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marcus hinz aedd4ba314 Kapitelübersichten - 1 - 3 
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
2026-06-05 16:48:32 +02:00

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<meta name="descrption" content="Ludwig Wittgenstein's Tractatus Logico-Philosophicus; side-by-side-by-side edition" />
<meta name="author" content="Ludwig Wittgenstein" />
<meta name="keywords" content="philosophy,logic,metaphysics,analytic philosophy,mysticisim" />
<meta name="creator" content="Ludwig Wittgenstein" />
<meta name="contributor" content="Kevin C. Klement" />
<meta name="subject" content="Philosophy" />
<meta name="date" content="Mon Feb 05 13:10:16 EST 2018" />
<meta name="source" content="German text plus Ogden-Ramsey and Pears-McGuinness translations" />
<meta name="rights" content="Public Domain" />
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["ger","gerpref","bigdivGerman"]
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["ogd","ogdpref","bigdivOgden"]
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["pmc","pmcpref","bigdivPearsMcGuinness"]
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<div id="coverpage" class="coverpageDiv">
<h1 class="englishtitle">Tractatus Logico-Philosophicus</h1>
<h1 class="germantitle">Logisch-philosophische Abhandlung</h1>
<h3 class="byline">By Ludwig Wittgenstein</h3>
<h3 class="pubinfo">First published by Kegan Paul (London), 1922.</h3>
<h3 class="pubinfo">Side-by-side-by-side edition, version 0.53 (5 February 2018), containing the original German, alongside both the Ogden/Ramsey, and Pears/McGuinness English translations.</h3>
<hr />
</div>
<div id="contents" class="contentsDiv">
<h2 class="majordivision" id="tableofcontents">Contents</h2>
<ul class="contentslist">
<li class="contentsitem introlink"><a href="#intro" class="contentslink">Introduction (by Bertrand Russell)</a></li>
<li class="contentsitem dedlink"><a href="#dedication" class="contentslink">Dedication page</a></li>
<li class="contentsitem gertoc">German text
<ul>
<li class="contentsitem preflink"><a href="#prefaceGerman" class="contentslink">Vorwort (preface)</a></li>
<li class="contentsitem"><a href="#bodytextGerman" class="contentslink">Logisch-philosophische Abhandlung</a></li>
</ul>
</li>
<li class="contentsitem ogdtoc">Ogden translation
<ul>
<li class="contentsitem preflink"><a href="#prefaceOgden" class="contentslink">Preface</a></li>
<li class="contentsitem"><a href="#bodytextOgden" class="contentslink">Tractatus Logico-Philosophicus</a></li>
</ul>
</li>
<li class="contentsitem pmctoc">Pears/McGuinness translation
<ul>
<li class="contentsitem preflink"><a href="#prefacePearsMcGuinness" class="contentslink">Preface</a></li>
<li class="contentsitem"><a href="#bodytextPearsMcGuinness" class="contentslink">Tractatus Logico-Philosophicus</a></li>
</ul>
</li>
<li class="contentsitem indextoc"><a href="#index" class="contentslink">Index</a></li>
</ul>
<hr />
</div>
<div class="russellsintro">
<h2 class="majordivision" id="intro">Introduction</h2>
<h3 class="bylinebr">By Bertrand Russell, F.&thinsp;R.&thinsp;S.</h3>
<p class="openingpar"><span class="textsc">Mr. Wittgenstein’s</span> <em>Tractatus Logico-Philosophicus</em>, whether or not it prove to give the ultimate truth on the matters with which it deals, certainly deserves, by its breadth and scope and profundity, to be considered an important event in the philosophical world. Starting from the principles of Symbolism and the relations which are necessary between words and things in any language, it applies the result of this inquiry to various departments of traditional philosophy, showing in each case how traditional philosophy and traditional solutions arise out of ignorance of the principles of Symbolism and out of misuse of language.</p>
<p>The logical structure of propositions and the nature of logical inference are first dealt with. Thence we pass successively to Theory of Knowledge, Principles of Physics, Ethics, and finally the Mystical (<em>das Mystische</em>).</p>
<p>In order to understand Mr. Wittgenstein’s book, it is necessary to realize what is the problem with which he is concerned. In the part of his theory which deals with Symbolism he is concerned with the conditions which would have to be fulfilled by a logically perfect language. There are various problems as regards language. First, there is the problem what actually occurs in our minds when we use language with the intention of meaning something by it; this problem belongs to psychology. Secondly, there is the problem as to what is the relation subsisting between thoughts, words, or sentences, and that which they refer to or mean; this problem belongs to epistemology. Thirdly, there is the problem of using sentences so as to convey truth rather that falsehood; this belongs to the special sciences dealing with the subject-matter of the sentences in question. Fourthly, there is the question: what relation must one fact (such as a sentence) have to another in order to be <em>capable</em> of being a symbol for that other? This last is a logical question, and is the one with which Mr. Wittgenstein is concerned. He is concerned with the conditions for <em>accurate</em> Symbolism, i.e. for Symbolism in which a sentence “means” something quite definite. In practice, language is always more or less vague, so that what we assert is never quite precise. Thus, logic has two problems to deal with in regard to Symbolism: (1) the conditions for sense rather than nonsense in combinations of symbols; (2) the conditions for uniqueness of meaning or reference in symbols or combinations of symbols. A logically perfect language has rules of syntax which prevent nonsense, and has single symbols which always have a definite and unique meaning. Mr. Wittgenstein is concerned with the conditions for a logically perfect language—not that any language is logically perfect, or that we believe ourselves capable, here and now, of constructing a logically perfect language, but that the whole function of language is to have meaning, and it only fulfills this function in proportion as it approaches to the ideal language which we postulate.</p>
<p>The essential business of language is to assert or deny facts. Given the syntax of language, the meaning of a sentence is determined as soon as the meaning of the component words is known. In order that a certain sentence should assert a certain fact there must, however the language may be constructed, be something in common between the structure of the sentence and the structure of the fact. This is perhaps the most fundamental thesis of Mr. Wittgenstein’s theory. That which has to be in common between the sentence and the fact cannot, he contends, be itself in turn <em>said</em> in language. It can, in his phraseology, only be <em>shown</em>, not said, for whatever we may say will still need to have the same structure.</p>
<p>The first requisite of an ideal language would be that there should be one name for every simple, and never the same name for two different simples. A name is a simple symbol in the sense that it has no parts which are themselves symbols. In a logically perfect language nothing that is not simple will have a simple symbol. The symbol for the whole will be a “complex”, containing the symbols for the parts. (In speaking of a “complex” we are, as will appear later, sinning against the rules of philosophical grammar, but this is unavoidable at the outset. “Most propositions and questions that have been written about philosophical matters are not false but senseless. We cannot, therefore, answer questions of this kind at all, but only state their senselessness. Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language. They are of the same kind as the question whether the Good is more or less identical than the Beautiful” (4.003).) What is complex in the world is a fact. Facts which are not compounded of other facts are what Mr. Wittgenstein calls <em>Sachverhalte</em>, whereas a fact which may consist of two or more facts is a <em>Tatsache</em>: thus, for example “Socrates is wise” is a <em>Sachverhalt</em>, as well as a <em>Tatsache</em>, whereas “Socrates is wise and Plato is his pupil” is a <em>Tatsache</em> but not a <em>Sachverhalt</em>.</p>
<p>He compares linguistic expression to projection in geometry. A geometrical figure may be projected in many ways: each of these ways corresponds to a different language, but the projective properties of the original figure remain unchanged whichever of these ways may be adopted. These projective properties correspond to that which in his theory the proposition and the fact must have in common, if the proposition is to assert the fact.</p>
<p>In certain elementary ways this is, of course, obvious. It is impossible, for example, to make a statement about two men (assuming for the moment that the men may be treated as simples), without employing two names, and if you are going to assert a relation between the two men it will be necessary that the sentence in which you make the assertion shall establish a relation between the two names. If we say “Plato loves Socrates”, the word “loves” which occurs between the word “Plato” and the word “Socrates” establishes a certain relation between these two words, and it is owing to this fact that our sentence is able to assert a relation between the persons named by the words “Plato” and “Socrates”. “We must not say, the complex sign ‘<span class="mathmode"><var>aRb</var></span>’ says that ‘<span class="mathmode"><var>a</var></span> stands in a certain relation <span class="mathmode"><var>R</var></span> to <span class="mathmode"><var>b</var></span>’; but we must say, that ‘<span class="mathmode"><var>a</var></span>’ stands in a certain relation to ‘<span class="mathmode"><var>b</var></span>’ says <em>that</em> <span class="mathmode"><var>aRb</var></span>” (3.1432).</p>
<p>Mr. Wittgenstein begins his theory of Symbolism with the statement (2.1): “We make to ourselves pictures of facts.” A picture, he says, is a model of the reality, and to the objects in the reality correspond the elements of the picture: the picture itself is a fact. The fact that things have a certain relation to each other is represented by the fact that in the picture its elements have a certain relation to one another. “In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all. What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation” (2.161, 2.17).</p>
<p>We speak of a logical picture of a reality when we wish to imply only so much resemblance as is essential to its being a picture in any sense, that is to say, when we wish to imply no more than identity of logical form. The logical picture of a fact, he says, is a <em>Gedanke</em>. A picture can correspond or not correspond with the fact and be accordingly true or false, but in both cases it shares the logical form with the fact. The sense in which he speaks of pictures is illustrated by his statement: “The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation which holds between language and the world. To all of them the logical structure is common. (Like the two youths, their two horses and their lilies in the story. They are all in a certain sense one)” (4.014). The possibility of a proposition representing a fact rests upon the fact that in it objects are represented by signs. The so-called logical “constants” are not represented by signs, but are themselves present in the proposition as in the fact. The proposition and the fact must exhibit the same logical “manifold”, and this cannot be itself represented since it has to be in common between the fact and the picture. Mr. Wittgenstein maintains that everything properly philosophical belongs to what can only be shown, or to what is in common between a fact and its logical picture. It results from this view that nothing correct can be said in philosophy. Every philosophical proposition is bad grammar, and the best that we can hope to achieve by philosophical discussion is to lead people to see that philosophical discussion is a mistake. “Philosophy is not one of the natural sciences. (The word ‘philosophy’ must mean something which stands above or below, but not beside the natural sciences.) The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory but an activity. A philosophical work consists essentially of elucidations. The result of philosophy is not a number of ‘philosophical propositions’, but to make propositions clear. Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred” (4.111 and 4.112). In accordance with this principle the things that have to be said in leading the reader to understand Mr. Wittgenstein’s theory are all of them things which that theory itself condemns as meaningless. With this proviso we will endeavour to convey the picture of the world which seems to underlie his system.</p>
<p>The world consists of facts: facts cannot strictly speaking be defined, but we can explain what we mean by saying that facts are what makes propositions true, or false. Facts may contain parts which are facts or may contain no such parts; for example: “Socrates was a wise Athenian”, consists of the two facts, “Socrates was wise”, and “Socrates was an Athenian.” A fact which has no parts that are facts is called by Mr. Wittgenstein a <em>Sachverhalt</em>. This is the same thing that he calls an atomic fact. An atomic fact, although it contains no parts that are facts, nevertheless does contain parts. If we may regard “Socrates is wise” as an atomic fact we perceive that it contains the constituents “Socrates” and “wise”. If an atomic fact is analyzed as fully as possible (theoretical, not practical possibility is meant) the constituents finally reached may be called “simples” or “objects”. It is a logical necessity demanded by theory, like an electron. His ground for maintaining that there must be simples is that every complex presupposes a fact. It is not necessarily assumed that the complexity of facts is finite; even if every fact consisted of an infinite number of atomic facts and if every atomic fact consisted of an infinite number of objects there would still be objects and atomic facts (4.2211). The assertion that there is a certain complex reduces to the assertion that its constituents are related in a certain way, which is the assertion of a <em>fact</em>: thus if we give a name to the complex the name only has meaning in virtue of the truth of a certain proposition, namely the proposition asserting the relatedness of the constituents of the complex. Thus the naming of complexes presupposes propositions, while propositions presuppose the naming of simples. In this way the naming of simples is shown to be what is logically first in logic.</p>
<p>The world is fully described if all atomic facts are known, together with the fact that these are all of them. The world is not described by merely naming all the objects in it; it is necessary also to know the atomic facts of which these objects are constituents. Given this totality of atomic facts, every true proposition, however complex, can theoretically be inferred. A proposition (true or false) asserting an atomic fact is called an atomic proposition. All atomic propositions are logically independent of each other. No atomic proposition implies any other or is inconsistent with any other. Thus the whole business of logical inference is concerned with propositions which are not atomic. Such propositions may be called molecular.</p>
<p>Wittgenstein’s theory of molecular propositions turns upon his theory of the construction of truth-functions.</p>
<p>A truth-function of a proposition <span class="mathmode"><var>p</var></span> is a proposition containing <span class="mathmode"><var>p</var></span> and such that its truth or falsehood depends only upon the truth or falsehood of <span class="mathmode"><var>p</var></span>, and similarly a truth-function of several propositions <span class="mathmode"><var>p</var>, <var>q</var>, <var>r</var>,<span class="mathrel">…</span></span> is one containing <span class="mathmode"><var>p</var>, <var>q</var>, <var>r</var>,<span class="mathrel">…</span></span> and such that its truth or falsehood depends only upon the truth or falsehood of <span class="mathmode"><var>p</var>, <var>q</var>, <var>r</var>,<span class="mathrel">…</span></span> It might seem at first sight as though there were other functions of propositions besides truth-functions; such, for example, would be “A believes <span class="mathmode"><var>p</var></span>”, for in general A will believe some true propositions and some false ones: unless he is an exceptionally gifted individual, we cannot infer that <span class="mathmode"><var>p</var></span> is true from the fact that he believes it or that <span class="mathmode"><var>p</var></span> is false from the fact that he does not believe it. Other apparent exceptions would be such as “<span class="mathmode"><var>p</var></span> is a very complex proposition” or “<span class="mathmode"><var>p</var></span> is a proposition about Socrates”. Mr. Wittgenstein maintains, however, for reasons which will appear presently, that such exceptions are only apparent, and that every function of a proposition is really a truth-function. It follows that if we can define truth-functions generally, we can obtain a general definition of all propositions in terms of the original set of atomic propositions. This Wittgenstein proceeds to do.</p>
<p>It has been shown by Dr. Sheffer (<em>Trans. Am. Math. Soc.</em>, Vol. XIV. pp. 481–488) that all truth-functions of a given set of propositions can be constructed out of either of the two functions “not-<span class="mathmode"><var>p</var></span> or not-<span class="mathmode"><var>q</var></span>” or “not-<span class="mathmode"><var>p</var></span> and not-<span class="mathmode"><var>q</var></span>”. Wittgenstein makes use of the latter, assuming a knowledge of Dr. Sheffer’s work. The manner in which other truth-functions are constructed out of “not-<span class="mathmode"><var>p</var></span> and not-<span class="mathmode"><var>q</var></span>” is easy to see. “Not-<span class="mathmode"><var>p</var></span> and not-<span class="mathmode"><var>p</var></span>” is equivalent to “not-<span class="mathmode"><var>p</var></span>”, hence we obtain a definition of negation in terms of our primitive function: hence we can define “<span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>”, since this is the negation of “not-<span class="mathmode"><var>p</var></span> and not-<span class="mathmode"><var>q</var></span>”, i.e. of our primitive function. The development of other truth-functions out of “not-<span class="mathmode"><var>p</var></span>” and “<span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>” is given in detail at the beginning of <em>Principia Mathematica</em>. This gives all that is wanted when the propositions which are arguments to our truth-function are given by enumeration. Wittgenstein, however, by a very interesting analysis succeeds in extending the process to general propositions, i.e. to cases where the propositions which are arguments to our truth-function are not given by enumeration but are given as all those satisfying some condition. For example, let <span class="mathmode"><var>fx</var></span> be a propositional function (i.e. a function whose values are propositions), such as “<span class="mathmode"><var>x</var></span> is human”—then the various values of <span class="mathmode"><var>fx</var></span> form a set of propositions. We may extend the idea “not-<span class="mathmode"><var>p</var></span> and not-<span class="mathmode"><var>q</var></span>” so as to apply to the simultaneous denial of all the propositions which are values of <span class="mathmode"><var>fx</var></span>. In this way we arrive at the proposition which is ordinarily represented in mathematical logic by the words “<span class="mathmode"><var>fx</var></span> is false for all values of <span class="mathmode"><var>x</var></span>”. The negation of this would be the proposition “there is at least one <span class="mathmode"><var>x</var></span> for which <span class="mathmode"><var>fx</var></span> is true” which is represented by “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>”. If we had started with not-<span class="mathmode"><var>fx</var></span> instead of <span class="mathmode"><var>fx</var></span> we should have arrived at the proposition “<span class="mathmode"><var>fx</var></span> is true for all values of <span class="mathmode"><var>x</var></span>” which is represented by “<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>”. Wittgenstein’s method of dealing with general propositions [i.e. “<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>” and “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>”] differs from previous methods by the fact that the generality comes only in specifying the set of propositions concerned, and when this has been done the building up of truth-functions proceeds exactly as it would in the case of a finite number of enumerated arguments <span class="mathmode"><var>p</var>, <var>q</var>, <var>r</var>,<span class="mathrel">…</span></span></p>
<p>Mr. Wittgenstein’s explanation of his symbolism at this point is not quite fully given in the text. The symbol he uses is <span class="mathmode">[<span class="overlined"><var>p</var></span>, <span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)].</span> The following is the explanation of this symbol:</p>
<ul class="desc">
<li><span class="mathmode"><span class="overlined"><var>p</var></span></span> stands for all atomic propositions.</li>
<li><span class="mathmode"><span class="overlined"><var>ξ</var></span></span> stands for any set of propositions.</li>
<li><span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)</span> stands for the negation of all the propositions making up <span class="mathmode"><span class="overlined"><var>ξ</var></span></span>.</li>
</ul>
<p>The whole symbol <span class="mathmode">[<span class="overlined"><var>p</var></span>, <span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)]</span> means whatever can be obtained by taking any selection of atomic propositions, negating them all, then taking any selection of the set of propositions now obtained, together with any of the originals—and so on indefinitely. This is, he says, the general truth-function and also the general form of proposition. What is meant is somewhat less complicated than it sounds. The symbol is intended to describe a process by the help of which, given the atomic propositions, all others can be manufactured. The process depends upon:</p>
<p>(a). Sheffer’s proof that all truth-functions can be obtained out of simultaneous negation, i.e. out of “not-<span class="mathmode"><var>p</var></span> and not-<span class="mathmode"><var>q</var></span>”;</p>
<p>(b). Mr. Wittgenstein’s theory of the derivation of general propositions from conjunctions and disjunctions;</p>
<p>(c). The assertion that a proposition can only occur in another proposition as argument to a truth-function. Given these three foundations, it follows that all propositions which are not atomic can be derived from such as are, by a uniform process, and it is this process which is indicated by Mr. Wittgenstein’s symbol.</p>
<p>From this uniform method of construction we arrive at an amazing simplification of the theory of inference, as well as a definition of the sort of propositions that belong to logic. The method of generation which has just been described, enables Wittgenstein to say that all propositions can be constructed in the above manner from atomic propositions, and in this way the totality of propositions is defined. (The apparent exceptions which we mentioned above are dealt with in a manner which we shall consider later.) Wittgenstein is enabled to assert that propositions are all that follows from the totality of atomic propositions (together with the fact that it is the totality of them); that a proposition is always a truth-function of atomic propositions; and that if <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span> the meaning of <span class="mathmode"><var>p</var></span> is contained in the meaning of <span class="mathmode"><var>q</var></span>, from which of course it results that nothing can be deduced from an atomic proposition. All the propositions of logic, he maintains, are tautologies, such, for example, as “<span class="mathmode"><var>p</var></span> or not <span class="mathmode"><var>p</var></span>”.</p>
<p>The fact that nothing can be deduced from an atomic proposition has interesting applications, for example, to causality. There cannot, in Wittgenstein’s logic, be any such thing as a causal nexus. “The events of the future”, he says, “<em>cannot</em> be inferred from those of the present. Superstition is the belief in the causal nexus.” That the sun will rise to-morrow is a hypothesis. We do not in fact know whether it will rise, since there is no compulsion according to which one thing must happen because another happens.</p>
<p>Let us now take up another subject—that of names. In Wittgenstein’s theoretical logical language, names are only given to simples. We do not give two names to one thing, or one name to two things. There is no way whatever, according to him, by which we can describe the totality of things that can be named, in other words, the totality of what there is in the world. In order to be able to do this we should have to know of some property which must belong to every thing by a logical necessity. It has been sought to find such a property in self-identity, but the conception of identity is subjected by Wittgenstein to a destructive criticism from which there seems no escape. The definition of identity by means of the identity of indiscernibles is rejected, because the identity of indiscernibles appears to be not a logically necessary principle. According to this principle <span class="mathmode"><var>x</var></span> is identical with <span class="mathmode"><var>y</var></span> if every property of <span class="mathmode"><var>x</var></span> is a property of <span class="mathmode"><var>y</var></span>, but it would, after all be logically possible for two things to have exactly the same properties. If this does not in fact happen that is an accidental characteristic of the world, not a logically necessary characteristic, and accidental characteristics of the world must, of course, not be admitted into the structure of logic. Mr. Wittgenstein accordingly banishes identity and adopts the convention that different letters are to mean different things. In practice, identity is needed as between a name and a description or between two descriptions. It is needed for such propositions as “Socrates is the philosopher who drank the hemlock”, or “The even prime is the next number after 1.” For such uses of identity it is easy to provide on Wittgenstein’s system.</p>
<p>The rejection of identity removes one method of speaking of the totality of things, and it will be found that any other method that may be suggested is equally fallacious: so, at least, Wittgenstein contends and, I think, rightly. This amounts to saying that “object” is a pseudo-concept. To say “<span class="mathmode"><var>x</var></span> is an object” is to say nothing. It follows from this that we cannot make such statements as “there are more than three objects in the world”, or “there are an infinite number of objects in the world”. Objects can only be mentioned in connexion with some definite property. We can say “there are more than three objects which are human”, or “there are more than three objects which are red”, for in these statements the word object can be replaced by a variable in the language of logic, the variable being one which satisfies in the first case the function “<span class="mathmode"><var>x</var></span> is human”; in the second the function “<span class="mathmode"><var>x</var></span> is red”. But when we attempt to say “there are more than three objects”, this substitution of the variable for the word “object” becomes impossible, and the proposition is therefore seen to be meaningless.</p>
<p>We here touch one instance of Wittgenstein’s fundamental thesis, that it is impossible to say anything about the world as a whole, and that whatever can be said has to be about bounded portions of the world. This view may have been originally suggested by notation, and if so, that is much in its favor, for a good notation has a subtlety and suggestiveness which at times make it seem almost like a live teacher. Notational irregularities are often the first sign of philosophical errors, and a perfect notation would be a substitute for thought. But although notation may have first suggested to Mr. Wittgenstein the limitation of logic to things within the world as opposed to the world as a whole, yet the view, once suggested, is seen to have much else to recommend it. Whether it is ultimately true I do not, for my part, profess to know. In this Introduction I am concerned to expound it, not to pronounce upon it. According to this view we could only say things about the world as a whole if we could get outside the world, if, that is to say, it ceased to be for us the whole world. Our world may be bounded for some superior being who can survey it from above, but for us, however finite it may be, it cannot have a boundary, since it has nothing outside it. Wittgenstein uses, as an analogy, the field of vision. Our field of vision does not, for us, have a visual boundary, just because there is nothing outside it, and in like manner our logical world has no logical boundary because our logic knows of nothing outside it. These considerations lead him to a somewhat curious discussion of Solipsism. Logic, he says, fills the world. The boundaries of the world are also its boundaries. In logic, therefore, we cannot say, there is this and this in the world, but not that, for to say so would apparently presuppose that we exclude certain possibilities, and this cannot be the case, since it would require that logic should go beyond the boundaries of the world as if it could contemplate these boundaries from the other side also. What we cannot think we cannot think, therefore we also cannot say what we cannot think.</p>
<p>This, he says, gives the key to solipsism. What Solipsism intends is quite correct, but this cannot be said, it can only be shown. That the world is <em>my</em> world appears in the fact that the boundaries of language (the only language I understand) indicate the boundaries of my world. The metaphysical subject does not belong to the world but is a boundary of the world.</p>
<p>We must take up next the question of molecular propositions which are at first sight not truth-functions, of the propositions that they contain, such, for example, as “A believes <span class="mathmode"><var>p</var></span>.”</p>
<p>Wittgenstein introduces this subject in the statement of his position, namely, that all molecular functions are truth-functions. He says (5.54): “In the general propositional form, propositions occur in a proposition only as bases of truth-operations.” At first sight, he goes on to explain, it seems as if a propositions could also occur in other ways, e.g. “A believes <span class="mathmode"><var>p</var></span>.” Here it seems superficially as if the proposition <span class="mathmode"><var>p</var></span> stood in a sort of relation to the object A. “But it is clear that ‘A believes that <span class="mathmode"><var>p</var></span>,’ ‘A thinks <span class="mathmode"><var>p</var></span>,’ ‘A says <span class="mathmode"><var>p</var></span>’ are of the form “‘<span class="mathmode"><var>p</var></span>’ says <span class="mathmode"><var>p</var></span>”; and here we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination of their objects” (5.542).</p>
<p>What Mr. Wittgenstein says here is said so shortly that its point is not likely to be clear to those who have not in mind the controversies with which he is concerned. The theory which which he is disagreeing will be found in my articles on the nature of truth and falsehood in <em>Philosophical Essays</em> and <em>Proceedings of the Aristotelian Society</em>, 1906–7. The problem at issue is the problem of the logical form of belief, i.e. what is the schema representing what occurs when a man believes. Of course, the problem applies not only to belief, but also to a host of other mental phenomena which may be called propositional attitudes: doubting, considering, desiring, etc. In all these cases it seems natural to express the phenomenon in the form “A doubts <span class="mathmode"><var>p</var></span>”, “A considers <span class="mathmode"><var>p</var></span>”, “A desires <span class="mathmode"><var>p</var></span>”, etc., which makes it appear as though we were dealing with a relation between a person and a proposition. This cannot, of course, be the ultimate analysis, since persons are fictions and so are propositions, except in the sense in which they are facts on their own account. A proposition, considered as a fact on its own account, may be a set of words which a man says over to himself, or a complex image, or train of images passing through his mind, or a set of incipient bodily movements. It may be any one of innumerable different things. The proposition as a fact on its own account, for example, the actual set of words the man pronounces to himself, is not relevant to logic. What is relevant to logic is that common element among all these facts, which enables him, as we say, to <em>mean</em> the fact which the proposition asserts. To psychology, of course, more is relevant; for a symbol does not mean what it symbolizes in virtue of a logical relation alone, but in virtue also of a psychological relation of intention, or association, or what-not. The psychological part of meaning, however, does not concern the logician. What does concern him in this problem of belief is the logical schema. It is clear that, when a person believes a proposition, the person, considered as a metaphysical subject, does not have to be assumed in order to explain what is happening. What has to be explained is the relation between the set of words which is the proposition considered as a fact on its own account, and the “objective” fact which makes the proposition true or false. This reduces ultimately to the question of the meaning of propositions, that is to say, the meaning of propositions is the only non-psychological portion of the problem involved in the analysis of belief. This problem is simply one of a relation of two facts, namely, the relation between the series of words used by the believer and the fact which makes these words true or false. The series of words is a fact just as much as what makes it true or false is a fact. The relation between these two facts is not unanalyzable, since the meaning of a proposition results from the meaning of its constituent words. The meaning of the series of words which is a proposition is a function of the meaning of the separate words. Accordingly, the proposition as a whole does not really enter into what has to be explained in explaining the meaning of a propositions. It would perhaps help to suggest the point of view which I am trying to indicate, to say that in the cases which have been considering the proposition occurs as a fact, not as a proposition. Such a statement, however, must not be taken too literally. The real point is that in believing, desiring, etc., what is logically fundamental is the relation of a proposition <em>considered as a fact</em>, to the fact which makes it true or false, and that this relation of two facts is reducible to a relation of their constituents. Thus the proposition does not occur at all in the same sense in which it occurs in a truth-function.</p>
<p>There are some respects, in which, as it seems to me, Mr. Wittgenstein’s theory stands in need of greater technical development. This applies in particular to his theory of number (6.02ff.) which, as it stands, is only capable of dealing with finite numbers. No logic can be considered adequate until it has been shown to be capable of dealing with transfinite numbers. I do not think there is anything in Mr. Wittgenstein’s system to make it impossible for him to fill this lacuna.</p>
<p>More interesting than such questions of comparative detail is Mr. Wittgenstein’s attitude towards the mystical. His attitude upon this grows naturally out of his doctrine in pure logic, according to which the logical proposition is a picture (true or false) of the fact, and has in common with the fact a certain structure. It is this common structure which makes it capable of being a picture of the fact, but the structure cannot itself be put into words, since it is a structure <em>of</em> words, as well as of the fact to which they refer. Everything, therefore, which is involved in the very idea of the expressiveness of language must remain incapable of being expressed in language, and is, therefore, inexpressible in a perfectly precise sense. This inexpressible contains, according to Mr. Wittgenstein, the whole of logic and philosophy. The right method of teaching philosophy, he says, would be to confine oneself to propositions of the sciences, stated with all possible clearness and exactness, leaving philosophical assertions to the learner, and proving to him, whenever he made them, that they are meaningless. It is true that the fate of Socrates might befall a man who attempted this method of teaching, but we are not to be deterred by that fear, if it is the only right method. It is not this that causes some hesitation in accepting Mr. Wittgenstein’s position, in spite of the very powerful arguments which he brings to its support. What causes hesitation is the fact that, after all, Mr. Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the sceptical reader that possibly there may be some loophole through a hierarchy of languages, or by some other exit. The whole subject of ethics, for example, is placed by Mr. Wittgenstein in the mystical, inexpressible region. Nevertheless he is capable of conveying his ethical opinions. His defence would be that what he calls the mystical can be shown, although it cannot be said. It may be that this defence is adequate, but, for my part, I confess that it leaves me with a certain sense of intellectual discomfort.</p>
<p>There is one purely logical problem in regard to which these difficulties are peculiarly acute. I mean the problem of generality. In the theory of generality it is necessary to consider all propositions of the form <span class="mathmode"><var>fx</var></span> where <span class="mathmode"><var>fx</var></span> is a given propositional function. This belongs to the part of logic which can be expressed, according to Mr. Wittgenstein’s system. But the totality of possible values of <span class="mathmode"><var>x</var></span> which might seem to be involved in the totality of propositions of the form <span class="mathmode"><var>fx</var></span> is not admitted by Mr. Wittgenstein among the things that can be spoken of, for this is no other than the totality of things in the world, and thus involves the attempt to conceive the world as a whole; “the feeling of the world as a bounded whole is the mystical”; hence the totality of the values of <span class="mathmode"><var>x</var></span> is mystical (6.45). This is expressly argued when Mr. Wittgenstein denies that we can make propositions as to how many things there are in the world, as for example, that there are more than three.</p>
<p>These difficulties suggest to my mind some such possibility as this: that every language has, as Mr. Wittgenstein says, a structure concerning which <em>in the language</em>, nothing can be said, but that there may be another language dealing with the structure of the first language, and having itself a new structure, and that to this hierarchy of languages there may be no limit. Mr. Wittgenstein would of course reply that his whole theory is applicable unchanged to the totality of such languages. The only retort would be to deny that there is any such totality. The totalities concerning which Mr. Wittgenstein holds that it is impossible to speak logically are nevertheless thought by him to exist, and are the subject-matter of his mysticism. The totality resulting from our hierarchy would be not merely logically inexpressible, but a fiction, a mere delusion, and in this way the supposed sphere of the mystical would be abolished. Such a hypothesis is very difficult, and I can see objections to it which at the moment I do not know how to answer. Yet I do not see how any easier hypothesis can escape from Mr. Wittgenstein’s conclusions. Even if this very difficult hypothesis should prove tenable, it would leave untouched a very large part of Mr. Wittgenstein’s theory, though possibly not the part upon which he himself would wish to lay most stress. As one with a long experience of the difficulties of logic and of the deceptiveness of theories which seem irrefutable, I find myself unable to be sure of the rightness of a theory, merely on the ground that I cannot see any point on which it is wrong. But to have constructed a theory of logic which is not at any point obviously wrong is to have achieved a work of extraordinary difficulty and importance. This merit, in my opinion, belongs to Mr. Wittgenstein’s book, and makes it one which no serious philosopher can afford to neglect.</p>
<p class="flushright"><span class="textsc">Bertrand Russell.</span><span class="phantom" style="visibility: hidden;">xxx</span></p>
<p><em>May</em> 1922.</p>
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<h2 class="majordivision" id="dedication">Tractatus Logico-Philosophicus</h2>
<div class="dedicationtext">Dedicated<br />to the Memory of My Friend<br />David H. Pinsent<br /></div>
<div class="motto"><em class="germph">Motto:</em> &hellip; und alles, was man weiss, nicht bloss rauschen und brausen gehört hat, lässt sich in drei Worten sagen. –KÜRNBERGER.</div>
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<h2 class="majordivision" id="prefaceGerman">Vorwort (Preface)</h2>
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<p>Dieses Buch wird vielleicht nur der verstehen, der die Gedanken, die darin ausgedrückt sind – oder doch ähnliche Gedanken – schon selbst einmal gedacht hat. – Es ist also kein Lehrbuch. – Sein Zweck wäre erreicht, wenn es Einem, der es mit Verständnis liest Vergnügen bereitete.</p>
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<p>Das Buch behandelt die philosophischen Probleme und zeigt – wie ich glaube – dass die Fragestellung dieser Probleme auf dem Mißverständnis der Logik unserer Sprache beruht. Man könnte den ganzen Sinn des Buches etwa in die Worte fassen: Was sich überhaupt sagen lässt, lässt sich klar sagen; und wovon man nicht reden kann, darüber muss man schweigen.</p>
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<p>Das Buch will also dem Denken eine Grenze ziehen, oder vielmehr – nicht dem Denken, sondern dem Ausdruck der Gedanken: Denn um dem Denken eine Grenze zu ziehen, müssten wir beide Seiten dieser Grenze denken können (wir müssten also denken können, was sich nicht denken lässt).</p>
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<p>Die Grenze wird also nur in der Sprache gezogen werden können und was jenseits der Grenze liegt, wird einfach Unsinn sein.</p>
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<p>Wieweit meine Bestrebungen mit denen anderer Philosophen zusammenfallen, will ich nicht beurteilen. Ja, was ich hier geschrieben habe macht im Einzelnen überhaupt nicht den Anspruch auf Neuheit; und darum gebe ich auch keine Quellen an, weil es mir gleichgültig ist, ob das was ich gedacht habe, vor mir schon ein anderer gedacht hat.</p>
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<p>Nur das will ich erwähnen, dass ich den großartigen Werken Freges und den Arbeiten meines Freundes Herrn Bertrand Russell einen großen Teil der Anregung zu meinen Gedanken schulde.</p>
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<p>Wenn diese Arbeit einen Wert hat, so besteht er in Zweierlei. Erstens darin, dass in ihr Gedanken ausgedrückt sind, und dieser Wert wird umso größer sein, je besser die Gedanken ausgedrückt sind. Je mehr der Nagel auf den Kopf getroffen ist. – Hier bin ich mir bewusst, weit hinter dem Möglichen zurückgeblieben zu sein. Einfach darum, weil meine Kraft zur Bewältigung der Aufgabe zu gering ist. – Mögen andere kommen und es besser machen.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref8GER"> GER [→<a class="ogdlink" href="#pref8OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref8PM">P/M</a>]</span></div>
<p>Dagegen scheint mir die <em class="germph">Wahrheit</em> der hier mitgeteilten Gedanken unantastbar und definitiv. Ich bin also der Meinung, die Probleme im Wesentlichen endgültig gelöst zu haben. Und wenn ich mich hierin nicht irre, so besteht nun der Wert dieser Arbeit zweitens darin, dass sie zeigt, wie wenig damit getan ist, dass diese Probleme gelöst sind.</p>
<p>&nbsp; <!-- flushright --> L. W.<br />
<em>Wien, 1918</em></p>
</div>
<h2 class="majordivision" id="bodytextGerman">Logisch-philosophische Abhandlung (German text)</h2>
<div class="corelinks tlpdepth0"><strong>1</strong><a href="#fn1GER" id="fn1markerGER">*</a><span class="linkarray tlpdepth0" id="p1GER"> GER [→<a class="ogdlink" href="#p1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Die Welt ist alles, was der Fall ist.</div>
<div class="corelinks tlpdepth1"><strong>1.1</strong><span class="linkarray tlpdepth1" id="p1.1GER"> GER [→<a class="ogdlink" href="#p1.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Die Welt ist die Gesamtheit der Tatsachen, nicht der Dinge.</div>
<div class="corelinks tlpdepth2"><strong>1.11</strong><span class="linkarray tlpdepth2" id="p1.11GER"> GER [→<a class="ogdlink" href="#p1.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Welt ist durch die Tatsachen bestimmt und dadurch, dass es <em class="germph">alle</em> Tatsachen sind.</div>
<div class="corelinks tlpdepth2"><strong>1.12</strong><span class="linkarray tlpdepth2" id="p1.12GER"> GER [→<a class="ogdlink" href="#p1.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Denn, die Gesamtheit der Tatsachen bestimmt, was der Fall ist und auch, was alles nicht der Fall ist.</div>
<div class="corelinks tlpdepth2"><strong>1.13</strong><span class="linkarray tlpdepth2" id="p1.13GER"> GER [→<a class="ogdlink" href="#p1.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Tatsachen im logischen Raum sind die Welt.</div>
<div class="corelinks tlpdepth1"><strong>1.2</strong><span class="linkarray tlpdepth1" id="p1.2GER"> GER [→<a class="ogdlink" href="#p1.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Die Welt zerfällt in Tatsachen.</div>
<div class="corelinks tlpdepth2"><strong>1.21</strong><span class="linkarray tlpdepth2" id="p1.21GER"> GER [→<a class="ogdlink" href="#p1.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Eines kann der Fall sein oder nicht der Fall sein und alles übrige gleich bleiben.</div>
<div class="corelinks tlpdepth0"><strong>2</strong><span class="linkarray tlpdepth0" id="p2GER"> GER [→<a class="ogdlink" href="#p2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten.</div>
<div class="corelinks tlpdepth2"><strong>2.01</strong><span class="linkarray tlpdepth2" id="p2.01GER"> GER [→<a class="ogdlink" href="#p2.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Sachverhalt ist eine Verbindung von Gegenständen. (Sachen, Dingen.)</div>
<div class="corelinks tlpdepth3"><strong>2.011</strong><span class="linkarray tlpdepth3" id="p2.011GER"> GER [→<a class="ogdlink" href="#p2.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.011PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist dem Ding wesentlich, der Bestandteil eines Sachverhaltes sein zu können.</div>
<div class="corelinks tlpdepth3"><strong>2.012</strong><span class="linkarray tlpdepth3" id="p2.012GER"> GER [→<a class="ogdlink" href="#p2.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.012PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In der Logik ist nichts zufällig: Wenn das Ding im Sachverhalt vorkommen <em class="germph">kann</em>, so muss die Möglichkeit des Sachverhaltes im Ding bereits präjudiziert sein.</div>
<div class="corelinks tlpdepth4"><strong>2.0121</strong><span class="linkarray tlpdepth4" id="p2.0121GER"> GER [→<a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es erschiene gleichsam als Zufall, wenn dem Ding, das allein für sich bestehen könnte, nachträglich eine Sachlage passen würde.</div>
<div class="para tlpdepth4">Wenn die Dinge in Sachverhalten vorkommen können, so muss dies schon in ihnen liegen.</div>
<div class="para tlpdepth4">(Etwas Logisches kann nicht nur-möglich sein. Die Logik handelt von jeder Möglichkeit und alle Möglichkeiten sind ihre Tatsachen.)</div>
<div class="para tlpdepth4">Wie wir uns räumliche Gegenstände überhaupt nicht außerhalb des Raumes, zeitliche nicht außerhalb der Zeit denken können, so können wir uns <em class="germph">keinen</em> Gegenstand außerhalb der Möglichkeit seiner Verbindung mit anderen denken.</div>
<div class="para tlpdepth4">Wenn ich mir den Gegenstand im Verbande des Sachverhalts denken kann, so kann ich ihn nicht außerhalb der <em class="germph">Möglichkeit</em> dieses Verbandes denken.</div>
<div class="corelinks tlpdepth4"><strong>2.0122</strong><span class="linkarray tlpdepth4" id="p2.0122GER"> GER [→<a class="ogdlink" href="#p2.0122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0122PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das Ding ist selbständig, insofern es in allen <em class="germph">möglichen</em> Sachlagen vorkommen kann, aber diese Form der Selbständigkeit ist eine Form des Zusammenhangs mit dem Sachverhalt, eine Form der Unselbständigkeit. (Es ist unmöglich, dass Worte in zwei verschiedenen Weisen auftreten, allein und im Satz.)</div>
<div class="corelinks tlpdepth4"><strong>2.0123</strong><span class="linkarray tlpdepth4" id="p2.0123GER"> GER [→<a class="ogdlink" href="#p2.0123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0123PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wenn ich den Gegenstand kenne, so kenne ich auch sämtliche Möglichkeiten seines Vorkommens in Sachverhalten.</div>
<div class="para tlpdepth4">(Jede solche Möglichkeit muss in der Natur des Gegenstandes liegen.)</div>
<div class="para tlpdepth4">Es kann nicht nachträglich eine neue Möglichkeit gefunden werden.</div>
<div class="corelinks tlpdepth5"><strong>2.01231</strong><span class="linkarray tlpdepth5" id="p2.01231GER"> GER [→<a class="ogdlink" href="#p2.01231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01231PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Um einen Gegenstand zu kennen, muss ich zwar nicht seine externen – aber ich muss alle seine internen Eigenschaften kennen.</div>
<div class="corelinks tlpdepth4"><strong>2.0124</strong><span class="linkarray tlpdepth4" id="p2.0124GER"> GER [→<a class="ogdlink" href="#p2.0124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0124PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Sind alle Gegenstände gegeben, so sind damit auch alle <em class="germph">möglichen</em> Sachverhalte gegeben.</div>
<div class="corelinks tlpdepth3"><strong>2.013</strong><span class="linkarray tlpdepth3" id="p2.013GER"> GER [→<a class="ogdlink" href="#p2.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.013PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Jedes Ding ist, gleichsam, in einem Raume möglicher Sachverhalte. Diesen Raum kann ich mir leer denken, nicht aber das Ding ohne den Raum.</div>
<div class="corelinks tlpdepth4"><strong>2.0131</strong><span class="linkarray tlpdepth4" id="p2.0131GER"> GER [→<a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Der räumliche Gegenstand muss im unendlichen Raume liegen. (Der Raumpunkt ist eine Argumentstelle.)</div>
<div class="para tlpdepth4">Der Fleck im Gesichtsfeld muss zwar nicht rot sein, aber eine Farbe muss er haben: er hat sozusagen den Farbenraum um sich. Der Ton muss <em class="germph">eine</em> Höhe haben, der Gegenstand des Tastsinnes <em class="germph">eine</em> Härte, usw.</div>
<div class="corelinks tlpdepth3"><strong>2.014</strong><span class="linkarray tlpdepth3" id="p2.014GER"> GER [→<a class="ogdlink" href="#p2.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.014PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Gegenstände enthalten die Möglichkeit aller Sachlagen.</div>
<div class="corelinks tlpdepth4"><strong>2.0141</strong><span class="linkarray tlpdepth4" id="p2.0141GER"> GER [→<a class="ogdlink" href="#p2.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0141PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Möglichkeit seines Vorkommens in Sachverhalten, ist die Form des Gegenstandes.</div>
<div class="corelinks tlpdepth2"><strong>2.02</strong><span class="linkarray tlpdepth2" id="p2.02GER"> GER [→<a class="ogdlink" href="#p2.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Gegenstand ist einfach.</div>
<div class="corelinks tlpdepth4"><strong>2.0201</strong><span class="linkarray tlpdepth4" id="p2.0201GER"> GER [→<a class="ogdlink" href="#p2.0201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Jede Aussage über Komplexe lässt sich in eine Aussage über deren Bestandteile und in diejenigen Sätze zerlegen, welche die Komplexe vollständig beschreiben.</div>
<div class="corelinks tlpdepth3"><strong>2.021</strong><span class="linkarray tlpdepth3" id="p2.021GER"> GER [→<a class="ogdlink" href="#p2.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.021PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Gegenstände bilden die Substanz der Welt. Darum können sie nicht zusammengesetzt sein.</div>
<div class="corelinks tlpdepth4"><strong>2.0211</strong><span class="linkarray tlpdepth4" id="p2.0211GER"> GER [→<a class="ogdlink" href="#p2.0211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0211PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Hätte die Welt keine Substanz, so würde, ob ein Satz Sinn hat, davon abhängen, ob ein anderer Satz wahr ist.</div>
<div class="corelinks tlpdepth4"><strong>2.0212</strong><span class="linkarray tlpdepth4" id="p2.0212GER"> GER [→<a class="ogdlink" href="#p2.0212OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0212PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es wäre dann unmöglich, ein Bild der Welt (wahr oder falsch) zu entwerfen.</div>
<div class="corelinks tlpdepth3"><strong>2.022</strong><span class="linkarray tlpdepth3" id="p2.022GER"> GER [→<a class="ogdlink" href="#p2.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.022PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist offenbar, dass auch eine von der wirklichen noch so verschieden gedachte Welt Etwas – eine Form – mit der wirklichen gemein haben muss.</div>
<div class="corelinks tlpdepth3"><strong>2.023</strong><span class="linkarray tlpdepth3" id="p2.023GER"> GER [→<a class="ogdlink" href="#p2.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.023PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Diese feste Form besteht eben aus den Gegenständen.</div>
<div class="corelinks tlpdepth4"><strong>2.0231</strong><span class="linkarray tlpdepth4" id="p2.0231GER"> GER [→<a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Substanz der Welt <em class="germph">kann</em> nur eine Form und keine materiellen Eigenschaften bestimmen. Denn diese werden erst durch die Sätze dargestellt – erst durch die Konfiguration der Gegenstände gebildet.</div>
<div class="corelinks tlpdepth4"><strong>2.0232</strong><span class="linkarray tlpdepth4" id="p2.0232GER"> GER [→<a class="ogdlink" href="#p2.0232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0232PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Beiläufig gesprochen: Die Gegenstände sind farblos.</div>
<div class="corelinks tlpdepth4"><strong>2.0233</strong><span class="linkarray tlpdepth4" id="p2.0233GER"> GER [→<a class="ogdlink" href="#p2.0233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0233PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Zwei Gegenstände von der gleichen logischen Form sind – abgesehen von ihren externen Eigenschaften – von einander nur dadurch unterschieden, dass sie verschieden sind.</div>
<div class="corelinks tlpdepth5"><strong>2.02331</strong><span class="linkarray tlpdepth5" id="p2.02331GER"> GER [→<a class="ogdlink" href="#p2.02331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02331PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Entweder ein Ding hat Eigenschaften, die kein anderes hat, dann kann man es ohneweiteres durch eine Beschreibung aus den anderen herausheben, und darauf hinweisen; oder aber, es gibt mehrere Dinge, die ihre sämtlichen Eigenschaften gemeinsam haben, dann ist es überhaupt unmöglich auf eines von ihnen zu zeigen.</div>
<div class="para tlpdepth5">Denn, ist das Ding durch nichts hervorgehoben, so kann ich es nicht hervorheben, denn sonst ist es eben hervorgehoben.</div>
<div class="corelinks tlpdepth3"><strong>2.024</strong><span class="linkarray tlpdepth3" id="p2.024GER"> GER [→<a class="ogdlink" href="#p2.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.024PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Substanz ist das, was unabhängig von dem was der Fall ist, besteht.</div>
<div class="corelinks tlpdepth3"><strong>2.025</strong><span class="linkarray tlpdepth3" id="p2.025GER"> GER [→<a class="ogdlink" href="#p2.025OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.025PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Sie ist Form und Inhalt.</div>
<div class="corelinks tlpdepth4"><strong>2.0251</strong><span class="linkarray tlpdepth4" id="p2.0251GER"> GER [→<a class="ogdlink" href="#p2.0251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0251PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Raum, Zeit und Farbe (Färbigkeit) sind Formen der Gegenstände.</div>
<div class="corelinks tlpdepth3"><strong>2.026</strong><span class="linkarray tlpdepth3" id="p2.026GER"> GER [→<a class="ogdlink" href="#p2.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.026PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Nur wenn es Gegenstände gibt, kann es eine feste Form der Welt geben.</div>
<div class="corelinks tlpdepth3"><strong>2.027</strong><span class="linkarray tlpdepth3" id="p2.027GER"> GER [→<a class="ogdlink" href="#p2.027OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.027PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Feste, das Bestehende und der Gegenstand sind Eins.</div>
<div class="corelinks tlpdepth4"><strong>2.0271</strong><span class="linkarray tlpdepth4" id="p2.0271GER"> GER [→<a class="ogdlink" href="#p2.0271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0271PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Der Gegenstand ist das Feste, Bestehende; die Konfiguration ist das Wechselnde, Unbeständige.</div>
<div class="corelinks tlpdepth4"><strong>2.0272</strong><span class="linkarray tlpdepth4" id="p2.0272GER"> GER [→<a class="ogdlink" href="#p2.0272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0272PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Konfiguration der Gegenstände bildet den Sachverhalt.</div>
<div class="corelinks tlpdepth2"><strong>2.03</strong><span class="linkarray tlpdepth2" id="p2.03GER"> GER [→<a class="ogdlink" href="#p2.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.03PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Im Sachverhalt hängen die Gegenstände ineinander, wie die Glieder einer Kette.</div>
<div class="corelinks tlpdepth3"><strong>2.031</strong><span class="linkarray tlpdepth3" id="p2.031GER"> GER [→<a class="ogdlink" href="#p2.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.031PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Im Sachverhalt verhalten sich die Gegenstände in bestimmter Art und Weise zueinander.</div>
<div class="corelinks tlpdepth3"><strong>2.032</strong><span class="linkarray tlpdepth3" id="p2.032GER"> GER [→<a class="ogdlink" href="#p2.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.032PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Art und Weise, wie die Gegenstände im Sachverhalt zusammenhängen, ist die Struktur des Sachverhaltes.</div>
<div class="corelinks tlpdepth3"><strong>2.033</strong><span class="linkarray tlpdepth3" id="p2.033GER"> GER [→<a class="ogdlink" href="#p2.033OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.033PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Form ist die Möglichkeit der Struktur.</div>
<div class="corelinks tlpdepth3"><strong>2.034</strong><span class="linkarray tlpdepth3" id="p2.034GER"> GER [→<a class="ogdlink" href="#p2.034OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.034PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Struktur der Tatsache besteht aus den Strukturen der Sachverhalte.</div>
<div class="corelinks tlpdepth2"><strong>2.04</strong><span class="linkarray tlpdepth2" id="p2.04GER"> GER [→<a class="ogdlink" href="#p2.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.04PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Gesamtheit der bestehenden Sachverhalte ist die Welt.</div>
<div class="corelinks tlpdepth2"><strong>2.05</strong><span class="linkarray tlpdepth2" id="p2.05GER"> GER [→<a class="ogdlink" href="#p2.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.05PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Gesamtheit der bestehenden Sachverhalte bestimmt auch, welche Sachverhalte nicht bestehen.</div>
<div class="corelinks tlpdepth2"><strong>2.06</strong><span class="linkarray tlpdepth2" id="p2.06GER"> GER [→<a class="ogdlink" href="#p2.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.06PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Bestehen und Nichtbestehen von Sachverhalten ist die Wirklichkeit.</div>
<div class="para tlpdepth2">(Das Bestehen von Sachverhalten nennen wir auch eine positive, das Nichtbestehen eine negative Tatsache.)</div>
<div class="corelinks tlpdepth3"><strong>2.061</strong><span class="linkarray tlpdepth3" id="p2.061GER"> GER [→<a class="ogdlink" href="#p2.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.061PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Sachverhalte sind von einander unabhängig.</div>
<div class="corelinks tlpdepth3"><strong>2.062</strong><span class="linkarray tlpdepth3" id="p2.062GER"> GER [→<a class="ogdlink" href="#p2.062OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.062PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Aus dem Bestehen oder Nichtbestehen eines Sachverhaltes kann nicht auf das Bestehen oder Nichtbestehen eines anderen geschlossen werden.</div>
<div class="corelinks tlpdepth3"><strong>2.063</strong><span class="linkarray tlpdepth3" id="p2.063GER"> GER [→<a class="ogdlink" href="#p2.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.063PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die gesamte Wirklichkeit ist die Welt.</div>
<div class="corelinks tlpdepth1"><strong>2.1</strong><span class="linkarray tlpdepth1" id="p2.1GER"> GER [→<a class="ogdlink" href="#p2.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Wir machen uns Bilder der Tatsachen.</div>
<div class="corelinks tlpdepth2"><strong>2.11</strong><span class="linkarray tlpdepth2" id="p2.11GER"> GER [→<a class="ogdlink" href="#p2.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Bild stellt die Sachlage im logischen Raume, das Bestehen und Nichtbestehen von Sachverhalten vor.</div>
<div class="corelinks tlpdepth2"><strong>2.12</strong><span class="linkarray tlpdepth2" id="p2.12GER"> GER [→<a class="ogdlink" href="#p2.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Bild ist ein Modell der Wirklichkeit.</div>
<div class="corelinks tlpdepth2"><strong>2.13</strong><span class="linkarray tlpdepth2" id="p2.13GER"> GER [→<a class="ogdlink" href="#p2.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Den Gegenständen entsprechen im Bilde die Elemente des Bildes.</div>
<div class="corelinks tlpdepth3"><strong>2.131</strong><span class="linkarray tlpdepth3" id="p2.131GER"> GER [→<a class="ogdlink" href="#p2.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.131PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Elemente des Bildes vertreten im Bild die Gegenstände.</div>
<div class="corelinks tlpdepth2"><strong>2.14</strong><span class="linkarray tlpdepth2" id="p2.14GER"> GER [→<a class="ogdlink" href="#p2.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.14PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Bild besteht darin, dass sich seine Elemente in bestimmter Art und Weise zu einander verhalten.</div>
<div class="corelinks tlpdepth3"><strong>2.141</strong><span class="linkarray tlpdepth3" id="p2.141GER"> GER [→<a class="ogdlink" href="#p2.141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.141PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bild ist eine Tatsache.</div>
<div class="corelinks tlpdepth2"><strong>2.15</strong><span class="linkarray tlpdepth2" id="p2.15GER"> GER [→<a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Dass sich die Elemente des Bildes in bestimmter Art und Weise zu einander verhalten, stellt vor, dass sich die Sachen so zu einander verhalten.</div>
<div class="para tlpdepth2">Dieser Zusammenhang der Elemente des Bildes heiße seine Struktur und ihre Möglichkeit seine Form der Abbildung.</div>
<div class="corelinks tlpdepth3"><strong>2.151</strong><span class="linkarray tlpdepth3" id="p2.151GER"> GER [→<a class="ogdlink" href="#p2.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.151PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Form der Abbildung ist die Möglichkeit, dass sich die Dinge so zu einander verhalten, wie die Elemente des Bildes.</div>
<div class="corelinks tlpdepth4"><strong>2.1511</strong><span class="linkarray tlpdepth4" id="p2.1511GER"> GER [→<a class="ogdlink" href="#p2.1511OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1511PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das Bild ist <em class="germph">so</em> mit der Wirklichkeit verknüpft – es reicht bis zu ihr.</div>
<div class="corelinks tlpdepth4"><strong>2.1512</strong><span class="linkarray tlpdepth4" id="p2.1512GER"> GER [→<a class="ogdlink" href="#p2.1512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1512PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es ist wie ein Maßstab an die Wirklichkeit angelegt.</div>
<div class="corelinks tlpdepth5"><strong>2.15121</strong><span class="linkarray tlpdepth5" id="p2.15121GER"> GER [→<a class="ogdlink" href="#p2.15121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15121PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Nur die äußersten Punkte der Teilstriche <em class="germph">berühren</em> den zu messenden Gegenstand.</div>
<div class="corelinks tlpdepth4"><strong>2.1513</strong><span class="linkarray tlpdepth4" id="p2.1513GER"> GER [→<a class="ogdlink" href="#p2.1513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1513PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Nach dieser Auffassung gehört also zum Bilde auch noch die abbildende Beziehung, die es zum Bild macht.</div>
<div class="corelinks tlpdepth4"><strong>2.1514</strong><span class="linkarray tlpdepth4" id="p2.1514GER"> GER [→<a class="ogdlink" href="#p2.1514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1514PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die abbildende Beziehung besteht aus den Zuordnungen der Elemente des Bildes und der Sachen.</div>
<div class="corelinks tlpdepth4"><strong>2.1515</strong><span class="linkarray tlpdepth4" id="p2.1515GER"> GER [→<a class="ogdlink" href="#p2.1515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1515PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Diese Zuordnungen sind gleichsam die Fühler der Bildelemente, mit denen das Bild die Wirklichkeit berührt.</div>
<div class="corelinks tlpdepth2"><strong>2.16</strong><span class="linkarray tlpdepth2" id="p2.16GER"> GER [→<a class="ogdlink" href="#p2.16OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.16PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Tatsache muss, um Bild zu sein, etwas mit dem Abgebildeten gemeinsam haben.</div>
<div class="corelinks tlpdepth3"><strong>2.161</strong><span class="linkarray tlpdepth3" id="p2.161GER"> GER [→<a class="ogdlink" href="#p2.161OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.161PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In Bild und Abgebildetem muss etwas identisch sein, damit das eine überhaupt ein Bild des anderen sein kann.</div>
<div class="corelinks tlpdepth2"><strong>2.17</strong><span class="linkarray tlpdepth2" id="p2.17GER"> GER [→<a class="ogdlink" href="#p2.17OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.17PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Was das Bild mit der Wirklichkeit gemein haben muss, um sie auf seine Art und Weise – richtig oder falsch – abbilden zu können, ist seine Form der Abbildung.</div>
<div class="corelinks tlpdepth3"><strong>2.171</strong><span class="linkarray tlpdepth3" id="p2.171GER"> GER [→<a class="ogdlink" href="#p2.171OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.171PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bild kann jede Wirklichkeit abbilden, deren Form es hat.</div>
<div class="para tlpdepth3">Das räumliche Bild alles Räumliche, das farbige alles Farbige, etc.</div>
<div class="corelinks tlpdepth3"><strong>2.172</strong><span class="linkarray tlpdepth3" id="p2.172GER"> GER [→<a class="ogdlink" href="#p2.172OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.172PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Seine Form der Abbildung aber, kann das Bild nicht abbilden; es weist sie auf.</div>
<div class="corelinks tlpdepth3"><strong>2.173</strong><span class="linkarray tlpdepth3" id="p2.173GER"> GER [→<a class="ogdlink" href="#p2.173OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.173PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bild stellt sein Objekt von außerhalb dar (sein Standpunkt ist seine Form der Darstellung), darum stellt das Bild sein Objekt richtig oder falsch dar.</div>
<div class="corelinks tlpdepth3"><strong>2.174</strong><span class="linkarray tlpdepth3" id="p2.174GER"> GER [→<a class="ogdlink" href="#p2.174OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.174PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bild kann sich aber nicht außerhalb seiner Form der Darstellung stellen.</div>
<div class="corelinks tlpdepth2"><strong>2.18</strong><span class="linkarray tlpdepth2" id="p2.18GER"> GER [→<a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Was jedes Bild, welcher Form immer, mit der Wirklichkeit gemein haben muss, um sie überhaupt – richtig oder falsch – abbilden zu können, ist die logische Form, das ist, die Form der Wirklichkeit.</div>
<div class="corelinks tlpdepth3"><strong>2.181</strong><span class="linkarray tlpdepth3" id="p2.181GER"> GER [→<a class="ogdlink" href="#p2.181OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.181PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ist die Form der Abbildung die logische Form, so heißt das Bild das logische Bild.</div>
<div class="corelinks tlpdepth3"><strong>2.182</strong><span class="linkarray tlpdepth3" id="p2.182GER"> GER [→<a class="ogdlink" href="#p2.182OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.182PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Jedes Bild ist <em class="germph">auch</em> ein logisches. (Dagegen ist z. B. nicht jedes Bild ein räumliches.)</div>
<div class="corelinks tlpdepth2"><strong>2.19</strong><span class="linkarray tlpdepth2" id="p2.19GER"> GER [→<a class="ogdlink" href="#p2.19OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.19PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das logische Bild kann die Welt abbilden.</div>
<div class="corelinks tlpdepth1"><strong>2.2</strong><span class="linkarray tlpdepth1" id="p2.2GER"> GER [→<a class="ogdlink" href="#p2.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Das Bild hat mit dem Abgebildeten die logische Form der Abbildung gemein.</div>
<div class="corelinks tlpdepth3"><strong>2.201</strong><span class="linkarray tlpdepth3" id="p2.201GER"> GER [→<a class="ogdlink" href="#p2.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.201PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bild bildet die Wirklichkeit ab, indem es eine Möglichkeit des Bestehens und Nichtbestehens von Sachverhalten darstellt.</div>
<div class="corelinks tlpdepth3"><strong>2.202</strong><span class="linkarray tlpdepth3" id="p2.202GER"> GER [→<a class="ogdlink" href="#p2.202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.202PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bild stellt eine mögliche Sachlage im logischen Raume dar.</div>
<div class="corelinks tlpdepth3"><strong>2.203</strong><span class="linkarray tlpdepth3" id="p2.203GER"> GER [→<a class="ogdlink" href="#p2.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.203PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bild enthält die Möglichkeit der Sachlage, die es darstellt.</div>
<div class="corelinks tlpdepth2"><strong>2.21</strong><span class="linkarray tlpdepth2" id="p2.21GER"> GER [→<a class="ogdlink" href="#p2.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Bild stimmt mit der Wirklichkeit überein oder nicht; es ist richtig oder unrichtig, wahr oder falsch.</div>
<div class="corelinks tlpdepth2"><strong>2.22</strong><span class="linkarray tlpdepth2" id="p2.22GER"> GER [→<a class="ogdlink" href="#p2.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Bild stellt dar, was es darstellt, unabhängig von seiner Wahr- oder Falschheit, durch die Form der Abbildung.</div>
<div class="corelinks tlpdepth3"><strong>2.221</strong><span class="linkarray tlpdepth3" id="p2.221GER"> GER [→<a class="ogdlink" href="#p2.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.221PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Was das Bild darstellt, ist sein Sinn.</div>
<div class="corelinks tlpdepth3"><strong>2.222</strong><span class="linkarray tlpdepth3" id="p2.222GER"> GER [→<a class="ogdlink" href="#p2.222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.222PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In der Übereinstimmung oder Nichtübereinstimmung seines Sinnes mit der Wirklichkeit, besteht seine Wahrheit oder Falschheit.</div>
<div class="corelinks tlpdepth3"><strong>2.223</strong><span class="linkarray tlpdepth3" id="p2.223GER"> GER [→<a class="ogdlink" href="#p2.223OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.223PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Um zu erkennen, ob das Bild wahr oder falsch ist, müssen wir es mit der Wirklichkeit vergleichen.</div>
<div class="corelinks tlpdepth3"><strong>2.224</strong><span class="linkarray tlpdepth3" id="p2.224GER"> GER [→<a class="ogdlink" href="#p2.224OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.224PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Aus dem Bild allein ist nicht zu erkennen, ob es wahr oder falsch ist.</div>
<div class="corelinks tlpdepth3"><strong>2.225</strong><span class="linkarray tlpdepth3" id="p2.225GER"> GER [→<a class="ogdlink" href="#p2.225OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.225PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ein a priori wahres Bild gibt es nicht.</div>
<div class="corelinks tlpdepth0"><strong>3</strong><span class="linkarray tlpdepth0" id="p3GER"> GER [→<a class="ogdlink" href="#p3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Das logische Bild der Tatsachen ist der Gedanke.</div>
<div class="corelinks tlpdepth3"><strong>3.001</strong><span class="linkarray tlpdepth3" id="p3.001GER"> GER [→<a class="ogdlink" href="#p3.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.001PM">P/M</a>]</span></div>
<div class="para tlpdepth3">„Ein Sachverhalt ist denkbar“ heißt: Wir können uns ein Bild von ihm machen.</div>
<div class="corelinks tlpdepth2"><strong>3.01</strong><span class="linkarray tlpdepth2" id="p3.01GER"> GER [→<a class="ogdlink" href="#p3.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Gesamtheit der wahren Gedanken sind ein Bild der Welt.</div>
<div class="corelinks tlpdepth2"><strong>3.02</strong><span class="linkarray tlpdepth2" id="p3.02GER"> GER [→<a class="ogdlink" href="#p3.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Gedanke enthält die Möglichkeit der Sachlage, die er denkt. Was denkbar ist, ist auch möglich.</div>
<div class="corelinks tlpdepth2"><strong>3.03</strong><span class="linkarray tlpdepth2" id="p3.03GER"> GER [→<a class="ogdlink" href="#p3.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.03PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wir können nichts Unlogisches denken, weil wir sonst unlogisch denken müssten.</div>
<div class="corelinks tlpdepth3"><strong>3.031</strong><span class="linkarray tlpdepth3" id="p3.031GER"> GER [→<a class="ogdlink" href="#p3.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.031PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Man sagte einmal, dass Gott alles schaffen könne, nur nichts, was den logischen Gesetzen zuwider wäre. – Wir können nämlich von einer „unlogischen“ Welt nicht <em class="germph">sagen</em>, wie sie aussähe.</div>
<div class="corelinks tlpdepth3"><strong>3.032</strong><span class="linkarray tlpdepth3" id="p3.032GER"> GER [→<a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Etwas „der Logik widersprechendes“ in der Sprache darstellen, kann man ebensowenig, wie in der Geometrie eine den Gesetzen des Raumes widersprechende Figur durch ihre Koordinaten darstellen; oder die Koordinaten eines Punktes angeben, welcher nicht existiert.</div>
<div class="corelinks tlpdepth4"><strong>3.0321</strong><span class="linkarray tlpdepth4" id="p3.0321GER"> GER [→<a class="ogdlink" href="#p3.0321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.0321PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wohl können wir einen Sachverhalt räumlich darstellen, welcher den Gesetzen der Physik, aber keinen, der den Gesetzen der Geometrie zuwiderliefe.</div>
<div class="corelinks tlpdepth2"><strong>3.04</strong><span class="linkarray tlpdepth2" id="p3.04GER"> GER [→<a class="ogdlink" href="#p3.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.04PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Ein a priori richtiger Gedanke wäre ein solcher, dessen Möglichkeit seine Wahrheit bedingte.</div>
<div class="corelinks tlpdepth2"><strong>3.05</strong><span class="linkarray tlpdepth2" id="p3.05GER"> GER [→<a class="ogdlink" href="#p3.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.05PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Nur so könnten wir a priori wissen, dass ein Gedanke wahr ist, wenn aus dem Gedanken selbst (ohne Vergleichsobjekt) seine Wahrheit zu erkennen wäre.</div>
<div class="corelinks tlpdepth1"><strong>3.1</strong><span class="linkarray tlpdepth1" id="p3.1GER"> GER [→<a class="ogdlink" href="#p3.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Im Satz drückt sich der Gedanke sinnlich wahrnehmbar aus.</div>
<div class="corelinks tlpdepth2"><strong>3.11</strong><span class="linkarray tlpdepth2" id="p3.11GER"> GER [→<a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wir benützen das sinnlich wahrnehmbare Zeichen (Laut- oder Schriftzeichen etc.) des Satzes als Projektion der möglichen Sachlage.</div>
<div class="para tlpdepth2">Die Projektionsmethode ist das Denken des Satz-Sinnes.</div>
<div class="corelinks tlpdepth2"><strong>3.12</strong><span class="linkarray tlpdepth2" id="p3.12GER"> GER [→<a class="ogdlink" href="#p3.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Zeichen, durch welches wir den Gedanken ausdrücken, nenne ich das Satzzeichen. Und der Satz ist das Satzzeichen in seiner projektiven Beziehung zur Welt.</div>
<div class="corelinks tlpdepth2"><strong>3.13</strong><span class="linkarray tlpdepth2" id="p3.13GER"> GER [→<a class="ogdlink" href="#p3.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Zum Satz gehört alles, was zur Projektion gehört; aber nicht das Projizierte.</div>
<div class="para tlpdepth2">Also die Möglichkeit des Projizierten, aber nicht dieses selbst.</div>
<div class="para tlpdepth2">Im Satz ist also sein Sinn noch nicht enthalten, wohl aber die Möglichkeit, ihn auszudücken.</div>
<div class="para tlpdepth2">(„Der Inhalt des Satzes“ heißt der Inhalt des sinnvollen Satzes.)</div>
<div class="para tlpdepth2">Im Satz ist die Form seines Sinnes enthalten, aber nicht dessen Inhalt.</div>
<div class="corelinks tlpdepth2"><strong>3.14</strong><span class="linkarray tlpdepth2" id="p3.14GER"> GER [→<a class="ogdlink" href="#p3.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.14PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Satzzeichen besteht darin, dass sich seine Elemente, die Wörter, in ihm auf bestimmte Art und Weise zu einander verhalten.</div>
<div class="para tlpdepth2">Das Satzzeichen ist eine Tatsache.</div>
<div class="corelinks tlpdepth3"><strong>3.141</strong><span class="linkarray tlpdepth3" id="p3.141GER"> GER [→<a class="ogdlink" href="#p3.141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.141PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Satz ist kein Wörtergemisch. – (Wie das musikalische Thema kein Gemisch von Tönen.)</div>
<div class="para tlpdepth3">Der Satz ist artikuliert.</div>
<div class="corelinks tlpdepth3"><strong>3.142</strong><span class="linkarray tlpdepth3" id="p3.142GER"> GER [→<a class="ogdlink" href="#p3.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.142PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Nur Tatsachen können einen Sinn ausdrücken, eine Klasse von Namen kann es nicht.</div>
<div class="corelinks tlpdepth3"><strong>3.143</strong><span class="linkarray tlpdepth3" id="p3.143GER"> GER [→<a class="ogdlink" href="#p3.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Dass das Satzzeichen eine Tatsache ist, wird durch die gewöhnliche Ausdrucksform der Schrift oder des Druckes verschleiert.</div>
<div class="para tlpdepth3">Denn im gedruckten Satz z. B. sieht das Satzzeichen nicht wesentlich verschieden aus vom Wort.</div>
<div class="para tlpdepth3">(So war es möglich, dass Frege den Satz einen zusammengesetzten Namen nannte.)</div>
<div class="corelinks tlpdepth4"><strong>3.1431</strong><span class="linkarray tlpdepth4" id="p3.1431GER"> GER [→<a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Sehr klar wird das Wesen des Satzzeichens, wenn wir es uns, statt aus Schriftzeichen, aus räumlichen Gegenständen (etwa Tischen, Stühlen, Büchern) zusammengesetzt denken.</div>
<div class="para tlpdepth4">Die gegenseitige räumliche Lage dieser Dinge drückt dann den Sinn des Satzes aus.</div>
<div class="corelinks tlpdepth4"><strong>3.1432</strong><span class="linkarray tlpdepth4" id="p3.1432GER"> GER [→<a class="ogdlink" href="#p3.1432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1432PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Nicht: „Das komplexe Zeichen ‚<span class="mathmode"><var>aRb</var></span>‘ sagt, dass <span class="mathmode"><var>a</var></span> in der Beziehung <span class="mathmode"><var>R</var></span> zu <span class="mathmode"><var>b</var></span> steht“, sondern: <em class="germph">Dass</em> „<span class="mathmode"><var>a</var></span>“ in einer gewissen Beziehung zu „<span class="mathmode"><var>b</var></span>“ steht, sagt, <em class="germph">dass</em> <span class="mathmode"><var>aRb</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>3.144</strong><span class="linkarray tlpdepth3" id="p3.144GER"> GER [→<a class="ogdlink" href="#p3.144OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.144PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Sachlagen kann man beschreiben, nicht <em class="germph">benennen</em>.</div>
<div class="para tlpdepth3">(Namen gleichen Punkten, Sätze Pfeilen, sie haben Sinn.)</div>
<div class="corelinks tlpdepth1"><strong>3.2</strong><span class="linkarray tlpdepth1" id="p3.2GER"> GER [→<a class="ogdlink" href="#p3.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Im Satze kann der Gedanke so ausgedrückt sein, dass den Gegenständen des Gedankens Elemente des Satzzeichens entsprechen.</div>
<div class="corelinks tlpdepth3"><strong>3.201</strong><span class="linkarray tlpdepth3" id="p3.201GER"> GER [→<a class="ogdlink" href="#p3.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.201PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Diese Elemente nenne ich „einfache Zeichen“ und den Satz „vollständig analysiert“.</div>
<div class="corelinks tlpdepth3"><strong>3.202</strong><span class="linkarray tlpdepth3" id="p3.202GER"> GER [→<a class="ogdlink" href="#p3.202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.202PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die im Satze angewandten einfachen Zeichen heißen Namen.</div>
<div class="corelinks tlpdepth3"><strong>3.203</strong><span class="linkarray tlpdepth3" id="p3.203GER"> GER [→<a class="ogdlink" href="#p3.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.203PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Name bedeutet den Gegenstand. Der Gegenstand ist seine Bedeutung. („<span class="mathmode"><var>A</var></span>“ ist dasselbe Zeichen wie „<span class="mathmode"><var>A</var></span>“.)</div>
<div class="corelinks tlpdepth2"><strong>3.21</strong><span class="linkarray tlpdepth2" id="p3.21GER"> GER [→<a class="ogdlink" href="#p3.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Konfiguration der einfachen Zeichen im Satzzeichen entspricht die Konfiguration der Gegenstände in der Sachlage.</div>
<div class="corelinks tlpdepth2"><strong>3.22</strong><span class="linkarray tlpdepth2" id="p3.22GER"> GER [→<a class="ogdlink" href="#p3.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Name vertritt im Satz den Gegenstand.</div>
<div class="corelinks tlpdepth3"><strong>3.221</strong><span class="linkarray tlpdepth3" id="p3.221GER"> GER [→<a class="ogdlink" href="#p3.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Gegenstände kann ich nur <em class="germph">nennen</em>. Zeichen vertreten sie. Ich kann nur <em class="germph">von</em> ihnen sprechen, <em class="germph">sie aussprechen</em> kann ich nicht. Ein Satz kann nur sagen, <em class="germph">wie</em> ein Ding ist, nicht <em class="germph">was</em> es ist.</div>
<div class="corelinks tlpdepth2"><strong>3.23</strong><span class="linkarray tlpdepth2" id="p3.23GER"> GER [→<a class="ogdlink" href="#p3.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.23PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Forderung der Möglichkeit der einfachen Zeichen ist die Forderung der Bestimmtheit des Sinnes.</div>
<div class="corelinks tlpdepth2"><strong>3.24</strong><span class="linkarray tlpdepth2" id="p3.24GER"> GER [→<a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Satz, welcher vom Komplex handelt, steht in interner Beziehung zum Satze, der von dessen Bestandteil handelt.</div>
<div class="para tlpdepth2">Der Komplex kann nur durch seine Beschreibung gegeben sein, und diese wird stimmen oder nicht stimmen. Der Satz, in welchem von einem Komplex die Rede ist, wird, wenn dieser nicht existiert, nicht unsinnig, sondern einfach falsch sein.</div>
<div class="para tlpdepth2">Dass ein Satzelement einen Komplex bezeichnet, kann man aus einer Unbestimmtheit in den Sätzen sehen, worin es vorkommt. Wir <em class="germph">wissen</em>, durch diesen Satz ist noch nicht alles bestimmt. (Die Allgemeinheitsbezeichnung <em class="germph">enthält</em> ja ein Urbild.)</div>
<div class="para tlpdepth2">Die Zusammenfassung des Symbols eines Komplexes in ein einfaches Symbol kann durch eine Definition ausgedrückt werden.</div>
<div class="corelinks tlpdepth2"><strong>3.25</strong><span class="linkarray tlpdepth2" id="p3.25GER"> GER [→<a class="ogdlink" href="#p3.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.25PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Es gibt eine und nur eine vollständige Analyse des Satzes.</div>
<div class="corelinks tlpdepth3"><strong>3.251</strong><span class="linkarray tlpdepth3" id="p3.251GER"> GER [→<a class="ogdlink" href="#p3.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.251PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Satz drückt auf bestimmte, klar angebbare Weise aus, was er ausdrückt: Der Satz ist artikuliert.</div>
<div class="corelinks tlpdepth2"><strong>3.26</strong><span class="linkarray tlpdepth2" id="p3.26GER"> GER [→<a class="ogdlink" href="#p3.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.26PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Name ist durch keine Definition weiter zu zergliedern: er ist ein Urzeichen.</div>
<div class="corelinks tlpdepth3"><strong>3.261</strong><span class="linkarray tlpdepth3" id="p3.261GER"> GER [→<a class="ogdlink" href="#p3.261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Jedes definierte Zeichen bezeichnet <em class="germph">über</em> jene Zeichen, durch welche es definiert wurde; und die Definitionen weisen den Weg.</div>
<div class="para tlpdepth3">Zwei Zeichen, ein Urzeichen, und ein durch Urzeichen definiertes, können nicht auf dieselbe Art und Weise bezeichnen. Namen <em class="germph">kann</em> man nicht durch Definitionen auseinanderlegen. (Kein Zeichen, welches allein, selbständig eine Bedeutung hat.)</div>
<div class="corelinks tlpdepth3"><strong>3.262</strong><span class="linkarray tlpdepth3" id="p3.262GER"> GER [→<a class="ogdlink" href="#p3.262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.262PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Was in den Zeichen nicht zum Ausdruck kommt, das zeigt ihre Anwendung. Was die Zeichen verschlucken, das spricht ihre Anwendung aus.</div>
<div class="corelinks tlpdepth3"><strong>3.263</strong><span class="linkarray tlpdepth3" id="p3.263GER"> GER [→<a class="ogdlink" href="#p3.263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Bedeutung von Urzeichen können durch Erläuterungen erklärt werden. Erläuterungen sind Sätze, welche die Urzeichen enthalten. Sie können also nur verstanden werden, wenn die Bedeutungen dieser Zeichen bereits bekannt sind.</div>
<div class="corelinks tlpdepth1"><strong>3.3</strong><span class="linkarray tlpdepth1" id="p3.3GER"> GER [→<a class="ogdlink" href="#p3.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Nur der Satz hat Sinn; nur im Zusammenhang des Satzes hat ein Name Bedeutung.</div>
<div class="corelinks tlpdepth2"><strong>3.31</strong><span class="linkarray tlpdepth2" id="p3.31GER"> GER [→<a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Jeden Teil des Satzes, der seinen Sinn charakterisiert, nenne ich einen Ausdruck (ein Symbol).</div>
<div class="para tlpdepth2">(Der Satz selbst ist ein Ausdruck.)</div>
<div class="para tlpdepth2">Ausdruck ist alles, für den Sinn des Satzes wesentliche, was Sätze miteinander gemein haben können.</div>
<div class="para tlpdepth2">Der Ausdruck kennzeichnet eine Form und einen Inhalt.</div>
<div class="corelinks tlpdepth3"><strong>3.311</strong><span class="linkarray tlpdepth3" id="p3.311GER"> GER [→<a class="ogdlink" href="#p3.311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.311PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Ausdruck setzt die Formen aller Sätze voraus, in welchem er vorkommen kann. Er ist das gemeinsame charakteristische Merkmal einer Klasse von Sätzen.</div>
<div class="corelinks tlpdepth3"><strong>3.312</strong><span class="linkarray tlpdepth3" id="p3.312GER"> GER [→<a class="ogdlink" href="#p3.312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.312PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Er wird also dargestellt durch die allgemeine Form der Sätze, die er charakterisiert.</div>
<div class="para tlpdepth3">Und zwar wird in dieser Form der Ausdruck <em class="germph">konstant</em> und alles übrige <em class="germph">variabel</em> sein.</div>
<div class="corelinks tlpdepth3"><strong>3.313</strong><span class="linkarray tlpdepth3" id="p3.313GER"> GER [→<a class="ogdlink" href="#p3.313OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.313PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Ausdruck wird also durch eine Variable dargestellt, deren Werte die Sätze sind, die den Ausdruck enthalten.</div>
<div class="para tlpdepth3">(Im Grenzfall wird die Variable zur Konstanten, der Ausdruck zum Satz.)</div>
<div class="para tlpdepth3">Ich nenne eine solche Variable „Satzvariable“.</div>
<div class="corelinks tlpdepth3"><strong>3.314</strong><span class="linkarray tlpdepth3" id="p3.314GER"> GER [→<a class="ogdlink" href="#p3.314OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.314PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Ausdruck hat nur im Satz Bedeutung. Jede Variable lässt sich als Satzvariable auffassen.</div>
<div class="para tlpdepth3">(Auch der variable Name.)</div>
<div class="corelinks tlpdepth3"><strong>3.315</strong><span class="linkarray tlpdepth3" id="p3.315GER"> GER [→<a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Verwandeln wir einen Bestandteil eines Satzes in eine Variable, so gibt es eine Klasse von Sätzen, welche sämtlich Werte des so entstandenen variablen Satzes sind. Diese Klasse hängt im allgemeinen noch davon ab, was wir, nach willkürlicher Übereinkunft, mit Teilen jenes Satzes meinen. Verwandeln wir aber alle jene Zeichen, deren Bedeutung willkürlich bestimmt wurde, in Variable, so gibt es nun noch immer eine solche Klasse. Diese aber ist nun von keiner Übereinkunft abhängig, sondern nur noch von der Natur des Satzes. Sie entspricht einer logischen Form – einem logischen Urbild.</div>
<div class="corelinks tlpdepth3"><strong>3.316</strong><span class="linkarray tlpdepth3" id="p3.316GER"> GER [→<a class="ogdlink" href="#p3.316OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.316PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Welche Werte die Satzvariable annehmen darf, wird festgesetzt.</div>
<div class="para tlpdepth3">Die Festsetzung der Werte <em class="germph">ist</em> die Variable.</div>
<div class="corelinks tlpdepth3"><strong>3.317</strong><span class="linkarray tlpdepth3" id="p3.317GER"> GER [→<a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Festsetzung der Werte der Satzvariablen ist die <em class="germph">Angabe der Sätze</em>, deren gemeinsames Merkmal die Variable ist.</div>
<div class="para tlpdepth3">Die Festsetzung ist eine Beschreibung dieser Sätze.</div>
<div class="para tlpdepth3">Die Festsetzung wird also nur von Symbolen, nicht von deren Bedeutung handeln.</div>
<div class="para tlpdepth3">Und <em class="germph">nur</em> dies ist der Festsetzung wesentlich, <em class="germph">dass sie nur eine Beschreibung von Symbolen ist und nicht über das Bezeichnete aussagt</em>.</div>
<div class="para tlpdepth3">Wie die Beschreibung der Sätze geschieht, ist unwesentlich.</div>
<div class="corelinks tlpdepth3"><strong>3.318</strong><span class="linkarray tlpdepth3" id="p3.318GER"> GER [→<a class="ogdlink" href="#p3.318OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.318PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Den Satz fasse ich – wie Frege und Russell – als Funktion der in ihm enthaltenen Ausdrücke auf.</div>
<div class="corelinks tlpdepth2"><strong>3.32</strong><span class="linkarray tlpdepth2" id="p3.32GER"> GER [→<a class="ogdlink" href="#p3.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.32PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Zeichen ist das sinnlich Wahrnehmbare am Symbol.</div>
<div class="corelinks tlpdepth3"><strong>3.321</strong><span class="linkarray tlpdepth3" id="p3.321GER"> GER [→<a class="ogdlink" href="#p3.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.321PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Zwei verschiedene Symbole können also das Zeichen (Schriftzeichen oder Lautzeichen etc.) miteinander gemein haben – sie bezeichnen dann auf verschiedene Art und Weise.</div>
<div class="corelinks tlpdepth3"><strong>3.322</strong><span class="linkarray tlpdepth3" id="p3.322GER"> GER [→<a class="ogdlink" href="#p3.322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es kann nie das gemeinsame Merkmal zweier Gegenstände anzeigen, dass wir sie mit demselben Zeichen, aber durch zwei verschiedene <em class="germph">Bezeichnungsweisen</em> bezeichnen. Denn das Zeichen ist ja willkürlich. Man könnte also auch zwei verschiedene Zeichen wählen, und wo bliebe dann das Gemeinsame in der Bezeichnung?</div>
<div class="corelinks tlpdepth3"><strong>3.323</strong><span class="linkarray tlpdepth3" id="p3.323GER"> GER [→<a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In der Umgangssprache kommt es ungemein häufig vor, dass dasselbe Wort auf verschiedene Art und Weise bezeichnet – also verschiedene Symbolen angehört –, oder, dass zwei Wörter, die auf verschiedene Art und Weise bezeichnen, äußerlich in der gleichen Weise im Satz angewandt werden.</div>
<div class="para tlpdepth3">So erscheint das Wort „ist“ als Kopula, als Gleichheitszeichen und als Ausdruck der Existenz; „existieren“ als intransitives Zeitwort wie „gehen“; „identisch“ als Eigenschaftswort; wir reden von <em class="germph">Etwas</em>, aber auch davon, dass <em class="germph">etwas</em> geschieht.</div>
<div class="para tlpdepth3">(Im Satze „Grün ist grün“ – wo das erste Wort ein Personenname, das letzte ein Eigenschaftswort ist – haben diese Worte nicht einfach verschiedene Bedeutung, sondern es sind <em class="germph">verschiedene Symbole</em>.)</div>
<div class="corelinks tlpdepth3"><strong>3.324</strong><span class="linkarray tlpdepth3" id="p3.324GER"> GER [→<a class="ogdlink" href="#p3.324OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.324PM">P/M</a>]</span></div>
<div class="para tlpdepth3">So entstehen leicht die fundamentalsten Verwechselungen (deren die ganze Philosophie voll ist).</div>
<div class="corelinks tlpdepth3"><strong>3.325</strong><span class="linkarray tlpdepth3" id="p3.325GER"> GER [→<a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Um diesen Irrtümern zu entgehen, müssen wir eine Zeichensprache verwenden, welche sie ausschließt, indem sie nicht das gleiche Zeichen in verschiedenen Symbolen, und Zeichen, welche auf verschiedene Art bezeichnen, nicht äußerlich auf die gleiche Art verwendet. Eine Zeichensprache also, die der <em class="germph">logischen</em> Grammatik – der logischen Syntax – gehorcht.</div>
<div class="para tlpdepth3">(Die Begriffsschrift Freges und Russells ist eine solche Sprache, die allerdings noch nicht alle Fehler ausschließt.)</div>
<div class="corelinks tlpdepth3"><strong>3.326</strong><span class="linkarray tlpdepth3" id="p3.326GER"> GER [→<a class="ogdlink" href="#p3.326OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.326PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Um das Symbol am Zeichen zu erkennen, muss man auf den sinnvollen Gebrauch achten.</div>
<div class="corelinks tlpdepth3"><strong>3.327</strong><span class="linkarray tlpdepth3" id="p3.327GER"> GER [→<a class="ogdlink" href="#p3.327OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.327PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Zeichen bestimmt erst mit seiner logisch-syntaktischen Verwendung zusammen eine logische Form.</div>
<div class="corelinks tlpdepth3"><strong>3.328</strong><span class="linkarray tlpdepth3" id="p3.328GER"> GER [→<a class="ogdlink" href="#p3.328OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.328PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wird ein Zeichen <em class="germph">nicht gebraucht</em>, so ist es bedeutungslos. Das ist der Sinn der Devise Occams.</div>
<div class="para tlpdepth3">(Wenn sich alles so verhält als hätte ein Zeichen Bedeutung, dann hat es auch Bedeutung.)</div>
<div class="corelinks tlpdepth2"><strong>3.33</strong><span class="linkarray tlpdepth2" id="p3.33GER"> GER [→<a class="ogdlink" href="#p3.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.33PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In der logischen Syntax darf nie die Bedeutung eines Zeichens eine Rolle spielen; sie muss sich aufstellen lassen, ohne dass dabei von der <em class="germph">Bedeutung</em> eines Zeichens die Rede wäre, sie darf <em class="germph">nur</em> die Beschreibung der Ausdrücke voraussetzen.</div>
<div class="corelinks tlpdepth3"><strong>3.331</strong><span class="linkarray tlpdepth3" id="p3.331GER"> GER [→<a class="ogdlink" href="#p3.331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.331PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Von dieser Bemerkung sehen wir in Russells „Theory of types“ hinüber: Der Irrtum Russells zeigt sich darin, dass er bei der Aufstellung der Zeichenregeln von der Bedeutung der Zeichen reden musste.</div>
<div class="corelinks tlpdepth3"><strong>3.332</strong><span class="linkarray tlpdepth3" id="p3.332GER"> GER [→<a class="ogdlink" href="#p3.332OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.332PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Kein Satz kann etwas über sich selbst aussagen, weil das Satzzeichen nicht in sich selbst enthalten sein kann (das ist die ganze „Theory of types“).</div>
<div class="corelinks tlpdepth3"><strong>3.333</strong><span class="linkarray tlpdepth3" id="p3.333GER"> GER [→<a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Eine Funktion kann darum nicht ihr eigenes Argument sein, weil das Funktionszeichen bereits das Urbild seines Arguments enthält und es sich nicht selbst enthalten kann.</div>
<div class="para tlpdepth3">Nehmen wir nämlich an, die Funktion <span class="mathmode"><var>F</var>(<var>fx</var>)</span> könnte ihr eigenes Argument sein; dann gäbe es also einen Satz: „<span class="mathmode"><var>F</var>(<var>F</var>(<var>fx</var>))</span>“ und in diesem müssen die äußere Funktion <span class="mathmode"><var>F</var></span> und die innere Funtion <span class="mathmode"><var>F</var></span> verschiedene Bedeutungen haben, denn die innere hat die Form <span class="mathmode"><var>φ</var>(<var>fx</var>)</span>, die äußere die Form <span class="mathmode"><var>ψ</var>(<var>φ</var>(<var>fx</var>))</span>. Gemeinsam ist den beiden Funktionen nur der Buchstabe „<span class="mathmode"><var>F</var></span>“, der aber allein nichts bezeichnet.</div>
<div class="para tlpdepth3">Dies wird sofort klar, wenn wir statt „<span class="mathmode"><var>F</var>(<var>Fu</var>)</span>“ schreiben „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>φ</var>):</span><var>F</var>(<var>φu</var>)<span class="mathrel">.</span><var>φu</var><span class="mathrel">=</span><var>Fu</var></span>“.</div>
<div class="para tlpdepth3">Hiermit erledigt sich Russells Paradox.</div>
<div class="corelinks tlpdepth3"><strong>3.334</strong><span class="linkarray tlpdepth3" id="p3.334GER"> GER [→<a class="ogdlink" href="#p3.334OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.334PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Regeln der logischen Syntax müssen sich von selbst verstehen, wenn man nur weiß, wie ein jedes Zeichen bezeichnet.</div>
<div class="corelinks tlpdepth2"><strong>3.34</strong><span class="linkarray tlpdepth2" id="p3.34GER"> GER [→<a class="ogdlink" href="#p3.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.34PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Satz besitzt wesentliche und zufällige Züge.</div>
<div class="para tlpdepth2">Zufällig sind die Züge, die von der besonderen Art der Hervorbringung des Satzzeichens herrühren. Wesentlich diejenigen, welche allein den Satz befähigen, seinen Sinn auszudrücken.</div>
<div class="corelinks tlpdepth3"><strong>3.341</strong><span class="linkarray tlpdepth3" id="p3.341GER"> GER [→<a class="ogdlink" href="#p3.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.341PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Wesentliche am Satz ist also das, was allen Sätzen, welche den gleichen Sinn ausdrücken können, gemeinsam ist.</div>
<div class="para tlpdepth3">Und ebenso ist allgemein das Wesentliche am Symbol das, was alle Symbole, die denselben Zweck erfüllen können, gemeinsam haben.</div>
<div class="corelinks tlpdepth4"><strong>3.3411</strong><span class="linkarray tlpdepth4" id="p3.3411GER"> GER [→<a class="ogdlink" href="#p3.3411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3411PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Man könnte also sagen: Der eigentliche Name ist das, was alle Symbole, die den Gegenstand bezeichnen, gemeinsam haben. Es würde sich so successive ergeben, dass keinerlei Zusammensetzung für den Namen wesentlich ist.</div>
<div class="corelinks tlpdepth3"><strong>3.342</strong><span class="linkarray tlpdepth3" id="p3.342GER"> GER [→<a class="ogdlink" href="#p3.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.342PM">P/M</a>]</span></div>
<div class="para tlpdepth3">An unseren Notationen ist zwar etwas willkürlich, aber <em class="germph">das</em> ist nicht willkürlich: Dass, <em class="germph">wenn</em> wir etwas willkürlich bestimmt haben, dann etwas anderes der Fall sein muss. (Dies hängt von dem <em class="germph">Wesen</em> der Notation ab.)</div>
<div class="corelinks tlpdepth4"><strong>3.3421</strong><span class="linkarray tlpdepth4" id="p3.3421GER"> GER [→<a class="ogdlink" href="#p3.3421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3421PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Eine besondere Bezeichnungsweise mag unwichtig sein, aber wichtig ist es immer, dass diese eine <em class="germph">mögliche</em> Bezeichnungsweise ist. Und so verhält es sich in der Philosophie überhaupt: Das Einzelne erweist sich immer wieder als unwichtig, aber die Möglichkeit jedes Einzelnen gibt uns einen Aufschluss über das Wesen der Welt.</div>
<div class="corelinks tlpdepth3"><strong>3.343</strong><span class="linkarray tlpdepth3" id="p3.343GER"> GER [→<a class="ogdlink" href="#p3.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.343PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Definitionen sind Regeln der Übersetzung von einer Sprache in eine andere. Jede richtige Zeichensprache muss sich in jede andere nach solchen Regeln übersetzen lassen: <em class="germph">Dies</em> ist, was sie alle gemeinsam haben.</div>
<div class="corelinks tlpdepth3"><strong>3.344</strong><span class="linkarray tlpdepth3" id="p3.344GER"> GER [→<a class="ogdlink" href="#p3.344OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.344PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das, was am Symbol bezeichnet, ist das Gemeinsame aller jener Symbole, durch die das erste den Regeln der logischen Syntax zufolge ersetzt werden kann.</div>
<div class="corelinks tlpdepth4"><strong>3.3441</strong><span class="linkarray tlpdepth4" id="p3.3441GER"> GER [→<a class="ogdlink" href="#p3.3441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Man kann z. B. das Gemeinsame aller Notationen für die Wahrheitsfunktionen so ausdrücken: Es ist ihnen gemeinsam, dass sich alle – z. B. – durch die Notation von „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ („nicht <span class="mathmode"><var>p</var></span>“) und „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>“ („<span class="mathmode"><var>p</var></span> oder <span class="mathmode"><var>q</var></span>“) <em class="germph">ersetzen lassen</em>.</div>
<div class="para tlpdepth4">(Hiermit ist die Art und Weise gekennzeichnet, wie eine spezielle mögliche Notation uns allgemeine Aufschlüsse geben kann.)</div>
<div class="corelinks tlpdepth4"><strong>3.3442</strong><span class="linkarray tlpdepth4" id="p3.3442GER"> GER [→<a class="ogdlink" href="#p3.3442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3442PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das Zeichen des Komplexes löst sich auch bei der Analyse nicht willkürlich auf, so dass etwa seine Auflösung in jedem Satzgefüge eine andere wäre.</div>
<div class="corelinks tlpdepth1"><strong>3.4</strong><span class="linkarray tlpdepth1" id="p3.4GER"> GER [→<a class="ogdlink" href="#p3.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.4PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Der Satz bestimmt einen Ort im logischen Raum. Die Existenz dieses logischen Ortes ist durch die Existenz der Bestandteile allein verbürgt, durch die Existenz des sinnvollen Satzes.</div>
<div class="corelinks tlpdepth2"><strong>3.41</strong><span class="linkarray tlpdepth2" id="p3.41GER"> GER [→<a class="ogdlink" href="#p3.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.41PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Satzzeichen und die logischen Koordinaten: Das ist der logische Ort.</div>
<div class="corelinks tlpdepth3"><strong>3.411</strong><span class="linkarray tlpdepth3" id="p3.411GER"> GER [→<a class="ogdlink" href="#p3.411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.411PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der geometrische und der logische Ort stimmen darin überein, dass beide die Möglichkeit einer Existenz sind.</div>
<div class="corelinks tlpdepth2"><strong>3.42</strong><span class="linkarray tlpdepth2" id="p3.42GER"> GER [→<a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Obwohl der Satz nur einen Ort des logischen Raumes bestimmen darf, so muss doch durch ihn schon der ganze logische Raum gegeben sein.</div>
<div class="para tlpdepth2">(Sonst würden durch die Verneinung, die logische Summe, das logische Produkt, etc. immer neue Elemente – in Koordinaten – eingeführt.)</div>
<div class="para tlpdepth2">(Das logische Gerüst um das Bild herum bestimmt den logischen Raum. Der Satz durchgreift den ganzen logischen Raum.)</div>
<div class="corelinks tlpdepth1"><strong>3.5</strong><span class="linkarray tlpdepth1" id="p3.5GER"> GER [→<a class="ogdlink" href="#p3.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.5PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Das angewandte, gedachte Satzeichen ist der Gedanke.</div>
<div class="corelinks tlpdepth0"><strong>4</strong><span class="linkarray tlpdepth0" id="p4GER"> GER [→<a class="ogdlink" href="#p4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Der Gedanke ist der sinnvolle Satz.</div>
<div class="corelinks tlpdepth3"><strong>4.001</strong><span class="linkarray tlpdepth3" id="p4.001GER"> GER [→<a class="ogdlink" href="#p4.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.001PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Gesamtheit der Sätze ist die Sprache.</div>
<div class="corelinks tlpdepth3"><strong>4.002</strong><span class="linkarray tlpdepth3" id="p4.002GER"> GER [→<a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Mensch besitzt die Fähigkeit Sprachen zu bauen, womit sich jeder Sinn ausdrücken lässt, ohne eine Ahnung davon zu haben, wie und was jedes Wort bedeutet. – Wie man auch spricht, ohne zu wissen, wie die einzelnen Laute hervorgebracht werden.</div>
<div class="para tlpdepth3">Die Umgangssprache ist ein Teil des menschlichen Organismus und nicht weniger kompliziert als dieser.</div>
<div class="para tlpdepth3">Es ist menschenunmöglich, die Sprachlogik aus ihr unmittelbar zu entnehmen.</div>
<div class="para tlpdepth3">Die Sprache verkleidet den Gedanken. Und zwar so, dass man nach der äußeren Form des Kleides, nicht auf deie Form des bekleideten Gedankens schließen kann; weil die äußere Form des Kleides nach ganz anderen Zwecken gebildet ist als danach, die Form des Körpers erkennen zu lassen.</div>
<div class="para tlpdepth3">Die stillschweigenden Abmachungen zum Verständnis der Umgangssprache sind enorm kompliziert.</div>
<div class="corelinks tlpdepth3"><strong>4.003</strong><span class="linkarray tlpdepth3" id="p4.003GER"> GER [→<a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die meisten Sätze und Fragen, welche über philosophische Dinge geschrieben worden sind, sind nicht falsch, sondern unsinnig. Wir können daher Fragen dieser Art überhaupt nicht beantworten, sondern nur ihre Unsinnigkeit feststellen. Die meisten Fragen und Sätze der Philosophen beruhen darauf, dass wir unsere Sprachlogik nicht verstehen.</div>
<div class="para tlpdepth3">(Sie sind von der Art der Frage, ob das Gute mehr oder weniger identisch sei als das Schöne.)</div>
<div class="para tlpdepth3">Und es ist nicht verwunderlich, dass die tiefsten Probleme eigentlich <em class="germph">keine</em> Probleme sind.</div>
<div class="corelinks tlpdepth4"><strong>4.0031</strong><span class="linkarray tlpdepth4" id="p4.0031GER"> GER [→<a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Alle Philosophie ist „Sprachkritik“. (Allerdings nicht im Sinne Mauthners.) Russells Verdienst ist es, gezeigt zu haben, dass die scheinbar logische Form des Satzes nicht seine wirkliche sein muss.</div>
<div class="corelinks tlpdepth2"><strong>4.01</strong><span class="linkarray tlpdepth2" id="p4.01GER"> GER [→<a class="ogdlink" href="#p4.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Satz ist ein Bild der Wirklichkeit.</div>
<div class="para tlpdepth2">Der Satz ist ein Modell der Wirklichkeit, so wie wir sie uns denken.</div>
<div class="corelinks tlpdepth3"><strong>4.011</strong><span class="linkarray tlpdepth3" id="p4.011GER"> GER [→<a class="ogdlink" href="#p4.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.011PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Auf den ersten Blick scheint der Satz – wie er etwa auf dem Papier gedruckt steht – kein Bild der Wirklichkeit zu sein, von der er handelt. Aber auch die Notenschrift scheint auf den ersten Blick kein Bild der Musik zu sein, und unsere Lautzeichen-(Buchstaben-)Schrift kein Bild unserer Lautsprache.</div>
<div class="para tlpdepth3">Und doch erweisen sich diese Zeichensprachen auch im gewöhnlichen Sinne als Bilder dessen, was sie darstellen.</div>
<div class="corelinks tlpdepth3"><strong>4.012</strong><span class="linkarray tlpdepth3" id="p4.012GER"> GER [→<a class="ogdlink" href="#p4.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.012PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Offenbar ist, dass wir einen Satz von der Form „<span class="mathmode"><var>aRb</var></span>“ als Bild empfinden. Hier ist das Zeichen offenbar ein Gleichnis des Bezeichneten.</div>
<div class="corelinks tlpdepth3"><strong>4.013</strong><span class="linkarray tlpdepth3" id="p4.013GER"> GER [→<a class="ogdlink" href="#p4.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.013PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Und wenn wir in das Wesentliche dieser Bildhaftigkeit eindringen, so sehen wir, dass dieselbe durch <em class="germph">scheinbare Unregelmäßigkeiten</em> (wie die Verwendung von <span class="mathmode"><span class="symbol">♯</span></span> und <span class="mathmode"><span class="symbol">♭</span></span> in der Notenschrift) <em class="germph">nicht</em> gestört wird.</div>
<div class="para tlpdepth3">Denn auch diese Unregelmäßigkeiten bilden das ab, was sie ausdrücken sollen; nur auf eine andere Art und Weise.</div>
<div class="corelinks tlpdepth3"><strong>4.014</strong><span class="linkarray tlpdepth3" id="p4.014GER"> GER [→<a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Grammophonplatte, der musikalische Gedanke, die Notenschrift, die Schallwellen, stehen alle in jener abbildenden internen Beziehung zu einander, die zwischen Sprache und Welt besteht.</div>
<div class="para tlpdepth3">Ihnen allen ist der logische Bau gemeinsam.</div>
<div class="para tlpdepth3">(Wie im Märchen die zwei Jünglinge, ihre zwei Pferde und ihre Lilien. Sie sind alle in gewissem Sinne Eins.)</div>
<div class="corelinks tlpdepth4"><strong>4.0141</strong><span class="linkarray tlpdepth4" id="p4.0141GER"> GER [→<a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dass es eine allgemeine Regel gibt, durch die der Musiker aus der Partitur die Symphonie entnehmen kann, durch welche man aus der Linie auf der Grammophonplatte die Symphonie und nach der ersten Regel wieder die Partitur ableiten kann, darin besteht eben die innere Ähnlichkeit dieser scheinbar so ganz verschiedenen Gebilde. Und jene Regel ist das Gesetz der Projektion, welches die Symphonie in die Notensprache projiziert. Sie ist die Regel der Übersetzung der Notensprache in die Sprache der Grammophonplatte.</div>
<div class="corelinks tlpdepth3"><strong>4.015</strong><span class="linkarray tlpdepth3" id="p4.015GER"> GER [→<a class="ogdlink" href="#p4.015OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.015PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Möglichkeit aller Gleichnisse, der ganzen Bildhaftigkeit unserer Ausdrucksweise, ruht in der Logik der Abbildung.</div>
<div class="corelinks tlpdepth3"><strong>4.016</strong><span class="linkarray tlpdepth3" id="p4.016GER"> GER [→<a class="ogdlink" href="#p4.016OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.016PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Um das Wesen des Satzes zu verstehen, denken wir an die Hieroglyphenschrift, welche die Tatsachen die sie beschreibt abbildet.</div>
<div class="para tlpdepth3">Und aus ihr wurde die Buchstabenschrift, ohne das Wesentliche der Abbildung zu verlieren.</div>
<div class="corelinks tlpdepth2"><strong>4.02</strong><span class="linkarray tlpdepth2" id="p4.02GER"> GER [→<a class="ogdlink" href="#p4.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Dies sehen wir daraus, dass wir den Sinn des Satzzeichens verstehen, ohne dass er uns erklärt wurde.</div>
<div class="corelinks tlpdepth3"><strong>4.021</strong><span class="linkarray tlpdepth3" id="p4.021GER"> GER [→<a class="ogdlink" href="#p4.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Satz ist ein Bild der Wirklichkeit: Denn ich kenne die von ihm dargestellte Sachlage, wenn ich den Satz verstehe. Und den Satz verstehe ich, ohne dass mir sein Sinn erklärt wurde.</div>
<div class="corelinks tlpdepth3"><strong>4.022</strong><span class="linkarray tlpdepth3" id="p4.022GER"> GER [→<a class="ogdlink" href="#p4.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.022PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Satz <em class="germph">zeigt</em> seinen Sinn.</div>
<div class="para tlpdepth3">Der Satz <em class="germph">zeigt</em>, wie es sich verhält, <em class="germph">wenn</em> er wahr ist. Und er <em class="germph">sagt</em>, <em class="germph">dass</em> es sich so verhält.</div>
<div class="corelinks tlpdepth3"><strong>4.023</strong><span class="linkarray tlpdepth3" id="p4.023GER"> GER [→<a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Wirklichkeit muss durch den Satz auf ja oder nein fixiert sein.</div>
<div class="para tlpdepth3">Dazu muss sie durch ihn vollständig beschrieben werden.</div>
<div class="para tlpdepth3">Der Satz ist die Beschreibung eines Sachverhaltes.</div>
<div class="para tlpdepth3">Wie die Beschreibung einen Gegenstand nach seinen externen Eigenschaften, so beschreibt der Satz die Wirklichkeit nach ihren internen Eigenschaften.</div>
<div class="para tlpdepth3">Der Satz konstruiert eine Welt mit Hilfe eines logischen Gerüstes und darum kann man am Satz auch sehen, wie sich alles Logische verhält, <em class="germph">wenn</em> er wahr ist. Man kann aus einem falschen Satz <em class="germph">Schlüsse ziehen</em>.</div>
<div class="corelinks tlpdepth3"><strong>4.024</strong><span class="linkarray tlpdepth3" id="p4.024GER"> GER [→<a class="ogdlink" href="#p4.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.024PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Einen Satz verstehen, heißt, wissen was der Fall ist, wenn er wahr ist.</div>
<div class="para tlpdepth3">(Man kann ihn also verstehen, ohne zu wissen, ob er wahr ist.)</div>
<div class="para tlpdepth3">Man versteht ihn, wenn man seine Bestandteile versteht.</div>
<div class="corelinks tlpdepth3"><strong>4.025</strong><span class="linkarray tlpdepth3" id="p4.025GER"> GER [→<a class="ogdlink" href="#p4.025OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.025PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Übersetzung einer Sprache in eine andere geht nicht so vor sich, dass man jeden <em class="germph">Satz</em> der einen in einen <em class="germph">Satz</em> der anderen übersetzt, sondern nur die Satzbestandteile werden übersetzt.</div>
<div class="para tlpdepth3">(Und das Wörterbuch übersetzt nicht nur Substantiva, sondern auch Zeit-, Eigenschafts- und Bindewörter etc.; und es behandelt sie alle gleich.)</div>
<div class="corelinks tlpdepth3"><strong>4.026</strong><span class="linkarray tlpdepth3" id="p4.026GER"> GER [→<a class="ogdlink" href="#p4.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Bedeutung der einfachen Zeichen (der Wörter) müssen uns erklärt werden, dass wir sie verstehen.</div>
<div class="para tlpdepth3">Mit den Sätzen aber verständigen wir uns.</div>
<div class="corelinks tlpdepth3"><strong>4.027</strong><span class="linkarray tlpdepth3" id="p4.027GER"> GER [→<a class="ogdlink" href="#p4.027OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.027PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es liegt im Wesen des Satzes, dass er uns einen <em class="germph">neuen</em> Sinn mitteilen kann.</div>
<div class="corelinks tlpdepth2"><strong>4.03</strong><span class="linkarray tlpdepth2" id="p4.03GER"> GER [→<a class="ogdlink" href="#p4.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Ein Satz muss mit alten Ausdrücken einen neuen Sinn mitteilen.</div>
<div class="para tlpdepth2">Der Satz teilt uns eine Sachlage mit, also muss er <em class="germph">wesentlich</em> mit der Sachlage zusammenhängen.</div>
<div class="para tlpdepth2">Und der Zusammenhang ist eben, dass er ihr logisches Bild ist.</div>
<div class="para tlpdepth2">Der Satz sagt nur insoweit etwas aus, als er ein Bild ist.</div>
<div class="corelinks tlpdepth3"><strong>4.031</strong><span class="linkarray tlpdepth3" id="p4.031GER"> GER [→<a class="ogdlink" href="#p4.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.031PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Im Satz wird gleichsam eine Sachlage probeweise zusammengestellt.</div>
<div class="para tlpdepth3">Man kann geradezu sagen: statt, dieser Satz hat diesen und diesen Sinn; dieser Satz stellt diese und diese Sachlage dar.</div>
<div class="corelinks tlpdepth4"><strong>4.0311</strong><span class="linkarray tlpdepth4" id="p4.0311GER"> GER [→<a class="ogdlink" href="#p4.0311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Ein Name steht für ein Ding, ein anderer für ein anderes Ding und untereinander sind sie verbunden, so stellt das Ganze – wie ein lebendes Bild – den Sachverhalt vor.</div>
<div class="corelinks tlpdepth4"><strong>4.0312</strong><span class="linkarray tlpdepth4" id="p4.0312GER"> GER [→<a class="ogdlink" href="#p4.0312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Möglichkeit des Satzes beruht auf dem Prinzip der Vertretung von Gegenständen durch Zeichen.</div>
<div class="para tlpdepth4">Mein Grundgedanke ist, dass die „logischen Konstanten“ nicht vertreten. Dass sich die <em class="germph">Logik</em> der Tatsachen nicht vertreten lässt.</div>
<div class="corelinks tlpdepth3"><strong>4.032</strong><span class="linkarray tlpdepth3" id="p4.032GER"> GER [→<a class="ogdlink" href="#p4.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.032PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Nur insoweit ist der Satz ein Bild der Sachlage, als er logisch gegliedert ist.</div>
<div class="para tlpdepth3">(Auch der Satz: „ambulo“, ist zusammengesetzt, denn sein Stamm ergibt mit einer anderen Endung, und seine Endung mit einem anderen Stamm, einen anderen Sinn.)</div>
<div class="corelinks tlpdepth2"><strong>4.04</strong><span class="linkarray tlpdepth2" id="p4.04GER"> GER [→<a class="ogdlink" href="#p4.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Am Satz muss gerade soviel zu unterscheiden sein, als an der Sachlage, die er darstellt.</div>
<div class="para tlpdepth2">Die beiden müssen die gleiche logische (mathematische) Mannigfaltigkeit besitzen. (Vergleiche Hertz’s „Mechanik“, über dynamische Modelle.)</div>
<div class="corelinks tlpdepth3"><strong>4.041</strong><span class="linkarray tlpdepth3" id="p4.041GER"> GER [→<a class="ogdlink" href="#p4.041OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.041PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Diese mathematische Mannigfaltigkeit kann man natürlich nicht selbst wieder abbilden. Aus ihr kann man beim Abbilden nicht heraus.</div>
<div class="corelinks tlpdepth4"><strong>4.0411</strong><span class="linkarray tlpdepth4" id="p4.0411GER"> GER [→<a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wollten wir z. B. das, was wir durch „<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>“ ausdrücken, durch Vorsetzen eines Indexes von „<span class="mathmode"><var>fx</var></span>“ ausdrücken – etwa so: „<span class="mathmode"><span class="mathop"><span class="mathrm">Alg.</span></span><var>fx</var></span>“ – es würde nicht genügen – wir wüssten nicht, was verallgemeinert wurde. Wollten wir es durch einen Index „<span class="mathmode"><sub><var>a</var></sub></span>“ anzeigen – etwa so: „<span class="mathmode"><var>f</var>(<var>x</var><sub><var>a</var></sub>)</span>“ – es würde auch nicht genügen – wir wüssten nicht den Bereich der Allgemeinheitsbezeichnung.</div>
<div class="para tlpdepth4">Wollten wir es durch Einführung einer Marke in die Argumentstellen versuchen – etwa so: „<span class="mathmode"><span class="mathop">(<var>A</var>, <var>A</var>).</span> <var>F</var>(<var>A</var>, <var>A</var>)</span>“ – es würde nicht genügen – wir könnten die Identität der Variablen nicht feststellen. U.s.w.</div>
<div class="para tlpdepth4">Alle diese Bezeichnungsweisen genügen nicht, weil sie nicht die notwendige mathematische Mannigfaltigkeit haben.</div>
<div class="corelinks tlpdepth4"><strong>4.0412</strong><span class="linkarray tlpdepth4" id="p4.0412GER"> GER [→<a class="ogdlink" href="#p4.0412OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0412PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Aus demselben Grunde genügt die idealistische Erklärung des Sehens der räumlichen Beziehung durch die „Raumbrille“ nicht, weil sie nicht die Mannigfaltigkeit dieser Beziehungen erklären kann.</div>
<div class="corelinks tlpdepth2"><strong>4.05</strong><span class="linkarray tlpdepth2" id="p4.05GER"> GER [→<a class="ogdlink" href="#p4.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.05PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Wirklichkeit wird mit dem Satz verglichen.</div>
<div class="corelinks tlpdepth2"><strong>4.06</strong><span class="linkarray tlpdepth2" id="p4.06GER"> GER [→<a class="ogdlink" href="#p4.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.06PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Nur dadurch kann der Satz wahr oder falsch sein, indem er ein Bild der Wirklichkeit ist.</div>
<div class="corelinks tlpdepth3"><strong>4.061</strong><span class="linkarray tlpdepth3" id="p4.061GER"> GER [→<a class="ogdlink" href="#p4.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.061PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Beachtet man nicht, dass der Satz einen von den Tatsachen unabhängigen Sinn hat, so kann man leicht glauben, dass wahr und falsch gleichberechtigte Beziehungen von Zeichen und Bezeichnetem sind.</div>
<div class="para tlpdepth3">Man könnte dann z. B. sagen, dass „<span class="mathmode"><var>p</var></span>“ auch die wahre Art bezeichnet, was „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ auf die falsche Art, etc.</div>
<div class="corelinks tlpdepth3"><strong>4.062</strong><span class="linkarray tlpdepth3" id="p4.062GER"> GER [→<a class="ogdlink" href="#p4.062OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.062PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Kann man sich nicht mit falschen Sätzen, wie bisher mit wahren, verständigen? Solange man nur weiß, dass sie falsch gemeint sind. Nein! Denn, wahr ist ein Satz, wenn es sich so verhält, wie wir es durch ihn sagen; und wenn wir mit „<span class="mathmode"><var>p</var></span>“ <span class="mathmode"><span class="mathop">~</span><var>p</var></span> meinen, und es sich so verhält wie wir es meinen, so ist „<span class="mathmode"><var>p</var></span>“ in der neuen Auffassung wahr und nicht falsch.</div>
<div class="corelinks tlpdepth4"><strong>4.0621</strong><span class="linkarray tlpdepth4" id="p4.0621GER"> GER [→<a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dass aber die Zeichen „<span class="mathmode"><var>p</var></span>“ und „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ das gleiche sagen <em class="germph">können</em>, ist wichtig. Denn es zeigt, dass dem Zeichen „~“ in der Wirklichkeit nichts entspricht.</div>
<div class="para tlpdepth4">Dass in einem Satz die Verneinung vorkommt, ist noch kein Merkmal seines Sinnes (<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var><span class="mathrel">=</span><var>p</var></span>).</div>
<div class="para tlpdepth4">Die Sätze „<span class="mathmode"><var>p</var></span>“ und „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ haben entgegengesetzten Sinn, aber es entspricht ihnen eine und dieselbe Wirklichkeit.</div>
<div class="corelinks tlpdepth3"><strong>4.063</strong><span class="linkarray tlpdepth3" id="p4.063GER"> GER [→<a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ein Bild zur Erklärung des Wahrheitsbegriffes: Schwarzer Fleck auf weißem Papier; die Form des Fleckes kann man beschreiben, indem man für jeden Punkt der Fläche angibt, ob er weiß oder schwarz ist. Der Tatsache, dass ein Punkt schwarz ist, entspricht eine positive – der, dass ein Punkt weiß (nicht schwarz) ist, eine negative Tatsache. Bezeichne ich einen Punkt der Fläche (einen Fregeschen Wahrheitswert), so entspricht dies der Annahme, die zur Beurteilung aufgestellt wird, etc. etc.</div>
<div class="para tlpdepth3">Um aber sagen zu können, ein Punkt sei schwarz oder weiß, muss ich vorerst wissen, wann man einen Punkt schwarz und wann man ihn weiß nennt; um sagen zu können: „<span class="mathmode"><var>p</var></span>“ ist wahr (oder falsch), muss ich bestimmt haben, unter welchen Umständen ich „<span class="mathmode"><var>p</var></span>“ wahr nenne, und damit bestimme ich den Sinn des Satzes.</div>
<div class="para tlpdepth3">Der Punkt, an dem das Gleichnis hinkt ist nun der: Wir können auf einen Punkt des Papiers zeigen, auch ohne zu wissen, was weiß und schwarz ist; einem Satz ohne Sinn aber entspricht gar nichts, denn er bezeichnet kein Ding (Wahrheitswert) dessen Eigenschaften etwa „falsch“ oder „wahr“ hießen; das Verbum eines Satzes ist nicht „ist wahr“ oder „ist falsch“ – wie Frege glaubte –, sondern das, was „wahr ist“, muss das Verbum schon enthalten.</div>
<div class="corelinks tlpdepth3"><strong>4.064</strong><span class="linkarray tlpdepth3" id="p4.064GER"> GER [→<a class="ogdlink" href="#p4.064OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.064PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Jeder Satz muss <em class="germph">schon</em> einen Sinn haben; die Bejahung kann ihn ihm nicht geben, denn sie bejaht ja gerade den Sinn. Und dasselbe gilt von der Verneinung, etc.</div>
<div class="corelinks tlpdepth4"><strong>4.0641</strong><span class="linkarray tlpdepth4" id="p4.0641GER"> GER [→<a class="ogdlink" href="#p4.0641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0641PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Man könnte sagen: Die Verneinung bezieht sich schon auf den logischen Ort, den der verneinte Satz bestimmt.</div>
<div class="para tlpdepth4">Der verneinende Satz bestimmt einen <em class="germph">anderen</em> logischen Ort als der verneinte.</div>
<div class="para tlpdepth4">Der verneinende Satz bestimmt einen logischen Ort mit Hilfe des logischen Ortes des verneinten Satzes, indem er jenen als außerhalb diesem liegend beschreibt.</div>
<div class="para tlpdepth4">Dass man den verneinten Satz wieder verneinen kann, zeigt schon, dass das, was verneint wird, schon ein Satz und nicht erst die Vorbereitung zu einem Satze ist.</div>
<div class="corelinks tlpdepth1"><strong>4.1</strong><span class="linkarray tlpdepth1" id="p4.1GER"> GER [→<a class="ogdlink" href="#p4.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Der Satz stellt das Bestehen und Nichtbestehen der Sachverhalte dar.</div>
<div class="corelinks tlpdepth2"><strong>4.11</strong><span class="linkarray tlpdepth2" id="p4.11GER"> GER [→<a class="ogdlink" href="#p4.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Gesamtheit der wahren Sätze ist die gesamte Naturwissenschaft (oder die Gesamtheit der Naturwissenschaften).</div>
<div class="corelinks tlpdepth3"><strong>4.111</strong><span class="linkarray tlpdepth3" id="p4.111GER"> GER [→<a class="ogdlink" href="#p4.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.111PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Philosophie ist keine der Naturwissenschaften.</div>
<div class="para tlpdepth3">(Das Wort „Philosophie“ muss etwas bedeuten, was über oder unter, aber nicht neben den Naturwissenschaften steht.)</div>
<div class="corelinks tlpdepth3"><strong>4.112</strong><span class="linkarray tlpdepth3" id="p4.112GER"> GER [→<a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Zweck der Philosophie ist die logische Klärung der Gedanken.</div>
<div class="para tlpdepth3">Die Philosophie ist keine Lehre, sondern eine Tätigkeit.</div>
<div class="para tlpdepth3">Ein philosophisches Werk besteht wesentlich aus Erläuterungen.</div>
<div class="para tlpdepth3">Das Resultat der Philosophie sind nicht „philosophische Sätze“, sondern das Klarwerden von Sätzen.</div>
<div class="para tlpdepth3">Die Philosophie soll die Gedanken, die sonst, gleichsam, trübe und verschwommen sind, klar machen und scharf abgrenzen.</div>
<div class="corelinks tlpdepth4"><strong>4.1121</strong><span class="linkarray tlpdepth4" id="p4.1121GER"> GER [→<a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Psychologie ist der Philosophie nicht verwandter als irgend eine andere Naturwissenschaft.</div>
<div class="para tlpdepth4">Erkenntnistheorie ist die Philosophie der Psychologie.</div>
<div class="para tlpdepth4">Entspricht nicht mein Studium der Zeichensprache dem Studium der Denkprozesse, welches die Philosophen für die Philosophie der Logik für so wesentlich hielten? Nur verwickelten sie sich meistens in unwesentliche psychologische Untersuchungen und eine analoge Gefahr gibt es auch bei meiner Methode.</div>
<div class="corelinks tlpdepth4"><strong>4.1122</strong><span class="linkarray tlpdepth4" id="p4.1122GER"> GER [→<a class="ogdlink" href="#p4.1122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1122PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Darwinsche Theorie hat mit der Philosophie nicht mehr zu schaffen als irgendeine andere Hypothese der Naturwissenschaft.</div>
<div class="corelinks tlpdepth3"><strong>4.113</strong><span class="linkarray tlpdepth3" id="p4.113GER"> GER [→<a class="ogdlink" href="#p4.113OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.113PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Philosophie begrenzt das bestreitbare Gebiet der Naturwissenschaft.</div>
<div class="corelinks tlpdepth3"><strong>4.114</strong><span class="linkarray tlpdepth3" id="p4.114GER"> GER [→<a class="ogdlink" href="#p4.114OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.114PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Sie soll das Denkbare abgrenzen und damit das Undenkbare.</div>
<div class="para tlpdepth3">Sie soll das Undenkbare von innen durch das Denkbare begrenzen.</div>
<div class="corelinks tlpdepth3"><strong>4.115</strong><span class="linkarray tlpdepth3" id="p4.115GER"> GER [→<a class="ogdlink" href="#p4.115OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.115PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Sie wird das Unsagbare bedeuten, indem sie das Sagbare klar darstellt.</div>
<div class="corelinks tlpdepth3"><strong>4.116</strong><span class="linkarray tlpdepth3" id="p4.116GER"> GER [→<a class="ogdlink" href="#p4.116OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.116PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Alles was überhaupt gedacht werden kann, kann klar gedacht werden. Alles, was sich aussprechen lässt, lässt sich klar aussprechen.</div>
<div class="corelinks tlpdepth2"><strong>4.12</strong><span class="linkarray tlpdepth2" id="p4.12GER"> GER [→<a class="ogdlink" href="#p4.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Satz kann die gesamte Wirklichkeit darstellen, aber er kann nicht das darstellen, was er mit der Wirklichkeit gemein haben muss, um sie darstellen zu können – die logische Form.</div>
<div class="para tlpdepth2">Um die logische Form darstellen zu können, müssten wir uns mit dem Satze außerhalb der Logik aufstellen können, das heißt außerhalb der Welt.</div>
<div class="corelinks tlpdepth3"><strong>4.121</strong><span class="linkarray tlpdepth3" id="p4.121GER"> GER [→<a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Satz kann die logische Form nicht darstellen, sie spiegelt sich in ihm.</div>
<div class="para tlpdepth3">Was sich in der Sprache spiegelt, kann sie nicht darstellen.</div>
<div class="para tlpdepth3">Was <em class="germph">sich</em> in der Sprache ausdrückt, können <em class="germph">wir</em> nicht durch sie ausdrücken.</div>
<div class="para tlpdepth3">Der Satz <em class="germph">zeigt</em> die logische Form der Wirklichkeit.</div>
<div class="para tlpdepth3">Er weist sie auf.</div>
<div class="corelinks tlpdepth4"><strong>4.1211</strong><span class="linkarray tlpdepth4" id="p4.1211GER"> GER [→<a class="ogdlink" href="#p4.1211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span></div>
<div class="para tlpdepth4">So zeigt ein Satz „<span class="mathmode"><var>fa</var></span>“, dass in seinem Sinn der Gegenstand <span class="mathmode"><var>a</var></span> vorkommt, zwei Sätze „<span class="mathmode"><var>fa</var></span>“ und „<span class="mathmode"><var>ga</var></span>“, dass in ihnen beiden von demselben Gegenstand die Rede ist.</div>
<div class="para tlpdepth4">Wenn zwei Sätze einander widersprechen. So zeigt dies ihre Struktur; ebenso, wenn einer aus dem anderen folgt. U.s.w.</div>
<div class="corelinks tlpdepth4"><strong>4.1212</strong><span class="linkarray tlpdepth4" id="p4.1212GER"> GER [→<a class="ogdlink" href="#p4.1212OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1212PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Was gezeigt werden <em class="germph">kann</em>, <em class="germph">kann</em> nicht gesagt werden.</div>
<div class="corelinks tlpdepth4"><strong>4.1213</strong><span class="linkarray tlpdepth4" id="p4.1213GER"> GER [→<a class="ogdlink" href="#p4.1213OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1213PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Jetzt verstehen wir auch unser Gefühl: dass wir im Besitze einer richtigen logischen Auffassung seien, wenn nur einmal alles in unserer Zeichensprache stimmt.</div>
<div class="corelinks tlpdepth3"><strong>4.122</strong><span class="linkarray tlpdepth3" id="p4.122GER"> GER [→<a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wir können in gewissem Sinne von formalen Eigenschaften der Gegenstände und Sachverhalte bezw. von Eigenschaften der Struktur der Tatsachen reden, und in demselben Sinne von formalen Relationen und Relationen von Strukturen.</div>
<div class="para tlpdepth3">(Statt Eigenschaft der Struktur sage ich auch „interne Eigenschaft“; statt Relation der Strukturen „interne Relation“.</div>
<div class="para tlpdepth3">Ich führe diese Ausdrücke ein, um den Grund der bei den Philosophen sehr verbreiteten Verwechslung zwischen den internen Relationen und den eigentlichen (externen) Relationen zu zeigen.)</div>
<div class="para tlpdepth3">Das Bestehen solcher interner Eigenschaften und Relationen kann aber nicht durch Sätze behauptet werden, sondern es zeigt sich in den Sätzen, welche jene Sachverhalte darstellen und von jenen Gegenständen handeln.</div>
<div class="corelinks tlpdepth4"><strong>4.1221</strong><span class="linkarray tlpdepth4" id="p4.1221GER"> GER [→<a class="ogdlink" href="#p4.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1221PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Eine interne Eigenschaft einer Tatsache können wir auch einen Zug dieser Tatsache nennen. (In dem Sinn, in welchem wir etwa von Gesichtszügen sprechen.)</div>
<div class="corelinks tlpdepth3"><strong>4.123</strong><span class="linkarray tlpdepth3" id="p4.123GER"> GER [→<a class="ogdlink" href="#p4.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.123PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Eine Eigenschaft ist intern, wenn es undenkbar ist, dass ihr Gegenstand sie nicht besitzt.</div>
<div class="para tlpdepth3">(Diese blaue Farbe und jene stehen in der internen Relation von heller und dunkler eo ipso. Es ist undenkbar, dass <em class="germph">diese</em> beiden Gegenstände nicht in dieser Relation stünden.)</div>
<div class="para tlpdepth3">(Hier entspricht dem schwankenden Gebrauch der Worte „Eigenschaft“ und „Relation“ der schwankende Gebrauch des Wortes „Gegenstand“.)</div>
<div class="corelinks tlpdepth3"><strong>4.124</strong><span class="linkarray tlpdepth3" id="p4.124GER"> GER [→<a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bestehen einer internen Eigenschaft einer möglichen Sachlage wird nicht durch einen Satz ausgedrückt, sondern es drückt sich in dem sie darstellenden Satz durch eine interne Eigenschaft dieses Satzes aus.</div>
<div class="para tlpdepth3">Es wäre ebenso unsinnig, dem Satze eine formale Eigenschaft zuzusprechen, als sie ihm abzusprechen.</div>
<div class="corelinks tlpdepth4"><strong>4.1241</strong><span class="linkarray tlpdepth4" id="p4.1241GER"> GER [→<a class="ogdlink" href="#p4.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1241PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Formen kann man nicht dadurch voneinander unterscheiden, dass man sagt, die eine habe diese, die andere aber jene Eigenschaft; denn dies setzt voraus, dass es einen Sinn habe, beide Eigenschaften von beiden Formen auszusagen.</div>
<div class="corelinks tlpdepth3"><strong>4.125</strong><span class="linkarray tlpdepth3" id="p4.125GER"> GER [→<a class="ogdlink" href="#p4.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Bestehen einer internen Relation zwischen möglichen Sachlagen drückt sich sprachlich durch eine interne Relation zwischen den sie darstellenden Sätzen aus.</div>
<div class="corelinks tlpdepth4"><strong>4.1251</strong><span class="linkarray tlpdepth4" id="p4.1251GER"> GER [→<a class="ogdlink" href="#p4.1251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1251PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Hier erledigt sich nun die Streitfrage, „ob alle Relationen intern oder extern seien“.</div>
<div class="corelinks tlpdepth4"><strong>4.1252</strong><span class="linkarray tlpdepth4" id="p4.1252GER"> GER [→<a class="ogdlink" href="#p4.1252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Reihen, welche durch <em class="germph">interne</em> Relationen geordnet sind, nenne ich Formenreihen.</div>
<div class="para tlpdepth4">Die Zahlenreihe ist nicht nach einer externen, sondern nach einer internen Relation geordnet.</div>
<div class="para tlpdepth4">Ebenso die Reihe der Sätze „<span class="mathmode"><var>aRb</var></span>“,</div>
<div class="para tlpdepth4">„<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRb</var></span>“,</div>
<div class="para tlpdepth4">„<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRy</var><span class="mathrel">.</span><var>yRb</var></span>“, u. s. f.</div>
<div class="para tlpdepth4">(Steht <span class="mathmode"><var>b</var></span> in einer dieser Beziehungen zu <span class="mathmode"><var>a</var></span>, so nenne ich <span class="mathmode"><var>b</var></span> einen Nachfolder von <span class="mathmode"><var>a</var></span>.)</div>
<div class="corelinks tlpdepth3"><strong>4.126</strong><span class="linkarray tlpdepth3" id="p4.126GER"> GER [→<a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In dem Sinne, in welchem wir von formalen Eigenschaften sprechen, können wir nun auch von formalen Begriffen reden.</div>
<div class="para tlpdepth3">(Ich führe diesen Ausdruck ein, um den Grund der Verwechslung der formalen Begriffe mit den eigentlichen Begriffen, welche die ganze alte Logik durchzieht, klar zu machen.)</div>
<div class="para tlpdepth3">Dass etwas unter einen formalen Begriff als dessen Gegenstand fällt, kann nicht durch einen Satz ausgedrückt werden. Sondern es zeigt sich an dem Zeichen dieses Gegenstandes selbst. (Der Name zeigt, dass er einen Gegenstand bezeichnet, das Zahlenzeichen, dass es eine Zahl bezeichnet etc.)</div>
<div class="para tlpdepth3">Die formalen Begriffe können ja nicht, wie die eigentlichen Begriffe, durch eine Funktion dargestellt werden.</div>
<div class="para tlpdepth3">Denn ihre Merkmale, die formalen Eigenschaften, werden nicht durch Funktionen ausgedrückt.</div>
<div class="para tlpdepth3">Der Ausdruck der formalen Eigenschaft ist ein Zug gewisser Symbole.</div>
<div class="para tlpdepth3">Das Zeichen der Merkmale eines formalen Begriffes ist also ein charakteristischer Zug aller Symbole, deren Bedeutungen unter den Begriff fallen.</div>
<div class="para tlpdepth3">Der Ausdruck des formalen Begriffes, also, eine Satzvariable, in welcher nur dieser charakteristische Zug konstant ist.</div>
<div class="corelinks tlpdepth3"><strong>4.127</strong><span class="linkarray tlpdepth3" id="p4.127GER"> GER [→<a class="ogdlink" href="#p4.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.127PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Satzvariable bezeichnet den formalen Begriff und ihre Werte die Gegenstände, welche unter diesen Begriff fallen.</div>
<div class="corelinks tlpdepth4"><strong>4.1271</strong><span class="linkarray tlpdepth4" id="p4.1271GER"> GER [→<a class="ogdlink" href="#p4.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Jede Variable ist das Zeichen eines formalen Begriffes.</div>
<div class="para tlpdepth4">Denn jede Variable stellt eine konstante Form dar, welche alle ihre Werte besitzen, und die als formale Eigenschaft dieser Werte aufgefasst werden kann.</div>
<div class="corelinks tlpdepth4"><strong>4.1272</strong><span class="linkarray tlpdepth4" id="p4.1272GER"> GER [→<a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span></div>
<div class="para tlpdepth4">So ist der variable Name „<span class="mathmode"><var>x</var></span>“ das eigentliche Zeichen des Scheinbegriffes <em class="germph">Gegenstand</em>.</div>
<div class="para tlpdepth4">Wo immer das Wort „Gegenstand“ („Ding“, „Sache“, etc.) richtig gebraucht wird, wird es in der Begriffsschrift durch den variablen Namen ausgedrückt.</div>
<div class="para tlpdepth4">Zum Beispiel in dem Satz „es gibt 2 Gegenstände, welche …“ durch „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>)</span><span class="mathrel">…</span></span>“.</div>
<div class="para tlpdepth4">Wo immer es anders, also als eigentliches Begriffswort gebraucht wird, entstehen unsinnige Scheinsätze.</div>
<div class="para tlpdepth4">So kann man z. B. nicht sagen „Es gibt Gegenstände“, wie man etwa sagt: „Es gibt Bücher“. Und ebenso wenig: „Es gibt 100 Gegenstände“, oder „Es gibt <span class="mathmode"><span class="symbol">ℵ</span><sub>0</sub></span> Gegenstände“.</div>
<div class="para tlpdepth4">Und es ist unsinnig, von der <em class="germph">Anzahl aller Gegenstände</em> zu sprechen.</div>
<div class="para tlpdepth4">Dasselbe gilt von den Worten „Komplex“, „Tatsache“, „Funktion“, „Zahl“, etc.</div>
<div class="para tlpdepth4">Sie alle bezeichnen formale Begriffe und werden in der Begriffsschrift durch Variable, nicht durch Funktionen oder Klassen dargestellt. (Wie Frege und Russell glaubten.)</div>
<div class="para tlpdepth4">Ausdrücke wie „1 ist eine Zahl“, „Es gibt nur Eine Null“ und alle ähnlichen sind unsinnig.</div>
<div class="para tlpdepth4">(Es ist ebenso unsinnig zu sagen: „Es gibt nur Eine 1“, als es unsinnig wäre, zu sagen: „<span class="mathmode">2<span class="mathrel">+</span>2</span> ist um 3 Uhr gleich 4“.)</div>
<div class="corelinks tlpdepth5"><strong>4.12721</strong><span class="linkarray tlpdepth5" id="p4.12721GER"> GER [→<a class="ogdlink" href="#p4.12721OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12721PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Der formale Begriff ist mit einem Gegenstand, der unter ihn fällt, bereits gegeben. Man kann also nicht Gegenstände eines formalen Begriffes <em class="germph">und</em> den formalen Begriff selbst als Grundbegriffe einführen. Man kann also z. B. nicht den Begriff der Funktion, und auch spezielle Funktionen (wie Russell) als Grundbegriffe einführen; oder den Begriff der Zahl und bestimmte Zahlen.</div>
<div class="corelinks tlpdepth4"><strong>4.1273</strong><span class="linkarray tlpdepth4" id="p4.1273GER"> GER [→<a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wollen wir den allgemeinen Satz: „<span class="mathmode"><var>b</var></span> ist ein Nachfolger von <span class="mathmode"><var>a</var></span>“ in der Begriffsschrift ausdrücken, so brauchen wir hierzu einen Ausdruck für das allgemeine Glied der Formenreihe:</div>
<div class="para tlpdepth4"><div class="centered"><span class="mathmode"><var>aRb</var></span>,<br />
<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRb</var></span>,<br />
<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRy</var><span class="mathrel">.</span><var>yRb</var></span>,<br />
…&nbsp; .</div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> Das allgemeine Glied einer Formenreihe kann man nur durch eine Variable ausdrücken, denn der Begriff: Glied dieser Formenreihe, ist ein <em class="germph">formaler</em> Begriff. (Dies haben Frege und Russell übersehen; die Art und Weise, wie sie allgemeine Sätze wie den obigen ausdrücken wollen, ist daher falsch; sie enthält einen circulus vitiosus.)</div>
<div class="para tlpdepth4">Wir können das allgemeine Glied der Formenreihe bestimmen, indem wir ihr erstes Glied angeben und die allgemeine Form der Operation, welche das folgende Glied aus dem vorhergehenden Satz erzeugt.</div>
<div class="corelinks tlpdepth4"><strong>4.1274</strong><span class="linkarray tlpdepth4" id="p4.1274GER"> GER [→<a class="ogdlink" href="#p4.1274OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Frage nach der Existenz eines formalen Begriffes ist unsinnig. Denn kein Satz kann eine solche Frage beantworten.</div>
<div class="para tlpdepth4">(Man kann also z. B. nicht fragen: „Gibt es unanalysierbare Subjekt-Prädikatsätze?“)</div>
<div class="corelinks tlpdepth3"><strong>4.128</strong><span class="linkarray tlpdepth3" id="p4.128GER"> GER [→<a class="ogdlink" href="#p4.128OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die logischen Formen sind zah<em class="germph">llos</em>.</div>
<div class="para tlpdepth3">Darum gibt es in der Logik keine ausgezeichneten Zahlen und darum gibt es keinen philosophischen Monismus oder Dualismus, etc.</div>
<div class="corelinks tlpdepth1"><strong>4.2</strong><span class="linkarray tlpdepth1" id="p4.2GER"> GER [→<a class="ogdlink" href="#p4.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Der Sinn des Satzes ist seine Übereinstimmung und Nichtübereinstimmung mit den Möglichkeiten des Bestehens und Nichtbestehens der Sachverhalte.</div>
<div class="corelinks tlpdepth2"><strong>4.21</strong><span class="linkarray tlpdepth2" id="p4.21GER"> GER [→<a class="ogdlink" href="#p4.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der einfachste Satz, der Elementarsatz, behauptet das Bestehen eines Sachverhaltes.</div>
<div class="corelinks tlpdepth3"><strong>4.211</strong><span class="linkarray tlpdepth3" id="p4.211GER"> GER [→<a class="ogdlink" href="#p4.211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.211PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ein Zeichen des Elementarsatzes ist es, dass kein Elementarsatz mit ihm in Widerspruch stehen kann.</div>
<div class="corelinks tlpdepth2"><strong>4.22</strong><span class="linkarray tlpdepth2" id="p4.22GER"> GER [→<a class="ogdlink" href="#p4.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Elementarsatz besteht aus Namen. Er ist ein Zusammenhang, eine Verkettung, von Namen.</div>
<div class="corelinks tlpdepth3"><strong>4.221</strong><span class="linkarray tlpdepth3" id="p4.221GER"> GER [→<a class="ogdlink" href="#p4.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.221PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist offenbar, dass wir bei der Analyse der Sätze auf Elementarsätze kommen müssen, die aus Namen in unmittelbarer Verbindung bestehen.</div>
<div class="para tlpdepth3">Es frägt sich hier, wie kommt der Satzverband zustande.</div>
<div class="corelinks tlpdepth4"><strong>4.2211</strong><span class="linkarray tlpdepth4" id="p4.2211GER"> GER [→<a class="ogdlink" href="#p4.2211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Auch wenn die Welt unendlich komplex ist, so dass jede Tatsache aus unendlich vielen Sachverhalten besteht und jeder Sachverhalt aus unendlich vielen Gegenständen zusammengesetzt ist, auch dann müsste es Gegenstände und Sachverhalte geben.</div>
<div class="corelinks tlpdepth2"><strong>4.23</strong><span class="linkarray tlpdepth2" id="p4.23GER"> GER [→<a class="ogdlink" href="#p4.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.23PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Name kommt im Satz nur im Zusammenhange des Elementarsatzes vor.</div>
<div class="corelinks tlpdepth2"><strong>4.24</strong><span class="linkarray tlpdepth2" id="p4.24GER"> GER [→<a class="ogdlink" href="#p4.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.24PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Namen sind die einfachen Symbole, ich deute sie durch einzelne Buchstaben („<span class="mathmode"><var>x</var></span>“, „<span class="mathmode"><var>y</var></span>“, „<span class="mathmode"><var>z</var></span>“) an.</div>
<div class="para tlpdepth2">Den Elementarsatz schreibe ich als Funktion der Namen in der Form: „<span class="mathmode"><var>fx</var></span>“, „<span class="mathmode"><var>φ</var>(<var>x</var>,<var>y</var>)</span>“, etc.</div>
<div class="para tlpdepth2">Oder ich deute ihn durch die Buchstaben <span class="mathmode"><var>p</var></span>, <span class="mathmode"><var>q</var></span>, <span class="mathmode"><var>r</var></span> an.</div>
<div class="corelinks tlpdepth3"><strong>4.241</strong><span class="linkarray tlpdepth3" id="p4.241GER"> GER [→<a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Gebrauche ich zwei Zeichen in ein und derselben Bedeutung, so drücke ich dies aus, indem ich zwischen beide das Zeichen „=“ setze.</div>
<div class="para tlpdepth3">„<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span>“ heißt also: das Zeichen „<span class="mathmode"><var>a</var></span>“ ist durch das Zeichen „<span class="mathmode"><var>b</var></span>“ ersetzbar.</div>
<div class="para tlpdepth3">(Führe ich durch eine Gleichung ein neues Zeichen „<span class="mathmode"><var>b</var></span>“ ein, indem ich bestimme, es solle ein bereits bekanntes Zeichen „<span class="mathmode"><var>a</var></span>“ ersetzen, so schreibe ich die Gleichung – Definition – (wie Russell) in der Form „<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span> Def.“. Die Definition ist eine Zeichenregel.)</div>
<div class="corelinks tlpdepth3"><strong>4.242</strong><span class="linkarray tlpdepth3" id="p4.242GER"> GER [→<a class="ogdlink" href="#p4.242OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.242PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ausdrücke von der Form „<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span>“ sind also nur Behelfe der Darstellung; sie sagen nichts über die Bedeutung der Zeichen „<span class="mathmode"><var>a</var></span>“, „<span class="mathmode"><var>b</var></span>“ aus.</div>
<div class="corelinks tlpdepth3"><strong>4.243</strong><span class="linkarray tlpdepth3" id="p4.243GER"> GER [→<a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Können wir zwei Namen verstehen, ohne zu wissen, ob sie dasselbe Ding oder zwei verschiedene Dinge bezeichnen? – Können wir einen Satz, worin zwei Namen vorkommen, verstehen, ohne zu wissen, ob sie Dasselbe oder Verschiedenes bedeuten?</div>
<div class="para tlpdepth3">Kenne ich etwa die Bedeutung eines englischen und eines gleichbedeutenden deutschen Wortes, so ist es unmöglich, dass ich nicht weiß, dass die beiden gleichbedeutend sind; es ist unmöglich, dass ich sie nicht ineinander übersetzen kann.</div>
<div class="para tlpdepth3">Ausdrücke wie „<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>“, oder von diesen abgeleitete, sind weder Elementarsätze, noch sonst sinnvolle Zeichen. (Dies wird sich später zeigen.)</div>
<div class="corelinks tlpdepth2"><strong>4.25</strong><span class="linkarray tlpdepth2" id="p4.25GER"> GER [→<a class="ogdlink" href="#p4.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.25PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Ist der Elementarsatz wahr, so besteht der Sachverhalt; ist der Elementarsatz falsch, so besteht der Sachverhalt nicht.</div>
<div class="corelinks tlpdepth2"><strong>4.26</strong><span class="linkarray tlpdepth2" id="p4.26GER"> GER [→<a class="ogdlink" href="#p4.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.26PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Angabe aller wahren Elementarsätze beschreibt die Welt vollständig. Die Welt ist vollständig beschrieben durch die Angaben aller Elementarsätze plus der Angabe, welche von ihnen wahr und welche falsch sind.</div>
<div class="corelinks tlpdepth2"><strong>4.27</strong><span class="linkarray tlpdepth2" id="p4.27GER"> GER [→<a class="ogdlink" href="#p4.27OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.27PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Bezüglich des Bestehens und Nichtbestehens von <span class="mathmode"><var>n</var></span> Sachverhalten gibt es <table class="possibilities"><tr><td rowspan="3" class="middleright"><span class="mathmode">K<sub><var>n</var></sub> = </span></td><td class="summationtop"><span class="mathmode"><var class="smallvar">n</var></span></td><td rowspan="3" class="middleright"><span class="largeparen">(</span></td><td rowspan="3" class="middlecenter"><span class="mathmode"><var>n</var></span><br /><span class="mathmode"><var>ν</var></span></td><td rowspan="3" class="middleleft"><span class="largeparen">)</span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="largeop">∑</span></span></td></tr><tr><td class="summationbottom"><span class="mathmode"><span class="smallvar"><var>ν</var> = 0</span></span></td></tr></table> Möglichkeiten.</div>
<div class="para tlpdepth2">Es können alle Kombinationen der Sachverhalte bestehen, die andern nicht bestehen.</div>
<div class="corelinks tlpdepth2"><strong>4.28</strong><span class="linkarray tlpdepth2" id="p4.28GER"> GER [→<a class="ogdlink" href="#p4.28OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.28PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Diesen Kombinationen entsprechen ebenso viele Möglichkeiten der Wahrheit – und Falschheit – von <span class="mathmode"><var>n</var></span> Elementarsätzen.</div>
<div class="corelinks tlpdepth1"><strong>4.3</strong><span class="linkarray tlpdepth1" id="p4.3GER"> GER [→<a class="ogdlink" href="#p4.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.3PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Die Wahrheitsmöglichkeiten der Elementarsätze bedeuten die Möglichkeiten des Bestehens und Nichtbestehens der Sachverhalte.</div>
<div class="corelinks tlpdepth2"><strong>4.31</strong><span class="linkarray tlpdepth2" id="p4.31GER"> GER [→<a class="ogdlink" href="#p4.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.31PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Wahrheitsmöglichkeiten können wir durch Schemata folgender Art darstellen („W“ bedeutet „wahr“, „F“, „falsch“. Die Reihen der „W“ und „F“ unter der Reihe der Elementarsätze bedeuten in leichtverständlicher Symbolik deren Wahrheitsmöglichkeiten):</div>
<div class="para tlpdepth2"><div class="centered"><table class="truthtable"><tr><th class="l"><span class="mathmode"><var>p</var></span></th><th class="m"><span class="mathmode"><var>q</var></span></th><th class="e"><span class="mathmode"><var>r</var></span></th></tr><tr><td class="l">W</td><td class="m">W</td><td class="e">W</td></tr><tr><td class="l">F</td><td class="m">W</td><td class="e">W</td></tr><tr><td class="l">W</td><td class="m">F</td><td class="e">W</td></tr><tr><td class="l">W</td><td class="m">W</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="m">F</td><td class="e">W</td></tr><tr><td class="l">F</td><td class="m">W</td><td class="e">F</td></tr><tr><td class="l">W</td><td class="m">F</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="m">F</td><td class="e">F</td></tr></table><span class="padrthree"></span><table class="truthtable"><tr><th class="l"><span class="mathmode"><var>p</var></span></th><th class="e"><span class="mathmode"><var>q</var></span></th></tr><tr><td class="l">W</td><td class="e">W</td></tr><tr><td class="l">F</td><td class="e">W</td></tr><tr><td class="l">W</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="e">F</td></tr></table><span class="padrthree"></span><table class="truthtable"><tr><th class="e"><span class="mathmode"><var>p</var></span></th></tr><tr><td class="e">W</td></tr><tr><td class="e">F</td></tr></table></div></div>
<div class="corelinks tlpdepth1"><strong>4.4</strong><span class="linkarray tlpdepth1" id="p4.4GER"> GER [→<a class="ogdlink" href="#p4.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Der Satz ist der Ausdruck der Übereinstimmung und Nichtübereinstimmung mit den Wahrheitsmöglichkeiten der Elementarsätze.</div>
<div class="corelinks tlpdepth2"><strong>4.41</strong><span class="linkarray tlpdepth2" id="p4.41GER"> GER [→<a class="ogdlink" href="#p4.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.41PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Wahrheitsmöglichkeiten der Elementarsätze sind die Bedingungen der Wahrheit und Falschheit der Sätze.</div>
<div class="corelinks tlpdepth3"><strong>4.411</strong><span class="linkarray tlpdepth3" id="p4.411GER"> GER [→<a class="ogdlink" href="#p4.411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.411PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist von vornherein wahrscheinlich, dass die Einführung der Elementarsätze für das Verständnis aller anderen Satzarten grundlegend ist. Ja, das Verständnis der allgemeinen Sätze hängt <em class="germph">fühlbar</em> von dem der Elementarsätze ab.</div>
<div class="corelinks tlpdepth2"><strong>4.42</strong><span class="linkarray tlpdepth2" id="p4.42GER"> GER [→<a class="ogdlink" href="#p4.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.42PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Bezüglich der Übereinstimmung und Nichtübereinstimmung eines Satzes mit den Wahrheitsmöglichkeiten von <span class="mathmode"><var>n</var></span> Elementarsätzen gibt es <table class="possibilities"><tr><td class="summationtop"><span class="mathmode"><span class="smallvar">K<sub><var>n</var></sub></span></span></td><td class="middleright" rowspan="3"><span class="largeparen">(</span></td><td class="middlecenter" rowspan="3"><span class="mathode">K<sub><var>n</var></sub></span><br /><span class="mathmode"><var>κ</var></span></td><td class="middleright" rowspan="3"><span class="mathomde"><span class="largeparen">)</span> = L<sub><var>n</var></sub></span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="largeop">∑</span></span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="smallvar"><var>κ</var> = 0</span></span></td></tr></table> Möglichkeiten.</div>
<div class="corelinks tlpdepth2"><strong>4.43</strong><span class="linkarray tlpdepth2" id="p4.43GER"> GER [→<a class="ogdlink" href="#p4.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.43PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Übereinstimmung mit den Wahrheitsmöglichkeiten können wir dadurch ausdrücken, indem wir ihnen im Schema etwa das Abzeichen „W“ (wahr) zuordnen.</div>
<div class="para tlpdepth2">Das Fehlen dieses Abzeichens bedeutet die Nichtübereinstimmung.</div>
<div class="corelinks tlpdepth3"><strong>4.431</strong><span class="linkarray tlpdepth3" id="p4.431GER"> GER [→<a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Ausdruck der Übereinstimmung und Nichtübereinstimmung mit den Wahrheitsmöglichkeiten der Elementarsätze drückt die Wahrheitsbedingungen des Satzes aus.</div>
<div class="para tlpdepth3">Der Satz ist der Ausdruck seiner Wahrheitsbedingungen.</div>
<div class="para tlpdepth3">(Frege hat sie daher ganz richtig als Erklärung der Zeichen seiner Begriffsschrift vorausgeschickt. Nur ist die Erklärung des Wahrheitsbegriffes bei Frege falsch: Wären „das Wahre“ und „das Falsche“ wirklich Gegenstände und die Argumente in <span class="mathmode"><span class="mathop">~</span><var>p</var></span> etc. dann wäre nach Freges Bestimmung der Sinn von „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ keineswegs bestimmt.)</div>
<div class="corelinks tlpdepth2"><strong>4.44</strong><span class="linkarray tlpdepth2" id="p4.44GER"> GER [→<a class="ogdlink" href="#p4.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.44PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Zeichen, welches durch die Zuordnung jener Abzeichen „W“ und der Wahrheitsmöglichkeiten entsteht, ist ein Satzzeichen.</div>
<div class="corelinks tlpdepth3"><strong>4.441</strong><span class="linkarray tlpdepth3" id="p4.441GER"> GER [→<a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist klar, dass dem Komplex der Zeichen „F“ und „W“ kein Gegenstand (oder Komplex von Gegenständen) entspricht; so wenig, wie den horizontalen und vertikalen Strichen oder den Klammern. – „Logische Gegenstände“ gibt es nicht.</div>
<div class="para tlpdepth3">Analoges gilt natürlich für alle Zeichen, die dasselbe ausdrücken wie die Schemata der „W“ und „F“.</div>
<div class="corelinks tlpdepth3"><strong>4.442</strong><span class="linkarray tlpdepth3" id="p4.442GER"> GER [→<a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist z. B.:</div>
<div class="para tlpdepth3 noindent"><!-- noindent --><div class="centered"><table class="truthtable"><tr><th></th><th class="l"><span class="mathmode"><var>p</var></span></th><th class="m"><span class="mathmode"><var>q</var></span></th><th class="e"></th><th>“</th></tr><tr><td></td><td class="l">W</td><td class="m">W</td><td class="e">W</td><td></td></tr><tr><td></td><td class="l">F</td><td class="m">W</td><td class="e">W</td><td></td></tr><tr><td></td><td class="l">W</td><td class="m">F</td><td class="e"></td><td></td></tr><tr><td>„</td><td class="l">F</td><td class="m">F</td><td class="e">W</td><td></td></tr></table></div></div>
<div class="para tlpdepth3 flushright"><!-- flushright --> ein Satzzeichen.</div>
<div class="para tlpdepth3">(Frege’s „Urteilsstrich“ „<span class="mathmode">⊢</span>“ ist logisch ganz bedeutunglos; er zeigt bei Frege (und Russell) nur an, dass diese Autoren die so bezeichneten Sätze für wahr halten.
„<span class="mathmode">⊢</span>“ gehört daher ebenso wenig zum Satzgefüge, wie etwa die Nummer des Satzes. Ein Satz kann unmöglich von sich selbst aussagen, dass er wahr ist.)</div>
<div class="para tlpdepth3">Ist die Reihenfolge der Wahrheitsmöglichkeiten im Schema durch eine Kombinationsregel ein für allemal festgesetzt, dann ist die letzte Kolonne allein schon ein Ausdruck der Wahrheitsbedingungen. Schreiben wir diese Kolonne als Reihe hin, so wird das Satzzeichen zu</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode"> „ <span class="mathop">(<span class="mathrm">WW–W</span>)</span>&nbsp; (<var>p</var>, <var>q</var>)“ </span></div><span class="mathmode"></span></div>
<div class="para tlpdepth3 noindent"><!-- noindent --> oder deutlicher</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode"> „ <span class="mathop">(<span class="mathrm">WWFW</span>)</span>&nbsp; (<var>p</var>, <var>q</var>)“. </span></div><span class="mathmode"></span></div>
<div class="para tlpdepth3">(Die Anzahl der Stellen in der linken Klammer ist durch die Anzahl der Glieder in der rechten bestimmt.)</div>
<div class="corelinks tlpdepth2"><strong>4.45</strong><span class="linkarray tlpdepth2" id="p4.45GER"> GER [→<a class="ogdlink" href="#p4.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.45PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Für <span class="mathmode"><var>n</var></span> Elementarsätze gibt es <span class="mathmode"><span class="mathrm">L</span><sub><var>n</var></sub></span> mögliche Gruppen von Wahrheitsbedingungen.</div>
<div class="para tlpdepth2">Die Gruppen von Wahrheitsbedingungen, welche zu den Wahrheitsmöglichkeiten einer Anzahl von Elementarsätzen gehören, lassen sich in eine Reihe ordnen.</div>
<div class="corelinks tlpdepth2"><strong>4.46</strong><span class="linkarray tlpdepth2" id="p4.46GER"> GER [→<a class="ogdlink" href="#p4.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Unter den möglichen Gruppen von Wahrheitsbedingungen gibt es zwei extreme Fälle.</div>
<div class="para tlpdepth2">In dem einen Fall ist der Satz für sämtliche Wahrheitsmöglichkeiten der Elementarsätze wahr. Wir sagen, die Wahrheitsbedingungen sind <em class="germph">tautologisch</em>.</div>
<div class="para tlpdepth2">Im zweiten Fall ist der Satz für sämtliche Wahrheitsmöglichkeiten falsch: Die Wahrheitsbedingungen sind <em class="germph">kontradiktorisch</em>.</div>
<div class="para tlpdepth2">Im ersten Fall nennen wir den Satz eine Tautologie, im zweiten Fall eine Kontradiktion.</div>
<div class="corelinks tlpdepth3"><strong>4.461</strong><span class="linkarray tlpdepth3" id="p4.461GER"> GER [→<a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Satz zeigt was er sagt, die Tautologie und die Kontradiktion, dass sie nichts sagen.</div>
<div class="para tlpdepth3">Die Tautologie hat keine Wahrheitsbedingungen, denn sie ist bedingungslos wahr; und die Kontradiktion ist unter keiner Bedingung wahr.</div>
<div class="para tlpdepth3">Tautologie und Kontradiktion sind sinnlos.</div>
<div class="para tlpdepth3">(Wie der Punkt, von dem zwei Pfeile in entgegengesetzter Richtung auseinandergehen.)</div>
<div class="para tlpdepth3">(Ich weiß z. B. nichts über das Wetter, wenn ich weiß, dass es regnet oder nicht regnet.)</div>
<div class="corelinks tlpdepth4"><strong>4.4611</strong><span class="linkarray tlpdepth4" id="p4.4611GER"> GER [→<a class="ogdlink" href="#p4.4611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4611PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Tautologie und Kontradiktion sind aber nicht unsinnig; sie gehören zum Symbolismus, und zwar ähnlich wie die „0“ zum Symbolismus der Arithmetik.</div>
<div class="corelinks tlpdepth3"><strong>4.462</strong><span class="linkarray tlpdepth3" id="p4.462GER"> GER [→<a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Tautologie und Kontradiktion sind nicht Bilder der Wirklichkeit. Sie stellen keine mögliche Sachlage dar. Denn jene lässt <em class="germph">jede</em> mögliche Sachlage zu, diese <em class="germph">keine</em>.</div>
<div class="para tlpdepth3">In der Tautologie heben die Bedingungen der Übereinstimmung mit der Welt – die darstellenden Beziehungen – einander auf, so dass sie in keiner darstellenden Beziehung zur Wirklichkeit steht.</div>
<div class="corelinks tlpdepth3"><strong>4.463</strong><span class="linkarray tlpdepth3" id="p4.463GER"> GER [→<a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Wahrheitsbedingungen bestimmen den Spielraum, der den Tatsachen durch den Satz gelassen wird.</div>
<div class="para tlpdepth3">(Der Satz, das Bild, das Modell, sind im negativen Sinne wie ein fester Körper, der die Bewegungsfreiheit der anderen beschränkt; im positiven Sinne, wie der von fester Substanz begrenzte Raum, worin ein Körper Platz hat.)</div>
<div class="para tlpdepth3">Die Tautologie lässt der Wirklichkeit den ganzen – unendlichen – logischen Raum; die Kontradiktion erfüllt den ganzen logischen Raum und lässt der Wirklichkeit keinen Punkt. Keine von beiden kann daher die Wirklichkeit irgendwie bestimmen.</div>
<div class="corelinks tlpdepth3"><strong>4.464</strong><span class="linkarray tlpdepth3" id="p4.464GER"> GER [→<a class="ogdlink" href="#p4.464OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.464PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Wahrheit der Tautologie ist gewiss, des Satzes möglich, der Kontradiktion unmöglich.</div>
<div class="para tlpdepth3">(Gewiss, möglich, unmöglich: Hier haben wir das Anzeichen jener Gradation, die wir in der Wahrscheinlichkeitslehre brauchen.)</div>
<div class="corelinks tlpdepth3"><strong>4.465</strong><span class="linkarray tlpdepth3" id="p4.465GER"> GER [→<a class="ogdlink" href="#p4.465OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.465PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das logische Produkt einer Tautologie und eines Satzes sagt dasselbe, wie der Satz. Also ist jenes Produkt identisch mit dem Satz. Denn man kann das Wesentliche des Symbols nicht ändern, ohne seinen Sinn zu ändern.</div>
<div class="corelinks tlpdepth3"><strong>4.466</strong><span class="linkarray tlpdepth3" id="p4.466GER"> GER [→<a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Einer bestimmten logischen Verbindung von Zeichen entspricht eine bestimmte logische Verbindung ihrer Bedeutungen; <em class="germph">jede beliebige</em> Verbindung entspricht nur den unverbundenen Zeichen.</div>
<div class="para tlpdepth3">Das heißt, Sätze, die für jede Sachlage wahr sind, können überhaupt keine Zeichenverbindungen sein, denn sonst könnten ihnen nur bestimmte Verbindungen von Gegenständen entsprechen.</div>
<div class="para tlpdepth3">(Und keiner logischen Verbindung entspricht <em class="germph">keine</em> Verbindung der Gegenstände.)</div>
<div class="para tlpdepth3">Tautologie und Kontradiktion sind die Grenzfälle der Zeichenverbindung, nämlich ihre Auflösung.</div>
<div class="corelinks tlpdepth4"><strong>4.4661</strong><span class="linkarray tlpdepth4" id="p4.4661GER"> GER [→<a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Freilich sind auch in der Tautologie und Kontradiktion die Zeichen noch mit einander verbunden, d. h. sie stehen in Beziehungen zu einander, aber diese Beziehungen sind bedeutungslos, dem <em class="germph">Symbol</em> unwesentlich.</div>
<div class="corelinks tlpdepth1"><strong>4.5</strong><span class="linkarray tlpdepth1" id="p4.5GER"> GER [→<a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Nun scheint es möglich zu sein, die allgemeinste Satzform anzugeben: das heißt, eine Beschreibung der Sätze <em class="germph">irgend einer</em> Zeichensprache zu geben, so dass jeder mögliche Sinn durch ein Symbol, auf welches die Beschreibung passt, ausgedrückt werden kann, und dass jedes Symbol, worauf die Beschreibung passt, einen Sinn ausdrücken kann, wenn die Bedeutungen der Namen entsprechend gewählt werden.</div>
<div class="para tlpdepth1">Es ist klar, dass bei der Beschreibung der allgemeinsten Satzform <em class="germph">nur</em> ihr Wesentliches beschrieben werden darf, – sonst wäre sie nämlich nicht die allgemeinste.</div>
<div class="para tlpdepth1">Dass es eine allgemeine Satzform gibt, wird dadurch bewiesen, dass es keinen Satz geben darf, dessen Form man nicht hätte voraussehen (d. h. konstruieren) können. Die allgemeine Form des Satzes ist: Es verhält sich so und so.</div>
<div class="corelinks tlpdepth2"><strong>4.51</strong><span class="linkarray tlpdepth2" id="p4.51GER"> GER [→<a class="ogdlink" href="#p4.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.51PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Angenommen, mir wären <em class="germph">alle</em> Elementarsätze gegeben: Dann lässt sich einfach fragen: Welche Sätze kann ich aus ihnen bilden? Und das sind <em class="germph">alle</em> Sätze und <em class="germph">so</em> sind sie begrenzt.</div>
<div class="corelinks tlpdepth2"><strong>4.52</strong><span class="linkarray tlpdepth2" id="p4.52GER"> GER [→<a class="ogdlink" href="#p4.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.52PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Sätze sind alles, was aus der Gesamtheit aller Elementarsätze folgt (natürlich auch daraus, dass es die <em class="germph">Gesamtheit aller</em> ist). (So könnte man in gewissem Sinne sagen, dass <em class="germph">alle</em> Sätze Verallgemeinerungen der Elementarsätze sind.)</div>
<div class="corelinks tlpdepth2"><strong>4.53</strong><span class="linkarray tlpdepth2" id="p4.53GER"> GER [→<a class="ogdlink" href="#p4.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.53PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die allgemeine Satzform ist eine Variable.</div>
<div class="corelinks tlpdepth0"><strong>5</strong><span class="linkarray tlpdepth0" id="p5GER"> GER [→<a class="ogdlink" href="#p5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Der Satz ist eine Wahrheitsfunktion der Elementarsätze.</div>
<div class="para tlpdepth0">(Der Elementarsatz ist eine Wahrheitsfunktion seiner selbst.)</div>
<div class="corelinks tlpdepth2"><strong>5.01</strong><span class="linkarray tlpdepth2" id="p5.01GER"> GER [→<a class="ogdlink" href="#p5.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Elementarsätze sind die Wahrheitsargumente des Satzes.</div>
<div class="corelinks tlpdepth2"><strong>5.02</strong><span class="linkarray tlpdepth2" id="p5.02GER"> GER [→<a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Es liegt nahe, die Argumente von Funktionen mit den Indices von Namen zu verwechseln. Ich erkenne nämlich sowohl am Argument wie am Index die Bedeutung des sie enthaltenden Zeichens.</div>
<div class="para tlpdepth2">In Russells „<span class="mathmode"><span class="mathrel">+</span><sub><var>c</var></sub></span>“ ist z. B. „<span class="mathmode"><sub><var>c</var></sub></span>“ ein Index, der darauf hinweist, dass das ganze Zeichen das Additionszeichen für Kardinalzahlen ist. Aber diese Bezeichnung beruht auf willkürlicher Übereinkunft und man könnte statt „<span class="mathmode"><span class="mathrel">+</span><sub><var>c</var></sub></span>“ auch ein einfaches Zeichen wählen; in „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ aber ist „<span class="mathmode"><var>p</var></span>“ kein Index, sondern ein Argument: der Sinn von „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ <em class="germph">kann nicht</em> verstanden werden, ohne dass vorher der Sinn von „<span class="mathmode"><var>p</var></span>“ verstanden worden wäre. (Im Namen Julius Cäsar ist „Julius“ ein Index. Der Index ist immer ein Teil einer Beschreibung des Gegenstandes, dessen Namen wir ihn anhängen. Z. B. <em class="germph">der</em> Cäsar aus dem Geschlechte der Julier.)</div>
<div class="para tlpdepth2">Die Verwechslung von Argument und Index liegt, wenn ich mich nicht irre, der Theorie Freges von der Bedeutung der Sätze und Funktionen zugrunde. Für Frege waren die Sätze der Logik Namen, und deren Argumente die Indices dieser Namen.</div>
<div class="corelinks tlpdepth1"><strong>5.1</strong><span class="linkarray tlpdepth1" id="p5.1GER"> GER [→<a class="ogdlink" href="#p5.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Die Wahrheitsfunktionen lassen sich in Reihen ordnen.</div>
<div class="para tlpdepth1">Das ist die Grundlage der Wahrscheinlichkeitslehre.</div>
<div class="corelinks tlpdepth3"><strong>5.101</strong><span class="linkarray tlpdepth3" id="p5.101GER"> GER [→<a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Wahrheitsfunktionen jeder Anzahl von Elementarsätzen lassen sich in einem Schema folgender Art hinschreiben:</div>
<div class="para tlpdepth3 noindent"><!-- noindent --><table class="fnlist"><tr><td class="righttight" >(</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >Tautologie&nbsp;</td><td >(Wenn <span class="mathmode"><var>p</var></span>, so <span class="mathmode"><var>p</var></span>; und wenn <span class="mathmode"><var>q</var></span>, so <span class="mathmode"><var>q</var></span>.) &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var><span class="mathrel">.</span><var>q</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >in&nbsp;Worten:&nbsp;</td><td >Nicht beides <span class="mathmode"><var>p</var></span> und <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><var>q</var>))</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Wenn <span class="mathmode"><var>q</var></span>, so <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>q</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Wenn <span class="mathmode"><var>p</var></span>, so <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span> oder <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Nicht <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<span class="mathop">~</span><var>q</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Nicht <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<span class="mathop">~</span><var>p</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span>, oder <span class="mathmode"><var>q</var></span>, aber nicht beide. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var><span class="mathrel">:<span class="symbol">∨</span>:</span><var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Wenn <span class="mathmode"><var>p</var></span>, so <span class="mathmode"><var>q</var></span>; und wenn <span class="mathmode"><var>q</var></span>, so <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">≡</span></span><var>q</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >W</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>q</var></span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Weder <span class="mathmode"><var>p</var></span> noch <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>)</span> oder <span class="mathmode">(<var>p</var><span class="mathrel">|</span><var>q</var>)</span></td></tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span> und nicht <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>q</var></span> und nicht <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >W</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>q</var></span> und <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>q</var><span class="mathrel">.</span><var>p</var>)</span></td> </tr><tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" colspan="2">Kontradiktion (<span class="mathmode"><var>p</var></span> und nicht <span class="mathmode"><var>p</var></span>; und <span class="mathmode"><var>q</var></span> und nicht <span class="mathmode"><var>q</var></span>.) &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>)</span></td></tr></table></div>
<div class="para tlpdepth3">Diejenigen Wahrheitsmöglichkeiten seiner Wahrheitsargumente, welche den Satz bewahrheiten, will ich seine <em class="germph">Wahrheitsgründe</em> nennen.</div>
<div class="corelinks tlpdepth2"><strong>5.11</strong><span class="linkarray tlpdepth2" id="p5.11GER"> GER [→<a class="ogdlink" href="#p5.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Sind die Wahrheitsgründe, die einer Anzahl von Sätzen gemeinsam sind, sämtlich auch Wahrheitsgründe eines bestimmten Satzes, so sagen wir, die Wahrheit dieses Satzes folge aus der Wahrheit jener Sätze.</div>
<div class="corelinks tlpdepth2"><strong>5.12</strong><span class="linkarray tlpdepth2" id="p5.12GER"> GER [→<a class="ogdlink" href="#p5.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Insbesondere folgt die Wahrheit eines Satzes „<span class="mathmode"><var>p</var></span>“ aus der Wahrheit eines anderen „<span class="mathmode"><var>q</var></span>“, wenn alle Wahrheitsgründe des zweiten Wahrheitsgründe des ersten sind.</div>
<div class="corelinks tlpdepth3"><strong>5.121</strong><span class="linkarray tlpdepth3" id="p5.121GER"> GER [→<a class="ogdlink" href="#p5.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.121PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Wahrheitsgründe des einen sind in denen des anderen enthalten; <span class="mathmode"><var>p</var></span> folgt aus <span class="mathmode"><var>q</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.122</strong><span class="linkarray tlpdepth3" id="p5.122GER"> GER [→<a class="ogdlink" href="#p5.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.122PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Folgt <span class="mathmode"><var>p</var></span> aus <span class="mathmode"><var>q</var></span>, so ist der Sinn von „<span class="mathmode"><var>p</var></span>“ im Sinne von „<span class="mathmode"><var>q</var></span>“ enthalten.</div>
<div class="corelinks tlpdepth3"><strong>5.123</strong><span class="linkarray tlpdepth3" id="p5.123GER"> GER [→<a class="ogdlink" href="#p5.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.123PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wenn ein Gott eine Welt erschafft, worin gewisse Sätze wahr sind, so schafft er damit auch schon eine Welt, in welcher alle ihre Folgesätze stimmen. Und ähnlich könnte er keine Welt schaffen, worin der Satz „<span class="mathmode"><var>p</var></span>“ wahr ist, ohne seine sämtlichen Gegenstände zu schaffen.</div>
<div class="corelinks tlpdepth3"><strong>5.124</strong><span class="linkarray tlpdepth3" id="p5.124GER"> GER [→<a class="ogdlink" href="#p5.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.124PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Satz bejaht jeden Satz, der aus ihm folgt.</div>
<div class="corelinks tlpdepth4"><strong>5.1241</strong><span class="linkarray tlpdepth4" id="p5.1241GER"> GER [→<a class="ogdlink" href="#p5.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1241PM">P/M</a>]</span></div>
<div class="para tlpdepth4">„<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>q</var></span>“ ist einer der Sätze, welche „<span class="mathmode"><var>p</var></span>“ bejahen, und zugleich einer der Sätze, welche „<span class="mathmode"><var>q</var></span>“ bejahen.</div>
<div class="para tlpdepth4">Zwei Sätze sind einander entgegengesetzt, wenn es keinen sinnvollen Satz gibt, der sie beide bejaht.</div>
<div class="para tlpdepth4">Jeder Satz der einem anderen widerspricht, verneint ihn.</div>
<div class="corelinks tlpdepth2"><strong>5.13</strong><span class="linkarray tlpdepth2" id="p5.13GER"> GER [→<a class="ogdlink" href="#p5.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Dass die Wahrheit eines Satzes aus der Wahrheit anderer Sätze folgt, ersehen wir aus der Struktur der Sätze.</div>
<div class="corelinks tlpdepth3"><strong>5.131</strong><span class="linkarray tlpdepth3" id="p5.131GER"> GER [→<a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Folgt die Wahrheit eines Satzes aus der Wahrheit anderer, so drückt sich dies durch Beziehungen aus, in welchen die Formen jener Sätze zu einander stehen; und zwar brauchen wir sie nicht erst in jene Beziehungen zu setzen, indem wir sie in einem Satz miteinander verbinden, sondern diese Beziehungen sind intern und bestehen, sobald, und dadurch dass, jene Sätze bestehen.</div>
<div class="corelinks tlpdepth4"><strong>5.1311</strong><span class="linkarray tlpdepth4" id="p5.1311GER"> GER [→<a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wenn wir von <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span> und <span class="mathmode"><span class="mathop">~</span><var>p</var></span> auf <span class="mathmode"><var>q</var></span> schließen, so ist hier durch die Bezeichnungsweise die Beziehung der Satzformen von „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>“ und „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ verhüllt. Schreiben wir aber z. B. statt „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>“ „<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>q</var><span class="mathrel">.|.</span><var>p</var><span class="mathrel">|</span><var>q</var></span>“ und statt „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ „<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>p</var></span>“ (<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>q</var></span> = weder <span class="mathmode"><var>p</var></span>, noch <span class="mathmode"><var>q</var></span>), so wird der innere Zusammenhang offenbar.</div>
<div class="para tlpdepth4">(Dass man aus <span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span> auf <span class="mathmode"><var>fa</var></span> schließen kann, das zeigt, dass die Allgemeinheit auch im Symbol „<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>“ vorhanden ist.)</div>
<div class="corelinks tlpdepth3"><strong>5.132</strong><span class="linkarray tlpdepth3" id="p5.132GER"> GER [→<a class="ogdlink" href="#p5.132OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.132PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Folgt <span class="mathmode"><var>p</var></span> aus <span class="mathmode"><var>q</var></span>, so kann ich von <span class="mathmode"><var>q</var></span> auf <span class="mathmode"><var>p</var></span> schließen; <span class="mathmode"><var>p</var></span> aus <span class="mathmode"><var>q</var></span> folgern.</div>
<div class="para tlpdepth3">Die Art des Schlusses ist allein aus den beiden Sätzen zu entnehmen.</div>
<div class="para tlpdepth3">Nur sie selbst können den Schluss rechtfertigen.</div>
<div class="para tlpdepth3">„Schlussgesetze“, welche – wie bei Frege und Russell – die Schlüsse rechtfertigen sollen, sind sinnlos, und wären überflüssig.</div>
<div class="corelinks tlpdepth3"><strong>5.133</strong><span class="linkarray tlpdepth3" id="p5.133GER"> GER [→<a class="ogdlink" href="#p5.133OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.133PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Alles Folgern geschieht a priori.</div>
<div class="corelinks tlpdepth3"><strong>5.134</strong><span class="linkarray tlpdepth3" id="p5.134GER"> GER [→<a class="ogdlink" href="#p5.134OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.134PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Aus einem Elementarsatz lässt sich kein anderer folgern.</div>
<div class="corelinks tlpdepth3"><strong>5.135</strong><span class="linkarray tlpdepth3" id="p5.135GER"> GER [→<a class="ogdlink" href="#p5.135OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.135PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Auf keine Weise kann aus dem Bestehen irgend einer Sachlage auf das Bestehen einer von ihr gänzlich verschiedenen Sachlage geschlossen werden.</div>
<div class="corelinks tlpdepth3"><strong>5.136</strong><span class="linkarray tlpdepth3" id="p5.136GER"> GER [→<a class="ogdlink" href="#p5.136OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.136PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Einen Kausalnexus, der einen solchen Schluss rechtfertigte, gibt es nicht.</div>
<div class="corelinks tlpdepth4"><strong>5.1361</strong><span class="linkarray tlpdepth4" id="p5.1361GER"> GER [→<a class="ogdlink" href="#p5.1361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1361PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Ereignisse der Zukunft <em class="germph">können</em> wir nicht aus den gegenwärtigen erschließen.</div>
<div class="para tlpdepth4">Der Glaube an den Kausalnexus ist der <em class="germph">Aberglaube</em>.</div>
<div class="corelinks tlpdepth4"><strong>5.1362</strong><span class="linkarray tlpdepth4" id="p5.1362GER"> GER [→<a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Willensfreiheit besteht darin, dass zukünftige Handlungen jetzt nicht gewusst werden können. Nur dann könnten wir sie wissen, wenn die Kausalität eine <em class="germph">innere</em> Notwendigkeit wäre, wie die des logischen Schlusses. – Der Zusammenhang von Wissen und Gewusstem ist der der logischen Notwendigkeit.</div>
<div class="para tlpdepth4">(„A weiß, dass <span class="mathmode"><var>p</var></span> der Fall ist“ ist sinnlos, wenn <span class="mathmode"><var>p</var></span> eine Tautologie ist.)</div>
<div class="corelinks tlpdepth4"><strong>5.1363</strong><span class="linkarray tlpdepth4" id="p5.1363GER"> GER [→<a class="ogdlink" href="#p5.1363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1363PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wenn daraus, dass ein Satz uns einleuchtet, nicht <em class="germph">folgt</em>, dass er wahr ist, so ist das Einleuchten auch keine Rechtfertigung für unseren Glauben an seine Wahrheit.</div>
<div class="corelinks tlpdepth2"><strong>5.14</strong><span class="linkarray tlpdepth2" id="p5.14GER"> GER [→<a class="ogdlink" href="#p5.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.14PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Folgt ein Satz aus einem anderen, so sagt dieser mehr als jener, jener weniger als dieser.</div>
<div class="corelinks tlpdepth3"><strong>5.141</strong><span class="linkarray tlpdepth3" id="p5.141GER"> GER [→<a class="ogdlink" href="#p5.141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.141PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Folgt <span class="mathmode"><var>p</var></span> aus <span class="mathmode"><var>q</var></span> und <span class="mathmode"><var>q</var></span> aus <span class="mathmode"><var>p</var></span>, so sind sie ein und derselbe Satz.</div>
<div class="corelinks tlpdepth3"><strong>5.142</strong><span class="linkarray tlpdepth3" id="p5.142GER"> GER [→<a class="ogdlink" href="#p5.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.142PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Tautologie folgt aus allen Sätzen: sie sagt nichts.</div>
<div class="corelinks tlpdepth3"><strong>5.143</strong><span class="linkarray tlpdepth3" id="p5.143GER"> GER [→<a class="ogdlink" href="#p5.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.143PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Kontradiktion ist das Gemeinsame der Sätze, was <em class="germph">kein</em> Satz mit einem anderen gemein hat. Die Tautologie ist das Gemeinsame aller Sätze, welche nichts miteinander gemein haben.</div>
<div class="para tlpdepth3">Die Kontradiktion verschwindet sozusagen außerhalb, die Tautologie innerhalb aller Sätze.</div>
<div class="para tlpdepth3">Die Kontradiktion ist die äußere Grenze der Sätze, die Tautologie ihr substanzloser Mittelpunkt.</div>
<div class="corelinks tlpdepth2"><strong>5.15</strong><span class="linkarray tlpdepth2" id="p5.15GER"> GER [→<a class="ogdlink" href="#p5.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.15PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Ist <span class="mathmode"><span class="mathrm">W</span><sub><var>r</var></sub></span> die Anzahl der Wahrheitsgründe des Satzes „<span class="mathmode"><var>r</var></span>“, <span class="mathmode"><span class="mathrm">W</span><sub><var>rs</var></sub></span> die Anzahl derjenigen Wahrheitsgründe des Satzes „<span class="mathmode"><var>s</var></span>“, die zugleich Wahrheitsgründe von „<span class="mathmode"><var>r</var></span>“ sind, dann nennen wir das Verhältnis: <span class="mathmode"><span class="mathrm">W</span><sub><var>rs</var></sub> : <span class="mathrm">W</span><sub><var>r</var></sub></span> das Maß der <em class="germph">Wahrscheinlichkeit</em>, welche der Satz „<span class="mathmode"><var>r</var></span>“ dem Satz „<span class="mathmode"><var>s</var></span>“ gibt.</div>
<div class="corelinks tlpdepth3"><strong>5.151</strong><span class="linkarray tlpdepth3" id="p5.151GER"> GER [→<a class="ogdlink" href="#p5.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.151PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Sei in einem Schema wie dem obigen in No. 5.101 <span class="mathmode"><span class="mathrm">W</span><sub><var>r</var></sub></span> die Anzahl der „W“ im Satze <span class="mathmode"><var>r</var></span>; <span class="mathmode"><span class="mathrm">W</span><sub><var>rs</var></sub></span> die Anzahl derjenigen „W“ im Satze <span class="mathmode"><var>s</var></span>, die in gleichen Kolonnen mit „W“ des Satzes <span class="mathmode"><var>r</var></span> stehen. Der Satz <span class="mathmode"><var>r</var></span> gibt dann dem Satze <span class="mathmode"><var>s</var></span> die Wahrscheinlichkeit: <span class="mathmode"><span class="mathrm">W</span><sub><var>rs</var></sub> : <span class="mathrm">W</span><sub><var>r</var></sub></span>.</div>
<div class="corelinks tlpdepth4"><strong>5.1511</strong><span class="linkarray tlpdepth4" id="p5.1511GER"> GER [→<a class="ogdlink" href="#p5.1511OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1511PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es gibt keinen besonderen Gegenstand, der den Wahrscheinlichkeitssätzen eigen wäre.</div>
<div class="corelinks tlpdepth3"><strong>5.152</strong><span class="linkarray tlpdepth3" id="p5.152GER"> GER [→<a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Sätze, welche keine Wahrheitsargumente mit einander gemein haben, nennen wir von einander unabhängig.</div>
<div class="para tlpdepth3">Zwei Elementarsätze geben einander die Wahrscheinlichkeit <span class="mathmode">½</span>.</div>
<div class="para tlpdepth3">Folgt <span class="mathmode"><var>p</var></span> aus <span class="mathmode"><var>q</var></span>, so gibt der Satz „<span class="mathmode"><var>q</var></span>“ dem Satz „<span class="mathmode"><var>p</var></span>“ die Wahrscheinlichkeit 1. Die Gewissheit des logischen Schlusses ist ein Grenzfall der Wahrscheinlichkeit.</div>
<div class="para tlpdepth3">(Anwendung auf Tautologie und Kontradiktion.)</div>
<div class="corelinks tlpdepth3"><strong>5.153</strong><span class="linkarray tlpdepth3" id="p5.153GER"> GER [→<a class="ogdlink" href="#p5.153OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.153PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ein Satz ist an sich weder wahrscheinlich noch unwahrscheinlich. Ein Ereignis trifft ein, oder es trifft nicht ein, ein Mittelding gibt es nicht.</div>
<div class="corelinks tlpdepth3"><strong>5.154</strong><span class="linkarray tlpdepth3" id="p5.154GER"> GER [→<a class="ogdlink" href="#p5.154OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.154PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In einer Urne seien gleichviel weiße und schwarze Kugeln (und keine anderen). Ich ziehe eine Kugel nach der anderen und lege sie wieder in die Urne zurück. Dann kann ich durch den Versuch feststellen, dass sich die Zahlen der gezogenen schwarzen und weißen Kugeln bei fortgesetztem Ziehen einander nähern.</div>
<div class="para tlpdepth3"><em class="germph">Das</em> ist also kein mathematisches Faktum.</div>
<div class="para tlpdepth3">Wenn ich nun sage: Es ist gleich wahrscheinlich, dass ich eine weiße Kugel wie eine schwarze ziehen werde, so heißt das: Alle mir bekannten Umstände (die hypothetisch angenommenen Naturgesetze mitinbegriffen) geben dem Eintreffen des einen Ereignisses nicht <em class="germph">mehr</em> Wahrscheinlichkeit als dem Eintreffen des anderen. Das heißt, sie geben – wie aus den obigen Erklärungen leicht zu entnehmen ist – jedem die Wahrscheinlichkeit <span class="mathmode">½</span>.</div>
<div class="para tlpdepth3">Was ich durch den Versuch bestätige ist, dass das Eintreffen der beiden Ereignisse von den Umständen, die ich nicht näher kenne, unabhängig ist.</div>
<div class="corelinks tlpdepth3"><strong>5.155</strong><span class="linkarray tlpdepth3" id="p5.155GER"> GER [→<a class="ogdlink" href="#p5.155OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.155PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Einheit des Wahrscheinlichkeitssatzes ist: Die Umstände – die ich sonst nicht weiter kenne – geben dem Eintreffen eines bestimmten Ereignisses den und den Grad der Wahrscheinlichkeit.</div>
<div class="corelinks tlpdepth3"><strong>5.156</strong><span class="linkarray tlpdepth3" id="p5.156GER"> GER [→<a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span></div>
<div class="para tlpdepth3">So ist die Wahrscheinlichkeit eine Verallgemeinerung.</div>
<div class="para tlpdepth3">Sie involviert eine allgemeine Beschreibung einer Satzform.</div>
<div class="para tlpdepth3">Nur in Ermanglung der Gewissheit gebrauchen wir die Wahrscheinlichkeit. – Wenn wir zwar eine Tatsache nicht vollkommen kennen, wohl aber <em class="germph">etwas</em> über ihre Form wissen.</div>
<div class="para tlpdepth3">(Ein Satz kann zwar ein unvollständiges Bild einer gewissen Sachlage sein, aber er ist immer <em class="germph">ein</em> vollständiges Bild.)</div>
<div class="para tlpdepth3">Der Wahrscheinlichkeitssatz ist gleichsam ein Auszug aus anderen Sätzen.</div>
<div class="corelinks tlpdepth1"><strong>5.2</strong><span class="linkarray tlpdepth1" id="p5.2GER"> GER [→<a class="ogdlink" href="#p5.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Die Strukturen der Sätze stehen in internen Beziehungen zu einander.</div>
<div class="corelinks tlpdepth2"><strong>5.21</strong><span class="linkarray tlpdepth2" id="p5.21GER"> GER [→<a class="ogdlink" href="#p5.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wir können diese internen Beziehungen dadurch in unserer Ausdrucksweise hervorheben, dass wir einen Satz als Resultat einer Operation darstellen, die ihn aus anderen Sätzen (den Basen der Operation) hervorbringt.</div>
<div class="corelinks tlpdepth2"><strong>5.22</strong><span class="linkarray tlpdepth2" id="p5.22GER"> GER [→<a class="ogdlink" href="#p5.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Operation ist der Ausdruck einer Beziehung zwischen den Strukturen ihres Resultats und ihrer Basen.</div>
<div class="corelinks tlpdepth2"><strong>5.23</strong><span class="linkarray tlpdepth2" id="p5.23GER"> GER [→<a class="ogdlink" href="#p5.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.23PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Operation ist das, was mit dem einen Satz geschehen muss, um aus ihm den anderen zu machen.</div>
<div class="corelinks tlpdepth3"><strong>5.231</strong><span class="linkarray tlpdepth3" id="p5.231GER"> GER [→<a class="ogdlink" href="#p5.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.231PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Und das wird natürlich von ihren formalen Eigenschaften, von der internen Ähnlichkeit ihrer Formen abhängen.</div>
<div class="corelinks tlpdepth3"><strong>5.232</strong><span class="linkarray tlpdepth3" id="p5.232GER"> GER [→<a class="ogdlink" href="#p5.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.232PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die interne Relation, die eine Reihe ordnet, ist äquivalent mit der Operation, durch welche ein Glied aus dem anderen entsteht.</div>
<div class="corelinks tlpdepth3"><strong>5.233</strong><span class="linkarray tlpdepth3" id="p5.233GER"> GER [→<a class="ogdlink" href="#p5.233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.233PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Operation kann erst dort auftreten, wo ein Satz auf logisch bedeutungsvolle Weise aus einem anderen entsteht. Also dort, wo die logische Konstruktion des Satzes anfängt.</div>
<div class="corelinks tlpdepth3"><strong>5.234</strong><span class="linkarray tlpdepth3" id="p5.234GER"> GER [→<a class="ogdlink" href="#p5.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.234PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Wahrheitsfunktionen der Elementarsätze sind Resultate von Operationen, die die Elementarsätze als Basen haben. (Ich nenne diese Operationen Wahrheitsoperationen.)</div>
<div class="corelinks tlpdepth4"><strong>5.2341</strong><span class="linkarray tlpdepth4" id="p5.2341GER"> GER [→<a class="ogdlink" href="#p5.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2341PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Der Sinn einer Wahrheitsfunktion von <span class="mathmode"><var>p</var></span> ist eine Funktion des Sinnes von <span class="mathmode"><var>p</var></span>.</div>
<div class="para tlpdepth4">Verneinung, logische Addition, logische Multiplikation, etc., etc. sind Operationen.</div>
<div class="para tlpdepth4">(Die Verneinung verkehrt den Sinn des Satzes.)</div>
<div class="corelinks tlpdepth2"><strong>5.24</strong><span class="linkarray tlpdepth2" id="p5.24GER"> GER [→<a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Operation zeigt sich in einer Variablen; sie zeigt, wie man von einer Form von Sätzen zu einer anderen gelangen kann.</div>
<div class="para tlpdepth2">Sie bringt den Unterschied der Formen zum Ausdruck.</div>
<div class="para tlpdepth2">(Und das Gemeinsame zwischen den Basen und dem Resultat der Operation sind eben die Basen.)</div>
<div class="corelinks tlpdepth3"><strong>5.241</strong><span class="linkarray tlpdepth3" id="p5.241GER"> GER [→<a class="ogdlink" href="#p5.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.241PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Operation kennzeichnet keine Form, sondern nur den Unterschied der Formen.</div>
<div class="corelinks tlpdepth3"><strong>5.242</strong><span class="linkarray tlpdepth3" id="p5.242GER"> GER [→<a class="ogdlink" href="#p5.242OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.242PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Dieselbe Operation, die „<span class="mathmode"><var>q</var></span>“ aus „<span class="mathmode"><var>p</var></span>“ macht, macht aus „<span class="mathmode"><var>q</var></span>“ „<span class="mathmode"><var>r</var></span>“ u. s. f. Dies kann nur darin ausgedrückt sein, dass „<span class="mathmode"><var>p</var></span>“, „<span class="mathmode"><var>q</var></span>“, „<span class="mathmode"><var>r</var></span>“, etc. Variable sind, die gewisse formale Relationen allgemein zum Ausdruck bringen.</div>
<div class="corelinks tlpdepth2"><strong>5.25</strong><span class="linkarray tlpdepth2" id="p5.25GER"> GER [→<a class="ogdlink" href="#p5.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.25PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Vorkommen der Operation charakterisiert den Sinn des Satzes nicht.</div>
<div class="para tlpdepth2">Die Operation sagt ja nichts aus, nur ihr Resultat, und dies hängt von den Basen der Operation ab.</div>
<div class="para tlpdepth2">(Operation und Funktion dürfen nicht miteinander verwechselt werden.)</div>
<div class="corelinks tlpdepth3"><strong>5.251</strong><span class="linkarray tlpdepth3" id="p5.251GER"> GER [→<a class="ogdlink" href="#p5.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.251PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Eine Funktion kann nicht ihr eigenes Argument sein, wohl aber kann das Resultat einer Operation ihre eigene Basis werden.</div>
<div class="corelinks tlpdepth3"><strong>5.252</strong><span class="linkarray tlpdepth3" id="p5.252GER"> GER [→<a class="ogdlink" href="#p5.252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Nur so ist das Fortschreiten von Glied zu Glied in einer Formenreihe (von Type zu Type in den Hierarchien Russells und Whiteheads) möglich. (Russell und Whitehead haben die Möglichkeit dieses Fortschreitens nicht zugegeben, aber immer wieder von ihr Gebrauch gemacht.)</div>
<div class="corelinks tlpdepth4"><strong>5.2521</strong><span class="linkarray tlpdepth4" id="p5.2521GER"> GER [→<a class="ogdlink" href="#p5.2521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2521PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die fortgesetzte Anwendung einer Operation auf ihr eigenes Resultat nenne ich ihre successive Anwendung („<span class="mathmode"><span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><var>a</var></span>“ ist das Resultat der dreimaligen successiven Anwendung von „<span class="mathmode"><span class="mathop"><span class="mathrm">O</span>’</span><var>ξ</var></span>“ auf „<span class="mathmode"><var>a</var></span>“).</div>
<div class="para tlpdepth4">In einem ähnlichen Sinne rede ich von der successiven Anwendung <em class="germph">mehrerer</em> Operationen auf eine Anzahl von Sätzen.</div>
<div class="corelinks tlpdepth4"><strong>5.2522</strong><span class="linkarray tlpdepth4" id="p5.2522GER"> GER [→<a class="ogdlink" href="#p5.2522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2522PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das allgemeine Glied einer Formenreihe <span class="mathmode"><var>a</var>, <span class="mathop"><span class="mathrm">O</span>’</span><var>a</var>, <span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><var>a</var>,<span class="mathrel">…</span></span> schreibe ich daher so: „<span class="mathmode">[<var>a</var>, <var>x</var>, <span class="mathop"><span class="mathrm">O</span>’</span><var>x</var>]</span>“. Dieser Klammerausdruck ist eine Variable. Das erste Glied des Klammerausdruckes ist der Anfang der Formenreihe, das zweite die Form eines beliebigen Gliedes <span class="mathmode"><var>x</var></span> der Reihe und das dritte die Form desjenigen Gliedes der Reihe, welches auf <span class="mathmode"><var>x</var></span> unmittelbar folgt.</div>
<div class="corelinks tlpdepth4"><strong>5.2523</strong><span class="linkarray tlpdepth4" id="p5.2523GER"> GER [→<a class="ogdlink" href="#p5.2523OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2523PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Der Begriff der successiven Anwendung der Operation ist äquivalent mit dem Begriff „und so weiter“.</div>
<div class="corelinks tlpdepth3"><strong>5.253</strong><span class="linkarray tlpdepth3" id="p5.253GER"> GER [→<a class="ogdlink" href="#p5.253OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.253PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Eine Operation kann die Wirkung einer anderen rückgängig machen. Operationen können einander aufheben.</div>
<div class="corelinks tlpdepth3"><strong>5.254</strong><span class="linkarray tlpdepth3" id="p5.254GER"> GER [→<a class="ogdlink" href="#p5.254OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.254PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Operation kann verschwinden (z. B. die Verneinung in „<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>“: <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var><span class="mathrel">=</span><var>p</var></span>).</div>
<div class="corelinks tlpdepth1"><strong>5.3</strong><span class="linkarray tlpdepth1" id="p5.3GER"> GER [→<a class="ogdlink" href="#p5.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.3PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Alle Sätze sind Resultate von Wahrheitsoperationen mit den Elementarsätzen.</div>
<div class="para tlpdepth1">Die Wahrheitsoperation ist die Art und Weise, wie aus den Elementarsätzen die Wahrheitsfunktion entsteht.</div>
<div class="para tlpdepth1">Nach dem Wesen der Wahrheitsoperation wird auf die gleiche Weise, wie aus den Elementarsätzen ihre Wahrheitsfunktion, aus Wahrheitsfunktionen eine neue. Jede Wahrheitsoperation erzeugt aus Wahrheitsfunktionen von Elementarsätzen wieder eine Wahrheitsfunktion von Elementarsätzen, einen Satz. Das Resultat jeder Wahrheitsoperation mit den Resultaten von Wahrheitsoperationen mit Elementarsätzen ist wieder das Resultat <em class="germph">Einer</em> Wahrheitsoperation mit Elementarsätzen.</div>
<div class="para tlpdepth1">Jeder Satz ist das Resultat von Wahrheitsoperationen mit Elementarsätzen.</div>
<div class="corelinks tlpdepth2"><strong>5.31</strong><span class="linkarray tlpdepth2" id="p5.31GER"> GER [→<a class="ogdlink" href="#p5.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.31PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Schemata No. 4.31 haben auch dann eine Bedeutung, wenn „<span class="mathmode"><var>p</var></span>“, „<span class="mathmode"><var>q</var></span>“, „<span class="mathmode"><var>r</var></span>“, etc. nicht Elementarsätze sind.</div>
<div class="para tlpdepth2">Und es ist leicht zu sehen, dass das Satzzeichen in No. 4.442, auch wenn „<span class="mathmode"><var>p</var></span>“ und „<span class="mathmode"><var>q</var></span>“ Wahrheitsfunktionen von Elementarsätzen sind, Eine Wahrheitsfunktion von Elementarsätzen ausdrückt.</div>
<div class="corelinks tlpdepth2"><strong>5.32</strong><span class="linkarray tlpdepth2" id="p5.32GER"> GER [→<a class="ogdlink" href="#p5.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.32PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Alle Wahrheitsfunktionen sind Resultate der successiven Anwendung einer endlichen Anzahl von Wahrheitsoperationen auf die Elementarsätze.</div>
<div class="corelinks tlpdepth1"><strong>5.4</strong><span class="linkarray tlpdepth1" id="p5.4GER"> GER [→<a class="ogdlink" href="#p5.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Hier zeigt es sich, dass es „logische Gegenstände“, „logische Konstante“ (im Sinne Freges und Russells) nicht gibt.</div>
<div class="corelinks tlpdepth2"><strong>5.41</strong><span class="linkarray tlpdepth2" id="p5.41GER"> GER [→<a class="ogdlink" href="#p5.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.41PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Denn: Alle Resultate von Wahrheitsoperationen mit Wahrheitsfunktionen sind identisch, welche eine und dieselbe Wahrheitsfunktion von Elementarsätzen sind.</div>
<div class="corelinks tlpdepth2"><strong>5.42</strong><span class="linkarray tlpdepth2" id="p5.42GER"> GER [→<a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Dass ∨, ⊃, etc. nicht Beziehungen im Sinne von rechts und links etc. sind, leuchtet ein.</div>
<div class="para tlpdepth2">Die Möglichkeit des kreuzweisen Definierens der logischen „Urzeichen“ Freges und Russells zeigt schon, dass diese keine Urzeichen sind, und schon erst recht, dass sie keine Relationen bezeichnen.</div>
<div class="para tlpdepth2">Und es ist offenbar, dass das „⊃“, welches wir durch „~“ und „∨“ definieren, identisch ist mit dem, durch welches wir „∨“ mit „~“ definieren, und dass dieses „∨“ mit dem ersten identisch ist. U. s. w.</div>
<div class="corelinks tlpdepth2"><strong>5.43</strong><span class="linkarray tlpdepth2" id="p5.43GER"> GER [→<a class="ogdlink" href="#p5.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Dass aus einer Tatsache <span class="mathmode"><var>p</var></span> unendlich viele <em class="germph">andere</em> folgen sollten, nämlich <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>, <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>, etc., ist doch von vornherein kaum zu glauben. Und nicht weniger merkwürdig ist, dass die unendliche Anzahl der Sätze der Logik (der Mathematik) aus einem halben Dutzend „Grundgesetzen“ folgen.</div>
<div class="para tlpdepth2">Alle Sätze der Logik sagen aber dasselbe. Nämlich nichts.</div>
<div class="corelinks tlpdepth2"><strong>5.44</strong><span class="linkarray tlpdepth2" id="p5.44GER"> GER [→<a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Wahrheitsfunktionen sind keine materiellen Funktionen.</div>
<div class="para tlpdepth2">Wenn man z. B. eine Bejahung durch doppelte Verneinung erzeugen kann, ist dann die Verneinung – in irgend einem Sinn – in der Bejahung enthalten? Verneint „<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>“ <span class="mathmode"><span class="mathop">~</span><var>p</var></span>, oder bejaht es <span class="mathmode"><var>p</var></span>; oder beides?</div>
<div class="para tlpdepth2">Der Satz „<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>“ handelt nicht von der Verneinung wie von einem Gegenstand; wohl aber ist die Möglichkeit der Verneinung in der Bejahung bereits präjudiziert.</div>
<div class="para tlpdepth2">Und gäbe es einen Gegenstand, der „~“ hieße, so müsste „<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>“ etwas anderes sagen als „<span class="mathmode"><var>p</var></span>“. Denn der eine Satz würde dann eben von ~ handeln, der andere nicht.</div>
<div class="corelinks tlpdepth3"><strong>5.441</strong><span class="linkarray tlpdepth3" id="p5.441GER"> GER [→<a class="ogdlink" href="#p5.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.441PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Dieses Verschwinden der scheinbaren logischen Konstanten tritt auch ein, wenn „<span class="mathmode"><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><span class="mathop">~</span><var>fx</var></span>“ dasselbe sagt wie „<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>“, oder „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>a</var></span>“ dasselbe wie „<span class="mathmode"><var>fa</var></span>“.</div>
<div class="corelinks tlpdepth3"><strong>5.442</strong><span class="linkarray tlpdepth3" id="p5.442GER"> GER [→<a class="ogdlink" href="#p5.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.442PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wenn uns ein Satz gegeben ist, so sind <em class="germph">mit ihm</em> auch schon die Resultate aller Wahrheitsoperationen, die ihn zur Basis haben, gegeben.</div>
<div class="corelinks tlpdepth2"><strong>5.45</strong><span class="linkarray tlpdepth2" id="p5.45GER"> GER [→<a class="ogdlink" href="#p5.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.45PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Gibt es logische Urzeichen, so muss eine richtige Logik ihre Stellung zueinander klar machen und ihr Dasein rechtfertigen. Der Bau der Logik <em class="germph">aus</em> ihren Urzeichen muss klar werden.</div>
<div class="corelinks tlpdepth3"><strong>5.451</strong><span class="linkarray tlpdepth3" id="p5.451GER"> GER [→<a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Hat die Logik Grundbegriffe, so müssen sie von einander unabhängig sein. Ist ein Grundbegriff eingeführt, so muss er in allen Verbindungen eingeführt sein, worin er überhaupt vorkommt. Man kann ihn also nicht zuerst für <em class="germph">eine</em> Verbindung, dann noch einmal für eine andere einführen. Z. B.: Ist die Verneinung eingeführt, so müssen wir sie jetzt in Sätzen von der Form „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ ebenso verstehen, wie in Sätzen wie „<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var>)</span>“, „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><span class="mathop">~</span><var>fx</var></span>“ u.&nbsp;a. Wir dürfen sie nicht erst für die eine Klasse von Fällen, dann für die andere einführen, denn es bliebe dann zweifelhaft, ob ihre Bedeutung in beiden Fällen die gleiche wäre und es wäre kein Grund vorhanden, in beiden Fällen dieselbe Art der Zeichenverbindung zu benützen.</div>
<div class="para tlpdepth3">(Kurz, für die Einführung der Urzeichen gilt, mutatis mutandis, dasselbe, was Frege („Grundgesetze der Arithmetik“) für die Einführung von Zeichen durch Definitionen gesagt hat.)</div>
<div class="corelinks tlpdepth3"><strong>5.452</strong><span class="linkarray tlpdepth3" id="p5.452GER"> GER [→<a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Einführung eines neuen Behelfes in den Symbolismus der Logik muss immer ein folgenschweres Ereignis sein. Kein neuer Behelf darf in die Logik – sozusagen, mit ganz unschuldiger Miene – in Klammern oder unter dem Striche eingeführt werden.</div>
<div class="para tlpdepth3">(So kommen in den „Principia Mathematica“ von Russell und Whitehead Definitionen und Grundgesetze in Worten vor. Warum hier plötzlich Worte? Dies bedürfte einer Rechtfertigung. Sie fehlt und muss fehlen, da das Vorgehen tatsächlich unerlaubt ist.)</div>
<div class="para tlpdepth3">Hat sich aber die Einführung eines neuen Behelfes an einer Stelle als nötig erwiesen, so muss man sich nun sofort fragen: Wo muss dieser Behelf nun <em class="germph">immer</em> angewandt werden? Seine Stellung in der Logik muss nun erklärt werden.</div>
<div class="corelinks tlpdepth3"><strong>5.453</strong><span class="linkarray tlpdepth3" id="p5.453GER"> GER [→<a class="ogdlink" href="#p5.453OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.453PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Alle Zahlen der Logik müssen sich rechtfertigen lassen.</div>
<div class="para tlpdepth3">Oder vielmehr: Es muss sich herausstellen, dass es in der Logik keine Zahlen gibt.</div>
<div class="para tlpdepth3">Es gibt keine ausgezeichneten Zahlen.</div>
<div class="corelinks tlpdepth3"><strong>5.454</strong><span class="linkarray tlpdepth3" id="p5.454GER"> GER [→<a class="ogdlink" href="#p5.454OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.454PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In der Logik gibt es kein Nebeneinander, kann es keine Klassifikation geben.</div>
<div class="para tlpdepth3">In der Logik kann es nicht Allgemeineres und Spezielleres geben.</div>
<div class="corelinks tlpdepth4"><strong>5.4541</strong><span class="linkarray tlpdepth4" id="p5.4541GER"> GER [→<a class="ogdlink" href="#p5.4541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Lösungen der logischen Probleme müssen einfach sein, denn sie setzen den Standard der Einfachheit.</div>
<div class="para tlpdepth4">Die Menschen haben immer geahnt, dass es ein Gebiet von Fragen geben müsse, deren Antworten – a priori – symmetrisch, und zu einem abgeschlossenen, regelmäßigen Gebilde vereint liegen.</div>
<div class="para tlpdepth4">Ein Gebiet, in dem der Satz gilt: simplex sigillum veri.</div>
<div class="corelinks tlpdepth2"><strong>5.46</strong><span class="linkarray tlpdepth2" id="p5.46GER"> GER [→<a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wenn man die logischen Zeichen richtig einführte, so hätte man damit auch schon den Sinn aller ihrer Kombinationen eingeführt; also nicht nur „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>“ sondern auch schon „<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>q</var>)</span>“ etc. etc. Man hätte damit auch schon die Wirkung aller nur möglichen Kombinationen von Klammern eingeführt. Und damit wäre es klar geworden, dass die eigentlichen allgemeinen Urzeichen nicht die „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var> </span>“, „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>“, etc. sind, sondern die allgemeinste Form ihrer Kombinationen.</div>
<div class="corelinks tlpdepth3"><strong>5.461</strong><span class="linkarray tlpdepth3" id="p5.461GER"> GER [→<a class="ogdlink" href="#p5.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Bedeutungsvoll ist die scheinbar unwichtige Tatsache, dass die logischen Scheinbeziehungen, wie ∨ und ⊃, der Klammern bedürfen – im Gegensatz zu den wirklichen Beziehungen.</div>
<div class="para tlpdepth3">Die Benützung der Klammern mit jenen scheinbaren Urzeichen deutet ja schon darauf hin, dass diese nicht die wirklichen Urzeichen sind. Und es wird doch wohl niemand glauben, dass die Klammern eine selbständige Bedeutung haben.</div>
<div class="corelinks tlpdepth4"><strong>5.4611</strong><span class="linkarray tlpdepth4" id="p5.4611GER"> GER [→<a class="ogdlink" href="#p5.4611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4611PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die logischen Operationszeichen sind Interpunktionen.</div>
<div class="corelinks tlpdepth2"><strong>5.47</strong><span class="linkarray tlpdepth2" id="p5.47GER"> GER [→<a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Es ist klar, dass alles, was sich überhaupt <em class="germph">von vornherein</em> über die Form aller Sätze sagen lässt, sich <em class="germph">auf einmal</em> sagen lassen muss.</div>
<div class="para tlpdepth2">Sind ja schon im Elementarsatze alle logischen Operationen enthalten. Denn „<span class="mathmode"><var>fa</var></span>“ sagt dasselbe wie</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode">„<span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>a</var>“.</span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">Wo Zusammengesetztheit ist, da ist Argument und Funktion, und wo diese sind, sind bereits alle logischen Konstanten.</div>
<div class="para tlpdepth2">Man könnte sagen: Die Eine logische Konstante ist das, was <em class="germph">alle</em> Sätze, ihrer Natur nach, mit einander gemein haben.</div>
<div class="para tlpdepth2">Das aber ist die allgemeine Satzform.</div>
<div class="corelinks tlpdepth3"><strong>5.471</strong><span class="linkarray tlpdepth3" id="p5.471GER"> GER [→<a class="ogdlink" href="#p5.471OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.471PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die allgemeine Satzform ist das Wesen des Satzes.</div>
<div class="corelinks tlpdepth4"><strong>5.4711</strong><span class="linkarray tlpdepth4" id="p5.4711GER"> GER [→<a class="ogdlink" href="#p5.4711OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4711PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das Wesen des Satzes angeben, heißt, das Wesen aller Beschreibung angeben, also das Wesen der Welt.</div>
<div class="corelinks tlpdepth3"><strong>5.472</strong><span class="linkarray tlpdepth3" id="p5.472GER"> GER [→<a class="ogdlink" href="#p5.472OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.472PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Beschreibung der allgemeinsten Satzform ist die Beschreibung des einen und einzigen allgemeinen Urzeichens der Logik.</div>
<div class="corelinks tlpdepth3"><strong>5.473</strong><span class="linkarray tlpdepth3" id="p5.473GER"> GER [→<a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Logik muss für sich selber sorgen.</div>
<div class="para tlpdepth3">Ein <em class="germph">mögliches</em> Zeichen muss auch bezeichnen können. Alles was in der Logik möglich ist, ist auch erlaubt. („Sokrates ist identisch“ heißt darum nichts, weil es keine Eigenschaft gibt, die „identisch“ heißt. Der Satz ist unsinnig, weil wir eine willkürliche Bestimmung nicht getroffen haben, aber nicht darum, weil das Symbol an und für sich unerlaubt wäre.)</div>
<div class="para tlpdepth3">Wir können uns, in gewissem Sinne, nicht in der Logik irren.</div>
<div class="corelinks tlpdepth4"><strong>5.4731</strong><span class="linkarray tlpdepth4" id="p5.4731GER"> GER [→<a class="ogdlink" href="#p5.4731OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das Einleuchten, von dem Russell so viel sprach, kann nur dadurch in der Logik entbehrlich werden, dass die Sprache selbst jeden logischen Fehler verhindert. – Dass die Logik a priori ist, besteht darin, dass nicht unlogisch gedacht werden <em class="germph">kann</em>.</div>
<div class="corelinks tlpdepth4"><strong>5.4732</strong><span class="linkarray tlpdepth4" id="p5.4732GER"> GER [→<a class="ogdlink" href="#p5.4732OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4732PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wir können einem Zeichen nicht den unrechten Sinn geben.</div>
<div class="corelinks tlpdepth5"><strong>5.47321</strong><span class="linkarray tlpdepth5" id="p5.47321GER"> GER [→<a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Occams Devise ist natürlich keine willkürliche, oder durch ihren praktischen Erfolg gerechtfertigte Regel: Sie besagt, dass <em class="germph">unnötige</em> Zeicheneinheiten nichts bedeuten.</div>
<div class="para tlpdepth5">Zeichen, die <em class="germph">Einen</em> Zweck erfüllen, sind logisch äquivalent, Zeichen, die <em class="germph">keinen</em> Zweck erfüllen, logisch bedeutungslos.</div>
<div class="corelinks tlpdepth4"><strong>5.4733</strong><span class="linkarray tlpdepth4" id="p5.4733GER"> GER [→<a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Frege sagt: Jeder rechtmäßig gebildete Satz muss einen Sinn haben; und ich sage: Jeder mögliche Satz ist rechtmäßig gebildet, und wenn er keinen Sinn hat, so kann das nur daran liegen, dass wir einigen seiner Bestandteile keine <em class="germph">Bedeutung</em> gegeben haben.</div>
<div class="para tlpdepth4">(Wenn wir auch glauben, es getan zu haben.)</div>
<div class="para tlpdepth4">So sagt „Sokrates ist identisch“ darum nichts, weil wir dem Wort „identisch“ als <em class="germph">Eigenschaftswort</em> <em class="germph">keine</em> Bedeutung gegeben haben. Denn, wenn es als Gleichheitszeichen auftritt, so symbolisiert es auf ganz andere Art und Weise – die bezeichnende Beziehung ist eine andere, – also ist auch das Symbol in beiden Fällen ganz verschieden; die beiden Symbole haben nur das Zeichen zufällig miteinander gemein.</div>
<div class="corelinks tlpdepth3"><strong>5.474</strong><span class="linkarray tlpdepth3" id="p5.474GER"> GER [→<a class="ogdlink" href="#p5.474OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.474PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Anzahl der nötigen Grundoperationen hängt <em class="germph">nur</em> von unserer Notation ab.</div>
<div class="corelinks tlpdepth3"><strong>5.475</strong><span class="linkarray tlpdepth3" id="p5.475GER"> GER [→<a class="ogdlink" href="#p5.475OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.475PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es kommt nur darauf an, ein Zeichensystem von einer bestimmten Anzahl von Dimensionen – von einer bestimmten mathematischen Mannigfaltigkeit – zu bilden.</div>
<div class="corelinks tlpdepth3"><strong>5.476</strong><span class="linkarray tlpdepth3" id="p5.476GER"> GER [→<a class="ogdlink" href="#p5.476OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.476PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist klar, dass es sich hier nicht um eine <em class="germph">Anzahl von Grundbegriffen</em> handelt, die bezeichnet werden müssen, sondern um den Ausdruck einer Regel.</div>
<div class="corelinks tlpdepth1"><strong>5.5</strong><span class="linkarray tlpdepth1" id="p5.5GER"> GER [→<a class="ogdlink" href="#p5.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Jede Wahrheitsfunktion ist ein Resultat der successiven Anwendung der Operation <span class="mathmode"><span class="mathop">(−−−−−<span class="mathrm">W</span>)</span> (<var>ξ</var>,&nbsp;.&nbsp;.&nbsp;.&nbsp;.&nbsp;.)</span> auf Elementarsätze.</div>
<div class="para tlpdepth1">Diese Operation verneint sämtliche Sätze in der rechten Klammer, und ich nenne sie die Negation dieser Sätze.</div>
<div class="corelinks tlpdepth3"><strong>5.501</strong><span class="linkarray tlpdepth3" id="p5.501GER"> GER [→<a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Einen Klammerausdruck, dessen Glieder Sätze sind, deute ich – wenn die Reihenfolge der Glieder in der Klammer gleichgültig ist – durch ein Zeichen von der Form „<span class="mathmode">(<span class="overlined"><var>ξ</var></span>)</span>“ an. „<span class="mathmode"><var>ξ</var></span>“ ist eine Variable, deren Werte die Glieder des Klammerausdruckes sind; und der Strich über der Variablen deutet an, dass sie ihre sämtlichen Werte in der Klammer vertritt.</div>
<div class="para tlpdepth3">(Hat also <span class="mathmode"><var>ξ</var></span> etwa die 3 Werte P, Q, R, so ist <span class="mathmode">(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span>(<span class="mathrm">P</span>, <span class="mathrm">Q</span>, <span class="mathrm">R</span>)</span>.)</div>
<div class="para tlpdepth3">Die Werte der Variablen werden festgesetzt.</div>
<div class="para tlpdepth3">Die Festsetzung ist die Beschreibung der Sätze, welche die Variable vertritt.</div>
<div class="para tlpdepth3">Wie die Beschreibung der Glieder des Klammerausdruckes geschieht, ist unwesentlich.</div>
<div class="para tlpdepth3">Wir <em class="germph">können</em> drei Arten der Beschreibung unterscheiden: 1. Die direkte Aufzählung. In diesem Fall können wir statt der Variablen einfach ihre konstanten Werte setzen. 2. Die Angabe einer Funktion <span class="mathmode"><var>fx</var></span>, deren Werte für alle Werte von <span class="mathmode"><var>x</var></span> die zu beschreibenden Sätze sind. 3. Die Angabe eines formalen Gesetzes, nach welchem jene Sätze gebildet sind. In diesem Falle sind die Glieder des Klammerausdrucks sämtliche Glieder einer Formenreihe.</div>
<div class="corelinks tlpdepth3"><strong>5.502</strong><span class="linkarray tlpdepth3" id="p5.502GER"> GER [→<a class="ogdlink" href="#p5.502OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.502PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ich schreibe also statt „<span class="mathmode"><span class="mathop">(−−−−−<span class="mathrm">W</span>)</span></span> <span class="mathmode">(<var>ξ</var>,&nbsp;.&nbsp;.&nbsp;.&nbsp;.&nbsp;.)</span>“ „<span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)</span>“.</div>
<div class="para tlpdepth3"><span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)</span> ist die Negation sämtlicher Werte der Satzvariablen <span class="mathmode"><var>ξ</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.503</strong><span class="linkarray tlpdepth3" id="p5.503GER"> GER [→<a class="ogdlink" href="#p5.503OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.503PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Da sich offenbar leicht ausdrücken lässt, wie mit dieser Operation Sätze gebildet werden können und wie Sätze mit ihr nicht zu bilden sind, so muss dies auch einen exakten Ausdruck finden können.</div>
<div class="corelinks tlpdepth2"><strong>5.51</strong><span class="linkarray tlpdepth2" id="p5.51GER"> GER [→<a class="ogdlink" href="#p5.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.51PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Hat <span class="mathmode"><var>ξ</var></span> nur einen Wert, so ist <span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><var>p</var></span> (nicht <span class="mathmode"><var>p</var></span>), hat es zwei Werte, so ist <span class="mathmode"><span class="nop">N</span> (<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var></span> (weder <span class="mathmode"><var>p</var></span> noch <span class="mathmode"><var>q</var></span>).</div>
<div class="corelinks tlpdepth3"><strong>5.511</strong><span class="linkarray tlpdepth3" id="p5.511GER"> GER [→<a class="ogdlink" href="#p5.511OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.511PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wie kann die allumfassende, weltspiegelnde Logik so spezielle Haken und Manipulationen gebrauchen? Nur, indem sich alle diese zu einem unendlich feinen Netzwerk, zu dem großen Spiegel, verknüpfen.</div>
<div class="corelinks tlpdepth3"><strong>5.512</strong><span class="linkarray tlpdepth3" id="p5.512GER"> GER [→<a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span></div>
<div class="para tlpdepth3">„<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ ist wahr, wenn „<span class="mathmode"><var>p</var></span>“ falsch ist. Also in dem wahren Satz „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ ist „<span class="mathmode"><var>p</var></span>“ ein falscher Satz. Wie kann ihn nun der Strich „~“ mit der Wirklichkeit zum Stimmen bringen?</div>
<div class="para tlpdepth3">Das, was in „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ verneint, ist aber nicht das „~“, sondern dasjenige, was allen Zeichen dieser Notation, welche <span class="mathmode"><var>p</var></span> verneinen, gemeinsam ist.</div>
<div class="para tlpdepth3">Also die gemeinsame Regel, nach welcher „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“, „<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>“, „<span class="mathmode"><span class="mathop">~</span><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>“, „<span class="mathmode"><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var></span>“, etc. etc. (ad inf.) gebildet werden. Und dies Gemeinsame spiegelt die Verneinung wieder.</div>
<div class="corelinks tlpdepth3"><strong>5.513</strong><span class="linkarray tlpdepth3" id="p5.513GER"> GER [→<a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Man könnte sagen: Das Gemeinsame aller Symbole, die sowohl <span class="mathmode"><var>p</var></span> als <span class="mathmode"><var>q</var></span> bejahen, ist der Satz „<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>q</var></span>“. Das Gemeinsame aller Symbole, die entweder <span class="mathmode"><var>p</var></span> oder <span class="mathmode"><var>q</var></span> bejahen, ist der Satz „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>“.</div>
<div class="para tlpdepth3">Und so kann man sagen: Zwei Sätze sind einander entgegengesetzt, wenn sie nichts miteinander gemein haben, und: Jeder Satz hat nur ein Negativ, weil es nur einen Satz gibt, der ganz außerhalb seiner liegt.</div>
<div class="para tlpdepth3">Es zeigt sich so auch in Russells Notation, dass „<span class="mathmode"><var>q</var><span class="mathrel">:</span><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>“ dasselbe sagt wie „<span class="mathmode"><var>q</var></span>“; dass „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>“ nichts sagt.</div>
<div class="corelinks tlpdepth3"><strong>5.514</strong><span class="linkarray tlpdepth3" id="p5.514GER"> GER [→<a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ist eine Notation festgelegt, so gibt es in ihr eine Regel, nach der alle <span class="mathmode"><var>p</var></span> verneinenden Sätze gebildet werden, eine Regel, nach der alle <span class="mathmode"><var>p</var></span> bejahenden Sätze gebildet werden, eine Regel, nach der alle <span class="mathmode"><var>p</var></span> oder <span class="mathmode"><var>q</var></span> bejahenden Sätze gebildet werden, u.&nbsp;s.&nbsp;f. Diese Regeln sind den Symbolen äquivalent und in ihnen spiegelt sich ihr Sinn wieder.</div>
<div class="corelinks tlpdepth3"><strong>5.515</strong><span class="linkarray tlpdepth3" id="p5.515GER"> GER [→<a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es muss sich an unseren Symbolen zeigen, dass das, was durch „∨“, „.“, etc. miteinander verbunden ist, Sätze sein müssen.</div>
<div class="para tlpdepth3">Und dies ist auch der Fall, denn das Symbol „<span class="mathmode"><var>p</var></span>“ und „<span class="mathmode"><var>q</var></span>“ setzt ja selbst das „∨“, „~“, etc. voraus. Wenn das Zeichen „<span class="mathmode"><var>p</var></span>“ in „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>“ nicht für ein komplexes Zeichen steht, dann kann es allein nicht Sinn haben; dann können aber auch die mit „<span class="mathmode"><var>p</var></span>“ gleichsinnigen Zeichen „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>p</var></span>“, „<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>p</var></span>“, etc. keinen Sinn haben. Wenn aber „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>p</var></span>“ keinen Sinn hat, dann kann auch „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>“ keinen Sinn haben.</div>
<div class="corelinks tlpdepth4"><strong>5.5151</strong><span class="linkarray tlpdepth4" id="p5.5151GER"> GER [→<a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Muss das Zeichen des negativen Satzes mit dem Zeichen des positiven gebildet werden? Warum sollte man den negativen Satz nicht durch eine negative Tatsache ausdrücken können. (Etwa: Wenn „<span class="mathmode"><var>a</var></span>“ nicht in einer bestimmten Beziehung zu „<span class="mathmode"><var>b</var></span>“ steht, könnte das ausdrücken, dass <span class="mathmode"><var>aRb</var></span> nicht der Fall ist.)</div>
<div class="para tlpdepth4">Aber auch hier ist ja der negative Satz indirekt durch den positiven gebildet.</div>
<div class="para tlpdepth4">Der positive <em class="germph">Satz</em> muss die Existenz des negativen <em class="germph">Satzes</em> voraussetzen und umgekehrt.</div>
<div class="corelinks tlpdepth2"><strong>5.52</strong><span class="linkarray tlpdepth2" id="p5.52GER"> GER [→<a class="ogdlink" href="#p5.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.52PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Sind die Werte von <span class="mathmode"><var>ξ</var></span> sämtliche Werte einer Funktion <span class="mathmode"><var>fx</var></span> für alle Werte von <span class="mathmode"><var>x</var></span>, so wird <span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.521</strong><span class="linkarray tlpdepth3" id="p5.521GER"> GER [→<a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ich trenne den Begriff <em class="germph">Alle</em> von der Wahrheitsfunktion.</div>
<div class="para tlpdepth3">Frege und Russell haben die Allgemeinheit in Verbindung mit dem logischen Produkt oder der logischen Summe eingeführt. So wurde es schwer, die Sätze „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>“ und „<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>“, in welchen beide Ideen beschlossen liegen, zu verstehen.</div>
<div class="corelinks tlpdepth3"><strong>5.522</strong><span class="linkarray tlpdepth3" id="p5.522GER"> GER [→<a class="ogdlink" href="#p5.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.522PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Eigentümliche der Allgemeinheitsbezeichnung ist erstens, dass sie auf ein logisches Urbild hinweist, und zweitens, dass sie Konstante hervorhebt.</div>
<div class="corelinks tlpdepth3"><strong>5.523</strong><span class="linkarray tlpdepth3" id="p5.523GER"> GER [→<a class="ogdlink" href="#p5.523OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.523PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Allgemeinheitsbezeichnung tritt als Argument auf.</div>
<div class="corelinks tlpdepth3"><strong>5.524</strong><span class="linkarray tlpdepth3" id="p5.524GER"> GER [→<a class="ogdlink" href="#p5.524OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.524PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wenn die Gegenstände gegeben sind, so sind uns damit auch schon <em class="germph">alle</em> Gegenstände gegeben.</div>
<div class="para tlpdepth3">Wenn die Elementarsätze gegeben sind, so sind damit auch <em class="germph">alle</em> Elementarsätze gegeben.</div>
<div class="corelinks tlpdepth3"><strong>5.525</strong><span class="linkarray tlpdepth3" id="p5.525GER"> GER [→<a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist unrichtig, den Satz „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>“ – wie Russell dies tut – in Worten durch „<span class="mathmode"><var>fx</var></span> ist <em class="germph">möglich</em>“ wiederzugeben.</div>
<div class="para tlpdepth3">Gewissheit, Möglichkeit oder Unmöglichkeit einer Sachlage wird nicht durch einen Satz ausgedrückt, sondern dadurch, dass ein Ausdruck eine Tautologie, ein sinnvoller Satz oder eine Kontradiktion ist.</div>
<div class="para tlpdepth3">Jener Präzedenzfall, auf den man sich immer berufen möchte, muss schon im Symbol selber liegen.</div>
<div class="corelinks tlpdepth3"><strong>5.526</strong><span class="linkarray tlpdepth3" id="p5.526GER"> GER [→<a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Man kann die Welt vollständig durch vollkommen verallgemeinerte Sätze beschreiben, das heißt also, ohne irgendeinen Namen von vornherein einem bestimmten Gegenstand zuzuordnen.</div>
<div class="para tlpdepth3">Um dann auf die gewöhnliche Ausdrucksweise zu kommen, muss man einfach nach einem Ausdruck: „Es gibt ein und nur ein <span class="mathmode"><var>x</var></span>, welches …“ sagen: Und dies <span class="mathmode"><var>x</var></span> ist <span class="mathmode"><var>a</var></span>.</div>
<div class="corelinks tlpdepth4"><strong>5.5261</strong><span class="linkarray tlpdepth4" id="p5.5261GER"> GER [→<a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Ein vollkommen verallgemeinerter Satz ist, wie jeder andere Satz, zusammengesetzt. (Dies zeigt sich daran, dass wir in „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>, <var>φ</var>).</span><var>φx</var></span>“ „<span class="mathmode"><var>φ</var></span>“ und „<span class="mathmode"><var>x</var></span>“ getrennt erwähnen müssen. Beide stehen unabhängig in bezeichnenden Beziehungen zur Welt, wie im unverallgemeinerten Satz.)</div>
<div class="para tlpdepth4">Kennzeichen des zusammengesetzten Symbols: Es hat etwas mit <em class="germph">anderen</em> Symbolen gemeinsam.</div>
<div class="corelinks tlpdepth4"><strong>5.5262</strong><span class="linkarray tlpdepth4" id="p5.5262GER"> GER [→<a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es verändert ja die Wahr- oder Falschheit <em class="germph">jedes</em> Satzes etwas am allgemeinen Bau der Welt. Und der Spielraum, welcher ihrem Bau durch die Gesamtheit der Elementarsätze gelassen wird, ist eben derjenige, welchen die ganz allgemeinen Sätze begrenzen.</div>
<div class="para tlpdepth4">(Wenn ein Elementarsatz wahr ist, so ist damit doch jedenfalls Ein Elementarsatz <em class="germph">mehr</em> wahr.)</div>
<div class="corelinks tlpdepth2"><strong>5.53</strong><span class="linkarray tlpdepth2" id="p5.53GER"> GER [→<a class="ogdlink" href="#p5.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.53PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Gleichheit des Gegenstandes drücke ich durch Gleichheit des Zeichens aus, und nicht mit Hilfe eines Gleichheitszeichens. Verschiedenheit der Gegenstände durch Verschiedenheit der Zeichen.</div>
<div class="corelinks tlpdepth4"><strong>5.5301</strong><span class="linkarray tlpdepth4" id="p5.5301GER"> GER [→<a class="ogdlink" href="#p5.5301OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dass die Identität keine Relation zwischen Gegenständen ist, leuchtet ein. Dies wird sehr klar, wenn man z. B. den Satz „<span class="mathmode"><span class="quant">(<var>x</var>):</span><var>fx</var><span class="mathrel">.<span class="symbol">⊃</span>.</span><var>x</var><span class="mathrel">=</span><var>a</var></span>“ betrachtet. Was dieser Satz sagt, ist einfach, dass <em class="germph">nur</em> <span class="mathmode"><var>a</var></span> der Funktion <span class="mathmode"><var>f</var></span> genügt, und nicht, dass nur solche Dinge der Funktion <span class="mathmode"><var>f</var></span> genügen, welche eine gewisse Beziehung zu <span class="mathmode"><var>a</var></span> haben.</div>
<div class="para tlpdepth4">Man könnte nun freilich sagen, dass eben <em class="germph">nur</em> <span class="mathmode"><var>a</var></span> diese Beziehung zu <span class="mathmode"><var>a</var></span> habe, aber, um dies auszudrücken, brauchten wir das Gleichheitszeichen selber.</div>
<div class="corelinks tlpdepth4"><strong>5.5302</strong><span class="linkarray tlpdepth4" id="p5.5302GER"> GER [→<a class="ogdlink" href="#p5.5302OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5302PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Russells Definition von „=“ genügt nicht; weil man nach ihr nicht sagen kann, dass zwei Gegenstände alle Eigenschaften gemeinsam haben. (Selbst wenn dieser Satz nie richtig ist, hat er doch <em class="germph">Sinn</em>.)</div>
<div class="corelinks tlpdepth4"><strong>5.5303</strong><span class="linkarray tlpdepth4" id="p5.5303GER"> GER [→<a class="ogdlink" href="#p5.5303OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5303PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Beiläufig gesprochen: Von <em class="germph">zwei</em> Dingen zu sagen, sie seien identisch, ist ein Unsinn, und von <em class="germph">Einem</em> zu sagen, es sei identisch mit sich selbst, sagt gar nichts.</div>
<div class="corelinks tlpdepth3"><strong>5.531</strong><span class="linkarray tlpdepth3" id="p5.531GER"> GER [→<a class="ogdlink" href="#p5.531OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.531PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ich schreibe also nicht „<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)<span class="mathrel">.</span><var>a</var><span class="mathrel">=</span><var>b</var></span>“, sondern „<span class="mathmode"><var>f</var>(<var>a</var>,<var>a</var>)</span>“ (oder „<span class="mathmode"><var>f</var>(<var>b</var>,<var>b</var>)</span>“). Und nicht „<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)<span class="mathrel">.</span><span class="mathop">~</span><var>a</var><span class="mathrel">=</span><var>b</var></span>“, sondern „<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)</span>“.</div>
<div class="corelinks tlpdepth3"><strong>5.532</strong><span class="linkarray tlpdepth3" id="p5.532GER"> GER [→<a class="ogdlink" href="#p5.532OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.532PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Und analog: Nicht „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>y</var></span>“, sondern „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>f</var>(<var>x</var>,<var>x</var>)</span>“; und nicht „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.</span><span class="mathop">~</span><var>x</var><span class="mathrel">=</span><var>y</var></span>“, sondern „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)</span>“.</div>
<div class="para tlpdepth3">(Also statt des Russellschen „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span></span> <span class="mathmode"><var>f</var>(<var>x</var>,<var>y</var>)</span>“: „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.<span class="symbol">∨</span>.</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>f</var>(<var>x</var>,<var>x</var>)</span>“.)</div>
<div class="corelinks tlpdepth4"><strong>5.5321</strong><span class="linkarray tlpdepth4" id="p5.5321GER"> GER [→<a class="ogdlink" href="#p5.5321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5321PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Statt „<span class="mathmode"><span class="quant">(<var>x</var>):</span><var>fx</var><span class="mathrel"><span class="symbol">⊃</span></span><var>x</var><span class="mathrel">=</span><var>a</var></span>“ schreiben wir also z. B. „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.<span class="symbol">⊃</span>.</span><var>fa</var><span class="mathrel">:</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>fx</var><span class="mathrel">.</span><var>fy</var></span>“.</div>
<div class="para tlpdepth4">Und der Satz: „<em class="germph">nur</em> Ein <span class="mathmode"><var>x</var></span> befriedigt <span class="mathmode"><var>f</var>(&nbsp;)</span>“ lautet: „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">:</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>fx</var><span class="mathrel">.</span><var>fy</var></span>“.</div>
<div class="corelinks tlpdepth3"><strong>5.533</strong><span class="linkarray tlpdepth3" id="p5.533GER"> GER [→<a class="ogdlink" href="#p5.533OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.533PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Gleichheitszeichen ist also kein wesentlicher Bestandteil der Begriffsschrift.</div>
<div class="corelinks tlpdepth3"><strong>5.534</strong><span class="linkarray tlpdepth3" id="p5.534GER"> GER [→<a class="ogdlink" href="#p5.534OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.534PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Und nun sehen wir, dass Scheinsätze wie: „<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>“, „<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var><span class="mathrel">.</span><var>b</var><span class="mathrel">=</span><var>c</var><span class="mathrel">.<span class="symbol">⊃</span></span><var>a</var><span class="mathrel">=</span><var>c</var></span>“, „<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>x</var></span>“, „<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>a</var></span>“, etc. sich in einer richtigen Begriffsschrift gar nicht hinschreiben lassen.</div>
<div class="corelinks tlpdepth3"><strong>5.535</strong><span class="linkarray tlpdepth3" id="p5.535GER"> GER [→<a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Damit erledigen sich auch alle Probleme, die an solche Scheinsätze geknüpft waren.</div>
<div class="para tlpdepth3">Alle Probleme, die Russells „Axiom of Infinity“ mit sich bringt, sind schon hier zu lösen.</div>
<div class="para tlpdepth3">Das, was das Axiom of Infinity sagen soll, würde sich in der Sprache dadurch ausdrücken, dass es unendlich viele Namen mit verschiedener Bedeutung gäbe.</div>
<div class="corelinks tlpdepth4"><strong>5.5351</strong><span class="linkarray tlpdepth4" id="p5.5351GER"> GER [→<a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es gibt gewisse Fälle, wo man in Versuchung gerät, Ausdrücke von der Form „<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>“ oder „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span>“ u. dgl. zu benützen. Und zwar geschieht dies, wenn man von dem Urbild: Satz, Ding, etc. reden möchte. So hat Russell in den „Principles of Mathematics“ den Unsinn „<span class="mathmode"><var>p</var></span> ist ein Satz“ in Symbolen durch „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span>“ wiedergegeben und als Hypothese vor gewisse Sätze gestellt, damit deren Argumentstellen nur von Sätzen besetzt werden könnten.</div>
<div class="para tlpdepth4">(Es ist schon darum Unsinn, die Hypothese <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span> vor einen Satz zu stellen, um ihm Argumente der richtigen Form zu sichern, weil die Hypothese für einen Nicht-Satz als Argument nicht falsch, sondern unsinnig wird, und weil der Satz selbst durch die unrichtige Gattung von Argumenten unsinnig wird, also sich selbst ebenso gut, oder so schlecht, vor den unrechten Argumenten bewahrt wie die zu diesem Zweck angehängte sinnlose Hypothese.)</div>
<div class="corelinks tlpdepth4"><strong>5.5352</strong><span class="linkarray tlpdepth4" id="p5.5352GER"> GER [→<a class="ogdlink" href="#p5.5352OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5352PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Ebenso wollte man „Es gibt keine <em class="germph">Dinge</em>“ ausdrücken durch „<span class="mathmode"><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>x</var></span>“. Aber selbst wenn dies ein Satz wäre – wäre er nicht auch wahr, wenn es zwar „Dinge gäbe“, aber diese nicht mit sich selbst identisch wären?</div>
<div class="corelinks tlpdepth2"><strong>5.54</strong><span class="linkarray tlpdepth2" id="p5.54GER"> GER [→<a class="ogdlink" href="#p5.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.54PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In der allgemeinen Satzform kommt der Satz im Satze nur als Basis der Wahrheitsoperationen vor.</div>
<div class="corelinks tlpdepth3"><strong>5.541</strong><span class="linkarray tlpdepth3" id="p5.541GER"> GER [→<a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Auf den ersten Blick scheint es, als könne ein Satz in einem anderen auch auf andere Weise vorkommen.</div>
<div class="para tlpdepth3">Besonders in gewissen Satzformen der Psychologie, wie „A glaubt, dass <span class="mathmode"><var>p</var></span> der Fall ist“, oder „A denkt <span class="mathmode"><var>p</var></span>“, etc.</div>
<div class="para tlpdepth3">Hier scheint es nämlich oberflächlich, als stünde der Satz <span class="mathmode"><var>p</var></span> zu einem Gegenstand A in einer Art von Relation.</div>
<div class="para tlpdepth3">(Und in der modernen Erkenntnistheorie (Russell, Moore, etc.) sind jene Sätze auch so aufgefasst worden.)</div>
<div class="corelinks tlpdepth3"><strong>5.542</strong><span class="linkarray tlpdepth3" id="p5.542GER"> GER [→<a class="ogdlink" href="#p5.542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist aber klar, dass „A glaubt, dass <span class="mathmode"><var>p</var></span>“, „A denkt <span class="mathmode"><var>p</var></span>“, „A sagt <span class="mathmode"><var>p</var></span>“ von der Form „‚<span class="mathmode"><var>p</var></span>‘ sagt <span class="mathmode"><var>p</var></span>“ sind: Und hier handelt es sich nicht um eine Zuordnung von einer Tatsache und einem Gegenstand, sondern um die Zuordnung von Tatsachen durch Zuordnung ihrer Gegenstände.</div>
<div class="corelinks tlpdepth4"><strong>5.5421</strong><span class="linkarray tlpdepth4" id="p5.5421GER"> GER [→<a class="ogdlink" href="#p5.5421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5421PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dies zeigt auch, dass die Seele – das Subjekt etc. – wie sie in der heutigen oberflächlichen Psychologie aufgefasst wird, ein Unding ist.</div>
<div class="para tlpdepth4">Eine zusammengesetzte Seele wäre nämlich keine Seele mehr.</div>
<div class="corelinks tlpdepth4"><strong>5.5422</strong><span class="linkarray tlpdepth4" id="p5.5422GER"> GER [→<a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die richtige Erklärung der Form des Satzes „A urteilt <span class="mathmode"><var>p</var></span>“ muss zeigen, dass es unmöglich ist, einen Unsinn zu urteilen. (Russells Theorie genügt dieser Bedingung nicht.)</div>
<div class="corelinks tlpdepth4"><strong>5.5423</strong><span class="linkarray tlpdepth4" id="p5.5423GER"> GER [→<a class="ogdlink" href="#p5.5423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5423PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Einen Komplex wahrnehmen heißt wahrnehmen, dass sich seine Bestandteile so und so zu einander verhalten.</div>
<div class="para tlpdepth4">Dies erklärt wohl auch, dass man die Figur </div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/thecube.svg" type="image/svg+xml" class="thecubesvg" ><img src="images/thecube.png" alt="Cube with a face and b face" class="thecubepng" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> auf zweierlei Art als Würfel sehen kann; und alle ähnlichen Erscheinungen. Denn wir sehen eben wirklich zwei verschiedene Tatsachen.</div>
<div class="para tlpdepth4">(Sehe ich erst auf die Ecken <span class="mathmode"><var>a</var></span> und nur flüchtig auf <span class="mathmode"><var>b</var></span>, so erscheint <span class="mathmode"><var>a</var></span> vorne; und umgekehrt.)</div>
<div class="corelinks tlpdepth2"><strong>5.55</strong><span class="linkarray tlpdepth2" id="p5.55GER"> GER [→<a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wir müssen nun die Frage nach allen möglichen Formen der Elementarsätze a priori beantworten.</div>
<div class="para tlpdepth2">Der Elementarsatz besteht aus Namen. Da wir aber die Anzahl der Namen von verschiedener Bedeutung nicht angeben können, so können wir auch nicht die Zusammensetzung des Elementarsatzes angeben.</div>
<div class="corelinks tlpdepth3"><strong>5.551</strong><span class="linkarray tlpdepth3" id="p5.551GER"> GER [→<a class="ogdlink" href="#p5.551OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.551PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Unser Grundsatz ist, dass jede Frage, die sich überhaupt durch die Logik entscheiden lässt, sich ohne weiteres entscheiden lassen muss.</div>
<div class="para tlpdepth3">(Und wenn wir in die Lage kommen, ein solches Problem durch Ansehen der Welt beantworten zu müssen, so zeigt dies, dass wir auf grundfalscher Fährte sind.)</div>
<div class="corelinks tlpdepth3"><strong>5.552</strong><span class="linkarray tlpdepth3" id="p5.552GER"> GER [→<a class="ogdlink" href="#p5.552OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.552PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die „Erfahrung“, die wir zum Verstehen der Logik brauchen, ist nicht die, dass sich etwas so und so verhält, sondern, dass etwas <em class="germph">ist</em>: aber das ist eben <em class="germph">keine</em> Erfahrung.</div>
<div class="para tlpdepth3">Die Logik ist <em class="germph">vor</em> jeder Erfahrung – dass etwas <em class="germph">so</em> ist.</div>
<div class="para tlpdepth3">Sie ist vor dem Wie, nicht vor dem Was.</div>
<div class="corelinks tlpdepth4"><strong>5.5521</strong><span class="linkarray tlpdepth4" id="p5.5521GER"> GER [→<a class="ogdlink" href="#p5.5521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5521PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Und wenn dies nicht so wäre, wie könnten wir die Logik anwenden? Man könnte sagen: Wenn es eine Logik gäbe, auch wenn es keine Welt gäbe, wie könnte es dann eine Logik geben, da es eine Welt gibt?</div>
<div class="corelinks tlpdepth3"><strong>5.553</strong><span class="linkarray tlpdepth3" id="p5.553GER"> GER [→<a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Russell sagte, es gäbe einfache Relationen zwischen verschiedenen Anzahlen von Dingen (Individuals). Aber zwischen welchen Anzahlen? Und wie soll sich das entscheiden? – Durch die Erfahrung?</div>
<div class="para tlpdepth3">(Eine ausgezeichnete Zahl gibt es nicht.)</div>
<div class="corelinks tlpdepth3"><strong>5.554</strong><span class="linkarray tlpdepth3" id="p5.554GER"> GER [→<a class="ogdlink" href="#p5.554OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.554PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Angabe jeder speziellen Form wäre vollkommen willkürlich.</div>
<div class="corelinks tlpdepth4"><strong>5.5541</strong><span class="linkarray tlpdepth4" id="p5.5541GER"> GER [→<a class="ogdlink" href="#p5.5541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5541PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es soll sich a priori angeben lassen, ob ich z. B. in die Lage kommen kann, etwas mit dem Zeichen einer 27-stelligen Relation bezeichnen zu müssen.</div>
<div class="corelinks tlpdepth4"><strong>5.5542</strong><span class="linkarray tlpdepth4" id="p5.5542GER"> GER [→<a class="ogdlink" href="#p5.5542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5542PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dürfen wir denn aber überhaupt so fragen? Können wir eine Zeichenform aufstellen und nicht wissen, ob ihr etwas entsprechen könne?</div>
<div class="para tlpdepth4">Hat die Frage einen Sinn: Was muss <em class="germph">sein</em>, damit etwas der-Fall-sein kann?</div>
<div class="corelinks tlpdepth3"><strong>5.555</strong><span class="linkarray tlpdepth3" id="p5.555GER"> GER [→<a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist klar, wir haben vom Elementarsatz einen Begriff, abgesehen von seiner besonderen logischen Form.</div>
<div class="para tlpdepth3">Wo man aber Symbole nach einem System bilden kann, dort ist dieses System das logisch wichtige und nicht die einzelnen Symbole.</div>
<div class="para tlpdepth3">Und wie wäre es auch möglich, dass ich es in der Logik mit Formen zu tun hätte, die ich erfinden kann; sondern mit dem muss ich es zu tun haben, was es mir möglich macht, sie zu erfinden.</div>
<div class="corelinks tlpdepth3"><strong>5.556</strong><span class="linkarray tlpdepth3" id="p5.556GER"> GER [→<a class="ogdlink" href="#p5.556OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.556PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Eine Hierarchie der Formen der Elementarsätze kann es nicht geben. Nur was wir selbst konstruieren, können wir voraussehen.</div>
<div class="corelinks tlpdepth4"><strong>5.5561</strong><span class="linkarray tlpdepth4" id="p5.5561GER"> GER [→<a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die empirische Realität ist begrenzt durch die Gesamtheit der Gegenstände. Die Grenze zeigt sich wieder in der Gesamtheit der Elementarsätze.</div>
<div class="para tlpdepth4">Die Hierarchien sind, und müssen unabhängig von der Realität sein.</div>
<div class="corelinks tlpdepth4"><strong>5.5562</strong><span class="linkarray tlpdepth4" id="p5.5562GER"> GER [→<a class="ogdlink" href="#p5.5562OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5562PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wissen wir aus rein logischen Gründen, dass es Elementarsätze geben muss, dann muss es jeder wissen, der die Sätze in ihrer unanalysierten Form versteht.</div>
<div class="corelinks tlpdepth4"><strong>5.5563</strong><span class="linkarray tlpdepth4" id="p5.5563GER"> GER [→<a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Alle Sätze unserer Umgangssprache sind tatsächlich, so wie sie sind, logisch vollkommen geordnet. – Jenes Einfachste, was wir hier angeben sollen, ist nicht ein Gleichnis der Wahrheit, sondern die volle Wahrheit selbst.</div>
<div class="para tlpdepth4">(Unsere Probleme sind nicht abstrakt, sondern vielleicht die konkretesten, die es gibt.)</div>
<div class="corelinks tlpdepth3"><strong>5.557</strong><span class="linkarray tlpdepth3" id="p5.557GER"> GER [→<a class="ogdlink" href="#p5.557OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.557PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die <em class="germph">Anwendung</em> der Logik entscheidet darüber, welche Elementarsätze es gibt.</div>
<div class="para tlpdepth3">Was in der Anwendung liegt, kann die Logik nicht vorausnehmen.</div>
<div class="para tlpdepth3">Das ist klar: Die Logik darf mit ihrer Anwendung nicht kollidieren.</div>
<div class="para tlpdepth3">Aber die Logik muss sich mit ihrer Anwendung berühren.</div>
<div class="para tlpdepth3">Also dürfen die Logik und ihre Anwendung einander nicht übergreifen.</div>
<div class="corelinks tlpdepth4"><strong>5.5571</strong><span class="linkarray tlpdepth4" id="p5.5571GER"> GER [→<a class="ogdlink" href="#p5.5571OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5571PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wenn ich die Elementarsätze nicht a priori angeben kann, dann muss es zu offenbarem Unsinn führen, sie angeben zu wollen.</div>
<div class="corelinks tlpdepth1"><strong>5.6</strong><span class="linkarray tlpdepth1" id="p5.6GER"> GER [→<a class="ogdlink" href="#p5.6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6PM">P/M</a>]</span></div>
<div class="para tlpdepth1"><em class="germph">Die Grenzen meiner Sprache</em> bedeuten die Grenzen meiner Welt.</div>
<div class="corelinks tlpdepth2"><strong>5.61</strong><span class="linkarray tlpdepth2" id="p5.61GER"> GER [→<a class="ogdlink" href="#p5.61OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.61PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Logik erfüllt die Welt; die Grenzen der Welt sind auch ihre Grenzen.</div>
<div class="para tlpdepth2">Wir können also in der Logik nicht sagen: Das und das gibt es in der Welt, jenes nicht.</div>
<div class="para tlpdepth2">Das würde nämlich scheinbar voraussetzen, dass wir gewisse Möglichkeiten ausschließen, und dies kann nicht der Fall sein, da sonst die Logik über die Grenzen der Welt hinaus müsste; wenn sie nämlich diese Grenzen auch von der anderen Seite betrachten könnte.</div>
<div class="para tlpdepth2">Was wir nicht denken können, das können wir nicht denken; wir können also auch nicht <em class="germph">sagen</em>, was wir nicht denken können.</div>
<div class="corelinks tlpdepth2"><strong>5.62</strong><span class="linkarray tlpdepth2" id="p5.62GER"> GER [→<a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Diese Bemerkung gibt den Schlüssel zur Entscheidung der Frage, inwieweit der Solipsismus eine Wahrheit ist.</div>
<div class="para tlpdepth2">Was der Solipsismus nämlich <em class="germph">meint</em>, ist ganz richtig, nur lässt es sich nicht <em class="germph">sagen</em>, sondern es zeigt sich.</div>
<div class="para tlpdepth2">Dass die Welt <em class="germph">meine</em> Welt ist, das zeigt sich darin, dass die Grenzen <em class="germph">der</em> Sprache (der Sprache, die allein ich verstehe) die Grenzen <em class="germph">meiner</em> Welt bedeuten.</div>
<div class="corelinks tlpdepth3"><strong>5.621</strong><span class="linkarray tlpdepth3" id="p5.621GER"> GER [→<a class="ogdlink" href="#p5.621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.621PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Welt und das Leben sind Eins.</div>
<div class="corelinks tlpdepth2"><strong>5.63</strong><span class="linkarray tlpdepth2" id="p5.63GER"> GER [→<a class="ogdlink" href="#p5.63OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.63PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Ich bin meine Welt. (Der Mikrokosmos.)</div>
<div class="corelinks tlpdepth3"><strong>5.631</strong><span class="linkarray tlpdepth3" id="p5.631GER"> GER [→<a class="ogdlink" href="#p5.631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das denkende, vorstellende, Subjekt gibt es nicht.</div>
<div class="para tlpdepth3">Wenn ich ein Buch schriebe „Die Welt, wie ich sie vorfand“, so wäre darin auch über meinen Leib zu berichten und zu sagen, welche Glieder meinem Willen unterstehen und welche nicht, etc., dies ist nämlich eine Methode, das Subjekt zu isolieren, oder vielmehr zu zeigen, dass es in einem wichtigen Sinne kein Subjekt gibt: Von ihm allein nämlich könnte in diesem Buche <em class="germph">nicht</em> die Rede sein.—</div>
<div class="corelinks tlpdepth3"><strong>5.632</strong><span class="linkarray tlpdepth3" id="p5.632GER"> GER [→<a class="ogdlink" href="#p5.632OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.632PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das Subjekt gehört nicht zur Welt, sondern es ist eine Grenze der Welt.</div>
<div class="corelinks tlpdepth3"><strong>5.633</strong><span class="linkarray tlpdepth3" id="p5.633GER"> GER [→<a class="ogdlink" href="#p5.633OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.633PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wo <em class="germph">in</em> der Welt ist ein metaphysisches Subjekt zu merken?</div>
<div class="para tlpdepth3">Du sagst, es verhält sich hier ganz wie mit Auge und Gesichtsfeld. Aber das Auge siehst du wirklich <em class="germph">nicht</em>.</div>
<div class="para tlpdepth3">Und nichts <em class="germph">am Gesichtsfeld</em> lässt darauf schließen, dass es von einem Auge gesehen wird.</div>
<div class="corelinks tlpdepth4"><strong>5.6331</strong><span class="linkarray tlpdepth4" id="p5.6331GER"> GER [→<a class="ogdlink" href="#p5.6331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6331PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das Gesichtsfeld hat nämlich nicht etwa eine solche Form:</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><span class="sfmiddle"><span class="lowered">Auge —</span><object data="images/theeye.svg" type="image/svg+xml" class="theeyesvg"><img src="images/theeye.png" alt="Eye image" class="theeyepng" /></object></span></div></div>
<div class="corelinks tlpdepth3"><strong>5.634</strong><span class="linkarray tlpdepth3" id="p5.634GER"> GER [→<a class="ogdlink" href="#p5.634OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.634PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Das hängt damit zusammen, dass kein Teil unserer Erfahrung auch a priori ist.</div>
<div class="para tlpdepth3">Alles, was wir sehen, könnte auch anders sein.</div>
<div class="para tlpdepth3">Alles, was wir überhaupt beschreiben können, könnte auch anders sein.</div>
<div class="para tlpdepth3">Es gibt keine Ordnung der Dinge a priori.</div>
<div class="corelinks tlpdepth2"><strong>5.64</strong><span class="linkarray tlpdepth2" id="p5.64GER"> GER [→<a class="ogdlink" href="#p5.64OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.64PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Hier sieht man, dass der Solipsismus, streng durchgeführt, mit dem reinen Realismus zusammenfällt. Das Ich des Solipsismus schrumpft zum ausdehnungslosen Punkt zusammen, und es bleibt die ihm koordinierte Realität.</div>
<div class="corelinks tlpdepth3"><strong>5.641</strong><span class="linkarray tlpdepth3" id="p5.641GER"> GER [→<a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es gibt also wirklich einen Sinn, in welchem in der Philosophie nichtpsychologisch vom Ich die Rede sein kann.</div>
<div class="para tlpdepth3">Das Ich tritt in die Philosophie dadurch ein, dass „die Welt meine Welt ist“.</div>
<div class="para tlpdepth3">Das philosophische Ich ist nicht der Mensch, nicht der menschliche Körper, oder die menschliche Seele, von der die Psychologie handelt, sondern das metaphysische Subjekt, die Grenze –nicht ein Teil – der Welt.</div>
<div class="corelinks tlpdepth0"><strong>6</strong><span class="linkarray tlpdepth0" id="p6GER"> GER [→<a class="ogdlink" href="#p6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Die allgemeine Form der Wahrheitsfunktion ist: <span class="mathmode">[<span class="overlined"><var>p</var></span>, <span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)]</span>.</div>
<div class="para tlpdepth0">Dies ist die allgemeine Form des Satzes.</div>
<div class="corelinks tlpdepth3"><strong>6.001</strong><span class="linkarray tlpdepth3" id="p6.001GER"> GER [→<a class="ogdlink" href="#p6.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.001PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Dies sagt nichts anderes, als dass jeder Satz ein Resultat der successiven Anwendung der Operation <span class="mathmode"><span class="mathop"><span class="nop">N</span>’</span>(<span class="overlined"><var>ξ</var></span>)</span> auf die Elementarsätze ist.</div>
<div class="corelinks tlpdepth3"><strong>6.002</strong><span class="linkarray tlpdepth3" id="p6.002GER"> GER [→<a class="ogdlink" href="#p6.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.002PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ist die allgemeine Form gegeben, wie ein Satz gebaut ist, so ist damit auch schon die allgemeine Form davon gegeben, wie aus einem Satz durch eine Operation ein anderer erzeugt werden kann.</div>
<div class="corelinks tlpdepth2"><strong>6.01</strong><span class="linkarray tlpdepth2" id="p6.01GER"> GER [→<a class="ogdlink" href="#p6.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die allgemeine Form der Operation <span class="mathmode"><span class="mathop">Ω’</span>(<span class="overlined"><var>η</var></span>)</span> ist also: <span class="mathmode"><span class="mathop">[<span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)]’</span> (<span class="overlined"><var>η</var></span>) (<span class="mathrel">=</span>[<span class="overlined"><var>η</var></span>, <span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)])</span>.</div>
<div class="para tlpdepth2">Das ist die allgemeinste Form des Überganges von einem Satz zum anderen.</div>
<div class="corelinks tlpdepth2"><strong>6.02</strong><span class="linkarray tlpdepth2" id="p6.02GER"> GER [→<a class="ogdlink" href="#p6.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Und <em class="germph">so</em> kommen wir zu den Zahlen: Ich definiere</div>
<div class="para tlpdepth2"><div class="centered"><table class="alignedmath"><tr><td class="righttight"><span class="mathmode"><var>x</var><span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode"><span class="mathop">Ω<sup>0</sup>’</span><var>x</var></span>&nbsp;&nbsp;Def. und</td></tr><tr><td class="righttight"><span class="mathmode"><span class="mathop">Ω’</span><span class="mathop">Ω<sup><var>ν</var></sup>’</span><var>x</var><span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode"><span class="mathop">Ω<sup><var>ν</var>+1</sup>’</span><var>x</var></span>&nbsp;&nbsp;Def.</td></tr></table></div></div>
<div class="para tlpdepth2">Nach diesen Zeichenregeln schreiben wir also die Reihe</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode"><var>x</var>, <span class="mathop">Ω’</span><var>x</var>, <span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var>, <span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var>,<span class="mathrel">…</span></span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">so:</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode"><span class="mathop">Ω<sup>0</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var>,<span class="mathrel">…</span></span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">Also schreibe ich statt „<span class="mathmode">[<var>x</var>, <var>ξ</var>, <span class="mathop">Ω’</span><var>ξ</var>]</span>“:</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode">„[<span class="mathop">Ω<sup>0</sup>’</span><var>x</var>, <span class="mathop">Ω<sup><var>ν</var></sup>’</span><var>x</var>, <span class="mathop">Ω<sup><var>ν</var><span class="mathrel">+</span>1</sup>’</span><var>x</var>]“.</span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">Und definiere:</div>
<div class="para tlpdepth2"><div class="centered"><table class="alignedmath"><tr><td class="lefttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">=</span>1</span>&nbsp;&nbsp;Def.</td></tr><tr><td class="lefttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">=</span>2</span>&nbsp;&nbsp;Def.</td></tr><tr><td class="lefttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">=</span>3</span>&nbsp;&nbsp;Def.</td></tr><tr><td class="lefttight">(u. s. f.)</td></tr></table></div></div>
<div class="corelinks tlpdepth3"><strong>6.021</strong><span class="linkarray tlpdepth3" id="p6.021GER"> GER [→<a class="ogdlink" href="#p6.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.021PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Zahl ist der Exponent einer Operation.</div>
<div class="corelinks tlpdepth3"><strong>6.022</strong><span class="linkarray tlpdepth3" id="p6.022GER"> GER [→<a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Zahlbegriff ist nichts anderes als das Gemeinsame aller Zahlen, die allgemeine Form der Zahl.</div>
<div class="para tlpdepth3">Der Zahlbegriff ist die variable Zahl.</div>
<div class="para tlpdepth3">Und der Begriff der Zahlengleichheit ist die allgemeine Form aller speziellen Zahlengleichheiten.</div>
<div class="corelinks tlpdepth2"><strong>6.03</strong><span class="linkarray tlpdepth2" id="p6.03GER"> GER [→<a class="ogdlink" href="#p6.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.03PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die allgemeine Form der ganzen Zahl ist: <span class="mathmode">[0, <var>ξ</var>, <var>ξ</var><span class="mathrel">+</span>1]</span>.</div>
<div class="corelinks tlpdepth3"><strong>6.031</strong><span class="linkarray tlpdepth3" id="p6.031GER"> GER [→<a class="ogdlink" href="#p6.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.031PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Theorie der Klassen ist in der Mathematik ganz überflüssig.</div>
<div class="para tlpdepth3">Dies hängt damit zusammen, dass die Allgemeinheit, welche wir in der Mathematik brauchen, nicht die <em class="germph">zufällige</em> ist.</div>
<div class="corelinks tlpdepth1"><strong>6.1</strong><span class="linkarray tlpdepth1" id="p6.1GER"> GER [→<a class="ogdlink" href="#p6.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Die Sätze der Logik sind Tautologien.</div>
<div class="corelinks tlpdepth2"><strong>6.11</strong><span class="linkarray tlpdepth2" id="p6.11GER"> GER [→<a class="ogdlink" href="#p6.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Sätze der Logik sagen also nichts. (Sie sind die analytischen Sätze.)</div>
<div class="corelinks tlpdepth3"><strong>6.111</strong><span class="linkarray tlpdepth3" id="p6.111GER"> GER [→<a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Theorien, die einen Satz der Logik gehaltvoll erscheinen lassen, sind immer falsch. Man könnte z. B. glauben, dass die Worte „wahr“ und „falsch“ zwei Eigenschaften unter anderen Eigenschaften bezeichnen, und da erschiene es als eine merkwürdige Tatsache, dass jeder Satz eine dieser Eigenschaften besitzt. Das scheint nun nichts weniger als selbstverständlich zu sein, ebensowenig selbstverständlich, wie etwa der Satz: „Alle Rosen sind entweder gelb oder rot“ klänge, auch wenn er wahr wäre. Ja, jener Satz bekommt nun ganz den Charakter eines naturwissenschaftlichen Satzes, und dies ist das sichere Anzeichen dafür, dass er falsch aufgefasst wurde.</div>
<div class="corelinks tlpdepth3"><strong>6.112</strong><span class="linkarray tlpdepth3" id="p6.112GER"> GER [→<a class="ogdlink" href="#p6.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.112PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die richtige Erklärung der logischen Sätze muss ihnen eine einzigartige Stellung unter allen Sätzen geben.</div>
<div class="corelinks tlpdepth3"><strong>6.113</strong><span class="linkarray tlpdepth3" id="p6.113GER"> GER [→<a class="ogdlink" href="#p6.113OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.113PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist das besondere Merkmal der logischen Sätze, dass man am Symbol allein erkennen kann, dass sie wahr sind, und diese Tatsache schließt die ganze Philosophie der Logik in sich. Und so ist es auch eine derwichtigsten Tatsachen, dass sich die Wahrheit oder Falschheit der nichtlogischen Sätze <em class="germph">nicht</em> am Satz allein erkennen lässt.</div>
<div class="corelinks tlpdepth2"><strong>6.12</strong><span class="linkarray tlpdepth2" id="p6.12GER"> GER [→<a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Dass die Sätze der Logik Tautologien sind, das <em class="germph">zeigt</em> die formalen – logischen – Eigenschaften der Sprache, der Welt.</div>
<div class="para tlpdepth2">Dass ihre Bestandteile <em class="germph">so</em> verknüpft eine Tautologie ergeben, das charakterisiert die Logik ihrer Bestandteile.</div>
<div class="para tlpdepth2">Damit Sätze, auf bestimmte Art und Weise verknüpft, eine Tautologie ergeben, dazu müssen sie bestimmte Eigenschaften der Struktur haben. Dass sie <em class="germph">so</em> verbunden eine Tautologie ergeben, zeigt also, dass sie diese Eigenschaften der Struktur besitzen.</div>
<div class="corelinks tlpdepth4"><strong>6.1201</strong><span class="linkarray tlpdepth4" id="p6.1201GER"> GER [→<a class="ogdlink" href="#p6.1201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1201PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dass z. B. die Sätze „<span class="mathmode"><var>p</var></span>“ und „<span class="mathmode"><span class="mathop">~</span><var>p</var></span>“ in der Verbindung „<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span>“ eine Tautologie ergeben, zeigt, dass sie einander widersprechen. Dass die Sätze „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>“, „<span class="mathmode"><var>p</var></span>“ und „<span class="mathmode"><var>q</var></span>“ in der Form „<span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>)<span class="mathrel">.</span>(<var>p</var>)<span class="mathrel">:<span class="symbol">⊃</span>:</span>(<var>q</var>)</span>“ miteinander verbunden eine Tautologie ergeben, zeigt, dass <span class="mathmode"><var>q</var></span> aus <span class="mathmode"><var>p</var></span> und <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span> folgt. Dass „<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var><span class="mathrel">:<span class="symbol">⊃</span>:</span><var>fa</var></span>“ eine Tautologie ist, dass <span class="mathmode"><var>fa</var></span> aus <span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span> folgt. etc. etc.</div>
<div class="corelinks tlpdepth4"><strong>6.1202</strong><span class="linkarray tlpdepth4" id="p6.1202GER"> GER [→<a class="ogdlink" href="#p6.1202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1202PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es ist klar, dass man zu demselben Zweck statt der Tautologien auch die Kontradiktionen verwenden könnte.</div>
<div class="corelinks tlpdepth4"><strong>6.1203</strong><span class="linkarray tlpdepth4" id="p6.1203GER"> GER [→<a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Um eine Tautologie als solche zu erkennen, kann man sich, in den Fällen, in welchen in der Tautologie keine Allgemeinheitsbezeichnung vorkommt, folgender anschaulichen Methode bedienen: Ich schreibe statt „<span class="mathmode"><var>p</var></span>“, „<span class="mathmode"><var>q</var></span>“, „<span class="mathmode"><var>r</var></span>“ etc. „<span class="mathmode"><span class="mathrm">W</span> <var>p</var> <span class="mathrm">F</span></span>“, „<span class="mathmode"><span class="mathrm">W</span> <var>q</var> <span class="mathrm">F</span></span>“, „<span class="mathmode"><span class="mathrm">W</span> <var>r</var> <span class="mathrm">F</span></span>“ etc. Die Wahrheitskombinationen drücke ich durch Klammern aus, z. B.:</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigureonegerman.svg" type="image/svg+xml" width="158" height="69" style="width: 158pt; height: 69pt;"><img src="images/abfigureonegerman.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> und die Zuordnung der Wahr- oder Falschheit des ganzen Satzes und der Wahrheitskombinationen der Wahrheitsargumente durch Striche auf folgende Weise:</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfiguretwogerman.svg" type="image/svg+xml" width="158" height="124" style="width: 158pt; height: 124pt;"><img src="images/abfiguretwogerman.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> Dies Zeichen würde also z. B. den Satz <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span> darstellen. Nun will ich z. B. den Satz <span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span> (Gesetz des Widerspruchs) daraufhin untersuchen, ob er eine Tautologie ist. Die Form „<span class="mathmode"><span class="mathop">~</span><var>ξ</var></span>“ wird in unserer Notation</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurethreegerman.svg" type="image/svg+xml" width="49" height="75" style="width: 49pt; height: 75pt;"><img src="images/abfigurethreegerman.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> geschrieben; die Form „<span class="mathmode"><var>ξ</var><span class="mathrel">.</span><var>η</var></span>“ so:</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurefourgerman.svg" type="image/svg+xml" width="158" height="116" style="width: 158pt; height: 116pt;"><img src="images/abfigurefourgerman.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent -->Daher lautet der Satz <span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>)</span> so:</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurefivegerman.svg" type="image/svg+xml" width="133" height="168" style="width: 133pt; height: 168pt;"><img src="images/abfigurefivegerman.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> Setzen wir statt „<span class="mathmode"><var>q</var></span>“ „<span class="mathmode"><var>p</var></span>“ ein und untersuchen die Verbindung der äußersten W und F mit den innersten, so ergibt sich, dass die Wahrheit des ganzen Satzes <em class="germph">allen</em> Wahrheitskombinationen seines Argumentes, seine Falschheit keiner der Wahrheitskombinationen zugeordnet ist.</div>
<div class="corelinks tlpdepth3"><strong>6.121</strong><span class="linkarray tlpdepth3" id="p6.121GER"> GER [→<a class="ogdlink" href="#p6.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Sätze der Logik demonstrieren die logischen Eigenschaften der Sätze, indem sie sie zu nichtssagenden Sätzen verbinden.</div>
<div class="para tlpdepth3">Diese Methode könnte man auch eine Nullmethode nennen. Im logischen Satz werden Sätze miteinander ins Gleichgewicht gebracht und der Zustand des Gleichgewichts zeigt dann an, wie diese Sätze logisch beschaffen sein müssen.</div>
<div class="corelinks tlpdepth3"><strong>6.122</strong><span class="linkarray tlpdepth3" id="p6.122GER"> GER [→<a class="ogdlink" href="#p6.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.122PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Daraus ergibt sich, dass wir auch ohne die logischen Sätze auskommen können, da wir ja in einer entsprechenden Notation die formalen Eigenschaften der Sätze durch das bloße Ansehen dieser Sätze erkennen können.</div>
<div class="corelinks tlpdepth4"><strong>6.1221</strong><span class="linkarray tlpdepth4" id="p6.1221GER"> GER [→<a class="ogdlink" href="#p6.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1221PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Ergeben z. B. zwei Sätze „<span class="mathmode"><var>p</var></span>“ und „<span class="mathmode"><var>q</var></span>“ in der Verbindung „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>“ eine Tautologie, so ist klar, dass <span class="mathmode"><var>q</var></span> aus <span class="mathmode"><var>p</var></span> folgt.</div>
<div class="para tlpdepth4">Dass z. B. „<span class="mathmode"><var>q</var></span>“ aus „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var><span class="mathrel">.</span><var>p</var></span>“ folgt, ersehen wir aus diesen beiden Sätzen selbst, aber wir können es auch <em class="germph">so</em> zeigen, indem wir sie zu „<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var><span class="mathrel">.</span><var>p</var><span class="mathrel">:<span class="symbol">⊃</span>:</span><var>q</var></span>“ verbinden und nun zeigen, dass dies eine Tautologie ist.</div>
<div class="corelinks tlpdepth4"><strong>6.1222</strong><span class="linkarray tlpdepth4" id="p6.1222GER"> GER [→<a class="ogdlink" href="#p6.1222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1222PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dies wirft ein Licht auf die Frage, warum die logischen Sätze nicht durch die Erfahrung bestätigt werden können, ebensowenig wie sie durch die Erfahrung widerlegt werden können. Nicht nur muss ein Satz der Logik durch keine mögliche Erfahrung widerlegt werden können, sondern er darf auch nicht durch eine solche bestätigt werden können.</div>
<div class="corelinks tlpdepth4"><strong>6.1223</strong><span class="linkarray tlpdepth4" id="p6.1223GER"> GER [→<a class="ogdlink" href="#p6.1223OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1223PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Nun wird klar, warum man oft fühlte, als wären die „logischen Wahrheiten“ von uns zu „<em class="germph">fordern</em>“: Wir können sie nämlich insofern fordern, als wir eine genügende Notation fordern können.</div>
<div class="corelinks tlpdepth4"><strong>6.1224</strong><span class="linkarray tlpdepth4" id="p6.1224GER"> GER [→<a class="ogdlink" href="#p6.1224OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1224PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es wird jetzt auch klar, warum die Logik die Lehre von den Formen und vom Schließen genannt wurde.</div>
<div class="corelinks tlpdepth3"><strong>6.123</strong><span class="linkarray tlpdepth3" id="p6.123GER"> GER [→<a class="ogdlink" href="#p6.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.123PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist klar: Die logischen Gesetze dürfen nicht selbst wieder logischen Gesetzen unterstehen.</div>
<div class="para tlpdepth3">(Es gibt nicht, wie Russell meinte, für jede „Type“ ein eigenes Gesetz des Widerspruches, sondern Eines genügt, da es auf sich selbst nicht angewendet wird.)</div>
<div class="corelinks tlpdepth4"><strong>6.1231</strong><span class="linkarray tlpdepth4" id="p6.1231GER"> GER [→<a class="ogdlink" href="#p6.1231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1231PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das Anzeichen des logischen Satzes ist <em class="germph">nicht</em> die Allgemeingültigkeit.</div>
<div class="para tlpdepth4">Allgemein sein heißt ja nur: zufälligerweise für alle Dinge gelten. Ein unverallgemeinerter Satz kann ja ebensowohl tautologisch sein als ein verallgemeinerter.</div>
<div class="corelinks tlpdepth4"><strong>6.1232</strong><span class="linkarray tlpdepth4" id="p6.1232GER"> GER [→<a class="ogdlink" href="#p6.1232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die logische Allgemeingültigkeit könnte man wesentlich nennen, im Gegensatz zu jener zufälligen, etwa des Satzes: „Alle Menschen sind sterblich“. Sätze wie Russells „Axiom of Reducibility“ sind nicht logische Sätze, und dies erklärt unser Gefühl: Dass sie, wenn wahr, so doch nur durch einen günstigen Zufall wahr sein könnten.</div>
<div class="corelinks tlpdepth4"><strong>6.1233</strong><span class="linkarray tlpdepth4" id="p6.1233GER"> GER [→<a class="ogdlink" href="#p6.1233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1233PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es lässt sich eine Welt denken, in der das Axiom of Reducibility nicht gilt. Es ist aber klar, dass die Logik nichts mit der Frage zu schaffen hat, ob unsere Welt wirklich so ist oder nicht.</div>
<div class="corelinks tlpdepth3"><strong>6.124</strong><span class="linkarray tlpdepth3" id="p6.124GER"> GER [→<a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die logischen Sätze beschreiben das Gerüst der Welt, oder vielmehr, sie stellen es dar. Sie „handeln“ von nichts. Sie setzen voraus, dass Namen Bedeutung, und Elementarsätze Sinn haben: Und dies ist ihre Verbindung mit der Welt. Es ist klar, dass es etwas über die Welt anzeigen muss, dass gewisse Verbindungen von Symbolen – welche wesentlich einen bestimmten Charakter haben – Tautologien sind. Hierin liegt das Entscheidende. Wir sagten, manches an den Symbolen, die wir gebrauchen, wäre willkürlich, manches nicht. In der Logik drückt nur dieses aus: Das heißt aber, in der Logik drücken nicht <em class="germph">wir</em> mit Hilfe der Zeichen aus, was wir wollen, sondern in der Logik sagt die Natur der naturnotwendigen Zeichen selbst aus: Wenn wir die logische Syntax irgendeiner Zeichensprache kennen, dann sind bereits alle Sätze der Logik gegeben.</div>
<div class="corelinks tlpdepth3"><strong>6.125</strong><span class="linkarray tlpdepth3" id="p6.125GER"> GER [→<a class="ogdlink" href="#p6.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.125PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist möglich, und zwar auch nach der alten Auffassung der Logik, von vornherein eine Beschreibung aller „wahren“ logischen Sätze zu geben.</div>
<div class="corelinks tlpdepth4"><strong>6.1251</strong><span class="linkarray tlpdepth4" id="p6.1251GER"> GER [→<a class="ogdlink" href="#p6.1251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1251PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Darum kann es in der Logik auch <em class="germph">nie</em> Überraschungen geben.</div>
<div class="corelinks tlpdepth3"><strong>6.126</strong><span class="linkarray tlpdepth3" id="p6.126GER"> GER [→<a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Ob ein Satz der Logik angehört, kann man berechnen, indem man die logischen Eigenschaften des <em class="germph">Symbols</em> berechnet.</div>
<div class="para tlpdepth3">Und dies tun wir, wenn wir einen logischen Satz „beweisen“. Denn, ohne uns um einen Sinn und eine Bedeutung zu kümmern, bilden wir den logischen Satz aus anderen nach bloßen <em class="germph">Zeichenregeln</em>.</div>
<div class="para tlpdepth3">Der Beweis der logischen Sätze besteht darin, dass wir sie aus anderen logischen Sätzen durch successive Anwendung gewisser Operationen entstehen lassen, die aus den ersten immer wieder Tautologien erzeugen. (Und zwar <em class="germph">folgen</em> aus einer Tautologie nur Tautologien.)</div>
<div class="para tlpdepth3">Natürlich ist diese Art zu zeigen, dass ihre Sätze Tautologien sind, der Logik durchaus unwesentlich. Schon darum, weil die Sätze, von welchen der Beweis ausgeht, ja ohne Beweis zeigen müssen, dass sie Tautologien sind.</div>
<div class="corelinks tlpdepth4"><strong>6.1261</strong><span class="linkarray tlpdepth4" id="p6.1261GER"> GER [→<a class="ogdlink" href="#p6.1261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1261PM">P/M</a>]</span></div>
<div class="para tlpdepth4">In der Logik sind Prozess und Resultat äquivalent. (Darum keine Überraschung.)</div>
<div class="corelinks tlpdepth4"><strong>6.1262</strong><span class="linkarray tlpdepth4" id="p6.1262GER"> GER [→<a class="ogdlink" href="#p6.1262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1262PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Der Beweis in der Logik ist nur ein mechanisches Hilfsmittel zum leichteren Erkennen der Tautologie, wo sie kompliziert ist.</div>
<div class="corelinks tlpdepth4"><strong>6.1263</strong><span class="linkarray tlpdepth4" id="p6.1263GER"> GER [→<a class="ogdlink" href="#p6.1263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1263PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es wäre ja auch zu merkwürdig, wenn man einen sinnvollen Satz <em class="germph">logisch</em> aus anderen beweisen könnte, und einen logischen Satz <em class="germph">auch</em>. Es ist von vornherein klar, dass der logische Beweis eines sinnvollen Satzes und der Beweis <em class="germph">in</em> der Logik zwei ganz verschiedene Dinge sein müssen.</div>
<div class="corelinks tlpdepth4"><strong>6.1264</strong><span class="linkarray tlpdepth4" id="p6.1264GER"> GER [→<a class="ogdlink" href="#p6.1264OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1264PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Der sinnvolle Satz sagt etwas aus, und sein Beweis zeigt, dass es so ist; in der Logik ist jeder Satz die Form eines Beweises.</div>
<div class="para tlpdepth4">Jeder Satz der Logik ist ein in Zeichen dargestellter modus ponens. (Und den modus ponens kann man nicht durch einen Satz ausdrücken.)</div>
<div class="corelinks tlpdepth4"><strong>6.1265</strong><span class="linkarray tlpdepth4" id="p6.1265GER"> GER [→<a class="ogdlink" href="#p6.1265OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1265PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Immer kann man die Logik so auffassen, dass jeder Satz sein eigener Beweis ist.</div>
<div class="corelinks tlpdepth3"><strong>6.127</strong><span class="linkarray tlpdepth3" id="p6.127GER"> GER [→<a class="ogdlink" href="#p6.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.127PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Alle Sätze der Logik sind gleichberechtigt, es gibt unter ihnen nicht wesentlich Grundgesetze und abgeleitete Sätze.</div>
<div class="para tlpdepth3">Jede Tautologie zeigt selbst, dass sie eine Tautologie ist.</div>
<div class="corelinks tlpdepth4"><strong>6.1271</strong><span class="linkarray tlpdepth4" id="p6.1271GER"> GER [→<a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Es ist klar, dass die Anzahl der „logischen Grundgesetze“ willkürlich ist, denn man könnte die Logik ja aus Einem Grundgesetz ableiten, indem man einfach z. B. aus Freges Grundgesetzen das logische Produkt bildet. (Frege würde vielleicht sagen, dass dieses Grundgesetz nun nicht mehr unmittelbar einleuchte. Aber es ist merkwürdig, dass ein so exakter Denker wie Frege sich auf den Grad des Einleuchtens als Kriterium des logischen Satzes berufen hat.)</div>
<div class="corelinks tlpdepth2"><strong>6.13</strong><span class="linkarray tlpdepth2" id="p6.13GER"> GER [→<a class="ogdlink" href="#p6.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt.</div>
<div class="para tlpdepth2">Die Logik ist transzendental.</div>
<div class="corelinks tlpdepth1"><strong>6.2</strong><span class="linkarray tlpdepth1" id="p6.2GER"> GER [→<a class="ogdlink" href="#p6.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Die Mathematik ist eine logische Methode.</div>
<div class="para tlpdepth1">Die Sätze der Mathematik sind Gleichungen, also Scheinsätze.</div>
<div class="corelinks tlpdepth2"><strong>6.21</strong><span class="linkarray tlpdepth2" id="p6.21GER"> GER [→<a class="ogdlink" href="#p6.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Satz der Mathematik drückt keinen Gedanken aus.</div>
<div class="corelinks tlpdepth3"><strong>6.211</strong><span class="linkarray tlpdepth3" id="p6.211GER"> GER [→<a class="ogdlink" href="#p6.211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.211PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Im Leben ist es ja nie der mathematische Satz, den wir brauchen, sondern wir benützen den mathematischen Satz <em class="germph">nur</em>, um aus Sätzen, welche nicht der Mathematik angehören, auf andere zu schließen, welche gleichfalls nicht der Mathematik angehören.</div>
<div class="para tlpdepth3">(In der Philosophie führt die Frage: „Wozu gebrauchen wir eigentlich jenes Wort, jenen Satz“ immer wieder zu wertvollen Einsichten.)</div>
<div class="corelinks tlpdepth2"><strong>6.22</strong><span class="linkarray tlpdepth2" id="p6.22GER"> GER [→<a class="ogdlink" href="#p6.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Logik der Welt, die die Sätze der Logik in den Tautologien zeigen, zeigt die Mathematik in den Gleichungen.</div>
<div class="corelinks tlpdepth2"><strong>6.23</strong><span class="linkarray tlpdepth2" id="p6.23GER"> GER [→<a class="ogdlink" href="#p6.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wenn zwei Ausdrücke durch das Gleichheitszeichen verbunden werden, so heißt das, sie sind durch einander ersetzbar. Ob dies aber der Fall ist, muss sich an den beiden Ausdrücken selbst zeigen.</div>
<div class="para tlpdepth2">Es charakterisiert die logische Form zweier Ausdrücke, dass sie durch einander ersetzbar sind.</div>
<div class="corelinks tlpdepth3"><strong>6.231</strong><span class="linkarray tlpdepth3" id="p6.231GER"> GER [→<a class="ogdlink" href="#p6.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.231PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist eine Eigenschaft der Bejahung, dass man sie als doppelte Verneinung auffassen kann.</div>
<div class="para tlpdepth3">Es ist eine Eigenschaft von „<span class="mathmode">1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</span>“, dass man es als „<span class="mathmode">(1<span class="mathrel">+</span>1)<span class="mathrel">+</span>(1<span class="mathrel">+</span>1)</span>“ auffassen kann.</div>
<div class="corelinks tlpdepth3"><strong>6.232</strong><span class="linkarray tlpdepth3" id="p6.232GER"> GER [→<a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Frege sagt, die beiden Ausdrücke haben dieselbe Bedeutung, aber verschiedenen Sinn.</div>
<div class="para tlpdepth3">Das Wesentliche an der Gleichung ist aber, dass sie nicht notwendig ist, um zu zeigen, dass die beiden Ausdrücke, die das Gleichheitszeichen verbindet, dieselbe Bedeutung haben, da sich dies aus den beiden Ausdrücken selbst ersehen lässt.</div>
<div class="corelinks tlpdepth4"><strong>6.2321</strong><span class="linkarray tlpdepth4" id="p6.2321GER"> GER [→<a class="ogdlink" href="#p6.2321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2321PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Und, dass die Sätze der Mathematik bewiesen werden können, heißt ja nichts anderes, als dass ihre Richtigkeit einzusehen ist, ohne dass das, was sie ausdrücken, selbst mit den Tatsachen auf seine Richtigkeit hin verglichen werden muss.</div>
<div class="corelinks tlpdepth4"><strong>6.2322</strong><span class="linkarray tlpdepth4" id="p6.2322GER"> GER [→<a class="ogdlink" href="#p6.2322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2322PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Identität der Bedeutung zweier Ausdrücke lässt sich nicht <em class="germph">behaupten</em>. Denn, um etwas von ihrer Bedeutung behaupten zu können, muss ich ihre Bedeutung kennen: und indem ich ihre Bedeutung kenne, weiß ich, ob sie dasselbe oder verschiedenes bedeuten.</div>
<div class="corelinks tlpdepth4"><strong>6.2323</strong><span class="linkarray tlpdepth4" id="p6.2323GER"> GER [→<a class="ogdlink" href="#p6.2323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2323PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Gleichung kennzeichnet nur den Standpunkt, von welchem ich die beiden Ausdrücke betrachte, nämlich vom Standpunkte ihrer Bedeutungsgleichheit.</div>
<div class="corelinks tlpdepth3"><strong>6.233</strong><span class="linkarray tlpdepth3" id="p6.233GER"> GER [→<a class="ogdlink" href="#p6.233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.233PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Frage, ob man zur Lösung der mathematischen Probleme die Anschauung brauche, muss dahin beantwortet werden, dass eben die Sprache hier die nötige Anschauung liefert.</div>
<div class="corelinks tlpdepth4"><strong>6.2331</strong><span class="linkarray tlpdepth4" id="p6.2331GER"> GER [→<a class="ogdlink" href="#p6.2331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2331PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Der Vorgang des <em class="germph">Rechnens</em> vermittelt eben diese Anschauung.</div>
<div class="para tlpdepth4">Die Rechnung ist kein Experiment.</div>
<div class="corelinks tlpdepth3"><strong>6.234</strong><span class="linkarray tlpdepth3" id="p6.234GER"> GER [→<a class="ogdlink" href="#p6.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.234PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Mathematik ist eine Methode der Logik.</div>
<div class="corelinks tlpdepth4"><strong>6.2341</strong><span class="linkarray tlpdepth4" id="p6.2341GER"> GER [→<a class="ogdlink" href="#p6.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2341PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Das Wesentliche der mathematischen Methode ist es, mit Gleichungen zu arbeiten. Auf dieser Methode beruht es nämlich, dass jeder Satz der Mathematik sich von selbst verstehen muss.</div>
<div class="corelinks tlpdepth2"><strong>6.24</strong><span class="linkarray tlpdepth2" id="p6.24GER"> GER [→<a class="ogdlink" href="#p6.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.24PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Methode der Mathematik, zu ihren Gleichungen zu kommen, ist die Substitutionsmethode.</div>
<div class="para tlpdepth2">Denn die Gleichungen drücken die Ersetzbarkeit zweier Ausdrücke aus und wir schreiten von einer Anzahl von Gleichungen zu neuen Gleichungen vor, indem wir, den Gleichungen entsprechend, Ausdrücke durch andere ersetzen.</div>
<div class="corelinks tlpdepth3"><strong>6.241</strong><span class="linkarray tlpdepth3" id="p6.241GER"> GER [→<a class="ogdlink" href="#p6.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.241PM">P/M</a>]</span></div>
<div class="para tlpdepth3">So lautet der Beweis des Satzes <span class="mathmode">2 × 2<span class="mathrel">=</span>4</span>:</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode"><span class="mathop">(Ω<sup><var>ν</var></sup>)<sup><var>μ</var></sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup><var>ν</var>× <var>μ</var></sup>’</span><var>x</var></span> Def.<br />
<span class="mathmode"><span class="mathop">Ω<sup>2 × 2</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω<sup>2</sup>)<sup>2</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω<sup>2</sup>)<sup>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>2</sup>’</span><span class="mathop">Ω<sup>2</sup>’</span><var>x</var></span><br />
<span class="mathmode"><span class="mathrel">=</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1</sup>’</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω’Ω)’</span><span class="mathop">(Ω’Ω)’</span> <var>x</var></span><br />
<span class="mathmode"><span class="mathrel">=</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>4</sup>’</span><var>x</var></span>.<br />
</div></div>
<div class="corelinks tlpdepth1"><strong>6.3</strong><span class="linkarray tlpdepth1" id="p6.3GER"> GER [→<a class="ogdlink" href="#p6.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Die Erforschung der Logik bedeutet die Erforschung <em class="germph">aller Gesetzmäßigkeit</em>. Und außerhalb der Logik ist alles Zufall.</div>
<div class="corelinks tlpdepth2"><strong>6.31</strong><span class="linkarray tlpdepth2" id="p6.31GER"> GER [→<a class="ogdlink" href="#p6.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.31PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das sogenannte Gesetz der Induktion kann jedenfalls kein logisches Gesetz sein, denn es ist offenbar ein sinnvoller Satz. – Und darum kann es auch kein Gesetz a priori sein.</div>
<div class="corelinks tlpdepth2"><strong>6.32</strong><span class="linkarray tlpdepth2" id="p6.32GER"> GER [→<a class="ogdlink" href="#p6.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.32PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Das Kausalitätsgesetz ist kein Gesetz, sondern die Form eines Gesetzes.</div>
<div class="corelinks tlpdepth3"><strong>6.321</strong><span class="linkarray tlpdepth3" id="p6.321GER"> GER [→<a class="ogdlink" href="#p6.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span></div>
<div class="para tlpdepth3">„Kausalitätsgesetz“, das ist ein Gattungsname. Und wie es in der Mechanik, sagen wir, Minimum-Gesetze gibt – etwa der kleinsten Wirkung – so gibt es in der Physik Kausalitätsgesetze, Gesetze von der Kausalitätsform.</div>
<div class="corelinks tlpdepth4"><strong>6.3211</strong><span class="linkarray tlpdepth4" id="p6.3211GER"> GER [→<a class="ogdlink" href="#p6.3211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3211PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Man hat ja auch davon eine Ahnung gehabt, dass es <em class="germph">ein</em> „Gesetz der kleinsten Wirkung“ geben müsse, ehe man genau wusste, wie es lautete. (Hier, wie immer, stellt sich das a priori Gewisse als etwas rein Logisches heraus.)</div>
<div class="corelinks tlpdepth2"><strong>6.33</strong><span class="linkarray tlpdepth2" id="p6.33GER"> GER [→<a class="ogdlink" href="#p6.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.33PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wir <em class="germph">glauben</em> nicht a priori an ein Erhaltungsgesetz, sondern wir <em class="germph">wissen</em> a priori die Möglichkeit einer logischen Form.</div>
<div class="corelinks tlpdepth2"><strong>6.34</strong><span class="linkarray tlpdepth2" id="p6.34GER"> GER [→<a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Alle jene Sätze, wie der Satz vom Grunde, von der Kontinuität in der Natur, vom kleinsten Aufwande in der Natur etc. etc., alle diese sind Einsichten a priori über die mögliche Formgebung der Sätze der Wissenschaft.</div>
<div class="corelinks tlpdepth3"><strong>6.341</strong><span class="linkarray tlpdepth3" id="p6.341GER"> GER [→<a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Newtonsche Mechanik z. B. bringt die Weltbeschreibung auf eine einheitliche Form. Denken wir uns eine weiße Fläche, auf der unregelmäßige schwarze Flecken wären. Wir sagen nun: Was für ein Bild immer hierdurch entsteht, immer kann ich seiner Beschreibung beliebig nahe kommen, indem ich die Fläche mit einem entsprechend feinen quadratischen Netzwerk bedecke und nun von jedem Quadrat sage, dass es weiß oder schwarz ist. Ich werde auf diese Weise die Beschreibung der Fläche auf eine einheitliche Form gebracht haben. Diese Form ist beliebig, denn ich hätte mit dem gleichen Erfolge ein Netz aus dreieckigen oder sechseckigen Maschen verwenden können. Es kann sein, dass die Beschreibung mit Hilfe eines Dreiecks-Netzes einfacher geworden wäre; das heißt, dass wir die Fläche mit einem gröberen Dreiecks-Netz genauer beschreiben könnten als mit einem feineren quadratischen (oder umgekehrt) usw. Den verschiedenen Netzen entsprechen verschiedene Systeme der Weltbeschreibung. Die Mechanik bestimmt eine Form der Weltbeschreibung, indem sie sagt: Alle Sätze der Weltbeschreibung müssen aus einer Anzahl gegebener Sätze – den mechanischen Axiomen – auf eine gegebene Art und Weise erhalten werden. Hierdurch liefert sie die Bausteine zum Bau des wissenschaftlichen Gebäudes und sagt: Welches Gebäude immer du aufführen willst, jedes musst du irgendwie mit diesen und nur diesen Bausteinen zusammenbringen.</div>
<div class="para tlpdepth3">(Wie man mit dem Zahlensystem jede beliebige Anzahl, so muss man mit dem System der Mechanik jeden beliebigen Satz der Physik hinschreiben können.)</div>
<div class="corelinks tlpdepth3"><strong>6.342</strong><span class="linkarray tlpdepth3" id="p6.342GER"> GER [→<a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Und nun sehen wir die gegenseitige Stellung von Logik und Mechanik. (Man könnte das Netz auch aus verschiedenartigen Figuren etwa aus Dreiecken und Sechsecken bestehen lassen.) Dass sich ein Bild, wie das vorhin erwähnte, durch ein Netz von gegebener Form beschreiben lässt, sagt über das Bild <em class="germph">nichts</em> aus. (Denn dies gilt für jedes Bild dieser Art.) Das aber charakterisiert das Bild, dass es sich durch ein bestimmtes Netz von <em class="germph">bestimmter</em> Feinheit <em class="germph">vollständig</em> beschreiben lässt.</div>
<div class="para tlpdepth3">So auch sagt es nichts über die Welt aus, dass sie sich durch die Newtonsche Mechanik beschreiben lässt; wohl aber, dass sie sich <em class="germph">so</em> durch jene beschreiben lässt, wie dies eben der Fall ist. Auch das sagt etwas über die Welt, dass sie sich durch die eine Mechanik einfacher beschreiben lässt als durch die andere.</div>
<div class="corelinks tlpdepth3"><strong>6.343</strong><span class="linkarray tlpdepth3" id="p6.343GER"> GER [→<a class="ogdlink" href="#p6.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.343PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Mechanik ist ein Versuch, alle <em class="germph">wahren</em> Sätze, die wir zur Weltbeschreibung brauchen, nach Einem Plane zu konstruieren.</div>
<div class="corelinks tlpdepth4"><strong>6.3431</strong><span class="linkarray tlpdepth4" id="p6.3431GER"> GER [→<a class="ogdlink" href="#p6.3431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3431PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Durch den ganzen logischen Apparat hindurch sprechen die physikalischen Gesetze doch von den Gegenständen der Welt.</div>
<div class="corelinks tlpdepth4"><strong>6.3432</strong><span class="linkarray tlpdepth4" id="p6.3432GER"> GER [→<a class="ogdlink" href="#p6.3432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3432PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wir dürfen nicht vergessen, dass die Weltbeschreibung durch die Mechanik immer die ganz allgemeine ist. Es ist in ihr z. B. nie von <em class="germph">bestimmten</em> materiellen Punkten die Rede, sondern immer nur von <em class="germph">irgend welchen</em>.</div>
<div class="corelinks tlpdepth2"><strong>6.35</strong><span class="linkarray tlpdepth2" id="p6.35GER"> GER [→<a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Obwohl die Flecke in unserem Bild geometrische Figuren sind, so kann doch selbstverständlich die Geometrie gar nichts über ihre tatsächliche Form und Lage sagen. Das Netz aber ist <em class="germph">rein</em> geometrisch, alle seine Eigenschaften können a priori angegeben werden.</div>
<div class="para tlpdepth2">Gesetze wie der Satz vom Grunde, etc. handeln vom Netz, nicht von dem, was das Netz beschreibt.</div>
<div class="corelinks tlpdepth2"><strong>6.36</strong><span class="linkarray tlpdepth2" id="p6.36GER"> GER [→<a class="ogdlink" href="#p6.36OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wenn es ein Kausalitätsgesetz gäbe, so könnte es lauten: „Es gibt Naturgesetze“.</div>
<div class="para tlpdepth2">Aber freilich kann man das nicht sagen: es zeigt sich.</div>
<div class="corelinks tlpdepth3"><strong>6.361</strong><span class="linkarray tlpdepth3" id="p6.361GER"> GER [→<a class="ogdlink" href="#p6.361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.361PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In der Ausdrucksweise Hertz’s könnte man sagen: Nur <em class="germph">gesetzmäßige</em> Zusammenhänge sind <em class="germph">denkbar</em>.</div>
<div class="corelinks tlpdepth4"><strong>6.3611</strong><span class="linkarray tlpdepth4" id="p6.3611GER"> GER [→<a class="ogdlink" href="#p6.3611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3611PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Wir können keinen Vorgang mit dem „Ablauf der Zeit“ vergleichen – diesen gibt es nicht –, sondern nur mit einem anderen Vorgang (etwa mit dem Gang des Chronometers).</div>
<div class="para tlpdepth4">Daher ist die Beschreibung des zeitlichen Verlaufs nur so möglich, dass wir uns auf einen anderen Vorgang stützen.</div>
<div class="para tlpdepth4">Ganz Analoges gilt für den Raum. Wo man z. B. sagt, es könne keines von zwei Ereignissen (die sich gegenseitig ausschließen) eintreten, weil <em class="germph">keine Ursache</em> vorhanden sei, warum das eine eher als das andere eintreten solle, da handelt es sich in Wirklichkeit darum, dass man gar nicht <em class="germph">eines</em> der beiden Ereignisse beschreiben kann, wenn nicht irgend eine Asymmetrie vorhanden ist. Und <em class="germph">wenn</em> eine solche Asymmetrie vorhanden <em class="germph">ist</em>, so können wir diese als <em class="germph">Ursache</em> des Eintreffens des einen und Nicht- Eintreffens des anderen auffassen.</div>
<div class="corelinks tlpdepth5"><strong>6.36111</strong><span class="linkarray tlpdepth5" id="p6.36111GER"> GER [→<a class="ogdlink" href="#p6.36111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36111PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Das Kant’sche Problem von der rechten und linken Hand, die man nicht zur Deckung bringen kann, besteht schon in der Ebene, ja im eindimensionalen Raum, wo die beiden kongruenten Figuren <span class="mathmode"><var>a</var></span> und <span class="mathmode"><var>b</var></span> auch nicht zur Deckung gebracht werden können, ohne aus diesem Raum</div>
<div class="para tlpdepth5 noindent"><!-- noindent --><div class="centeredsqueeze" ><b>–&nbsp;–&nbsp;–&nbsp;<span class="tight"><span class="symbol">○</span>————<span class="nudgedown"><span class="symbol">✕</span></span></span>&nbsp;–&nbsp;–&nbsp;<span class="tight"><span class="nudgedown"><span class="symbol">✕</span></span>————<span class="symbol">○</span></span>&nbsp;–&nbsp;–&nbsp;–</b><br /><var class="smallvar">a</var>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<var class="smallvar">b</var></div></div>
<div class="para tlpdepth5 noindent"><!-- noindent --> herausbewegt zu werden. Rechte und linke Hand sind tatsächlich vollkommen kongruent. Und dass man sie nicht zur Deckung bringen kann, hat damit nichts zu tun.</div>
<div class="para tlpdepth5">Den rechten Handschuh könnte man an die linke Hand ziehen, wenn man ihn im vierdimensionalen Raum umdrehen könnte.</div>
<div class="corelinks tlpdepth3"><strong>6.362</strong><span class="linkarray tlpdepth3" id="p6.362GER"> GER [→<a class="ogdlink" href="#p6.362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.362PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Was sich beschreiben lässt, das kann auch geschehen, und was das Kausalitätsgesetz ausschließen soll, das lässt sich auch nicht beschreiben.</div>
<div class="corelinks tlpdepth3"><strong>6.363</strong><span class="linkarray tlpdepth3" id="p6.363GER"> GER [→<a class="ogdlink" href="#p6.363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.363PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der Vorgang der Induktion besteht darin, dass wir das <em class="germph">einfachste</em> Gesetz annehmen, das mit unseren Erfahrungen in Einklang zu bringen ist.</div>
<div class="corelinks tlpdepth4"><strong>6.3631</strong><span class="linkarray tlpdepth4" id="p6.3631GER"> GER [→<a class="ogdlink" href="#p6.3631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3631PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dieser Vorgang hat aber keine logische, sondern nur eine psychologische Begründung.</div>
<div class="para tlpdepth4">Es ist klar, dass kein Grund vorhanden ist, zu glauben, es werde nun auch wirklich der einfachste Fall eintreten.</div>
<div class="corelinks tlpdepth5"><strong>6.36311</strong><span class="linkarray tlpdepth5" id="p6.36311GER"> GER [→<a class="ogdlink" href="#p6.36311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36311PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Dass die Sonne morgen aufgehen wird, ist eine Hypothese; und das heißt: wir <em class="germph">wissen</em> nicht, ob sie aufgehen wird.</div>
<div class="corelinks tlpdepth2"><strong>6.37</strong><span class="linkarray tlpdepth2" id="p6.37GER"> GER [→<a class="ogdlink" href="#p6.37OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.37PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Einen Zwang, nach dem Eines geschehen müsste, weil etwas anderes geschehen ist, gibt es nicht. Es gibt nur eine <em class="germph">logische</em> Notwendigkeit.</div>
<div class="corelinks tlpdepth3"><strong>6.371</strong><span class="linkarray tlpdepth3" id="p6.371GER"> GER [→<a class="ogdlink" href="#p6.371OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.371PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der ganzen modernen Weltanschauung liegt die Täuschung zugrunde, dass die sogenannten Naturgesetze die Erklärungen der Naturerscheinungen seien.</div>
<div class="corelinks tlpdepth3"><strong>6.372</strong><span class="linkarray tlpdepth3" id="p6.372GER"> GER [→<a class="ogdlink" href="#p6.372OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.372PM">P/M</a>]</span></div>
<div class="para tlpdepth3">So bleiben sie bei den Naturgesetzen als bei etwas Unantastbarem stehen, wie die Älteren bei Gott und dem Schicksal.</div>
<div class="para tlpdepth3">Und sie haben ja beide Recht, und Unrecht. Die Alten sind allerdings insofern klarer, als sie einen klaren Abschluss anerkennen, während es bei dem neuen System scheinen soll, als sei <em class="germph">alles</em> erklärt.</div>
<div class="corelinks tlpdepth3"><strong>6.373</strong><span class="linkarray tlpdepth3" id="p6.373GER"> GER [→<a class="ogdlink" href="#p6.373OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.373PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Welt ist unabhängig von meinem Willen.</div>
<div class="corelinks tlpdepth3"><strong>6.374</strong><span class="linkarray tlpdepth3" id="p6.374GER"> GER [→<a class="ogdlink" href="#p6.374OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Auch wenn alles, was wir wünschen, geschähe, so wäre dies doch nur, sozusagen, eine Gnade des Schicksals, denn es ist kein <em class="germph">logischer</em> Zusammenhang zwischen Willen und Welt, der dies verbürgte, und den angenommenen physikalischen Zusammenhang könnten wir doch nicht selbst wieder wollen.</div>
<div class="corelinks tlpdepth3"><strong>6.375</strong><span class="linkarray tlpdepth3" id="p6.375GER"> GER [→<a class="ogdlink" href="#p6.375OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.375PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wie es nur eine <em class="germph">logische</em> Notwendigkeit gibt, so gibt es auch nur eine <em class="germph">logische</em> Unmöglichkeit.</div>
<div class="corelinks tlpdepth4"><strong>6.3751</strong><span class="linkarray tlpdepth4" id="p6.3751GER"> GER [→<a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Dass z. B. zwei Farben zugleich an einem Ort des Gesichtsfeldes sind, ist unmöglich, und zwar logisch unmöglich, denn es ist durch die logische Struktur der Farbe ausgeschlossen.</div>
<div class="para tlpdepth4">Denken wir daran, wie sich dieser Widerspruch in der Physik darstellt: Ungefähr so, dass ein Teilchen nicht zu gleicher Zeit zwei Geschwindigkeiten haben kann; das heißt, dass es nicht zu gleicher Zeit an zwei Orten sein kann; das heißt, dass Teilchen an verschiedenen Orten zu Einer Zeit nicht identisch sein können.</div>
<div class="para tlpdepth4">(Es ist klar, dass das logische Produkt zweier Elementarsätze weder eine Tautologie noch eine Kontradiktion sein kann. Die Aussage, dass ein Punkt des Gesichtsfeldes zu gleicher Zeit zwei verschiedene Farben hat, ist eine Kontradiktion.)</div>
<div class="corelinks tlpdepth1"><strong>6.4</strong><span class="linkarray tlpdepth1" id="p6.4GER"> GER [→<a class="ogdlink" href="#p6.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Alle Sätze sind gleichwertig.</div>
<div class="corelinks tlpdepth2"><strong>6.41</strong><span class="linkarray tlpdepth2" id="p6.41GER"> GER [→<a class="ogdlink" href="#p6.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.41PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Der Sinn der Welt muss außerhalb ihrer liegen. In der Welt ist alles, wie es ist, und geschieht alles, wie es geschieht; es gibt <em class="germph">in</em> ihr keinen Wert – und wenn es ihn gäbe, so hätte er keinen Wert.</div>
<div class="para tlpdepth2">Wenn es einen Wert gibt, der Wert hat, so muss er außerhalb alles Geschehens und So-Seins liegen. Denn alles Geschehen und So-Sein ist zufällig.</div>
<div class="para tlpdepth2">Was es nichtzufällig macht, kann nicht <em class="germph">in</em> der Welt liegen, denn sonst wäre dies wieder zufällig.</div>
<div class="para tlpdepth2">Es muss außerhalb der Welt liegen.</div>
<div class="corelinks tlpdepth2"><strong>6.42</strong><span class="linkarray tlpdepth2" id="p6.42GER"> GER [→<a class="ogdlink" href="#p6.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.42PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Darum kann es auch keine Sätze der Ethik geben.</div>
<div class="para tlpdepth2">Sätze können nichts Höheres ausdrücken.</div>
<div class="corelinks tlpdepth3"><strong>6.421</strong><span class="linkarray tlpdepth3" id="p6.421GER"> GER [→<a class="ogdlink" href="#p6.421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.421PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es ist klar, dass sich die Ethik nicht aussprechen lässt.</div>
<div class="para tlpdepth3">Die Ethik ist transzendental.</div>
<div class="para tlpdepth3">(Ethik und Ästhetik sind Eins.)</div>
<div class="corelinks tlpdepth3"><strong>6.422</strong><span class="linkarray tlpdepth3" id="p6.422GER"> GER [→<a class="ogdlink" href="#p6.422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Der erste Gedanke bei der Aufstellung eines ethischen Gesetzes von der Form „Du sollst …“ ist: Und was dann, wenn ich es nicht tue? Es ist aber klar, dass die Ethik nichts mit Strafe und Lohn im gewöhnlichen Sinne zu tun hat. Also muss diese Frage nach den <em class="germph">Folgen</em> einer Handlung belanglos sein. – Zum Mindesten dürfen diese Folgen nicht Ereignisse sein. Denn etwas muss doch an jener Fragestellung richtig sein. Es muss zwar eine Art von ethischem Lohn und ethischer Strafe geben, aber diese müssen in der Handlung selbst liegen.</div>
<div class="para tlpdepth3">(Und das ist auch klar, dass der Lohn etwas Angenehmes, die Strafe etwas Unangenehmes sein muss.)</div>
<div class="corelinks tlpdepth3"><strong>6.423</strong><span class="linkarray tlpdepth3" id="p6.423GER"> GER [→<a class="ogdlink" href="#p6.423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.423PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Vom Willen als dem Träger des Ethischen kann nicht gesprochen werden.</div>
<div class="para tlpdepth3">Und der Wille als Phänomen interessiert nur die Psychologie.</div>
<div class="corelinks tlpdepth2"><strong>6.43</strong><span class="linkarray tlpdepth2" id="p6.43GER"> GER [→<a class="ogdlink" href="#p6.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.43PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wenn das gute oder böse Wollen die Welt ändert, so kann es nur die Grenzen der Welt ändern, nicht die Tatsachen; nicht das, was durch die Sprache ausgedrückt werden kann.</div>
<div class="para tlpdepth2">Kurz, die Welt muss dann dadurch überhaupt eine andere werden. Sie muss sozusagen als Ganzes abnehmen oder zunehmen.</div>
<div class="para tlpdepth2">Die Welt des Glücklichen ist eine andere als die des Unglücklichen.</div>
<div class="corelinks tlpdepth3"><strong>6.431</strong><span class="linkarray tlpdepth3" id="p6.431GER"> GER [→<a class="ogdlink" href="#p6.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.431PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Wie auch beim Tod die Welt sich nicht ändert, sondern aufhört.</div>
<div class="corelinks tlpdepth4"><strong>6.4311</strong><span class="linkarray tlpdepth4" id="p6.4311GER"> GER [→<a class="ogdlink" href="#p6.4311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Der Tod ist kein Ereignis des Lebens. Den Tod erlebt man nicht.</div>
<div class="para tlpdepth4">Wenn man unter Ewigkeit nicht unendliche Zeitdauer, sondern Unzeitlichkeit versteht, dann lebt der ewig, der in der Gegenwart lebt.</div>
<div class="para tlpdepth4">Unser Leben ist ebenso endlos, wie unser Gesichtsfeld grenzenlos ist.</div>
<div class="corelinks tlpdepth4"><strong>6.4312</strong><span class="linkarray tlpdepth4" id="p6.4312GER"> GER [→<a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die zeitliche Unsterblichkeit der Seele des Menschen, das heißt also ihr ewiges Fortleben auch nach dem Tode, ist nicht nur auf keine Weise verbürgt, sondern vor allem leistet diese Annahme gar nicht das, was man immer mit ihr erreichen wollte. Wird denn dadurch ein Rätsel gelöst, dass ich ewig fortlebe? Ist denn dieses ewige Leben dann nicht ebenso rätselhaft wie das gegenwärtige? Die Lösung des Rätsels des Lebens in Raum und Zeit liegt <em class="germph">außerhalb</em> von Raum und Zeit.</div>
<div class="para tlpdepth4">(Nicht Probleme der Naturwissenschaft sind ja zu lösen.)</div>
<div class="corelinks tlpdepth3"><strong>6.432</strong><span class="linkarray tlpdepth3" id="p6.432GER"> GER [→<a class="ogdlink" href="#p6.432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.432PM">P/M</a>]</span></div>
<div class="para tlpdepth3"><em class="germph">Wie</em> die Welt ist, ist für das Höhere vollkommen gleichgültig. Gott offenbart sich nicht <em class="germph">in</em> der Welt.</div>
<div class="corelinks tlpdepth4"><strong>6.4321</strong><span class="linkarray tlpdepth4" id="p6.4321GER"> GER [→<a class="ogdlink" href="#p6.4321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4321PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Die Tatsachen gehören alle nur zur Aufgabe, nicht zur Lösung.</div>
<div class="corelinks tlpdepth2"><strong>6.44</strong><span class="linkarray tlpdepth2" id="p6.44GER"> GER [→<a class="ogdlink" href="#p6.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.44PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Nicht <em class="germph">wie</em> die Welt ist, ist das Mystische, sondern <em class="germph">dass</em> sie ist.</div>
<div class="corelinks tlpdepth2"><strong>6.45</strong><span class="linkarray tlpdepth2" id="p6.45GER"> GER [→<a class="ogdlink" href="#p6.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.45PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die Anschauung der Welt sub specie aeterni ist ihre Anschauung als – begrenztes – Ganzes.</div>
<div class="para tlpdepth2">Das Gefühl der Welt als begrenztes Ganzes ist das mystische.</div>
<div class="corelinks tlpdepth1"><strong>6.5</strong><span class="linkarray tlpdepth1" id="p6.5GER"> GER [→<a class="ogdlink" href="#p6.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.5PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Zu einer Antwort, die man nicht aussprechen kann, kann man auch die Frage nicht aussprechen.</div>
<div class="para tlpdepth1"><em class="germph">Das Rätsel</em> gibt es nicht.</div>
<div class="para tlpdepth1">Wenn sich eine Frage überhaupt stellen lässt, so <em class="germph">kann</em> sie auch beantwortet werden.</div>
<div class="corelinks tlpdepth2"><strong>6.51</strong><span class="linkarray tlpdepth2" id="p6.51GER"> GER [→<a class="ogdlink" href="#p6.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.51PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Skeptizismus ist <em class="germph">nicht</em> unwiderleglich, sondern offenbar unsinnig, wenn er bezweifeln will, wo nicht gefragt werden kann.</div>
<div class="para tlpdepth2">Denn Zweifel kann nur bestehen, wo eine Frage besteht; eine Frage nur, wo eine Antwort besteht, und diese nur, wo etwas <em class="germph">gesagt</em> werden <em class="germph">kann</em>.</div>
<div class="corelinks tlpdepth2"><strong>6.52</strong><span class="linkarray tlpdepth2" id="p6.52GER"> GER [→<a class="ogdlink" href="#p6.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.52PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Wir fühlen, dass, selbst wenn alle <em class="germph">möglichen</em> wissenschaftlichen Fragen beantwortet sind, unsere Lebensprobleme noch gar nicht berührt sind. Freilich bleibt dann eben keine Frage mehr; und eben dies ist die Antwort.</div>
<div class="corelinks tlpdepth3"><strong>6.521</strong><span class="linkarray tlpdepth3" id="p6.521GER"> GER [→<a class="ogdlink" href="#p6.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.521PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Die Lösung des Problems des Lebens merkt man am Verschwinden dieses Problems.</div>
<div class="para tlpdepth3">(Ist nicht dies der Grund, warum Menschen, denen der Sinn des Lebens nach langen Zweifeln klar wurde, warum diese dann nicht sagen konnten, worin dieser Sinn bestand?)</div>
<div class="corelinks tlpdepth3"><strong>6.522</strong><span class="linkarray tlpdepth3" id="p6.522GER"> GER [→<a class="ogdlink" href="#p6.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.522PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Es gibt allerdings Unaussprechliches. Dies <em class="germph">zeigt</em> sich, es ist das Mystische.</div>
<div class="corelinks tlpdepth2"><strong>6.53</strong><span class="linkarray tlpdepth2" id="p6.53GER"> GER [→<a class="ogdlink" href="#p6.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Die richtige Methode der Philosophie wäre eigentlich die: Nichts zu sagen, als was sich sagen lässt, also Sätze der Naturwissenschaft – also etwas, was mit Philosophie nichts zu tun hat –&nbsp;, und dann immer, wenn ein anderer etwas Metaphysisches sagen wollte, ihm nachzuweisen, dass er gewissen Zeichen in seinen Sätzen keine Bedeutung gegeben hat. Diese Methode wäre für den anderen unbefriedigend – er hätte nicht das Gefühl, dass wir ihn Philosophie lehrten – aber <em class="germph">sie</em> wäre die einzig streng richtige.</div>
<div class="corelinks tlpdepth2"><strong>6.54</strong><span class="linkarray tlpdepth2" id="p6.54GER"> GER [→<a class="ogdlink" href="#p6.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.54PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Meine Sätze erläutern dadurch, dass sie der, welcher mich versteht, am Ende als unsinnig erkennt, wenn er durch sie – auf ihnen – über sie hinausgestiegen ist. (Er muss sozusagen die Leiter wegwerfen, nachdem er auf ihr hinaufgestiegen ist.)</div>
<div class="para tlpdepth2">Er muss diese Sätze überwinden, dann sieht er die Welt richtig.</div>
<div class="corelinks tlpdepth0"><strong>7</strong><span class="linkarray tlpdepth0" id="p7GER"> GER [→<a class="ogdlink" href="#p7OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p7PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Wovon man nicht sprechen kann, darüber muss man schweigen.</div>
<div id="footnotesGerman">
<h4 class="tlpdepth0">Footnote</h4>
<p class="footnote tlpdepth0" id="fn1GER"><a href="#fn1markerGER">*</a> <span id="germanfootnote1">Die Decimalzahlen als Nummern der einzelnen Sätze deuten das logische Gewicht der Sätze an, den Nachdruck, der auf ihnen in meiner Darstellung liegt. Die Sätze <var>n</var>.1, <var>n</var>.2, <var>n</var>.3, etc., sind Bemerkungen zum Sätze No. <var>n</var>; die Sätze <var>n</var>.<var>m</var>1, <var>n</var>.<var>m</var>2, etc. Bemerkungen zum Satze No. <var>n</var>.<var>m</var>; und so weiter.</span> <span class="linkarray">[→<a href="#fn1OGD" class="ogdlink">OGD</a><span class="beforepmclink"> | </span><a href="#fn1PM" class="pmclink">P/M</a>]</span></p>
</div>
<hr />
</div>
<div id="coredivOgden" class="versionbigdiv bigdivOgden">
<div id="prefacedivOgden" class="prefacediv">
<h2 class="majordivision" id="prefaceOgden">Preface (Ogden)</h2>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref1OGD"> OGD [→<a class="gerlink" href="#pref1GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref1PM">P/M</a>]</span></div>
<p>This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it—or similar thoughts. It is therefore not a text-book. Its object would be attained if there were one person who read it with understanding and to whom it afforded pleasure.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref2OGD"> OGD [→<a class="gerlink" href="#pref2GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span></div>
<p>The book deals with the problems of philosophy and shows, as I believe, that the method of formulating these problems rests on the misunderstanding of the logic of our language. Its whole meaning could be summed up somewhat as follows: What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref3OGD"> OGD [→<a class="gerlink" href="#pref3GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref3PM">P/M</a>]</span></div>
<p>The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought).</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref4OGD"> OGD [→<a class="gerlink" href="#pref4GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref4PM">P/M</a>]</span></div>
<p>The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref5OGD"> OGD [→<a class="gerlink" href="#pref5GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref5PM">P/M</a>]</span></div>
<p>How far my efforts agree with those of other philosophers I will not decide. Indeed what I have here written makes no claim to novelty in points of detail; and therefore I give no sources, because it is indifferent to me whether what I have thought has already been thought before me by another.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref6OGD"> OGD [→<a class="gerlink" href="#pref6GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref6PM">P/M</a>]</span></div>
<p>I will only mention that to the great works of Frege and the writings of my friend Bertrand Russell I owe in large measure the stimulation of my thoughts.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref7OGD"> OGD [→<a class="gerlink" href="#pref7GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref7PM">P/M</a>]</span></div>
<p>If this work has a value it consists in two things. First that in it thoughts are expressed, and this value will be the greater the better the thoughts are expressed. The more the nail has been hit on the head.—Here I am conscious that I have fallen far short of the possible. Simply because my powers are insufficient to cope with the task.—May others come and do it better.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref8OGD"> OGD [→<a class="gerlink" href="#pref8GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref8PM">P/M</a>]</span></div>
<p>On the other hand the <em>truth</em> of the thoughts communicated here seems to me unassailable and definitive. I am, therefore, of the opinion that the problems have in essentials been finally solved. And if I am not mistaken in this, then the value of this work secondly consists in the fact that it shows how little has been done when these problems have been solved.</p>
<p>&nbsp; <!-- flushright --> L. W.<br />
<em>Vienna, 1918</em></p>
</div>
<h2 class="majordivision" id="bodytextOgden">Tractatus Logico-Philosophicus (Ogden translation)</h2>
<div class="corelinks tlpdepth0"><strong>1</strong><a href="#fn1OGD" id="fn1markerOGD">*</a><span class="linkarray tlpdepth0" id="p1OGD"> OGD [→<a class="gerlink" href="#p1GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1PM">P/M</a>]</span></div>
<div class="para tlpdepth0">The world is everything that is the case.</div>
<div class="corelinks tlpdepth1"><strong>1.1</strong><span class="linkarray tlpdepth1" id="p1.1OGD"> OGD [→<a class="gerlink" href="#p1.1GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The world is the totality of facts, not of things.</div>
<div class="corelinks tlpdepth2"><strong>1.11</strong><span class="linkarray tlpdepth2" id="p1.11OGD"> OGD [→<a class="gerlink" href="#p1.11GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The world is determined by the facts, and by these being <em>all</em> the facts.</div>
<div class="corelinks tlpdepth2"><strong>1.12</strong><span class="linkarray tlpdepth2" id="p1.12OGD"> OGD [→<a class="gerlink" href="#p1.12GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">For the totality of facts determines both what is the case, and also all that is not the case.</div>
<div class="corelinks tlpdepth2"><strong>1.13</strong><span class="linkarray tlpdepth2" id="p1.13OGD"> OGD [→<a class="gerlink" href="#p1.13GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The facts in logical space are the world.</div>
<div class="corelinks tlpdepth1"><strong>1.2</strong><span class="linkarray tlpdepth1" id="p1.2OGD"> OGD [→<a class="gerlink" href="#p1.2GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The world divides into facts.</div>
<div class="corelinks tlpdepth2"><strong>1.21</strong><span class="linkarray tlpdepth2" id="p1.21OGD"> OGD [→<a class="gerlink" href="#p1.21GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Any one can either be the case or not be the case, and everything else remain the same.</div>
<div class="corelinks tlpdepth0"><strong>2</strong><span class="linkarray tlpdepth0" id="p2OGD"> OGD [→<a class="gerlink" href="#p2GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2PM">P/M</a>]</span></div>
<div class="para tlpdepth0">What is the case, the fact, is the existence of atomic facts.</div>
<div class="corelinks tlpdepth2"><strong>2.01</strong><span class="linkarray tlpdepth2" id="p2.01OGD"> OGD [→<a class="gerlink" href="#p2.01GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">An atomic fact is a combination of objects (entities, things).</div>
<div class="corelinks tlpdepth3"><strong>2.011</strong><span class="linkarray tlpdepth3" id="p2.011OGD"> OGD [→<a class="gerlink" href="#p2.011GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.011PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is essential to a thing that it can be a constituent part of an atomic fact.</div>
<div class="corelinks tlpdepth3"><strong>2.012</strong><span class="linkarray tlpdepth3" id="p2.012OGD"> OGD [→<a class="gerlink" href="#p2.012GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.012PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In logic nothing is accidental: if a thing <em>can</em> occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing.</div>
<div class="corelinks tlpdepth4"><strong>2.0121</strong><span class="linkarray tlpdepth4" id="p2.0121OGD"> OGD [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span></div>
<div class="para tlpdepth4">It would, so to speak, appear as an accident, when to a thing that could exist alone on its own account, subsequently a state of affairs could be made to fit.</div>
<div class="para tlpdepth4">If things can occur in atomic facts, this possibility must already lie in them.</div>
<div class="para tlpdepth4">(A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.)</div>
<div class="para tlpdepth4">Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of <em>any</em> object apart from the possibility of its connexion with other things.</div>
<div class="para tlpdepth4">If I can think of an object in the context of an atomic fact, I cannot think of it apart from the <em>possibility</em> of this context.</div>
<div class="corelinks tlpdepth4"><strong>2.0122</strong><span class="linkarray tlpdepth4" id="p2.0122OGD"> OGD [→<a class="gerlink" href="#p2.0122GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0122PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The thing is independent, in so far as it can occur in all <em>possible</em> circumstances, but this form of independence is a form of connexion with the atomic fact, a form of dependence. (It is impossible for words to occur in two different ways, alone and in the proposition.)</div>
<div class="corelinks tlpdepth4"><strong>2.0123</strong><span class="linkarray tlpdepth4" id="p2.0123OGD"> OGD [→<a class="gerlink" href="#p2.0123GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0123PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If I know an object, then I also know all the possibilities of its occurrence in atomic facts.</div>
<div class="para tlpdepth4">(Every such possibility must lie in the nature of the object.)</div>
<div class="para tlpdepth4">A new possibility cannot subsequently be found.</div>
<div class="corelinks tlpdepth5"><strong>2.01231</strong><span class="linkarray tlpdepth5" id="p2.01231OGD"> OGD [→<a class="gerlink" href="#p2.01231GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01231PM">P/M</a>]</span></div>
<div class="para tlpdepth5">In order to know an object, I must know not its external but all its internal qualities.</div>
<div class="corelinks tlpdepth4"><strong>2.0124</strong><span class="linkarray tlpdepth4" id="p2.0124OGD"> OGD [→<a class="gerlink" href="#p2.0124GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0124PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If all objects are given, then thereby are all <em>possible</em> atomic facts also given.</div>
<div class="corelinks tlpdepth3"><strong>2.013</strong><span class="linkarray tlpdepth3" id="p2.013OGD"> OGD [→<a class="gerlink" href="#p2.013GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.013PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.</div>
<div class="corelinks tlpdepth4"><strong>2.0131</strong><span class="linkarray tlpdepth4" id="p2.0131OGD"> OGD [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span></div>
<div class="para tlpdepth4">A spatial object must lie in infinite space. (A point in space is an argument place.)</div>
<div class="para tlpdepth4">A speck in a visual field need not be red, but it must have a colour; it has, so to speak, a colour space round it. A tone must have <em>a</em> pitch, the object of the sense of touch <em>a</em> hardness, etc.</div>
<div class="corelinks tlpdepth3"><strong>2.014</strong><span class="linkarray tlpdepth3" id="p2.014OGD"> OGD [→<a class="gerlink" href="#p2.014GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.014PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Objects contain the possibility of all states of affairs.</div>
<div class="corelinks tlpdepth4"><strong>2.0141</strong><span class="linkarray tlpdepth4" id="p2.0141OGD"> OGD [→<a class="gerlink" href="#p2.0141GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0141PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The possibility of its occurrence in atomic facts is the form of the object.</div>
<div class="corelinks tlpdepth2"><strong>2.02</strong><span class="linkarray tlpdepth2" id="p2.02OGD"> OGD [→<a class="gerlink" href="#p2.02GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The object is simple.</div>
<div class="corelinks tlpdepth4"><strong>2.0201</strong><span class="linkarray tlpdepth4" id="p2.0201OGD"> OGD [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Every statement about complexes can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.</div>
<div class="corelinks tlpdepth3"><strong>2.021</strong><span class="linkarray tlpdepth3" id="p2.021OGD"> OGD [→<a class="gerlink" href="#p2.021GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.021PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Objects form the substance of the world. Therefore they cannot be compound.</div>
<div class="corelinks tlpdepth4"><strong>2.0211</strong><span class="linkarray tlpdepth4" id="p2.0211OGD"> OGD [→<a class="gerlink" href="#p2.0211GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0211PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.</div>
<div class="corelinks tlpdepth4"><strong>2.0212</strong><span class="linkarray tlpdepth4" id="p2.0212OGD"> OGD [→<a class="gerlink" href="#p2.0212GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0212PM">P/M</a>]</span></div>
<div class="para tlpdepth4">It would then be impossible to form a picture of the world (true or false).</div>
<div class="corelinks tlpdepth3"><strong>2.022</strong><span class="linkarray tlpdepth3" id="p2.022OGD"> OGD [→<a class="gerlink" href="#p2.022GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.022PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is clear that however different from the real one an imagined world may be, it must have something—a form—in common with the real world.</div>
<div class="corelinks tlpdepth3"><strong>2.023</strong><span class="linkarray tlpdepth3" id="p2.023OGD"> OGD [→<a class="gerlink" href="#p2.023GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.023PM">P/M</a>]</span></div>
<div class="para tlpdepth3">This fixed form consists of the objects.</div>
<div class="corelinks tlpdepth4"><strong>2.0231</strong><span class="linkarray tlpdepth4" id="p2.0231OGD"> OGD [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The substance of the world <em>can</em> only determine a form and not any material properties. For these are first presented by the propositions—first formed by the configuration of the objects.</div>
<div class="corelinks tlpdepth4"><strong>2.0232</strong><span class="linkarray tlpdepth4" id="p2.0232OGD"> OGD [→<a class="gerlink" href="#p2.0232GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0232PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Roughly speaking: objects are colourless.</div>
<div class="corelinks tlpdepth4"><strong>2.0233</strong><span class="linkarray tlpdepth4" id="p2.0233OGD"> OGD [→<a class="gerlink" href="#p2.0233GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0233PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Two objects of the same logical form are—apart from their external properties—only differentiated from one another in that they are different.</div>
<div class="corelinks tlpdepth5"><strong>2.02331</strong><span class="linkarray tlpdepth5" id="p2.02331OGD"> OGD [→<a class="gerlink" href="#p2.02331GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02331PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Either a thing has properties which no other has, and then one can distinguish it straight away from the others by a description and refer to it; or, on the other hand, there are several things which have the totality of their properties in common, and then it is quite impossible to point to any one of them.</div>
<div class="para tlpdepth5">For if a thing is not distinguished by anything, I cannot distinguish it—for otherwise it would be distinguished.</div>
<div class="corelinks tlpdepth3"><strong>2.024</strong><span class="linkarray tlpdepth3" id="p2.024OGD"> OGD [→<a class="gerlink" href="#p2.024GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.024PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Substance is what exists independently of what is the case.</div>
<div class="corelinks tlpdepth3"><strong>2.025</strong><span class="linkarray tlpdepth3" id="p2.025OGD"> OGD [→<a class="gerlink" href="#p2.025GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.025PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is form and content.</div>
<div class="corelinks tlpdepth4"><strong>2.0251</strong><span class="linkarray tlpdepth4" id="p2.0251OGD"> OGD [→<a class="gerlink" href="#p2.0251GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0251PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Space, time and colour (colouredness) are forms of objects.</div>
<div class="corelinks tlpdepth3"><strong>2.026</strong><span class="linkarray tlpdepth3" id="p2.026OGD"> OGD [→<a class="gerlink" href="#p2.026GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.026PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Only if there are objects can there be a fixed form of the world.</div>
<div class="corelinks tlpdepth3"><strong>2.027</strong><span class="linkarray tlpdepth3" id="p2.027OGD"> OGD [→<a class="gerlink" href="#p2.027GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.027PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The fixed, the existent and the object are one.</div>
<div class="corelinks tlpdepth4"><strong>2.0271</strong><span class="linkarray tlpdepth4" id="p2.0271OGD"> OGD [→<a class="gerlink" href="#p2.0271GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0271PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The object is the fixed, the existent; the configuration is the changing, the variable.</div>
<div class="corelinks tlpdepth4"><strong>2.0272</strong><span class="linkarray tlpdepth4" id="p2.0272OGD"> OGD [→<a class="gerlink" href="#p2.0272GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0272PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The configuration of the objects forms the atomic fact.</div>
<div class="corelinks tlpdepth2"><strong>2.03</strong><span class="linkarray tlpdepth2" id="p2.03OGD"> OGD [→<a class="gerlink" href="#p2.03GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.03PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In the atomic fact objects hang one in another, like the links of a chain.</div>
<div class="corelinks tlpdepth3"><strong>2.031</strong><span class="linkarray tlpdepth3" id="p2.031OGD"> OGD [→<a class="gerlink" href="#p2.031GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.031PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In the atomic fact the objects are combined in a definite way.</div>
<div class="corelinks tlpdepth3"><strong>2.032</strong><span class="linkarray tlpdepth3" id="p2.032OGD"> OGD [→<a class="gerlink" href="#p2.032GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.032PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The way in which objects hang together in the atomic fact is the structure of the atomic fact.</div>
<div class="corelinks tlpdepth3"><strong>2.033</strong><span class="linkarray tlpdepth3" id="p2.033OGD"> OGD [→<a class="gerlink" href="#p2.033GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.033PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The form is the possibility of the structure.</div>
<div class="corelinks tlpdepth3"><strong>2.034</strong><span class="linkarray tlpdepth3" id="p2.034OGD"> OGD [→<a class="gerlink" href="#p2.034GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.034PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The structure of the fact consists of the structures of the atomic facts.</div>
<div class="corelinks tlpdepth2"><strong>2.04</strong><span class="linkarray tlpdepth2" id="p2.04OGD"> OGD [→<a class="gerlink" href="#p2.04GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.04PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The totality of existent atomic facts is the world.</div>
<div class="corelinks tlpdepth2"><strong>2.05</strong><span class="linkarray tlpdepth2" id="p2.05OGD"> OGD [→<a class="gerlink" href="#p2.05GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.05PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The totality of existent atomic facts also determines which atomic facts do not exist.</div>
<div class="corelinks tlpdepth2"><strong>2.06</strong><span class="linkarray tlpdepth2" id="p2.06OGD"> OGD [→<a class="gerlink" href="#p2.06GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.06PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The existence and non-existence of atomic facts is the reality.</div>
<div class="para tlpdepth2">(The existence of atomic facts we also call a positive fact, their non-existence a negative fact.)</div>
<div class="corelinks tlpdepth3"><strong>2.061</strong><span class="linkarray tlpdepth3" id="p2.061OGD"> OGD [→<a class="gerlink" href="#p2.061GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.061PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Atomic facts are independent of one another.</div>
<div class="corelinks tlpdepth3"><strong>2.062</strong><span class="linkarray tlpdepth3" id="p2.062OGD"> OGD [→<a class="gerlink" href="#p2.062GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.062PM">P/M</a>]</span></div>
<div class="para tlpdepth3">From the existence or non-existence of an atomic fact we cannot infer the existence or non-existence of another.</div>
<div class="corelinks tlpdepth3"><strong>2.063</strong><span class="linkarray tlpdepth3" id="p2.063OGD"> OGD [→<a class="gerlink" href="#p2.063GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.063PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The total reality is the world.</div>
<div class="corelinks tlpdepth1"><strong>2.1</strong><span class="linkarray tlpdepth1" id="p2.1OGD"> OGD [→<a class="gerlink" href="#p2.1GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">We make to ourselves pictures of facts.</div>
<div class="corelinks tlpdepth2"><strong>2.11</strong><span class="linkarray tlpdepth2" id="p2.11OGD"> OGD [→<a class="gerlink" href="#p2.11GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The picture presents the facts in logical space, the existence and non-existence of atomic facts.</div>
<div class="corelinks tlpdepth2"><strong>2.12</strong><span class="linkarray tlpdepth2" id="p2.12OGD"> OGD [→<a class="gerlink" href="#p2.12GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The picture is a model of reality.</div>
<div class="corelinks tlpdepth2"><strong>2.13</strong><span class="linkarray tlpdepth2" id="p2.13OGD"> OGD [→<a class="gerlink" href="#p2.13GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">To the objects correspond in the picture the elements of the picture.</div>
<div class="corelinks tlpdepth3"><strong>2.131</strong><span class="linkarray tlpdepth3" id="p2.131OGD"> OGD [→<a class="gerlink" href="#p2.131GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.131PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The elements of the picture stand, in the picture, for the objects.</div>
<div class="corelinks tlpdepth2"><strong>2.14</strong><span class="linkarray tlpdepth2" id="p2.14OGD"> OGD [→<a class="gerlink" href="#p2.14GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.14PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The picture consists in the fact that its elements are combined with one another in a definite way.</div>
<div class="corelinks tlpdepth3"><strong>2.141</strong><span class="linkarray tlpdepth3" id="p2.141OGD"> OGD [→<a class="gerlink" href="#p2.141GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.141PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The picture is a fact.</div>
<div class="corelinks tlpdepth2"><strong>2.15</strong><span class="linkarray tlpdepth2" id="p2.15OGD"> OGD [→<a class="gerlink" href="#p2.15GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span></div>
<div class="para tlpdepth2">That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another.</div>
<div class="para tlpdepth2">This connexion of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture.</div>
<div class="corelinks tlpdepth3"><strong>2.151</strong><span class="linkarray tlpdepth3" id="p2.151OGD"> OGD [→<a class="gerlink" href="#p2.151GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.151PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The form of representation is the possibility that the things are combined with one another as are the elements of the picture.</div>
<div class="corelinks tlpdepth4"><strong>2.1511</strong><span class="linkarray tlpdepth4" id="p2.1511OGD"> OGD [→<a class="gerlink" href="#p2.1511GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1511PM">P/M</a>]</span></div>
<div class="para tlpdepth4"><em>Thus</em> the picture is linked with reality; it reaches up to it.</div>
<div class="corelinks tlpdepth4"><strong>2.1512</strong><span class="linkarray tlpdepth4" id="p2.1512OGD"> OGD [→<a class="gerlink" href="#p2.1512GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1512PM">P/M</a>]</span></div>
<div class="para tlpdepth4">It is like a scale applied to reality.</div>
<div class="corelinks tlpdepth5"><strong>2.15121</strong><span class="linkarray tlpdepth5" id="p2.15121OGD"> OGD [→<a class="gerlink" href="#p2.15121GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15121PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Only the outermost points of the dividing lines <em>touch</em> the object to be measured.</div>
<div class="corelinks tlpdepth4"><strong>2.1513</strong><span class="linkarray tlpdepth4" id="p2.1513OGD"> OGD [→<a class="gerlink" href="#p2.1513GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1513PM">P/M</a>]</span></div>
<div class="para tlpdepth4">According to this view the representing relation which makes it a picture, also belongs to the picture.</div>
<div class="corelinks tlpdepth4"><strong>2.1514</strong><span class="linkarray tlpdepth4" id="p2.1514OGD"> OGD [→<a class="gerlink" href="#p2.1514GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1514PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The representing relation consists of the co-ordinations of the elements of the picture and the things.</div>
<div class="corelinks tlpdepth4"><strong>2.1515</strong><span class="linkarray tlpdepth4" id="p2.1515OGD"> OGD [→<a class="gerlink" href="#p2.1515GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1515PM">P/M</a>]</span></div>
<div class="para tlpdepth4">These co-ordinations are as it were the feelers of its elements with which the picture touches reality.</div>
<div class="corelinks tlpdepth2"><strong>2.16</strong><span class="linkarray tlpdepth2" id="p2.16OGD"> OGD [→<a class="gerlink" href="#p2.16GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.16PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In order to be a picture a fact must have something in common with what it pictures.</div>
<div class="corelinks tlpdepth3"><strong>2.161</strong><span class="linkarray tlpdepth3" id="p2.161OGD"> OGD [→<a class="gerlink" href="#p2.161GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.161PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.</div>
<div class="corelinks tlpdepth2"><strong>2.17</strong><span class="linkarray tlpdepth2" id="p2.17OGD"> OGD [→<a class="gerlink" href="#p2.17GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.17PM">P/M</a>]</span></div>
<div class="para tlpdepth2">What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation.</div>
<div class="corelinks tlpdepth3"><strong>2.171</strong><span class="linkarray tlpdepth3" id="p2.171OGD"> OGD [→<a class="gerlink" href="#p2.171GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.171PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The picture can represent every reality whose form it has.</div>
<div class="para tlpdepth3">The spatial picture, everything spatial, the coloured, everything coloured, etc.</div>
<div class="corelinks tlpdepth3"><strong>2.172</strong><span class="linkarray tlpdepth3" id="p2.172OGD"> OGD [→<a class="gerlink" href="#p2.172GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.172PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The picture, however, cannot represent its form of representation; it shows it forth.</div>
<div class="corelinks tlpdepth3"><strong>2.173</strong><span class="linkarray tlpdepth3" id="p2.173OGD"> OGD [→<a class="gerlink" href="#p2.173GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.173PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The picture represents its object from without (its standpoint is its form of representation), therefore the picture represents its object rightly or falsely.</div>
<div class="corelinks tlpdepth3"><strong>2.174</strong><span class="linkarray tlpdepth3" id="p2.174OGD"> OGD [→<a class="gerlink" href="#p2.174GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.174PM">P/M</a>]</span></div>
<div class="para tlpdepth3">But the picture cannot place itself outside of its form of representation.</div>
<div class="corelinks tlpdepth2"><strong>2.18</strong><span class="linkarray tlpdepth2" id="p2.18OGD"> OGD [→<a class="gerlink" href="#p2.18GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span></div>
<div class="para tlpdepth2">What every picture, of whatever form, must have in common with reality in order to be able to represent it at all—rightly or falsely—is the logical form, that is, the form of reality.</div>
<div class="corelinks tlpdepth3"><strong>2.181</strong><span class="linkarray tlpdepth3" id="p2.181OGD"> OGD [→<a class="gerlink" href="#p2.181GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.181PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If the form of representation is the logical form, then the picture is called a logical picture.</div>
<div class="corelinks tlpdepth3"><strong>2.182</strong><span class="linkarray tlpdepth3" id="p2.182OGD"> OGD [→<a class="gerlink" href="#p2.182GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.182PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Every picture is <em>also</em> a logical picture. (On the other hand, for example, not every picture is spatial.)</div>
<div class="corelinks tlpdepth2"><strong>2.19</strong><span class="linkarray tlpdepth2" id="p2.19OGD"> OGD [→<a class="gerlink" href="#p2.19GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.19PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The logical picture can depict the world.</div>
<div class="corelinks tlpdepth1"><strong>2.2</strong><span class="linkarray tlpdepth1" id="p2.2OGD"> OGD [→<a class="gerlink" href="#p2.2GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The picture has the logical form of representation in common with what it pictures.</div>
<div class="corelinks tlpdepth3"><strong>2.201</strong><span class="linkarray tlpdepth3" id="p2.201OGD"> OGD [→<a class="gerlink" href="#p2.201GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.201PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The picture depicts reality by representing a possibility of the existence and non-existence of atomic facts.</div>
<div class="corelinks tlpdepth3"><strong>2.202</strong><span class="linkarray tlpdepth3" id="p2.202OGD"> OGD [→<a class="gerlink" href="#p2.202GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.202PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The picture represents a possible state of affairs in logical space.</div>
<div class="corelinks tlpdepth3"><strong>2.203</strong><span class="linkarray tlpdepth3" id="p2.203OGD"> OGD [→<a class="gerlink" href="#p2.203GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.203PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The picture contains the possibility of the state of affairs which it represents.</div>
<div class="corelinks tlpdepth2"><strong>2.21</strong><span class="linkarray tlpdepth2" id="p2.21OGD"> OGD [→<a class="gerlink" href="#p2.21GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The picture agrees with reality or not; it is right or wrong, true or false.</div>
<div class="corelinks tlpdepth2"><strong>2.22</strong><span class="linkarray tlpdepth2" id="p2.22OGD"> OGD [→<a class="gerlink" href="#p2.22GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The picture represents what it represents, independently of its truth or falsehood, through the form of representation.</div>
<div class="corelinks tlpdepth3"><strong>2.221</strong><span class="linkarray tlpdepth3" id="p2.221OGD"> OGD [→<a class="gerlink" href="#p2.221GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.221PM">P/M</a>]</span></div>
<div class="para tlpdepth3">What the picture represents is its sense.</div>
<div class="corelinks tlpdepth3"><strong>2.222</strong><span class="linkarray tlpdepth3" id="p2.222OGD"> OGD [→<a class="gerlink" href="#p2.222GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.222PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In the agreement or disagreement of its sense with reality, its truth or falsity consists.</div>
<div class="corelinks tlpdepth3"><strong>2.223</strong><span class="linkarray tlpdepth3" id="p2.223OGD"> OGD [→<a class="gerlink" href="#p2.223GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.223PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In order to discover whether the picture is true or false we must compare it with reality.</div>
<div class="corelinks tlpdepth3"><strong>2.224</strong><span class="linkarray tlpdepth3" id="p2.224OGD"> OGD [→<a class="gerlink" href="#p2.224GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.224PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It cannot be discovered from the picture alone whether it is true or false.</div>
<div class="corelinks tlpdepth3"><strong>2.225</strong><span class="linkarray tlpdepth3" id="p2.225OGD"> OGD [→<a class="gerlink" href="#p2.225GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.225PM">P/M</a>]</span></div>
<div class="para tlpdepth3">There is no picture which is a priori true.</div>
<div class="corelinks tlpdepth0"><strong>3</strong><span class="linkarray tlpdepth0" id="p3OGD"> OGD [→<a class="gerlink" href="#p3GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3PM">P/M</a>]</span></div>
<div class="para tlpdepth0">The logical picture of the facts is the thought.</div>
<div class="corelinks tlpdepth3"><strong>3.001</strong><span class="linkarray tlpdepth3" id="p3.001OGD"> OGD [→<a class="gerlink" href="#p3.001GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.001PM">P/M</a>]</span></div>
<div class="para tlpdepth3">“An atomic fact is thinkable”—means: we can imagine it.</div>
<div class="corelinks tlpdepth2"><strong>3.01</strong><span class="linkarray tlpdepth2" id="p3.01OGD"> OGD [→<a class="gerlink" href="#p3.01GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The totality of true thoughts is a picture of the world.</div>
<div class="corelinks tlpdepth2"><strong>3.02</strong><span class="linkarray tlpdepth2" id="p3.02OGD"> OGD [→<a class="gerlink" href="#p3.02GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The thought contains the possibility of the state of affairs which it thinks. What is thinkable is also possible.</div>
<div class="corelinks tlpdepth2"><strong>3.03</strong><span class="linkarray tlpdepth2" id="p3.03OGD"> OGD [→<a class="gerlink" href="#p3.03GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.03PM">P/M</a>]</span></div>
<div class="para tlpdepth2">We cannot think anything unlogical, for otherwise we should have to think unlogically.</div>
<div class="corelinks tlpdepth3"><strong>3.031</strong><span class="linkarray tlpdepth3" id="p3.031OGD"> OGD [→<a class="gerlink" href="#p3.031GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.031PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It used to be said that God could create everything, except what was contrary to the laws of logic. The truth is, we could not <em>say</em> of an “unlogical” world how it would look.</div>
<div class="corelinks tlpdepth3"><strong>3.032</strong><span class="linkarray tlpdepth3" id="p3.032OGD"> OGD [→<a class="gerlink" href="#p3.032GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span></div>
<div class="para tlpdepth3">To present in language anything which “contradicts logic” is as impossible as in geometry to present by its co-ordinates a figure which contradicts the laws of space; or to give the co-ordinates of a point which does not exist.</div>
<div class="corelinks tlpdepth4"><strong>3.0321</strong><span class="linkarray tlpdepth4" id="p3.0321OGD"> OGD [→<a class="gerlink" href="#p3.0321GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.0321PM">P/M</a>]</span></div>
<div class="para tlpdepth4">We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.</div>
<div class="corelinks tlpdepth2"><strong>3.04</strong><span class="linkarray tlpdepth2" id="p3.04OGD"> OGD [→<a class="gerlink" href="#p3.04GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.04PM">P/M</a>]</span></div>
<div class="para tlpdepth2">An a priori true thought would be one whose possibility guaranteed its truth.</div>
<div class="corelinks tlpdepth2"><strong>3.05</strong><span class="linkarray tlpdepth2" id="p3.05OGD"> OGD [→<a class="gerlink" href="#p3.05GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.05PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Only if we could know a priori that a thought is true if its truth was to be recognized from the thought itself (without an object of comparison).</div>
<div class="corelinks tlpdepth1"><strong>3.1</strong><span class="linkarray tlpdepth1" id="p3.1OGD"> OGD [→<a class="gerlink" href="#p3.1GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">In the proposition the thought is expressed perceptibly through the senses.</div>
<div class="corelinks tlpdepth2"><strong>3.11</strong><span class="linkarray tlpdepth2" id="p3.11OGD"> OGD [→<a class="gerlink" href="#p3.11GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">We use the sensibly perceptible sign (sound or written sign, etc.) of the proposition as a projection of the possible state of affairs.</div>
<div class="para tlpdepth2">The method of projection is the thinking of the sense of the proposition.</div>
<div class="corelinks tlpdepth2"><strong>3.12</strong><span class="linkarray tlpdepth2" id="p3.12OGD"> OGD [→<a class="gerlink" href="#p3.12GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The sign through which we express the thought I call the propositional sign. And the proposition is the propositional sign in its projective relation to the world.</div>
<div class="corelinks tlpdepth2"><strong>3.13</strong><span class="linkarray tlpdepth2" id="p3.13OGD"> OGD [→<a class="gerlink" href="#p3.13GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">To the proposition belongs everything which belongs to the projection; but not what is projected.</div>
<div class="para tlpdepth2">Therefore the possibility of what is projected but not this itself.</div>
<div class="para tlpdepth2">In the proposition, therefore, its sense is not yet contained, but the possibility of expressing it.</div>
<div class="para tlpdepth2">(“The content of the proposition” means the content of the significant proposition.)</div>
<div class="para tlpdepth2">In the proposition the form of its sense is contained, but not its content.</div>
<div class="corelinks tlpdepth2"><strong>3.14</strong><span class="linkarray tlpdepth2" id="p3.14OGD"> OGD [→<a class="gerlink" href="#p3.14GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.14PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The propositional sign consists in the fact that its elements, the words, are combined in it in a definite way.</div>
<div class="para tlpdepth2">The propositional sign is a fact.</div>
<div class="corelinks tlpdepth3"><strong>3.141</strong><span class="linkarray tlpdepth3" id="p3.141OGD"> OGD [→<a class="gerlink" href="#p3.141GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.141PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The proposition is not a mixture of words (just as the musical theme is not a mixture of tones).</div>
<div class="para tlpdepth3">The proposition is articulate.</div>
<div class="corelinks tlpdepth3"><strong>3.142</strong><span class="linkarray tlpdepth3" id="p3.142OGD"> OGD [→<a class="gerlink" href="#p3.142GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.142PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Only facts can express a sense, a class of names cannot.</div>
<div class="corelinks tlpdepth3"><strong>3.143</strong><span class="linkarray tlpdepth3" id="p3.143OGD"> OGD [→<a class="gerlink" href="#p3.143GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span></div>
<div class="para tlpdepth3">That the propositional sign is a fact is concealed by the ordinary form of expression, written or printed.</div>
<div class="para tlpdepth3">For in the printed proposition, for example, the sign of a proposition does not appear essentially different from a word.</div>
<div class="para tlpdepth3">(Thus it was possible for Frege to call the proposition a compounded name.)</div>
<div class="corelinks tlpdepth4"><strong>3.1431</strong><span class="linkarray tlpdepth4" id="p3.1431OGD"> OGD [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.</div>
<div class="para tlpdepth4">The mutual spatial position of these things then expresses the sense of the proposition.</div>
<div class="corelinks tlpdepth4"><strong>3.1432</strong><span class="linkarray tlpdepth4" id="p3.1432OGD"> OGD [→<a class="gerlink" href="#p3.1432GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1432PM">P/M</a>]</span></div>
<div class="para tlpdepth4">We must not say, “The complex sign ‘<span class="mathmode"><var>aRb</var></span>’ says ‘<span class="mathmode"><var>a</var></span> stands in relation <span class="mathmode"><var>R</var></span> to <span class="mathmode"><var>b</var></span>’”; but we must say, “<em>That</em> ‘<span class="mathmode"><var>a</var></span>’ stands in a certain relation to ‘<span class="mathmode"><var>b</var></span>’ says <em>that</em> <span class="mathmode"><var>aRb</var></span>”.</div>
<div class="corelinks tlpdepth3"><strong>3.144</strong><span class="linkarray tlpdepth3" id="p3.144OGD"> OGD [→<a class="gerlink" href="#p3.144GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.144PM">P/M</a>]</span></div>
<div class="para tlpdepth3">States of affairs can be described but not <em>named</em>.</div>
<div class="para tlpdepth3">(Names resemble points; propositions resemble arrows, they have sense.)</div>
<div class="corelinks tlpdepth1"><strong>3.2</strong><span class="linkarray tlpdepth1" id="p3.2OGD"> OGD [→<a class="gerlink" href="#p3.2GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">In propositions thoughts can be so expressed that to the objects of the thoughts correspond the elements of the propositional sign.</div>
<div class="corelinks tlpdepth3"><strong>3.201</strong><span class="linkarray tlpdepth3" id="p3.201OGD"> OGD [→<a class="gerlink" href="#p3.201GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.201PM">P/M</a>]</span></div>
<div class="para tlpdepth3">These elements I call “simple signs” and the proposition “completely analysed”.</div>
<div class="corelinks tlpdepth3"><strong>3.202</strong><span class="linkarray tlpdepth3" id="p3.202OGD"> OGD [→<a class="gerlink" href="#p3.202GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.202PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The simple signs employed in propositions are called names.</div>
<div class="corelinks tlpdepth3"><strong>3.203</strong><span class="linkarray tlpdepth3" id="p3.203OGD"> OGD [→<a class="gerlink" href="#p3.203GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.203PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The name means the object. The object is its meaning. (“<span class="mathmode"><var>A</var></span>” is the same sign as “<span class="mathmode"><var>A</var></span>”.)</div>
<div class="corelinks tlpdepth2"><strong>3.21</strong><span class="linkarray tlpdepth2" id="p3.21OGD"> OGD [→<a class="gerlink" href="#p3.21GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">To the configuration of the simple signs in the propositional sign corresponds the configuration of the objects in the state of affairs.</div>
<div class="corelinks tlpdepth2"><strong>3.22</strong><span class="linkarray tlpdepth2" id="p3.22OGD"> OGD [→<a class="gerlink" href="#p3.22GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In the proposition the name represents the object.</div>
<div class="corelinks tlpdepth3"><strong>3.221</strong><span class="linkarray tlpdepth3" id="p3.221OGD"> OGD [→<a class="gerlink" href="#p3.221GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Objects I can only <em>name</em>. Signs represent them. I can only speak <em>of</em> them. I cannot <em>assert them</em>. A proposition can only say <em>how</em> a thing is, not <em>what</em> it is.</div>
<div class="corelinks tlpdepth2"><strong>3.23</strong><span class="linkarray tlpdepth2" id="p3.23OGD"> OGD [→<a class="gerlink" href="#p3.23GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.23PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The postulate of the possibility of the simple signs is the postulate of the determinateness of the sense.</div>
<div class="corelinks tlpdepth2"><strong>3.24</strong><span class="linkarray tlpdepth2" id="p3.24OGD"> OGD [→<a class="gerlink" href="#p3.24GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span></div>
<div class="para tlpdepth2">A proposition about a complex stands in internal relation to the proposition about its constituent part.</div>
<div class="para tlpdepth2">A
complex can only be given by its description, and this will either be
right or wrong. The proposition in which there is mention of a complex,
if this does not exist, becomes not nonsense but simply false.</div>
<div class="para tlpdepth2">That a propositional element signifies a complex can be seen from an indeterminateness in the propositions in which it occurs. We <em>know</em> that everything is not yet determined by this proposition. (The notation for generality <em>contains</em> a prototype.)</div>
<div class="para tlpdepth2">The combination of the symbols of a complex in a simple symbol can be expressed by a definition.</div>
<div class="corelinks tlpdepth2"><strong>3.25</strong><span class="linkarray tlpdepth2" id="p3.25OGD"> OGD [→<a class="gerlink" href="#p3.25GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.25PM">P/M</a>]</span></div>
<div class="para tlpdepth2">There is one and only one complete analysis of the proposition.</div>
<div class="corelinks tlpdepth3"><strong>3.251</strong><span class="linkarray tlpdepth3" id="p3.251OGD"> OGD [→<a class="gerlink" href="#p3.251GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.251PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The proposition expresses what it expresses in a definite and clearly specifiable way: the proposition is articulate.</div>
<div class="corelinks tlpdepth2"><strong>3.26</strong><span class="linkarray tlpdepth2" id="p3.26OGD"> OGD [→<a class="gerlink" href="#p3.26GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.26PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The name cannot be analysed further by any definition. It is a primitive sign.</div>
<div class="corelinks tlpdepth3"><strong>3.261</strong><span class="linkarray tlpdepth3" id="p3.261OGD"> OGD [→<a class="gerlink" href="#p3.261GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Every defined sign signifies <em>via</em> those signs by which it is defined, and the definitions show the way.</div>
<div class="para tlpdepth3">Two signs, one a primitive sign, and one defined by primitive signs, cannot signify in the same way. Names <em>cannot</em> be taken to pieces by definition (nor any sign which alone and independently has a meaning).</div>
<div class="corelinks tlpdepth3"><strong>3.262</strong><span class="linkarray tlpdepth3" id="p3.262OGD"> OGD [→<a class="gerlink" href="#p3.262GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.262PM">P/M</a>]</span></div>
<div class="para tlpdepth3">What does not get expressed in the sign is shown by its application. What the signs conceal, their application declares.</div>
<div class="corelinks tlpdepth3"><strong>3.263</strong><span class="linkarray tlpdepth3" id="p3.263OGD"> OGD [→<a class="gerlink" href="#p3.263GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The meanings of primitive signs can be explained by elucidations. Elucidations are propositions which contain the primitive signs. They can, therefore, only be understood when the meanings of these signs are already known.</div>
<div class="corelinks tlpdepth1"><strong>3.3</strong><span class="linkarray tlpdepth1" id="p3.3OGD"> OGD [→<a class="gerlink" href="#p3.3GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Only the proposition has sense; only in the context of a proposition has a name meaning.</div>
<div class="corelinks tlpdepth2"><strong>3.31</strong><span class="linkarray tlpdepth2" id="p3.31OGD"> OGD [→<a class="gerlink" href="#p3.31GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Every part of a proposition which characterizes its sense I call an expression (a symbol).</div>
<div class="para tlpdepth2">(The proposition itself is an expression.)</div>
<div class="para tlpdepth2">Expressions are everything—essential for the sense of the proposition—that propositions can have in common with one another.</div>
<div class="para tlpdepth2">An expression characterizes a form and a content.</div>
<div class="corelinks tlpdepth3"><strong>3.311</strong><span class="linkarray tlpdepth3" id="p3.311OGD"> OGD [→<a class="gerlink" href="#p3.311GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.311PM">P/M</a>]</span></div>
<div class="para tlpdepth3">An expression presupposes the forms of all propositions in which it can occur. It is the common characteristic mark of a class of propositions.</div>
<div class="corelinks tlpdepth3"><strong>3.312</strong><span class="linkarray tlpdepth3" id="p3.312OGD"> OGD [→<a class="gerlink" href="#p3.312GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.312PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is therefore represented by the general form of the propositions which it characterizes.</div>
<div class="para tlpdepth3">And in this form the expression is <em>constant</em> and everything else <em>variable</em>.</div>
<div class="corelinks tlpdepth3"><strong>3.313</strong><span class="linkarray tlpdepth3" id="p3.313OGD"> OGD [→<a class="gerlink" href="#p3.313GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.313PM">P/M</a>]</span></div>
<div class="para tlpdepth3">An expression is thus presented by a variable, whose values are the propositions which contain the expression.</div>
<div class="para tlpdepth3">(In the limiting case the variable becomes constant, the expression a proposition.)</div>
<div class="para tlpdepth3">I call such a variable a “propositional variable”.</div>
<div class="corelinks tlpdepth3"><strong>3.314</strong><span class="linkarray tlpdepth3" id="p3.314OGD"> OGD [→<a class="gerlink" href="#p3.314GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.314PM">P/M</a>]</span></div>
<div class="para tlpdepth3">An expression has meaning only in a proposition. Every variable can be conceived as a propositional variable.</div>
<div class="para tlpdepth3">(Including the variable name.)</div>
<div class="corelinks tlpdepth3"><strong>3.315</strong><span class="linkarray tlpdepth3" id="p3.315OGD"> OGD [→<a class="gerlink" href="#p3.315GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If we change a constituent part of a proposition into a variable, there is a class of propositions which are all the values of the resulting variable proposition. This class in general still depends on what, by arbitrary agreement, we mean by parts of that proposition. But if we change all those signs, whose meaning was arbitrarily determined, into variables, there always remains such a class. But this is now no longer dependent on any agreement; it depends only on the nature of the proposition. It corresponds to a logical form, to a logical prototype.</div>
<div class="corelinks tlpdepth3"><strong>3.316</strong><span class="linkarray tlpdepth3" id="p3.316OGD"> OGD [→<a class="gerlink" href="#p3.316GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.316PM">P/M</a>]</span></div>
<div class="para tlpdepth3">What values the propositional variable can assume is determined.</div>
<div class="para tlpdepth3">The determination of the values <em>is</em> the variable.</div>
<div class="corelinks tlpdepth3"><strong>3.317</strong><span class="linkarray tlpdepth3" id="p3.317OGD"> OGD [→<a class="gerlink" href="#p3.317GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The determination of the values of the propositional variable is done by <em>indicating the propositions</em> whose common mark the variable is.</div>
<div class="para tlpdepth3">The determination is a description of these propositions.</div>
<div class="para tlpdepth3">The determination will therefore deal only with symbols not with their meaning.</div>
<div class="para tlpdepth3">And <em>only</em> this is essential to the determination, <em>that it is only a description of symbols and asserts nothing about what is symbolized</em>.</div>
<div class="para tlpdepth3">The way in which we describe the propositions is not essential.</div>
<div class="corelinks tlpdepth3"><strong>3.318</strong><span class="linkarray tlpdepth3" id="p3.318OGD"> OGD [→<a class="gerlink" href="#p3.318GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.318PM">P/M</a>]</span></div>
<div class="para tlpdepth3">I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it.</div>
<div class="corelinks tlpdepth2"><strong>3.32</strong><span class="linkarray tlpdepth2" id="p3.32OGD"> OGD [→<a class="gerlink" href="#p3.32GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.32PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The sign is the part of the symbol perceptible by the senses.</div>
<div class="corelinks tlpdepth3"><strong>3.321</strong><span class="linkarray tlpdepth3" id="p3.321OGD"> OGD [→<a class="gerlink" href="#p3.321GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.321PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Two different symbols can therefore have the sign (the written sign or the sound sign) in common—they then signify in different ways.</div>
<div class="corelinks tlpdepth3"><strong>3.322</strong><span class="linkarray tlpdepth3" id="p3.322OGD"> OGD [→<a class="gerlink" href="#p3.322GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It can never indicate the common characteristic of two objects that we symbolize them with the same signs but by different <em>methods of symbolizing</em>. For the sign is arbitrary. We could therefore equally well choose two different signs and where then would be what was common in the symbolization?</div>
<div class="corelinks tlpdepth3"><strong>3.323</strong><span class="linkarray tlpdepth3" id="p3.323OGD"> OGD [→<a class="gerlink" href="#p3.323GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In the language of everyday life it very often happens that the same word signifies in two different ways—and therefore belongs to two different symbols—or that two words, which signify in different ways, are apparently applied in the same way in the proposition.</div>
<div class="para tlpdepth3">Thus the word “is” appears as the copula, as the sign of equality, and as the expression of existence; “to exist” as an intransitive verb like “to go”; “identical” as an adjective; we speak of <em>something</em> but also of the fact of <em>something</em> happening.</div>
<div class="para tlpdepth3">(In the proposition “Green is green”—where the first word is a proper name as the last an adjective—these words have not merely different meanings but they are <em>different symbols</em>.)</div>
<div class="corelinks tlpdepth3"><strong>3.324</strong><span class="linkarray tlpdepth3" id="p3.324OGD"> OGD [→<a class="gerlink" href="#p3.324GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.324PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Thus there easily arise the most fundamental confusions (of which the whole of philosophy is full).</div>
<div class="corelinks tlpdepth3"><strong>3.325</strong><span class="linkarray tlpdepth3" id="p3.325OGD"> OGD [→<a class="gerlink" href="#p3.325GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In order to avoid these errors, we must employ a symbolism which excludes them, by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways. A symbolism, that is to say, which obeys the rules of <em>logical</em> grammar—of logical syntax.</div>
<div class="para tlpdepth3">(The logical symbolism of Frege and Russell is such a language, which, however, does still not exclude all errors.)</div>
<div class="corelinks tlpdepth3"><strong>3.326</strong><span class="linkarray tlpdepth3" id="p3.326OGD"> OGD [→<a class="gerlink" href="#p3.326GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.326PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In order to recognize the symbol in the sign we must consider the significant use.</div>
<div class="corelinks tlpdepth3"><strong>3.327</strong><span class="linkarray tlpdepth3" id="p3.327OGD"> OGD [→<a class="gerlink" href="#p3.327GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.327PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The sign determines a logical form only together with its logical syntactic application.</div>
<div class="corelinks tlpdepth3"><strong>3.328</strong><span class="linkarray tlpdepth3" id="p3.328OGD"> OGD [→<a class="gerlink" href="#p3.328GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.328PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If a sign is <em>not necessary</em> then it is meaningless. That is the meaning of Occam’s razor.</div>
<div class="para tlpdepth3">(If everything in the symbolism works as though a sign had meaning, then it has meaning.)</div>
<div class="corelinks tlpdepth2"><strong>3.33</strong><span class="linkarray tlpdepth2" id="p3.33OGD"> OGD [→<a class="gerlink" href="#p3.33GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.33PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In logical syntax the meaning of a sign ought never to play a rôle; it must admit of being established without mention being thereby made of the <em>meaning</em> of a sign; it ought to presuppose <em>only</em> the description of the expressions.</div>
<div class="corelinks tlpdepth3"><strong>3.331</strong><span class="linkarray tlpdepth3" id="p3.331OGD"> OGD [→<a class="gerlink" href="#p3.331GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.331PM">P/M</a>]</span></div>
<div class="para tlpdepth3">From this observation we get a further view—into Russell’s <em>Theory of Types</em>. Russell’s error is shown by the fact that in drawing up his symbolic rules he has to speak about the things his signs mean.</div>
<div class="corelinks tlpdepth3"><strong>3.332</strong><span class="linkarray tlpdepth3" id="p3.332OGD"> OGD [→<a class="gerlink" href="#p3.332GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.332PM">P/M</a>]</span></div>
<div class="para tlpdepth3">No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the “whole theory of types”).</div>
<div class="corelinks tlpdepth3"><strong>3.333</strong><span class="linkarray tlpdepth3" id="p3.333OGD"> OGD [→<a class="gerlink" href="#p3.333GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span></div>
<div class="para tlpdepth3">A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself.</div>
<div class="para tlpdepth3">If, for example, we suppose that the function <span class="mathmode"><var>F</var>(<var>fx</var>)</span> could be its own argument, then there would be a proposition “<span class="mathmode"><var>F</var>(<var>F</var>(<var>fx</var>))</span>”, and in this the outer function <span class="mathmode"><var>F</var></span> and the inner function <span class="mathmode"><var>F</var></span> must have different meanings; for the inner has the form <span class="mathmode"><var>φ</var>(<var>fx</var>)</span>, the outer the form <span class="mathmode"><var>ψ</var>(<var>φ</var>(<var>fx</var>))</span>. Common to both functions is only the letter “<span class="mathmode"><var>F</var></span>”, which by itself signifies nothing.</div>
<div class="para tlpdepth3">This is at once clear, if instead of “<span class="mathmode"><var>F</var>(<var>Fu</var>)</span>” we write “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>φ</var>):</span><var>F</var>(<var>φu</var>)<span class="mathrel">.</span><var>φu</var><span class="mathrel">=</span><var>Fu</var></span>”.</div>
<div class="para tlpdepth3">Herewith Russell’s paradox vanishes.</div>
<div class="corelinks tlpdepth3"><strong>3.334</strong><span class="linkarray tlpdepth3" id="p3.334OGD"> OGD [→<a class="gerlink" href="#p3.334GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.334PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The rules of logical syntax must follow of themselves, if we only know how every single sign signifies.</div>
<div class="corelinks tlpdepth2"><strong>3.34</strong><span class="linkarray tlpdepth2" id="p3.34OGD"> OGD [→<a class="gerlink" href="#p3.34GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.34PM">P/M</a>]</span></div>
<div class="para tlpdepth2">A proposition possesses essential and accidental features.</div>
<div class="para tlpdepth2">Accidental are the features which are due to a particular way of producing the propositional sign. Essential are those which alone enable the proposition to express its sense.</div>
<div class="corelinks tlpdepth3"><strong>3.341</strong><span class="linkarray tlpdepth3" id="p3.341OGD"> OGD [→<a class="gerlink" href="#p3.341GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.341PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The essential in a proposition is therefore that which is common to all propositions which can express the same sense.</div>
<div class="para tlpdepth3">And in the same way in general the essential in a symbol is that which all symbols which can fulfill the same purpose have in common.</div>
<div class="corelinks tlpdepth4"><strong>3.3411</strong><span class="linkarray tlpdepth4" id="p3.3411OGD"> OGD [→<a class="gerlink" href="#p3.3411GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3411PM">P/M</a>]</span></div>
<div class="para tlpdepth4">One could therefore say the real name is that which all symbols, which signify an object, have in common. It would then follow, step by step, that no sort of composition was essential for a name.</div>
<div class="corelinks tlpdepth3"><strong>3.342</strong><span class="linkarray tlpdepth3" id="p3.342OGD"> OGD [→<a class="gerlink" href="#p3.342GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.342PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In our notations there is indeed something arbitrary, but <em>this</em> is not arbitrary, namely that <em>if</em> we have determined anything arbitrarily, then something else <em>must</em> be the case. (This results from the <em>essence</em> of the notation.)</div>
<div class="corelinks tlpdepth4"><strong>3.3421</strong><span class="linkarray tlpdepth4" id="p3.3421OGD"> OGD [→<a class="gerlink" href="#p3.3421GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3421PM">P/M</a>]</span></div>
<div class="para tlpdepth4">A particular method of symbolizing may be unimportant, but it is always important that this is a <em>possible</em> method of symbolizing. And this happens as a rule in philosophy: The single thing proves over and over again to be unimportant, but the possibility of every single thing reveals something about the nature of the world.</div>
<div class="corelinks tlpdepth3"><strong>3.343</strong><span class="linkarray tlpdepth3" id="p3.343OGD"> OGD [→<a class="gerlink" href="#p3.343GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.343PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Definitions are rules for the translation of one language into another. Every correct symbolism must be translatable into every other according to such rules. It is <em>this</em> which all have in common.</div>
<div class="corelinks tlpdepth3"><strong>3.344</strong><span class="linkarray tlpdepth3" id="p3.344OGD"> OGD [→<a class="gerlink" href="#p3.344GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.344PM">P/M</a>]</span></div>
<div class="para tlpdepth3">What signifies in the symbol is what is common to all those symbols by which it can be replaced according to the rules of logical syntax.</div>
<div class="corelinks tlpdepth4"><strong>3.3441</strong><span class="linkarray tlpdepth4" id="p3.3441OGD"> OGD [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span></div>
<div class="para tlpdepth4">We can, for example, express what is common to all notations for the truth-functions as follows: It is common to them that they all, for example, <em>can be replaced</em> by the notations of “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” (“not <span class="mathmode"><var>p</var></span>”) and “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>” (“<span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>”).</div>
<div class="para tlpdepth4">(Herewith is indicated the way in which a special possible notation can give us general information.)</div>
<div class="corelinks tlpdepth4"><strong>3.3442</strong><span class="linkarray tlpdepth4" id="p3.3442OGD"> OGD [→<a class="gerlink" href="#p3.3442GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3442PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The sign of the complex is not arbitrarily resolved in the analysis, in such a way that its resolution would be different in every propositional structure.</div>
<div class="corelinks tlpdepth1"><strong>3.4</strong><span class="linkarray tlpdepth1" id="p3.4OGD"> OGD [→<a class="gerlink" href="#p3.4GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.4PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The proposition determines a place in logical space: the existence of this logical place is guaranteed by the existence of the constituent parts alone, by the existence of the significant proposition.</div>
<div class="corelinks tlpdepth2"><strong>3.41</strong><span class="linkarray tlpdepth2" id="p3.41OGD"> OGD [→<a class="gerlink" href="#p3.41GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.41PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The propositional sign and the logical co-ordinates: that is the logical place.</div>
<div class="corelinks tlpdepth3"><strong>3.411</strong><span class="linkarray tlpdepth3" id="p3.411OGD"> OGD [→<a class="gerlink" href="#p3.411GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.411PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The geometrical and the logical place agree in that each is the possibility of an existence.</div>
<div class="corelinks tlpdepth2"><strong>3.42</strong><span class="linkarray tlpdepth2" id="p3.42OGD"> OGD [→<a class="gerlink" href="#p3.42GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Although a proposition may only determine one place in logical space, the whole logical space must already be given by it.</div>
<div class="para tlpdepth2">(Otherwise denial, the logical sum, the logical product, etc., would always introduce new elements—in co-ordination.)</div>
<div class="para tlpdepth2">(The logical scaffolding round the picture determines the logical space. The proposition reaches through the whole logical space.)</div>
<div class="corelinks tlpdepth1"><strong>3.5</strong><span class="linkarray tlpdepth1" id="p3.5OGD"> OGD [→<a class="gerlink" href="#p3.5GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.5PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The applied, thought, propositional sign, is the thought.</div>
<div class="corelinks tlpdepth0"><strong>4</strong><span class="linkarray tlpdepth0" id="p4OGD"> OGD [→<a class="gerlink" href="#p4GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4PM">P/M</a>]</span></div>
<div class="para tlpdepth0">The thought is the significant proposition.</div>
<div class="corelinks tlpdepth3"><strong>4.001</strong><span class="linkarray tlpdepth3" id="p4.001OGD"> OGD [→<a class="gerlink" href="#p4.001GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.001PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The totality of propositions is the language.</div>
<div class="corelinks tlpdepth3"><strong>4.002</strong><span class="linkarray tlpdepth3" id="p4.002OGD"> OGD [→<a class="gerlink" href="#p4.002GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Man possesses the capacity of constructing languages, in which every sense can be expressed, without having an idea how and what each word means—just as one speaks without knowing how the single sounds are produced.</div>
<div class="para tlpdepth3">Colloquial language is a part of the human organism and is not less complicated than it.</div>
<div class="para tlpdepth3">From it it is humanly impossible to gather immediately the logic of language.</div>
<div class="para tlpdepth3">Language disguises the thought; so that from the external form of the clothes one cannot infer the form of the thought they clothe, because the external form of the clothes is constructed with quite another object than to let the form of the body be recognized.</div>
<div class="para tlpdepth3">The silent adjustments to understand colloquial language are enormously complicated.</div>
<div class="corelinks tlpdepth3"><strong>4.003</strong><span class="linkarray tlpdepth3" id="p4.003OGD"> OGD [→<a class="gerlink" href="#p4.003GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Most propositions and questions, that have been written about philosophical matters, are not false, but senseless. We cannot, therefore, answer questions of this kind at all, but only state their senselessness. Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language.</div>
<div class="para tlpdepth3">(They are of the same kind as the question whether the Good is more or less identical than the Beautiful.)</div>
<div class="para tlpdepth3">And so it is not to be wondered at that the deepest problems are really <em>no</em> problems.</div>
<div class="corelinks tlpdepth4"><strong>4.0031</strong><span class="linkarray tlpdepth4" id="p4.0031OGD"> OGD [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span></div>
<div class="para tlpdepth4">All philosophy is “Critique of language” (but not at all in Mauthner’s sense). Russell’s merit is to have shown that the apparent logical form of the proposition need not be its real form.</div>
<div class="corelinks tlpdepth2"><strong>4.01</strong><span class="linkarray tlpdepth2" id="p4.01OGD"> OGD [→<a class="gerlink" href="#p4.01GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The proposition is a picture of reality.</div>
<div class="para tlpdepth2">The proposition is a model of the reality as we think it is.</div>
<div class="corelinks tlpdepth3"><strong>4.011</strong><span class="linkarray tlpdepth3" id="p4.011OGD"> OGD [→<a class="gerlink" href="#p4.011GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.011PM">P/M</a>]</span></div>
<div class="para tlpdepth3">At the first glance the proposition—say as it stands printed on paper—does not seem to be a picture of the reality of which it treats. But nor does the musical score appear at first sight to be a picture of a musical piece; nor does our phonetic spelling (letters) seem to be a picture of our spoken language.</div>
<div class="para tlpdepth3">And yet these symbolisms prove to be pictures—even in the ordinary sense of the word—of what they represent.</div>
<div class="corelinks tlpdepth3"><strong>4.012</strong><span class="linkarray tlpdepth3" id="p4.012OGD"> OGD [→<a class="gerlink" href="#p4.012GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.012PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is obvious that we perceive a proposition of the form <span class="mathmode"><var>aRb</var></span> as a picture. Here the sign is obviously a likeness of the signified.</div>
<div class="corelinks tlpdepth3"><strong>4.013</strong><span class="linkarray tlpdepth3" id="p4.013OGD"> OGD [→<a class="gerlink" href="#p4.013GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.013PM">P/M</a>]</span></div>
<div class="para tlpdepth3">And if we penetrate to the essence of this pictorial nature we see that this is not disturbed by <em>apparent irregularities</em> (like the use of <span class="mathmode"><span class="symbol">♯</span></span> and <span class="mathmode"><span class="symbol">♭</span></span> in the score).</div>
<div class="para tlpdepth3">For these irregularities also picture what they are to express; only in another way.</div>
<div class="corelinks tlpdepth3"><strong>4.014</strong><span class="linkarray tlpdepth3" id="p4.014OGD"> OGD [→<a class="gerlink" href="#p4.014GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation, which holds between language and the world.</div>
<div class="para tlpdepth3">To all of them the logical structure is common.</div>
<div class="para tlpdepth3">(Like the two youths, their two horses and their lilies in the story. They are all in a certain sense one.)</div>
<div class="corelinks tlpdepth4"><strong>4.0141</strong><span class="linkarray tlpdepth4" id="p4.0141OGD"> OGD [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span></div>
<div class="para tlpdepth4">In the fact that there is a general rule by which the musician is able to read the symphony out of the score, and that there is a rule by which one could reconstruct the symphony from the line on a gramophone record and from this again—by means of the first rule—construct the score, herein lies the internal similarity between these things which at first sight seem to be entirely different. And the rule is the law of projection which projects the symphony into the language of the musical score. It is the rule of translation of this language into the language of the gramophone record.</div>
<div class="corelinks tlpdepth3"><strong>4.015</strong><span class="linkarray tlpdepth3" id="p4.015OGD"> OGD [→<a class="gerlink" href="#p4.015GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.015PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The possibility of all similes, of all the images of our language, rests on the logic of representation.</div>
<div class="corelinks tlpdepth3"><strong>4.016</strong><span class="linkarray tlpdepth3" id="p4.016OGD"> OGD [→<a class="gerlink" href="#p4.016GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.016PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In order to understand the essence of the proposition, consider hieroglyphic writing, which pictures the facts it describes.</div>
<div class="para tlpdepth3">And from it came the alphabet without the essence of the representation being lost.</div>
<div class="corelinks tlpdepth2"><strong>4.02</strong><span class="linkarray tlpdepth2" id="p4.02OGD"> OGD [→<a class="gerlink" href="#p4.02GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">This we see from the fact that we understand the sense of the propositional sign, without having had it explained to us.</div>
<div class="corelinks tlpdepth3"><strong>4.021</strong><span class="linkarray tlpdepth3" id="p4.021OGD"> OGD [→<a class="gerlink" href="#p4.021GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The proposition is a picture of reality, for I know the state of affairs presented by it, if I understand the proposition. And I understand the proposition, without its sense having been explained to me.</div>
<div class="corelinks tlpdepth3"><strong>4.022</strong><span class="linkarray tlpdepth3" id="p4.022OGD"> OGD [→<a class="gerlink" href="#p4.022GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.022PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The proposition <em>shows</em> its sense.</div>
<div class="para tlpdepth3">The proposition <em>shows</em> how things stand, <em>if</em> it is true. And it <em>says</em>, that they do so stand.</div>
<div class="corelinks tlpdepth3"><strong>4.023</strong><span class="linkarray tlpdepth3" id="p4.023OGD"> OGD [→<a class="gerlink" href="#p4.023GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The proposition determines reality to this extent, that one only needs to say “Yes” or “No” to it to make it agree with reality.</div>
<div class="para tlpdepth3">Reality must therefore be completely described by the proposition.</div>
<div class="para tlpdepth3">A proposition is the description of a fact.</div>
<div class="para tlpdepth3">As the description of an object describes it by its external properties so propositions describe reality by its internal properties.</div>
<div class="para tlpdepth3">The proposition constructs a world with the help of a logical scaffolding, and therefore one can actually see in the proposition all the logical features possessed by reality <em>if</em> it is true. One can <em>draw conclusions</em> from a false proposition.</div>
<div class="corelinks tlpdepth3"><strong>4.024</strong><span class="linkarray tlpdepth3" id="p4.024OGD"> OGD [→<a class="gerlink" href="#p4.024GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.024PM">P/M</a>]</span></div>
<div class="para tlpdepth3">To understand a proposition means to know what is the case, if it is true.</div>
<div class="para tlpdepth3">(One can therefore understand it without knowing whether it is true or not.)</div>
<div class="para tlpdepth3">One understands it if one understands it constituent parts.</div>
<div class="corelinks tlpdepth3"><strong>4.025</strong><span class="linkarray tlpdepth3" id="p4.025OGD"> OGD [→<a class="gerlink" href="#p4.025GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.025PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The translation of one language into another is not a process of translating each proposition of the one into a proposition of the other, but only the constituent parts of propositions are translated.</div>
<div class="para tlpdepth3">(And the dictionary does not only translate substantives but also adverbs and conjunctions, etc., and it treats them all alike.)</div>
<div class="corelinks tlpdepth3"><strong>4.026</strong><span class="linkarray tlpdepth3" id="p4.026OGD"> OGD [→<a class="gerlink" href="#p4.026GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The meanings of the simple signs (the words) must be explained to us, if we are to understand them.</div>
<div class="para tlpdepth3">By means of propositions we explain ourselves.</div>
<div class="corelinks tlpdepth3"><strong>4.027</strong><span class="linkarray tlpdepth3" id="p4.027OGD"> OGD [→<a class="gerlink" href="#p4.027GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.027PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is essential to propositions, that they can communicate a <em>new</em> sense to us.</div>
<div class="corelinks tlpdepth2"><strong>4.03</strong><span class="linkarray tlpdepth2" id="p4.03OGD"> OGD [→<a class="gerlink" href="#p4.03GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span></div>
<div class="para tlpdepth2">A proposition must communicate a new sense with old words.</div>
<div class="para tlpdepth2">The proposition communicates to us a state of affairs, therefore it must be <em>essentially</em> connected with the state of affairs.</div>
<div class="para tlpdepth2">And the connexion is, in fact, that it is its logical picture.</div>
<div class="para tlpdepth2">The proposition only asserts something, in so far as it is a picture.</div>
<div class="corelinks tlpdepth3"><strong>4.031</strong><span class="linkarray tlpdepth3" id="p4.031OGD"> OGD [→<a class="gerlink" href="#p4.031GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.031PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In the proposition a state of affairs is, as it were, put together for the sake of experiment.</div>
<div class="para tlpdepth3">One can say, instead of, This proposition has such and such a sense, This proposition represents such and such a state of affairs.</div>
<div class="corelinks tlpdepth4"><strong>4.0311</strong><span class="linkarray tlpdepth4" id="p4.0311OGD"> OGD [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span></div>
<div class="para tlpdepth4">One name stands for one thing, and another for another thing, and they are connected together. And so the whole, like a living picture, presents the atomic fact.</div>
<div class="corelinks tlpdepth4"><strong>4.0312</strong><span class="linkarray tlpdepth4" id="p4.0312OGD"> OGD [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The possibility of propositions is based upon the principle of the representation of objects by signs.</div>
<div class="para tlpdepth4">My fundamental thought is that the “logical constants” do not represent. That the <em>logic</em> of the facts cannot be represented.</div>
<div class="corelinks tlpdepth3"><strong>4.032</strong><span class="linkarray tlpdepth3" id="p4.032OGD"> OGD [→<a class="gerlink" href="#p4.032GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.032PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The proposition is a picture of its state of affairs, only in so far as it is logically articulated.</div>
<div class="para tlpdepth3">(Even the proposition “ambulo” is composite, for its stem gives a different sense with another termination, or its termination with another stem.)</div>
<div class="corelinks tlpdepth2"><strong>4.04</strong><span class="linkarray tlpdepth2" id="p4.04OGD"> OGD [→<a class="gerlink" href="#p4.04GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In the proposition there must be exactly as many thing distinguishable as there are in the state of affairs, which it represents.</div>
<div class="para tlpdepth2">They must both possess the same logical (mathematical) multiplicity (cf. Hertz’s Mechanics, on Dynamic Models).</div>
<div class="corelinks tlpdepth3"><strong>4.041</strong><span class="linkarray tlpdepth3" id="p4.041OGD"> OGD [→<a class="gerlink" href="#p4.041GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.041PM">P/M</a>]</span></div>
<div class="para tlpdepth3">This mathematical multiplicity naturally cannot in its turn be represented. One cannot get outside it in the representation.</div>
<div class="corelinks tlpdepth4"><strong>4.0411</strong><span class="linkarray tlpdepth4" id="p4.0411OGD"> OGD [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If we tried, for example, to express what is expressed by “<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>” by putting an index before <span class="mathmode"><var>fx</var></span>, like: “<span class="mathmode"><span class="mathop"><span class="mathrm">Gen.</span></span> <var>fx</var></span>”, it would not do, we should not know what was generalized. If we tried to show it by an index <span class="mathmode"><var>g</var></span>, like: “<span class="mathmode"><var>f</var>(<var>x</var><sub><var>g</var></sub>)</span>” it would not do—we should not know the scope of the generalization.</div>
<div class="para tlpdepth4">If we were to try it by introducing a mark in the argument places, like “<span class="mathmode"><span class="mathop">(<var>G</var>, <var>G</var>).</span> <var>F</var>(<var>G</var>, <var>G</var>)</span>”, it would not do—we could not determine the identity of the variables, etc.</div>
<div class="para tlpdepth4">All these ways of symbolizing are inadequate because they have not the necessary mathematical multiplicity.</div>
<div class="corelinks tlpdepth4"><strong>4.0412</strong><span class="linkarray tlpdepth4" id="p4.0412OGD"> OGD [→<a class="gerlink" href="#p4.0412GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0412PM">P/M</a>]</span></div>
<div class="para tlpdepth4">For the same reason the idealist explanation of the seeing of spatial relations through “spatial spectacles” does not do, because it cannot explain the multiplicity of these relations.</div>
<div class="corelinks tlpdepth2"><strong>4.05</strong><span class="linkarray tlpdepth2" id="p4.05OGD"> OGD [→<a class="gerlink" href="#p4.05GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.05PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Reality is compared with the proposition.</div>
<div class="corelinks tlpdepth2"><strong>4.06</strong><span class="linkarray tlpdepth2" id="p4.06OGD"> OGD [→<a class="gerlink" href="#p4.06GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.06PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Propositions can be true or false only by being pictures of the reality.</div>
<div class="corelinks tlpdepth3"><strong>4.061</strong><span class="linkarray tlpdepth3" id="p4.061OGD"> OGD [→<a class="gerlink" href="#p4.061GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.061PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If one does not observe that propositions have a sense independent of the facts, one can easily believe that true and false are two relations between signs and things signified with equal rights.</div>
<div class="para tlpdepth3">One could, then, for example, say that “<span class="mathmode"><var>p</var></span>” signifies in the true way what “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” signifies in the false way, etc.</div>
<div class="corelinks tlpdepth3"><strong>4.062</strong><span class="linkarray tlpdepth3" id="p4.062OGD"> OGD [→<a class="gerlink" href="#p4.062GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.062PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Can we not make ourselves understood by means of false propositions as hitherto with true ones, so long as we know that they are meant to be false? No! For a proposition is true, if what we assert by means of it is the case; and if by “<span class="mathmode"><var>p</var></span>” we mean <span class="mathmode"><span class="mathop">~</span><var>p</var></span>, and what we mean is the case, then “<span class="mathmode"><var>p</var></span>” in the new conception is true and not false.</div>
<div class="corelinks tlpdepth4"><strong>4.0621</strong><span class="linkarray tlpdepth4" id="p4.0621OGD"> OGD [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span></div>
<div class="para tlpdepth4">That, however, the signs “<span class="mathmode"><var>p</var></span>” and “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” <em>can</em> say the same thing is important, for it shows that the sign “~” corresponds to nothing in reality.</div>
<div class="para tlpdepth4">That negation occurs in a proposition, is no characteristic of its sense (<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var><span class="mathrel">=</span><var>p</var></span>).</div>
<div class="para tlpdepth4">The propositions “<span class="mathmode"><var>p</var></span>” and “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” have opposite senses, but to them corresponds one and the same reality.</div>
<div class="corelinks tlpdepth3"><strong>4.063</strong><span class="linkarray tlpdepth3" id="p4.063OGD"> OGD [→<a class="gerlink" href="#p4.063GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span></div>
<div class="para tlpdepth3">An illustration to explain the concept of truth. A black spot on white paper; the form of the spot can be described by saying of each point of the plane whether it is white or black. To the fact that a point is black corresponds a positive fact; to the fact that a point is white (not black), a negative fact. If I indicate a point of the plane (a truth-value in Frege’s terminology), this corresponds to the assumption proposed for judgment, etc. etc.</div>
<div class="para tlpdepth3">But to be able to say that a point is black or white, I must first know under what conditions a point is called white or black; in order to be able to say “<span class="mathmode"><var>p</var></span>” is true (or false) I must have determined under what conditions I call “<span class="mathmode"><var>p</var></span>” true, and thereby I determine the sense of the proposition.</div>
<div class="para tlpdepth3">The point at which the simile breaks down is this: we can indicate a point on the paper, without knowing what white and black are; but to a proposition without a sense corresponds nothing at all, for it signifies no thing (truth-value) whose properties are called “false” or “true”; the verb of the proposition is not “is true” or “is false”—as Frege thought—but that which “is true” must already contain the verb.</div>
<div class="corelinks tlpdepth3"><strong>4.064</strong><span class="linkarray tlpdepth3" id="p4.064OGD"> OGD [→<a class="gerlink" href="#p4.064GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.064PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Every proposition must <em>already</em> have a sense; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc.</div>
<div class="corelinks tlpdepth4"><strong>4.0641</strong><span class="linkarray tlpdepth4" id="p4.0641OGD"> OGD [→<a class="gerlink" href="#p4.0641GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0641PM">P/M</a>]</span></div>
<div class="para tlpdepth4">One could say, the denial is already related to the logical place determined by the proposition that is denied.</div>
<div class="para tlpdepth4">The denying proposition determines a logical place <em>other</em> than does the proposition denied.</div>
<div class="para tlpdepth4">The denying proposition determines a logical place, with the help of the logical place of the proposition denied, by saying that it lies outside the latter place.</div>
<div class="para tlpdepth4">That one can deny again the denied proposition, shows that what is denied is already a proposition and not merely the preliminary to a proposition.</div>
<div class="corelinks tlpdepth1"><strong>4.1</strong><span class="linkarray tlpdepth1" id="p4.1OGD"> OGD [→<a class="gerlink" href="#p4.1GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">A proposition presents the existence and non-existence of atomic facts.</div>
<div class="corelinks tlpdepth2"><strong>4.11</strong><span class="linkarray tlpdepth2" id="p4.11OGD"> OGD [→<a class="gerlink" href="#p4.11GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The totality of true propositions is the total natural science (or the totality of the natural sciences).</div>
<div class="corelinks tlpdepth3"><strong>4.111</strong><span class="linkarray tlpdepth3" id="p4.111OGD"> OGD [→<a class="gerlink" href="#p4.111GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.111PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Philosophy is not one of the natural sciences.</div>
<div class="para tlpdepth3">(The word “philosophy” must mean something which stands above or below, but not beside the natural sciences.)</div>
<div class="corelinks tlpdepth3"><strong>4.112</strong><span class="linkarray tlpdepth3" id="p4.112OGD"> OGD [→<a class="gerlink" href="#p4.112GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The object of philosophy is the logical clarification of thoughts.</div>
<div class="para tlpdepth3">Philosophy is not a theory but an activity.</div>
<div class="para tlpdepth3">A philosophical work consists essentially of elucidations.</div>
<div class="para tlpdepth3">The result of philosophy is not a number of “philosophical propositions”, but to make propositions clear.</div>
<div class="para tlpdepth3">Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred.</div>
<div class="corelinks tlpdepth4"><strong>4.1121</strong><span class="linkarray tlpdepth4" id="p4.1121OGD"> OGD [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Psychology is no nearer related to philosophy, than is any other natural science.</div>
<div class="para tlpdepth4">The theory of knowledge is the philosophy of psychology.</div>
<div class="para tlpdepth4">Does not my study of sign-language correspond to the study of thought processes which philosophers held to be so essential to the philosophy of logic? Only they got entangled for the most part in unessential psychological investigations, and there is an analogous danger for my method.</div>
<div class="corelinks tlpdepth4"><strong>4.1122</strong><span class="linkarray tlpdepth4" id="p4.1122OGD"> OGD [→<a class="gerlink" href="#p4.1122GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1122PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The Darwinian theory has no more to do with philosophy than has any other hypothesis of natural science.</div>
<div class="corelinks tlpdepth3"><strong>4.113</strong><span class="linkarray tlpdepth3" id="p4.113OGD"> OGD [→<a class="gerlink" href="#p4.113GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.113PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Philosophy limits the disputable sphere of natural science.</div>
<div class="corelinks tlpdepth3"><strong>4.114</strong><span class="linkarray tlpdepth3" id="p4.114OGD"> OGD [→<a class="gerlink" href="#p4.114GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.114PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It should limit the thinkable and thereby the unthinkable.</div>
<div class="para tlpdepth3">It should limit the unthinkable from within through the thinkable.</div>
<div class="corelinks tlpdepth3"><strong>4.115</strong><span class="linkarray tlpdepth3" id="p4.115OGD"> OGD [→<a class="gerlink" href="#p4.115GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.115PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It will mean the unspeakable by clearly displaying the speakable.</div>
<div class="corelinks tlpdepth3"><strong>4.116</strong><span class="linkarray tlpdepth3" id="p4.116OGD"> OGD [→<a class="gerlink" href="#p4.116GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.116PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly.</div>
<div class="corelinks tlpdepth2"><strong>4.12</strong><span class="linkarray tlpdepth2" id="p4.12OGD"> OGD [→<a class="gerlink" href="#p4.12GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Propositions can represent the whole reality, but they cannot represent what they must have in common with reality in order to be able to represent it—the logical form.</div>
<div class="para tlpdepth2">To be able to represent the logical form, we should have to be able to put ourselves with the propositions outside logic, that is outside the world.</div>
<div class="corelinks tlpdepth3"><strong>4.121</strong><span class="linkarray tlpdepth3" id="p4.121OGD"> OGD [→<a class="gerlink" href="#p4.121GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Propositions cannot represent the logical form: this mirrors itself in the propositions.</div>
<div class="para tlpdepth3">That which mirrors itself in language, language cannot represent.</div>
<div class="para tlpdepth3">That which expresses <em>itself</em> in language, <em>we</em> cannot express by language.</div>
<div class="para tlpdepth3">The propositions <em>show</em> the logical form of reality.</div>
<div class="para tlpdepth3">They exhibit it.</div>
<div class="corelinks tlpdepth4"><strong>4.1211</strong><span class="linkarray tlpdepth4" id="p4.1211OGD"> OGD [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Thus a proposition “<span class="mathmode"><var>fa</var></span>” shows that in its sense the object <span class="mathmode"><var>a</var></span> occurs, two propositions “<span class="mathmode"><var>fa</var></span>” and “<span class="mathmode"><var>ga</var></span>” that they are both about the same object.</div>
<div class="para tlpdepth4">If two propositions contradict one another, this is shown by their structure; similarly if one follows from another, etc.</div>
<div class="corelinks tlpdepth4"><strong>4.1212</strong><span class="linkarray tlpdepth4" id="p4.1212OGD"> OGD [→<a class="gerlink" href="#p4.1212GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1212PM">P/M</a>]</span></div>
<div class="para tlpdepth4">What <em>can</em> be shown <em>cannot</em> be said.</div>
<div class="corelinks tlpdepth4"><strong>4.1213</strong><span class="linkarray tlpdepth4" id="p4.1213OGD"> OGD [→<a class="gerlink" href="#p4.1213GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1213PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Now we understand our feeling that we are in possession of the right logical conception, if only all is right in our symbolism.</div>
<div class="corelinks tlpdepth3"><strong>4.122</strong><span class="linkarray tlpdepth3" id="p4.122OGD"> OGD [→<a class="gerlink" href="#p4.122GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span></div>
<div class="para tlpdepth3">We can speak in a certain sense of formal properties of objects and atomic facts, or of properties of the structure of facts, and in the same sense of formal relations and relations of structures.</div>
<div class="para tlpdepth3">(Instead of property of the structure I also say “internal property”; instead of relation of structures “internal relation”.</div>
<div class="para tlpdepth3">I introduce these expressions in order to show the reason for the confusion, very widespread among philosophers, between internal relations and proper (external) relations.)</div>
<div class="para tlpdepth3">The holding of such internal properties and relations cannot, however, be asserted by propositions, but it shows itself in the propositions, which present the facts and treat of the objects in question.</div>
<div class="corelinks tlpdepth4"><strong>4.1221</strong><span class="linkarray tlpdepth4" id="p4.1221OGD"> OGD [→<a class="gerlink" href="#p4.1221GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1221PM">P/M</a>]</span></div>
<div class="para tlpdepth4">An internal property of a fact we also call a feature of this fact. (In the sense in which we speak of facial features.)</div>
<div class="corelinks tlpdepth3"><strong>4.123</strong><span class="linkarray tlpdepth3" id="p4.123OGD"> OGD [→<a class="gerlink" href="#p4.123GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.123PM">P/M</a>]</span></div>
<div class="para tlpdepth3">A property is internal if it is unthinkable that its object does not possess it.</div>
<div class="para tlpdepth3">(This bright blue colour and that stand in the internal relation of bright and darker eo ipso. It is unthinkable that <em>these</em> two objects should not stand in this relation.)</div>
<div class="para tlpdepth3">(Here to the shifting use of the words “property” and “relation” there corresponds the shifting use of the word “object”.)</div>
<div class="corelinks tlpdepth3"><strong>4.124</strong><span class="linkarray tlpdepth3" id="p4.124OGD"> OGD [→<a class="gerlink" href="#p4.124GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The existence of an internal property of a possible state of affairs is not expressed by a proposition, but it expresses itself in the proposition which presents that state of affairs, by an internal property of this proposition.</div>
<div class="para tlpdepth3">It would be as senseless to ascribe a formal property to a proposition as to deny it the formal property.</div>
<div class="corelinks tlpdepth4"><strong>4.1241</strong><span class="linkarray tlpdepth4" id="p4.1241OGD"> OGD [→<a class="gerlink" href="#p4.1241GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1241PM">P/M</a>]</span></div>
<div class="para tlpdepth4">One cannot distinguish forms from one another by saying that one has this property, the other that: for this assumes that there is a sense in asserting either property of either form.</div>
<div class="corelinks tlpdepth3"><strong>4.125</strong><span class="linkarray tlpdepth3" id="p4.125OGD"> OGD [→<a class="gerlink" href="#p4.125GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The existence of an internal relation between possible states of affairs expresses itself in language by an internal relation between the propositions presenting them.</div>
<div class="corelinks tlpdepth4"><strong>4.1251</strong><span class="linkarray tlpdepth4" id="p4.1251OGD"> OGD [→<a class="gerlink" href="#p4.1251GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1251PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Now this settles the disputed question “whether all relations are internal or external”.</div>
<div class="corelinks tlpdepth4"><strong>4.1252</strong><span class="linkarray tlpdepth4" id="p4.1252OGD"> OGD [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Series which are ordered by <em>internal</em> relations I call formal series.</div>
<div class="para tlpdepth4">The series of numbers is ordered not by an external, but by an internal relation.</div>
<div class="para tlpdepth4">Similarly the series of propositions “<span class="mathmode"><var>aRb</var></span>”,</div>
<div class="para tlpdepth4">“<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRb</var></span>”,</div>
<div class="para tlpdepth4">“<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRy</var><span class="mathrel">.</span><var>yRb</var></span>”, etc.</div>
<div class="para tlpdepth4">(If <span class="mathmode"><var>b</var></span> stands in one of these relations to <span class="mathmode"><var>a</var></span>, I call <span class="mathmode"><var>b</var></span> a successor of <span class="mathmode"><var>a</var></span>.)</div>
<div class="corelinks tlpdepth3"><strong>4.126</strong><span class="linkarray tlpdepth3" id="p4.126OGD"> OGD [→<a class="gerlink" href="#p4.126GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In the sense in which we speak of formal properties we can now speak also of formal concepts.</div>
<div class="para tlpdepth3">(I introduce this expression in order to make clear the confusion of formal concepts with proper concepts which runs through the whole of the old logic.)</div>
<div class="para tlpdepth3">That anything falls under a formal concept as an object belonging to it, cannot be expressed by a proposition. But it is shown in the symbol for the object itself. (The name shows that it signifies an object, the numerical sign that it signifies a number, etc.)</div>
<div class="para tlpdepth3">Formal concepts, cannot, like proper concepts, be presented by a function.</div>
<div class="para tlpdepth3">For their characteristics, the formal properties, are not expressed by the functions.</div>
<div class="para tlpdepth3">The expression of a formal property is a feature of certain symbols.</div>
<div class="para tlpdepth3">The sign that signifies the characteristics of a formal concept is, therefore, a characteristic feature of all symbols, whose meanings fall under the concept.</div>
<div class="para tlpdepth3">The expression of the formal concept is therefore a propositional variable in which only this characteristic feature is constant.</div>
<div class="corelinks tlpdepth3"><strong>4.127</strong><span class="linkarray tlpdepth3" id="p4.127OGD"> OGD [→<a class="gerlink" href="#p4.127GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.127PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The propositional variable signifies the formal concept, and its values signify the objects which fall under this concept.</div>
<div class="corelinks tlpdepth4"><strong>4.1271</strong><span class="linkarray tlpdepth4" id="p4.1271OGD"> OGD [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Every variable is the sign of a formal concept.</div>
<div class="para tlpdepth4">For every variable presents a constant form, which all its values possess, and which can be conceived as a formal property of these values.</div>
<div class="corelinks tlpdepth4"><strong>4.1272</strong><span class="linkarray tlpdepth4" id="p4.1272OGD"> OGD [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span></div>
<div class="para tlpdepth4">So the variable name “<span class="mathmode"><var>x</var></span>” is the proper sign of the pseudo-concept <em>object</em>.</div>
<div class="para tlpdepth4">Wherever the word “object” (“thing”, “entity”, etc.) is rightly used, it is expressed in logical symbolism by the variable name.</div>
<div class="para tlpdepth4">For example in the proposition “there are two objects which …”, by “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>)</span><span class="mathrel">…</span></span>”.</div>
<div class="para tlpdepth4">Wherever it is used otherwise, <em>i.e.</em> as a proper concept word, there arise senseless pseudo-propositions.</div>
<div class="para tlpdepth4">So one cannot, <em>e.g.</em> say “There are objects” as one says “There are books”. Nor “There are 100 objects” or “There are <span class="mathmode"><span class="symbol">ℵ</span><sub>0</sub></span> objects”.</div>
<div class="para tlpdepth4">And it is senseless to speak of the <em>number of all objects</em>.</div>
<div class="para tlpdepth4">The same holds of the words “Complex”, “Fact”, “Function”, “Number”, etc.</div>
<div class="para tlpdepth4">They all signify formal concepts and are presented in logical symbolism by variables, not by functions or classes (as Frege and Russell thought).</div>
<div class="para tlpdepth4">Expressions like “1 is a number”, “there is only one number nought”, and all like them are senseless.</div>
<div class="para tlpdepth4">(It is as senseless to say, “there is only one 1” as it would be to say: <span class="mathmode">2<span class="mathrel">+</span>2</span> is at 3 o’clock equal to 4.)</div>
<div class="corelinks tlpdepth5"><strong>4.12721</strong><span class="linkarray tlpdepth5" id="p4.12721OGD"> OGD [→<a class="gerlink" href="#p4.12721GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12721PM">P/M</a>]</span></div>
<div class="para tlpdepth5">The formal concept is already given with an object, which falls under it. One cannot, therefore, introduce both, the objects which fall under a formal concept <em>and</em> the formal concept itself, as primitive ideas. One cannot, therefore, <em>e.g.</em> introduce (as Russell does) the concept of function and also special functions as primitive ideas; or the concept of number and definite numbers.</div>
<div class="corelinks tlpdepth4"><strong>4.1273</strong><span class="linkarray tlpdepth4" id="p4.1273OGD"> OGD [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If we want to express in logical symbolism the general proposition “<span class="mathmode"><var>b</var></span> is a successor of <span class="mathmode"><var>a</var></span>” we need for this an expression for the general term of the formal series:</div>
<div class="para tlpdepth4"><div class="centered"><span class="mathmode"><var>aRb</var></span>,<br />
<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRb</var></span>,<br />
<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRy</var><span class="mathrel">.</span><var>yRb</var></span>,<br />
…&nbsp; .</div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> The general term of a formal series can only be expressed by a variable, for the concept symbolized by “term of this formal series” is a <em>formal</em> concept. (This Frege and Russell overlooked; the way in which they express general propositions like the above is, therefore, false; it contains a vicious circle.)</div>
<div class="para tlpdepth4">We can determine the general term of the formal series by giving its first term and the general form of the operation, which generates the following term out of the preceding proposition.</div>
<div class="corelinks tlpdepth4"><strong>4.1274</strong><span class="linkarray tlpdepth4" id="p4.1274OGD"> OGD [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The question about the existence of a formal concept is senseless. For no proposition can answer such a question.</div>
<div class="para tlpdepth4">(For example, one cannot ask: “Are there unanalysable subject-predicate propositions?”)</div>
<div class="corelinks tlpdepth3"><strong>4.128</strong><span class="linkarray tlpdepth3" id="p4.128OGD"> OGD [→<a class="gerlink" href="#p4.128GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The logical forms are <em>anumerical</em>.</div>
<div class="para tlpdepth3">Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc.</div>
<div class="corelinks tlpdepth1"><strong>4.2</strong><span class="linkarray tlpdepth1" id="p4.2OGD"> OGD [→<a class="gerlink" href="#p4.2GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of the atomic facts.</div>
<div class="corelinks tlpdepth2"><strong>4.21</strong><span class="linkarray tlpdepth2" id="p4.21OGD"> OGD [→<a class="gerlink" href="#p4.21GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The simplest proposition, the elementary proposition, asserts the existence of an atomic fact.</div>
<div class="corelinks tlpdepth3"><strong>4.211</strong><span class="linkarray tlpdepth3" id="p4.211OGD"> OGD [→<a class="gerlink" href="#p4.211GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.211PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is a sign of an elementary proposition, that no elementary proposition can contradict it.</div>
<div class="corelinks tlpdepth2"><strong>4.22</strong><span class="linkarray tlpdepth2" id="p4.22OGD"> OGD [→<a class="gerlink" href="#p4.22GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The elementary proposition consists of names. It is a connexion, a concatenation, of names.</div>
<div class="corelinks tlpdepth3"><strong>4.221</strong><span class="linkarray tlpdepth3" id="p4.221OGD"> OGD [→<a class="gerlink" href="#p4.221GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.221PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is obvious that in the analysis of propositions we must come to elementary propositions, which consist of names in immediate combination.</div>
<div class="para tlpdepth3">The question arises here, how the propositional connexion comes to be.</div>
<div class="corelinks tlpdepth4"><strong>4.2211</strong><span class="linkarray tlpdepth4" id="p4.2211OGD"> OGD [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Even if the world is infinitely complex, so that every fact consists of an infinite number of atomic facts and every atomic fact is composed of an infinite number of objects, even then there must be objects and atomic facts.</div>
<div class="corelinks tlpdepth2"><strong>4.23</strong><span class="linkarray tlpdepth2" id="p4.23OGD"> OGD [→<a class="gerlink" href="#p4.23GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.23PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The name occurs in the proposition only in the context of the elementary proposition.</div>
<div class="corelinks tlpdepth2"><strong>4.24</strong><span class="linkarray tlpdepth2" id="p4.24OGD"> OGD [→<a class="gerlink" href="#p4.24GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.24PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The names are the simple symbols, I indicate them by single letters (<span class="mathmode"><var>x</var></span>, <span class="mathmode"><var>y</var></span>, <span class="mathmode"><var>z</var></span>).</div>
<div class="para tlpdepth2">The elementary proposition I write as function of the names, in the form “<span class="mathmode"><var>fx</var></span>”, “<span class="mathmode"><var>φ</var>(<var>x</var>,<var>y</var>)</span>”, etc.</div>
<div class="para tlpdepth2">Or I indicate it by the letters <span class="mathmode"><var>p</var></span>, <span class="mathmode"><var>q</var></span>, <span class="mathmode"><var>r</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>4.241</strong><span class="linkarray tlpdepth3" id="p4.241OGD"> OGD [→<a class="gerlink" href="#p4.241GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If I use two signs with one and the same meaning, I express this by putting between them the sign “=”.</div>
<div class="para tlpdepth3">“<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span>” means then, that the sign “<span class="mathmode"><var>a</var></span>” is replaceable by the sign “<span class="mathmode"><var>b</var></span>”.</div>
<div class="para tlpdepth3">(If I introduce by an equation a new sign “<span class="mathmode"><var>b</var></span>”, by determining that it shall replace a previously known sign “<span class="mathmode"><var>a</var></span>”, I write the equation—definition—(like Russell) in the form “<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span> Def.”. A definition is a symbolic rule.)</div>
<div class="corelinks tlpdepth3"><strong>4.242</strong><span class="linkarray tlpdepth3" id="p4.242OGD"> OGD [→<a class="gerlink" href="#p4.242GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.242PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Expressions of the form “<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span>” are therefore only expedients in presentation: They assert nothing about the meaning of the signs “<span class="mathmode"><var>a</var></span>” and “<span class="mathmode"><var>b</var></span>”.</div>
<div class="corelinks tlpdepth3"><strong>4.243</strong><span class="linkarray tlpdepth3" id="p4.243OGD"> OGD [→<a class="gerlink" href="#p4.243GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Can we understand two names without knowing whether they signify the same thing or two different things? Can we understand a proposition in which two names occur, without knowing if they mean the same or different things?</div>
<div class="para tlpdepth3">If I know the meaning of an English and a synonymous German word, it is impossible for me not to know that they are synonymous, it is impossible for me not to be able to translate them into one another.</div>
<div class="para tlpdepth3">Expressions like “<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>”, or expressions deduced from these are neither elementary propositions nor otherwise significant signs. (This will be shown later.)</div>
<div class="corelinks tlpdepth2"><strong>4.25</strong><span class="linkarray tlpdepth2" id="p4.25OGD"> OGD [→<a class="gerlink" href="#p4.25GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.25PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If the elementary proposition is true, the atomic fact exists; if it is false the atomic fact does not exist.</div>
<div class="corelinks tlpdepth2"><strong>4.26</strong><span class="linkarray tlpdepth2" id="p4.26OGD"> OGD [→<a class="gerlink" href="#p4.26GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.26PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The specification of all true elementary propositions describes the world completely. The world is completely described by the specification of all elementary propositions plus the specification, which of them are true and which false.</div>
<div class="corelinks tlpdepth2"><strong>4.27</strong><span class="linkarray tlpdepth2" id="p4.27OGD"> OGD [→<a class="gerlink" href="#p4.27GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.27PM">P/M</a>]</span></div>
<div class="para tlpdepth2">With regard to the existence of <span class="mathmode"><var>n</var></span> atomic facts there are <table class="possibilities"><tr><td rowspan="3" class="middleright"><span class="mathmode">K<sub><var>n</var></sub> = </span></td><td class="summationtop"><span class="mathmode"><var class="smallvar">n</var></span></td><td rowspan="3" class="middleright"><span class="largeparen">(</span></td><td rowspan="3" class="middlecenter"><span class="mathmode"><var>n</var></span><br /><span class="mathmode"><var>ν</var></span></td><td rowspan="3" class="middleleft"><span class="largeparen">)</span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="largeop">∑</span></span></td></tr><tr><td class="summationbottom"><span class="mathmode"><span class="smallvar"><var>ν</var> = 0</span></span></td></tr></table> possibilities.</div>
<div class="para tlpdepth2">It is possible for all combinations of atomic facts to exist, and the others not to exist.</div>
<div class="corelinks tlpdepth2"><strong>4.28</strong><span class="linkarray tlpdepth2" id="p4.28OGD"> OGD [→<a class="gerlink" href="#p4.28GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.28PM">P/M</a>]</span></div>
<div class="para tlpdepth2">To these combinations correspond the same number of possibilities of the truth—and falsehood—of <span class="mathmode"><var>n</var></span> elementary propositions.</div>
<div class="corelinks tlpdepth1"><strong>4.3</strong><span class="linkarray tlpdepth1" id="p4.3OGD"> OGD [→<a class="gerlink" href="#p4.3GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.3PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The truth-possibilities of the elementary propositions mean the possibilities of the existence and non-existence of the atomic facts.</div>
<div class="corelinks tlpdepth2"><strong>4.31</strong><span class="linkarray tlpdepth2" id="p4.31OGD"> OGD [→<a class="gerlink" href="#p4.31GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.31PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The truth-possibilities can be presented by schemata of the following kind (“T” means “true”, “F” “false”. The rows of T’s and F’s under the row of the elementary propositions mean their truth-possibilities in an easily intelligible symbolism).</div>
<div class="para tlpdepth2"><div class="centered"><table class="truthtable"><tr><th class="l"><span class="mathmode"><var>p</var></span></th><th class="m"><span class="mathmode"><var>q</var></span></th><th class="e"><span class="mathmode"><var>r</var></span></th></tr><tr><td class="l">T</td><td class="m">T</td><td class="e">T</td></tr><tr><td class="l">F</td><td class="m">T</td><td class="e">T</td></tr><tr><td class="l">T</td><td class="m">F</td><td class="e">T</td></tr><tr><td class="l">T</td><td class="m">T</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="m">F</td><td class="e">T</td></tr><tr><td class="l">F</td><td class="m">T</td><td class="e">F</td></tr><tr><td class="l">T</td><td class="m">F</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="m">F</td><td class="e">F</td></tr></table><span class="padrthree"></span><table class="truthtable"><tr><th class="l"><span class="mathmode"><var>p</var></span></th><th class="e"><span class="mathmode"><var>q</var></span></th></tr><tr><td class="l">T</td><td class="e">T</td></tr><tr><td class="l">F</td><td class="e">T</td></tr><tr><td class="l">T</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="e">F</td></tr></table><span class="padrthree"></span><table class="truthtable"><tr><th class="e"><span class="mathmode"><var>p</var></span></th></tr><tr><td class="e">T</td></tr><tr><td class="e">F</td></tr></table></div></div>
<div class="corelinks tlpdepth1"><strong>4.4</strong><span class="linkarray tlpdepth1" id="p4.4OGD"> OGD [→<a class="gerlink" href="#p4.4GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4PM">P/M</a>]</span></div>
<div class="para tlpdepth1">A proposition is the expression of agreement and disagreement with the truth-possibilities of the elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>4.41</strong><span class="linkarray tlpdepth2" id="p4.41OGD"> OGD [→<a class="gerlink" href="#p4.41GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.41PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The truth-possibilities of the elementary propositions are the conditions of the truth and falsehood of the propositions.</div>
<div class="corelinks tlpdepth3"><strong>4.411</strong><span class="linkarray tlpdepth3" id="p4.411OGD"> OGD [→<a class="gerlink" href="#p4.411GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.411PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It seems probable even at first sight that the introduction of the elementary propositions is fundamental for the comprehension of the other kinds of propositions. Indeed the comprehension of the general propositions depends <em>palpably</em> on that of the elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>4.42</strong><span class="linkarray tlpdepth2" id="p4.42OGD"> OGD [→<a class="gerlink" href="#p4.42GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.42PM">P/M</a>]</span></div>
<div class="para tlpdepth2">With regard to the agreement and disagreement of a proposition with the truth-possibilities of <span class="mathmode"><var>n</var></span> elementary propositions there are <table class="possibilities"><tr><td class="summationtop"><span class="mathmode"><span class="smallvar">K<sub><var>n</var></sub></span></span></td><td class="middleright" rowspan="3"><span class="largeparen">(</span></td><td class="middlecenter" rowspan="3"><span class="mathode">K<sub><var>n</var></sub></span><br /><span class="mathmode"><var>κ</var></span></td><td class="middleright" rowspan="3"><span class="mathomde"><span class="largeparen">)</span> = L<sub><var>n</var></sub></span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="largeop">∑</span></span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="smallvar"><var>κ</var> = 0</span></span></td></tr></table> possibilities.</div>
<div class="corelinks tlpdepth2"><strong>4.43</strong><span class="linkarray tlpdepth2" id="p4.43OGD"> OGD [→<a class="gerlink" href="#p4.43GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.43PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Agreement with the truth-possibilities can be expressed by co-ordinating with them in the schema the mark “T” (true).</div>
<div class="para tlpdepth2">Absence of this mark means disagreement.</div>
<div class="corelinks tlpdepth3"><strong>4.431</strong><span class="linkarray tlpdepth3" id="p4.431OGD"> OGD [→<a class="gerlink" href="#p4.431GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The expression of the agreement and disagreement with the truth-possibilities of the elementary propositions expresses the truth-conditions of the proposition.</div>
<div class="para tlpdepth3">The proposition is the expression of its truth-conditions.</div>
<div class="para tlpdepth3">(Frege has therefore quite rightly put them at the beginning, as explaining the signs of his logical symbolism. Only Frege’s explanation of the truth-concept is false: if “the true” and “the false” were real objects and the arguments in <span class="mathmode"><span class="mathop">~</span><var>p</var></span>, etc., then the sense of <span class="mathmode"><span class="mathop">~</span><var>p</var></span> would by no means be determined by Frege’s determination.)</div>
<div class="corelinks tlpdepth2"><strong>4.44</strong><span class="linkarray tlpdepth2" id="p4.44OGD"> OGD [→<a class="gerlink" href="#p4.44GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.44PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The sign which arises from the co-ordination of that mark “T” with the truth-possibilities is a propositional sign.</div>
<div class="corelinks tlpdepth3"><strong>4.441</strong><span class="linkarray tlpdepth3" id="p4.441OGD"> OGD [→<a class="gerlink" href="#p4.441GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is clear that to the complex of the signs “F” and “T” no object (or complex of objects) corresponds; any more than to horizontal and vertical lines or to brackets. There are no “logical objects”.</div>
<div class="para tlpdepth3">Something analogous holds of course for all signs, which express the same as the schemata of “T” and “F”.</div>
<div class="corelinks tlpdepth3"><strong>4.442</strong><span class="linkarray tlpdepth3" id="p4.442OGD"> OGD [→<a class="gerlink" href="#p4.442GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Thus <em>e.g.</em></div>
<div class="para tlpdepth3 noindent"><!-- noindent --><div class="centered"><table class="truthtable"><tr><th>“</th><th class="l"><span class="mathmode"><var>p</var></span></th><th class="m"><span class="mathmode"><var>q</var></span></th><th class="e"></th><th></th></tr><tr><td></td><td class="l">T</td><td class="m">T</td><td class="e">T</td><td></td></tr><tr><td></td><td class="l">F</td><td class="m">T</td><td class="e">T</td><td></td></tr><tr><td></td><td class="l">T</td><td class="m">F</td><td class="e"></td><td></td></tr><tr><td></td><td class="l">F</td><td class="m">F</td><td class="e">T</td><td>”</td></tr></table></div></div>
<div class="para tlpdepth3 flushright"><!-- flushright --> is a propositional sign.</div>
<div class="para tlpdepth3">(Frege’s assertion sign “<span class="mathmode">⊢</span>” is logically altogether meaningless; in Frege (and Russell) it only shows that these authors hold as true the propositions marked in this way. “<span class="mathmode">⊢</span>” belongs therefore to the propositions no more than does the number of the proposition. A proposition cannot possibly assert of itself that it is true.)</div>
<div class="para tlpdepth3">If the sequence of the truth-possibilities in the schema is once for all determined by a rule of combination, then the last column is by itself an expression of the truth-conditions. If we write this column as a row the propositional sign becomes:</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode"> “<span class="mathop">(<span class="mathrm">TT–T</span>)</span>&nbsp; (<var>p</var>, <var>q</var>)”, </span></div><span class="mathmode"></span></div>
<div class="para tlpdepth3 noindent"><!-- noindent --> or more plainly:</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode">“<span class="mathop">(<span class="mathrm">TTFT</span>)</span>&nbsp; (<var>p</var>, <var>q</var>)”.</span></div><span class="mathmode"></span></div>
<div class="para tlpdepth3">(The number of places in the left-hand bracket is determined by the number of terms in the right-hand bracket.)</div>
<div class="corelinks tlpdepth2"><strong>4.45</strong><span class="linkarray tlpdepth2" id="p4.45OGD"> OGD [→<a class="gerlink" href="#p4.45GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.45PM">P/M</a>]</span></div>
<div class="para tlpdepth2">For <span class="mathmode"><var>n</var></span> elementary propositions there are <span class="mathmode"><span class="mathrm">L</span><sub><var>n</var></sub></span> possible groups of truth-conditions.</div>
<div class="para tlpdepth2">The groups of truth-conditions which belong to the truth-possibilities of a number of elementary propositions can be ordered in a series.</div>
<div class="corelinks tlpdepth2"><strong>4.46</strong><span class="linkarray tlpdepth2" id="p4.46OGD"> OGD [→<a class="gerlink" href="#p4.46GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Among the possible groups of truth-conditions there are two extreme cases.</div>
<div class="para tlpdepth2">In the one case the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are <em>tautological</em>.</div>
<div class="para tlpdepth2">In the second case the proposition is false for all the truth-possibilities. The truth-conditions are <em>self-contradictory</em>.</div>
<div class="para tlpdepth2">In the first case we call the proposition a tautology, in the second case a contradiction.</div>
<div class="corelinks tlpdepth3"><strong>4.461</strong><span class="linkarray tlpdepth3" id="p4.461OGD"> OGD [→<a class="gerlink" href="#p4.461GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The proposition shows what it says, the tautology and the contradiction that they say nothing.</div>
<div class="para tlpdepth3">The tautology has no truth-conditions, for it is unconditionally true; and the contradiction is on no condition true.</div>
<div class="para tlpdepth3">Tautology and contradiction are without sense.</div>
<div class="para tlpdepth3">(Like the point from which two arrows go out in opposite directions.)</div>
<div class="para tlpdepth3">(I know, <em>e.g.</em> nothing about the weather, when I know that it rains or does not rain.)</div>
<div class="corelinks tlpdepth4"><strong>4.4611</strong><span class="linkarray tlpdepth4" id="p4.4611OGD"> OGD [→<a class="gerlink" href="#p4.4611GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4611PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Tautology and contradiction are, however, not nonsensical; they are part of the symbolism, in the same way that “0” is part of the symbolism of Arithmetic.</div>
<div class="corelinks tlpdepth3"><strong>4.462</strong><span class="linkarray tlpdepth3" id="p4.462OGD"> OGD [→<a class="gerlink" href="#p4.462GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Tautology and contradiction are not pictures of the reality. They present no possible state of affairs. For the one allows <em>every</em> possible state of affairs, the other <em>none</em>.</div>
<div class="para tlpdepth3">In the tautology the conditions of agreement with the world—the presenting relations—cancel one another, so that it stands in no presenting relation to reality.</div>
<div class="corelinks tlpdepth3"><strong>4.463</strong><span class="linkarray tlpdepth3" id="p4.463OGD"> OGD [→<a class="gerlink" href="#p4.463GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The truth-conditions determine the range, which is left to the facts by the proposition.</div>
<div class="para tlpdepth3">(The proposition, the picture, the model, are in a negative sense like a solid body, which restricts the free movement of another: in a positive sense, like the space limited by solid substance, in which a body may be placed.)</div>
<div class="para tlpdepth3">Tautology leaves to reality the whole infinite logical space; contradiction fills the whole logical space and leaves no point to reality. Neither of them, therefore, can in any way determine reality.</div>
<div class="corelinks tlpdepth3"><strong>4.464</strong><span class="linkarray tlpdepth3" id="p4.464OGD"> OGD [→<a class="gerlink" href="#p4.464GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.464PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The truth of tautology is certain, of propositions possible, of contradiction impossible.</div>
<div class="para tlpdepth3">(Certain, possible, impossible: here we have an indication of that gradation which we need in the theory of probability.)</div>
<div class="corelinks tlpdepth3"><strong>4.465</strong><span class="linkarray tlpdepth3" id="p4.465OGD"> OGD [→<a class="gerlink" href="#p4.465GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.465PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The logical product of a tautology and a proposition says the same as the proposition. Therefore that product is identical with the proposition. For the essence of the symbol cannot be altered without altering its sense.</div>
<div class="corelinks tlpdepth3"><strong>4.466</strong><span class="linkarray tlpdepth3" id="p4.466OGD"> OGD [→<a class="gerlink" href="#p4.466GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span></div>
<div class="para tlpdepth3">To a definite logical combination of signs corresponds a definite logical combination of their meanings; <em>every arbitrary</em> combination only corresponds to the unconnected signs.</div>
<div class="para tlpdepth3">That is, propositions which are true for every state of affairs cannot be combinations of signs at all, for otherwise there could only correspond to them definite combinations of objects.</div>
<div class="para tlpdepth3">(And to no logical combination corresponds <em>no</em> combination of the objects.)</div>
<div class="para tlpdepth3">Tautology and contradiction are the limiting cases of the combination of symbols, namely their dissolution.</div>
<div class="corelinks tlpdepth4"><strong>4.4661</strong><span class="linkarray tlpdepth4" id="p4.4661OGD"> OGD [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Of course the signs are also combined with one another in the tautology and contradiction, <em>i.e.</em> they stand in relations to one another, but these relations are meaningless, unessential to the <em>symbol</em>.</div>
<div class="corelinks tlpdepth1"><strong>4.5</strong><span class="linkarray tlpdepth1" id="p4.5OGD"> OGD [→<a class="gerlink" href="#p4.5GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Now it appears to be possible to give the most general form of proposition; <em>i.e.</em> to give a description of the propositions of some one sign language, so that every possible sense can be expressed by a symbol, which falls under the description, and so that every symbol which falls under the description can express a sense, if the meanings of the names are chosen accordingly.</div>
<div class="para tlpdepth1">It is clear that in the description of the most general form of proposition <em>only</em> what is essential to it may be described—otherwise it would not be the most general form.</div>
<div class="para tlpdepth1">That there is a general form is proved by the fact that there cannot be a proposition whose form could not have been foreseen (<em>i.e.</em> constructed). The general form of proposition is: Such and such is the case.</div>
<div class="corelinks tlpdepth2"><strong>4.51</strong><span class="linkarray tlpdepth2" id="p4.51OGD"> OGD [→<a class="gerlink" href="#p4.51GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.51PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Suppose <em>all</em> elementary propositions were given me: then we can simply ask: what propositions I can build out of them. And these are <em>all</em> propositions and <em>so</em> are they limited.</div>
<div class="corelinks tlpdepth2"><strong>4.52</strong><span class="linkarray tlpdepth2" id="p4.52OGD"> OGD [→<a class="gerlink" href="#p4.52GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.52PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The propositions are everything which follows from the totality of all elementary propositions (of course also from the fact that it is the <em>totality of them all</em>). (So, in some sense, one could say, that <em>all</em> propositions are generalizations of the elementary propositions.)</div>
<div class="corelinks tlpdepth2"><strong>4.53</strong><span class="linkarray tlpdepth2" id="p4.53OGD"> OGD [→<a class="gerlink" href="#p4.53GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.53PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The general proposition form is a variable.</div>
<div class="corelinks tlpdepth0"><strong>5</strong><span class="linkarray tlpdepth0" id="p5OGD"> OGD [→<a class="gerlink" href="#p5GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Propositions are truth-functions of elementary propositions.</div>
<div class="para tlpdepth0">(An elementary proposition is a truth-function of itself.)</div>
<div class="corelinks tlpdepth2"><strong>5.01</strong><span class="linkarray tlpdepth2" id="p5.01OGD"> OGD [→<a class="gerlink" href="#p5.01GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The elementary propositions are the truth-arguments of propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.02</strong><span class="linkarray tlpdepth2" id="p5.02OGD"> OGD [→<a class="gerlink" href="#p5.02GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">It is natural to confuse the arguments of functions with the indices of names. For I recognize the meaning of the sign containing it from the argument just as much as from the index.</div>
<div class="para tlpdepth2">In Russell’s “<span class="mathmode"><span class="mathrel">+</span><sub><var>c</var></sub></span>”, for example, “<span class="mathmode"><sub><var>c</var></sub></span>” is an index which indicates that the whole sign is the addition sign for cardinal numbers. But this way of symbolizing depends on arbitrary agreement, and one could choose a simple sign instead of “<span class="mathmode"><span class="mathrel">+</span><sub><var>c</var></sub></span>”: but in “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” “<span class="mathmode"><var>p</var></span>” is not an index but an argument; the sense of “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” <em>cannot</em> be understood, unless the sense of “<span class="mathmode"><var>p</var></span>” has previously been understood. (In the name Julius Cæsar, Julius is an index. The index is always part of a description of the object to whose name we attach it, <em>e.g.</em> <em>The</em> Cæsar of the Julian gens.)</div>
<div class="para tlpdepth2">The confusion of argument and index is, if I am not mistaken, at the root of Frege’s theory of the meaning of propositions and functions. For Frege the propositions of logic were names and their arguments the indices of these names.</div>
<div class="corelinks tlpdepth1"><strong>5.1</strong><span class="linkarray tlpdepth1" id="p5.1OGD"> OGD [→<a class="gerlink" href="#p5.1GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The truth-functions can be ordered in series.</div>
<div class="para tlpdepth1">That is the foundation of the theory of probability.</div>
<div class="corelinks tlpdepth3"><strong>5.101</strong><span class="linkarray tlpdepth3" id="p5.101OGD"> OGD [→<a class="gerlink" href="#p5.101GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The truth-functions of every number of elementary propositions can be written in a schema of the following kind:</div>
<div class="para tlpdepth3 noindent"><!-- noindent --><table class="fnlist"> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >Tautology&nbsp;</td><td >(if <span class="mathmode"><var>p</var></span> then <span class="mathmode"><var>p</var></span>; and if <span class="mathmode"><var>q</var></span> then <span class="mathmode"><var>q</var></span>) &nbsp;&nbsp; <span class="mathmode">[<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var><span class="mathrel">.</span><var>q</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >in&nbsp;words:&nbsp;</td><td >Not both <span class="mathmode"><var>p</var></span> and <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">[<span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><var>q</var>)]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >If <span class="mathmode"><var>q</var></span> then <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">[<var>q</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >If <span class="mathmode"><var>p</var></span> then <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">[<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">[<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Not <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">[<span class="mathop">~</span><var>q</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Not <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">[<span class="mathop">~</span><var>p</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>, but not both. &nbsp;&nbsp; <span class="mathmode">[<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var><span class="mathrel">:<span class="symbol">∨</span>:</span><var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >If <span class="mathmode"><var>p</var></span>, then <span class="mathmode"><var>q</var></span>; and if <span class="mathmode"><var>q</var></span>, then <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">[<var>p</var><span class="mathrel"><span class="symbol">≡</span></span><var>q</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>q</var></span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td >Neither <span class="mathmode"><var>p</var></span> nor <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">[<span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var></span> or <span class="mathmode"><var>p</var><span class="mathrel">|</span><var>q</var>]</span></td></tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span> and not <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">[<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>q</var></span> and not <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">[<var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”</td><td ><span class="mathmode"><var>p</var></span> and <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">[<var>p</var><span class="mathrel">.</span><var>q</var>]</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" colspan="2">Contradiction (<span class="mathmode"><var>p</var></span> and not <span class="mathmode"><var>p</var></span>; and <span class="mathmode"><var>q</var></span> and not <span class="mathmode"><var>q</var></span>.) &nbsp;&nbsp; <span class="mathmode">[<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>]</span></td></tr></table></div>
<div class="para tlpdepth3">Those truth-possibilities of its truth-arguments, which verify the proposition, I shall call its <em>truth-grounds</em>.</div>
<div class="corelinks tlpdepth2"><strong>5.11</strong><span class="linkarray tlpdepth2" id="p5.11OGD"> OGD [→<a class="gerlink" href="#p5.11GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If the truth-grounds which are common to a number of propositions are all also truth-grounds of some one proposition, we say that the truth of this proposition follows from the truth of those propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.12</strong><span class="linkarray tlpdepth2" id="p5.12OGD"> OGD [→<a class="gerlink" href="#p5.12GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In particular the truth of a proposition <span class="mathmode"><var>p</var></span> follows from that of a proposition <span class="mathmode"><var>q</var></span>, if all the truth-grounds of the second are truth-grounds of the first.</div>
<div class="corelinks tlpdepth3"><strong>5.121</strong><span class="linkarray tlpdepth3" id="p5.121OGD"> OGD [→<a class="gerlink" href="#p5.121GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.121PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The truth-grounds of <span class="mathmode"><var>q</var></span> are contained in those of <span class="mathmode"><var>p</var></span>; <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.122</strong><span class="linkarray tlpdepth3" id="p5.122OGD"> OGD [→<a class="gerlink" href="#p5.122GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.122PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span>, the sense of “<span class="mathmode"><var>p</var></span>” is contained in that of “<span class="mathmode"><var>q</var></span>”.</div>
<div class="corelinks tlpdepth3"><strong>5.123</strong><span class="linkarray tlpdepth3" id="p5.123OGD"> OGD [→<a class="gerlink" href="#p5.123GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.123PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If a god creates a world in which certain propositions are true, he creates thereby also a world in which all propositions consequent on them are true. And similarly he could not create a world in which the proposition “<span class="mathmode"><var>p</var></span>” is true without creating all its objects.</div>
<div class="corelinks tlpdepth3"><strong>5.124</strong><span class="linkarray tlpdepth3" id="p5.124OGD"> OGD [→<a class="gerlink" href="#p5.124GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.124PM">P/M</a>]</span></div>
<div class="para tlpdepth3">A proposition asserts every proposition which follows from it.</div>
<div class="corelinks tlpdepth4"><strong>5.1241</strong><span class="linkarray tlpdepth4" id="p5.1241OGD"> OGD [→<a class="gerlink" href="#p5.1241GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1241PM">P/M</a>]</span></div>
<div class="para tlpdepth4">“<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>q</var></span>” is one of the propositions which assert “<span class="mathmode"><var>p</var></span>” and at the same time one of the propositions which assert “<span class="mathmode"><var>q</var></span>”.</div>
<div class="para tlpdepth4">Two propositions are opposed to one another if there is no significant proposition which asserts them both.</div>
<div class="para tlpdepth4">Every proposition which contradicts another, denies it.</div>
<div class="corelinks tlpdepth2"><strong>5.13</strong><span class="linkarray tlpdepth2" id="p5.13OGD"> OGD [→<a class="gerlink" href="#p5.13GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">That the truth of one proposition follows from the truth of other propositions, we perceive from the structure of the propositions.</div>
<div class="corelinks tlpdepth3"><strong>5.131</strong><span class="linkarray tlpdepth3" id="p5.131OGD"> OGD [→<a class="gerlink" href="#p5.131GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If the truth of one proposition follows from the truth of others, this expresses itself in relations in which the forms of these propositions stand to one another, and we do not need to put them in these relations first by connecting them with one another in a proposition; for these relations are internal, and exist as soon as, and by the very fact that, the propositions exist.</div>
<div class="corelinks tlpdepth4"><strong>5.1311</strong><span class="linkarray tlpdepth4" id="p5.1311OGD"> OGD [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span></div>
<div class="para tlpdepth4">When we conclude from <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span> and <span class="mathmode"><span class="mathop">~</span><var>p</var></span> to <span class="mathmode"><var>q</var></span> the relation between the forms of the propositions “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>” and “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” is here concealed by the method of symbolizing. But if we write, <em>e.g.</em> instead of “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>” “<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>q</var><span class="mathrel">.|.</span><var>p</var><span class="mathrel">|</span><var>q</var></span>” and instead of “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” “<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>p</var></span>” (<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>q</var></span> = neither <span class="mathmode"><var>p</var></span> nor <span class="mathmode"><var>q</var></span>), then the inner connexion becomes obvious.</div>
<div class="para tlpdepth4">(The fact that we can infer <span class="mathmode"><var>fa</var></span> from <span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span> shows that generality is present also in the symbol “<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>”.</div>
<div class="corelinks tlpdepth3"><strong>5.132</strong><span class="linkarray tlpdepth3" id="p5.132OGD"> OGD [→<a class="gerlink" href="#p5.132GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.132PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span>, I can conclude from <span class="mathmode"><var>q</var></span> to <span class="mathmode"><var>p</var></span>; infer <span class="mathmode"><var>p</var></span> from <span class="mathmode"><var>q</var></span>.</div>
<div class="para tlpdepth3">The method of inference is to be understood from the two propositions alone.</div>
<div class="para tlpdepth3">Only they themselves can justify the inference.</div>
<div class="para tlpdepth3">Laws of inference, which—as in Frege and Russell—are to justify the conclusions, are senseless and would be superfluous.</div>
<div class="corelinks tlpdepth3"><strong>5.133</strong><span class="linkarray tlpdepth3" id="p5.133OGD"> OGD [→<a class="gerlink" href="#p5.133GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.133PM">P/M</a>]</span></div>
<div class="para tlpdepth3">All inference takes place a priori.</div>
<div class="corelinks tlpdepth3"><strong>5.134</strong><span class="linkarray tlpdepth3" id="p5.134OGD"> OGD [→<a class="gerlink" href="#p5.134GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.134PM">P/M</a>]</span></div>
<div class="para tlpdepth3">From an elementary proposition no other can be inferred.</div>
<div class="corelinks tlpdepth3"><strong>5.135</strong><span class="linkarray tlpdepth3" id="p5.135OGD"> OGD [→<a class="gerlink" href="#p5.135GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.135PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In no way can an inference be made from the existence of one state of affairs to the existence of another entirely different from it.</div>
<div class="corelinks tlpdepth3"><strong>5.136</strong><span class="linkarray tlpdepth3" id="p5.136OGD"> OGD [→<a class="gerlink" href="#p5.136GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.136PM">P/M</a>]</span></div>
<div class="para tlpdepth3">There is no causal nexus which justifies such an inference.</div>
<div class="corelinks tlpdepth4"><strong>5.1361</strong><span class="linkarray tlpdepth4" id="p5.1361OGD"> OGD [→<a class="gerlink" href="#p5.1361GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1361PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The events of the future <em>cannot</em> be inferred from those of the present.</div>
<div class="para tlpdepth4">Superstition is the belief in the causal nexus.</div>
<div class="corelinks tlpdepth4"><strong>5.1362</strong><span class="linkarray tlpdepth4" id="p5.1362OGD"> OGD [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The freedom of the will consists in the fact that future actions cannot be known now. We could only know them if causality were an <em>inner</em> necessity, like that of logical deduction.—The connexion of knowledge and what is known is that of logical necessity.</div>
<div class="para tlpdepth4">(“A knows that <span class="mathmode"><var>p</var></span> is the case” is senseless if <span class="mathmode"><var>p</var></span> is a tautology.)</div>
<div class="corelinks tlpdepth4"><strong>5.1363</strong><span class="linkarray tlpdepth4" id="p5.1363OGD"> OGD [→<a class="gerlink" href="#p5.1363GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1363PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If from the fact that a proposition is obvious to us it does not <em>follow</em> that it is true, then obviousness is no justification for our belief in its truth.</div>
<div class="corelinks tlpdepth2"><strong>5.14</strong><span class="linkarray tlpdepth2" id="p5.14OGD"> OGD [→<a class="gerlink" href="#p5.14GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.14PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If a proposition follows from another, then the latter says more than the former, the former less than the latter.</div>
<div class="corelinks tlpdepth3"><strong>5.141</strong><span class="linkarray tlpdepth3" id="p5.141OGD"> OGD [→<a class="gerlink" href="#p5.141GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.141PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span> and <span class="mathmode"><var>q</var></span> from <span class="mathmode"><var>p</var></span> then they are one and the same proposition.</div>
<div class="corelinks tlpdepth3"><strong>5.142</strong><span class="linkarray tlpdepth3" id="p5.142OGD"> OGD [→<a class="gerlink" href="#p5.142GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.142PM">P/M</a>]</span></div>
<div class="para tlpdepth3">A tautology follows from all propositions: it says nothing.</div>
<div class="corelinks tlpdepth3"><strong>5.143</strong><span class="linkarray tlpdepth3" id="p5.143OGD"> OGD [→<a class="gerlink" href="#p5.143GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.143PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Contradiction is something shared by propositions, which <em>no</em> proposition has in common with another. Tautology is that which is shared by all propositions, which have nothing in common with one another.</div>
<div class="para tlpdepth3">Contradiction vanishes so to speak outside, tautology inside all propositions.</div>
<div class="para tlpdepth3">Contradiction is the external limit of the propositions, tautology their substanceless centre.</div>
<div class="corelinks tlpdepth2"><strong>5.15</strong><span class="linkarray tlpdepth2" id="p5.15OGD"> OGD [→<a class="gerlink" href="#p5.15GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.15PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If <span class="mathmode"><span class="mathrm">T</span><sub><var>r</var></sub></span> is the number of the truth-grounds of the proposition “<span class="mathmode"><var>r</var></span>”, <span class="mathmode"><span class="mathrm">T</span><sub><var>rs</var></sub></span> the number of those truth-grounds of the proposition “<span class="mathmode"><var>s</var></span>” which are at the same time truth-grounds of “<span class="mathmode"><var>r</var></span>”, then we call the ratio <span class="mathmode"><span class="mathrm">T</span><sub><var>rs</var></sub> : <span class="mathrm">T</span><sub><var>r</var></sub></span> the measure of the <em>probability</em> which the proposition “<span class="mathmode"><var>r</var></span>” gives to the proposition “<span class="mathmode"><var>s</var></span>”.</div>
<div class="corelinks tlpdepth3"><strong>5.151</strong><span class="linkarray tlpdepth3" id="p5.151OGD"> OGD [→<a class="gerlink" href="#p5.151GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.151PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Suppose in a schema like that above in No. 5.101 <span class="mathmode"><span class="mathrm">T</span><sub><var>r</var></sub></span> is the number of the “T” ’s in the proposition <span class="mathmode"><var>r</var></span>, <span class="mathmode"><span class="mathrm">T</span><sub><var>rs</var></sub></span> the number of those “T” ’s in the proposition <span class="mathmode"><var>s</var></span>, which stand in the same columns as “T” ’s of the proposition <span class="mathmode"><var>r</var></span>; then the proposition <span class="mathmode"><var>r</var></span> gives to the proposition <span class="mathmode"><var>s</var></span> the probability <span class="mathmode"><span class="mathrm">T</span><sub><var>rs</var></sub> : <span class="mathrm">T</span><sub><var>r</var></sub></span>.</div>
<div class="corelinks tlpdepth4"><strong>5.1511</strong><span class="linkarray tlpdepth4" id="p5.1511OGD"> OGD [→<a class="gerlink" href="#p5.1511GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1511PM">P/M</a>]</span></div>
<div class="para tlpdepth4">There is no special object peculiar to probability propositions.</div>
<div class="corelinks tlpdepth3"><strong>5.152</strong><span class="linkarray tlpdepth3" id="p5.152OGD"> OGD [→<a class="gerlink" href="#p5.152GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Propositions which have no truth-arguments in common with one another we call independent.</div>
<div class="para tlpdepth3">Independent propositions (<em>e.g.</em> any two elementary propositions) give to one another the probability <span class="mathmode">½</span>.</div>
<div class="para tlpdepth3">If <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span>, the proposition <span class="mathmode"><var>q</var></span> gives to the proposition <span class="mathmode"><var>p</var></span> the probability 1. The certainty of logical conclusion is a limiting case of probability.</div>
<div class="para tlpdepth3">(Application to tautology and contradiction.)</div>
<div class="corelinks tlpdepth3"><strong>5.153</strong><span class="linkarray tlpdepth3" id="p5.153OGD"> OGD [→<a class="gerlink" href="#p5.153GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.153PM">P/M</a>]</span></div>
<div class="para tlpdepth3">A proposition is in itself neither probable nor improbable. An event occurs or does not occur, there is no middle course.</div>
<div class="corelinks tlpdepth3"><strong>5.154</strong><span class="linkarray tlpdepth3" id="p5.154OGD"> OGD [→<a class="gerlink" href="#p5.154GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.154PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In an urn there are equal numbers of white and black balls (and no others). I draw one ball after another and put them back in the urn. Then I can determine by the experiment that the numbers of the black and white balls which are drawn approximate as the drawing continues.</div>
<div class="para tlpdepth3">So <em>this</em> is not a mathematical fact.</div>
<div class="para tlpdepth3">If then, I say, It is equally probable that I should draw a white and a black ball, this means, All the circumstances known to me (including the natural laws hypothetically assumed) give to the occurrence of the one event no more probability than to the occurrence of the other. That is they give—as can easily be understood from the above explanations—to each the probability <span class="mathmode">½</span>.</div>
<div class="para tlpdepth3">What I can verify by the experiment is that the occurrence of the two events is independent of the circumstances with which I have no closer acquaintance.</div>
<div class="corelinks tlpdepth3"><strong>5.155</strong><span class="linkarray tlpdepth3" id="p5.155OGD"> OGD [→<a class="gerlink" href="#p5.155GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.155PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The unit of the probability proposition is: The circumstances—with which I am not further acquainted—give to the occurrence of a definite event such and such a degree of probability.</div>
<div class="corelinks tlpdepth3"><strong>5.156</strong><span class="linkarray tlpdepth3" id="p5.156OGD"> OGD [→<a class="gerlink" href="#p5.156GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Probability is a generalization.</div>
<div class="para tlpdepth3">It involves a general description of a propositional form.</div>
<div class="para tlpdepth3">Only in default of certainty do we need probability. If we are not completely acquainted with a fact, but know <em>something</em> about its form.</div>
<div class="para tlpdepth3">(A proposition can, indeed, be an incomplete picture of a certain state of affairs, but it is always <em>a</em> complete picture.)</div>
<div class="para tlpdepth3">The probability proposition is, as it were, an extract from other propositions.</div>
<div class="corelinks tlpdepth1"><strong>5.2</strong><span class="linkarray tlpdepth1" id="p5.2OGD"> OGD [→<a class="gerlink" href="#p5.2GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The structures of propositions stand to one another in internal relations.</div>
<div class="corelinks tlpdepth2"><strong>5.21</strong><span class="linkarray tlpdepth2" id="p5.21OGD"> OGD [→<a class="gerlink" href="#p5.21GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">We can bring out these internal relations in our manner of expression, by presenting a proposition as the result of an operation which produces it from other propositions (the bases of the operation).</div>
<div class="corelinks tlpdepth2"><strong>5.22</strong><span class="linkarray tlpdepth2" id="p5.22OGD"> OGD [→<a class="gerlink" href="#p5.22GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The operation is the expression of a relation between the structures of its result and its bases.</div>
<div class="corelinks tlpdepth2"><strong>5.23</strong><span class="linkarray tlpdepth2" id="p5.23OGD"> OGD [→<a class="gerlink" href="#p5.23GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.23PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The operation is that which must happen to a proposition in order to make another out of it.</div>
<div class="corelinks tlpdepth3"><strong>5.231</strong><span class="linkarray tlpdepth3" id="p5.231OGD"> OGD [→<a class="gerlink" href="#p5.231GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.231PM">P/M</a>]</span></div>
<div class="para tlpdepth3">And that will naturally depend on their formal properties, on the internal similarity of their forms.</div>
<div class="corelinks tlpdepth3"><strong>5.232</strong><span class="linkarray tlpdepth3" id="p5.232OGD"> OGD [→<a class="gerlink" href="#p5.232GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.232PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The internal relation which orders a series is equivalent to the operation by which one term arises from another.</div>
<div class="corelinks tlpdepth3"><strong>5.233</strong><span class="linkarray tlpdepth3" id="p5.233OGD"> OGD [→<a class="gerlink" href="#p5.233GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.233PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The first place in which an operation can occur is where a proposition arises from another in a logically significant way; <em>i.e.</em> where the logical construction of the proposition begins.</div>
<div class="corelinks tlpdepth3"><strong>5.234</strong><span class="linkarray tlpdepth3" id="p5.234OGD"> OGD [→<a class="gerlink" href="#p5.234GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.234PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The truth-functions of elementary proposition, are results of operations which have the elementary propositions as bases. (I call these operations, truth-operations.)</div>
<div class="corelinks tlpdepth4"><strong>5.2341</strong><span class="linkarray tlpdepth4" id="p5.2341OGD"> OGD [→<a class="gerlink" href="#p5.2341GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2341PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The sense of a truth-function of <span class="mathmode"><var>p</var></span> is a function of the sense of <span class="mathmode"><var>p</var></span>.</div>
<div class="para tlpdepth4">Denial, logical addition, logical multiplication, etc., etc., are operations.</div>
<div class="para tlpdepth4">(Denial reverses the sense of a proposition.)</div>
<div class="corelinks tlpdepth2"><strong>5.24</strong><span class="linkarray tlpdepth2" id="p5.24OGD"> OGD [→<a class="gerlink" href="#p5.24GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span></div>
<div class="para tlpdepth2">An operation shows itself in a variable; it shows how we can proceed from one form of proposition to another.</div>
<div class="para tlpdepth2">It gives expression to the difference between the forms.</div>
<div class="para tlpdepth2">(And that which is common the the bases, and the result of an operation, is the bases themselves.)</div>
<div class="corelinks tlpdepth3"><strong>5.241</strong><span class="linkarray tlpdepth3" id="p5.241OGD"> OGD [→<a class="gerlink" href="#p5.241GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.241PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The operation does not characterize a form but only the difference between forms.</div>
<div class="corelinks tlpdepth3"><strong>5.242</strong><span class="linkarray tlpdepth3" id="p5.242OGD"> OGD [→<a class="gerlink" href="#p5.242GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.242PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The same operation which makes “<span class="mathmode"><var>q</var></span>” from “<span class="mathmode"><var>p</var></span>”, makes “<span class="mathmode"><var>r</var></span>” from “<span class="mathmode"><var>q</var></span>”, and so on. This can only be expressed by the fact that “<span class="mathmode"><var>p</var></span>”, “<span class="mathmode"><var>q</var></span>”, “<span class="mathmode"><var>r</var></span>”, etc., are variables which give general expression to certain formal relations.</div>
<div class="corelinks tlpdepth2"><strong>5.25</strong><span class="linkarray tlpdepth2" id="p5.25OGD"> OGD [→<a class="gerlink" href="#p5.25GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.25PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The occurrence of an operation does not characterize the sense of a proposition.</div>
<div class="para tlpdepth2">For an operation does not assert anything; only its result does, and this depends on the bases of the operation.</div>
<div class="para tlpdepth2">(Operation and function must not be confused with one another.)</div>
<div class="corelinks tlpdepth3"><strong>5.251</strong><span class="linkarray tlpdepth3" id="p5.251OGD"> OGD [→<a class="gerlink" href="#p5.251GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.251PM">P/M</a>]</span></div>
<div class="para tlpdepth3">A function cannot be its own argument, but the result of an operation can be its own basis.</div>
<div class="corelinks tlpdepth3"><strong>5.252</strong><span class="linkarray tlpdepth3" id="p5.252OGD"> OGD [→<a class="gerlink" href="#p5.252GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Only in this way is the progress from term to term in a formal series possible (from type to type in the hierarchy of Russell and Whitehead). (Russell and Whitehead have not admitted the possibility of this progress but have made use of it all the same.)</div>
<div class="corelinks tlpdepth4"><strong>5.2521</strong><span class="linkarray tlpdepth4" id="p5.2521OGD"> OGD [→<a class="gerlink" href="#p5.2521GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2521PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The repeated application of an operation to its own result I call its successive application (“<span class="mathmode"><span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><var>a</var></span>” is the result of the threefold successive application of “<span class="mathmode"><span class="mathop"><span class="mathrm">O</span>’</span><var>ξ</var></span>” to “<span class="mathmode"><var>a</var></span>”).</div>
<div class="para tlpdepth4">In a similar sense I speak of the successive application of <em>several</em> operations to a number of propositions.</div>
<div class="corelinks tlpdepth4"><strong>5.2522</strong><span class="linkarray tlpdepth4" id="p5.2522OGD"> OGD [→<a class="gerlink" href="#p5.2522GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2522PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The general term of the formal series <span class="mathmode"><var>a</var>, <span class="mathop"><span class="mathrm">O</span>’</span><var>a</var>, <span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><var>a</var>,<span class="mathrel">…</span></span>. I write thus: “<span class="mathmode">[<var>a</var>, <var>x</var>, <span class="mathop"><span class="mathrm">O</span>’</span><var>x</var>]</span>”. This expression in brackets is a variable. The first term of the expression is the beginning of the formal series, the second the form of an arbitrary term <span class="mathmode"><var>x</var></span> of the series, and the third the form of that term of the series which immediately follows <span class="mathmode"><var>x</var></span>.</div>
<div class="corelinks tlpdepth4"><strong>5.2523</strong><span class="linkarray tlpdepth4" id="p5.2523OGD"> OGD [→<a class="gerlink" href="#p5.2523GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2523PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The concept of the successive application of an operation is equivalent to the concept “and so on”.</div>
<div class="corelinks tlpdepth3"><strong>5.253</strong><span class="linkarray tlpdepth3" id="p5.253OGD"> OGD [→<a class="gerlink" href="#p5.253GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.253PM">P/M</a>]</span></div>
<div class="para tlpdepth3">One operation can reverse the effect of another. Operations can cancel one another.</div>
<div class="corelinks tlpdepth3"><strong>5.254</strong><span class="linkarray tlpdepth3" id="p5.254OGD"> OGD [→<a class="gerlink" href="#p5.254GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.254PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Operations can vanish (<em>e.g.</em> denial in “<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>”. <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var><span class="mathrel">=</span><var>p</var></span>).</div>
<div class="corelinks tlpdepth1"><strong>5.3</strong><span class="linkarray tlpdepth1" id="p5.3OGD"> OGD [→<a class="gerlink" href="#p5.3GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.3PM">P/M</a>]</span></div>
<div class="para tlpdepth1">All propositions are results of truth-operations on the elementary propositions.</div>
<div class="para tlpdepth1">The truth-operation is the way in which a truth-function arises from elementary propositions.</div>
<div class="para tlpdepth1">According to the nature of truth-operations, in the same way as out of elementary propositions arise their truth-functions, from truth-functions arises a new one. Every truth-operation creates from truth-functions of elementary propositions, another truth-function of elementary propositions <em>i.e.</em> a proposition. The result of every truth-operation on the results of truth-operations on elementary propositions is also the result of <em>one</em> truth-operation on elementary propositions.</div>
<div class="para tlpdepth1">Every proposition is the result of truth-operations on elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.31</strong><span class="linkarray tlpdepth2" id="p5.31OGD"> OGD [→<a class="gerlink" href="#p5.31GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.31PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The Schemata No. 4.31 are also significant, if “<span class="mathmode"><var>p</var></span>”, “<span class="mathmode"><var>q</var></span>”, “<span class="mathmode"><var>r</var></span>”, etc. are not elementary propositions.</div>
<div class="para tlpdepth2">And it is easy to see that the propositional sign in No. 4.442 expresses one truth-function of elementary propositions even when “<span class="mathmode"><var>p</var></span>” and “<span class="mathmode"><var>q</var></span>” are truth-functions of elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.32</strong><span class="linkarray tlpdepth2" id="p5.32OGD"> OGD [→<a class="gerlink" href="#p5.32GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.32PM">P/M</a>]</span></div>
<div class="para tlpdepth2">All truth-functions are results of the successive application of a finite number of truth-operations to elementary propositions.</div>
<div class="corelinks tlpdepth1"><strong>5.4</strong><span class="linkarray tlpdepth1" id="p5.4OGD"> OGD [→<a class="gerlink" href="#p5.4GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Here it becomes clear that there are no such things as “logical objects” or “logical constants” (in the sense of Frege and Russell).</div>
<div class="corelinks tlpdepth2"><strong>5.41</strong><span class="linkarray tlpdepth2" id="p5.41OGD"> OGD [→<a class="gerlink" href="#p5.41GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.41PM">P/M</a>]</span></div>
<div class="para tlpdepth2">For all those results of truth-operations on truth-functions are identical, which are one and the same truth-function of elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.42</strong><span class="linkarray tlpdepth2" id="p5.42OGD"> OGD [→<a class="gerlink" href="#p5.42GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span></div>
<div class="para tlpdepth2">That ∨, ⊃, etc., are not relations in the sense of right and left, etc., is obvious.</div>
<div class="para tlpdepth2">The possibility of crosswise definition of the logical “primitive signs” of Frege and Russell shows by itself that these are not primitive signs and that they signify no relations.</div>
<div class="para tlpdepth2">And it is obvious that the “⊃” which we define by means of “~” and “∨” is identical with that by which we define “∨” with the help of “~”, and that this “∨” is the same as the first, and so on.</div>
<div class="corelinks tlpdepth2"><strong>5.43</strong><span class="linkarray tlpdepth2" id="p5.43OGD"> OGD [→<a class="gerlink" href="#p5.43GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span></div>
<div class="para tlpdepth2">That from a fact <span class="mathmode"><var>p</var></span> an infinite number of <em>others</em> should follow, namely, <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>, <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>, etc., is indeed hardly to be believed, and it is no less wonderful that the infinite number of propositions of logic (of mathematics) should follow from half a dozen “primitive propositions”.</div>
<div class="para tlpdepth2">But the propositions of logic say the same thing. That is, nothing.</div>
<div class="corelinks tlpdepth2"><strong>5.44</strong><span class="linkarray tlpdepth2" id="p5.44OGD"> OGD [→<a class="gerlink" href="#p5.44GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Truth-functions are not material functions.</div>
<div class="para tlpdepth2">If <em>e.g.</em> an affirmation can be produced by repeated denial, is the denial—in any sense—contained in the affirmation? Does “<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>” deny <span class="mathmode"><span class="mathop">~</span><var>p</var></span>, or does it affirm <span class="mathmode"><var>p</var></span>; or both?</div>
<div class="para tlpdepth2">The proposition “<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>” does not treat of denial as an object, but the possibility of denial is already prejudged in affirmation.</div>
<div class="para tlpdepth2">And if there was an object called “~”, then “<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>” would have to say something other than “<span class="mathmode"><var>p</var></span>”. For the one proposition would then treat of ~, the other would not.</div>
<div class="corelinks tlpdepth3"><strong>5.441</strong><span class="linkarray tlpdepth3" id="p5.441OGD"> OGD [→<a class="gerlink" href="#p5.441GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.441PM">P/M</a>]</span></div>
<div class="para tlpdepth3">This disappearance of the apparent logical constants also occurs if “<span class="mathmode"><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><span class="mathop">~</span><var>fx</var></span>” says the same as “<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>”, or “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>a</var></span>” the same as “<span class="mathmode"><var>fa</var></span>”.</div>
<div class="corelinks tlpdepth3"><strong>5.442</strong><span class="linkarray tlpdepth3" id="p5.442OGD"> OGD [→<a class="gerlink" href="#p5.442GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.442PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If a proposition is given to us then the results of all truth-operations which have it as their basis are given <em>with</em> it.</div>
<div class="corelinks tlpdepth2"><strong>5.45</strong><span class="linkarray tlpdepth2" id="p5.45OGD"> OGD [→<a class="gerlink" href="#p5.45GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.45PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If there are logical primitive signs a correct logic must make clear their position relative to one another and justify their existence. The construction of logic <em>out of</em> its primitive signs must become clear.</div>
<div class="corelinks tlpdepth3"><strong>5.451</strong><span class="linkarray tlpdepth3" id="p5.451OGD"> OGD [→<a class="gerlink" href="#p5.451GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If logic has primitive ideas these must be independent of one another. If a primitive idea is introduced it must be introduced in all contexts in which it occurs at all. One cannot therefore introduce it for <em>one</em> context and then again for another. For example, if denial is introduced, we must understand it in propositions of the form “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>”, just as in propositions like “<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var>)</span>”, “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><span class="mathop">~</span><var>fx</var></span>” and others. We may not first introduce it for one class of cases and then for another, for it would then remain doubtful whether its meaning in the two cases was the same, and there would be no reason to use the same way of symbolizing in the two cases.</div>
<div class="para tlpdepth3">(In short, what Frege (“Grundgesetze der Arithmetik”) has said about the introduction of signs by definitions holds, mutatis mutandis, for the introduction of primitive signs also.)</div>
<div class="corelinks tlpdepth3"><strong>5.452</strong><span class="linkarray tlpdepth3" id="p5.452OGD"> OGD [→<a class="gerlink" href="#p5.452GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The introduction of a new expedient in the symbolism of logic must always be an event full of consequences. No new symbol may be introduced in logic in brackets or in the margin—with, so to speak, an entirely innocent face.</div>
<div class="para tlpdepth3">(Thus in the “Principia Mathematica” of Russell and Whitehead there occur definitions and primitive propositions in words. Why suddenly words here? This would need a justification. There was none, and can be none for the process is actually not allowed.)</div>
<div class="para tlpdepth3">But if the introduction of a new expedient has proved necessary in one place, we must immediately ask: Where is this expedient <em>always</em> to be used? Its position in logic must be made clear.</div>
<div class="corelinks tlpdepth3"><strong>5.453</strong><span class="linkarray tlpdepth3" id="p5.453OGD"> OGD [→<a class="gerlink" href="#p5.453GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.453PM">P/M</a>]</span></div>
<div class="para tlpdepth3">All numbers in logic must be capable of justification.</div>
<div class="para tlpdepth3">Or rather it must become plain that there are no numbers in logic.</div>
<div class="para tlpdepth3">There are no pre-eminent numbers.</div>
<div class="corelinks tlpdepth3"><strong>5.454</strong><span class="linkarray tlpdepth3" id="p5.454OGD"> OGD [→<a class="gerlink" href="#p5.454GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.454PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In logic there is no side by side, there can be no classification.</div>
<div class="para tlpdepth3">In logic there cannot be a more general and a more special.</div>
<div class="corelinks tlpdepth4"><strong>5.4541</strong><span class="linkarray tlpdepth4" id="p5.4541OGD"> OGD [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The solution of logical problems must be neat for they set the standard of neatness.</div>
<div class="para tlpdepth4">Men have always thought that there must be a sphere of questions whose answers—a priori—are symmetrical and united into a closed regular structure.</div>
<div class="para tlpdepth4">A sphere in which the proposition, simplex sigillum veri, is valid.</div>
<div class="corelinks tlpdepth2"><strong>5.46</strong><span class="linkarray tlpdepth2" id="p5.46OGD"> OGD [→<a class="gerlink" href="#p5.46GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span></div>
<div class="para tlpdepth2">When we have rightly introduced the logical signs, the sense of all their combinations has been already introduced with them: therefore not only “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>” but also “<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>q</var>)</span>”, etc. etc. We should then already have introduced the effect of all possible combinations of brackets; and it would then have become clear that the proper general primitive signs are not “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>”, “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>”, etc., but the most general form of their combinations.</div>
<div class="corelinks tlpdepth3"><strong>5.461</strong><span class="linkarray tlpdepth3" id="p5.461OGD"> OGD [→<a class="gerlink" href="#p5.461GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The apparently unimportant fact that the apparent relations like ∨ and ⊃ need brackets—unlike real relations—is of great importance.</div>
<div class="para tlpdepth3">The use of brackets with these apparent primitive signs shows that these are not the real primitive signs; and nobody of course would believe that the brackets have meaning by themselves.</div>
<div class="corelinks tlpdepth4"><strong>5.4611</strong><span class="linkarray tlpdepth4" id="p5.4611OGD"> OGD [→<a class="gerlink" href="#p5.4611GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4611PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Logical operation signs are punctuations.</div>
<div class="corelinks tlpdepth2"><strong>5.47</strong><span class="linkarray tlpdepth2" id="p5.47OGD"> OGD [→<a class="gerlink" href="#p5.47GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span></div>
<div class="para tlpdepth2">It is clear that everything which can be said <em>beforehand</em> about the form of <em>all</em> propositions at all can be said <em>on one occasion</em>.</div>
<div class="para tlpdepth2">For all logical operations are already contained in the elementary proposition. For “<span class="mathmode"><var>fa</var></span>” says the same as</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode">“<span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>a</var>”.</span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">Where there is composition, there is argument and function, and where these are, all logical constants already are.</div>
<div class="para tlpdepth2">One could say: the one logical constant is that which <em>all</em> propositions, according to their nature, have in common with one another.</div>
<div class="para tlpdepth2">That however is the general form of proposition.</div>
<div class="corelinks tlpdepth3"><strong>5.471</strong><span class="linkarray tlpdepth3" id="p5.471OGD"> OGD [→<a class="gerlink" href="#p5.471GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.471PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The general form of proposition is the essence of proposition.</div>
<div class="corelinks tlpdepth4"><strong>5.4711</strong><span class="linkarray tlpdepth4" id="p5.4711OGD"> OGD [→<a class="gerlink" href="#p5.4711GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4711PM">P/M</a>]</span></div>
<div class="para tlpdepth4">To give the essence of proposition means to give the essence of all description, therefore the essence of the world.</div>
<div class="corelinks tlpdepth3"><strong>5.472</strong><span class="linkarray tlpdepth3" id="p5.472OGD"> OGD [→<a class="gerlink" href="#p5.472GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.472PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The description of the most general propositional form is the description of the one and only general primitive sign in logic.</div>
<div class="corelinks tlpdepth3"><strong>5.473</strong><span class="linkarray tlpdepth3" id="p5.473OGD"> OGD [→<a class="gerlink" href="#p5.473GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Logic must take care of itself.</div>
<div class="para tlpdepth3">A <em>possible</em> sign must also be able to signify. Everything which is possible in logic is also permitted. (“Socrates is identical” means nothing because there is no property which is called “identical”. The proposition is senseless because we have not made some arbitrary determination, not because the symbol is in itself unpermissible.)</div>
<div class="para tlpdepth3">In a certain sense we cannot make mistakes in logic.</div>
<div class="corelinks tlpdepth4"><strong>5.4731</strong><span class="linkarray tlpdepth4" id="p5.4731OGD"> OGD [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Self-evidence, of which Russell has said so much, can only be discard in logic by language itself preventing every logical mistake. That logic is a priori consists in the fact that we <em>cannot</em> think illogically.</div>
<div class="corelinks tlpdepth4"><strong>5.4732</strong><span class="linkarray tlpdepth4" id="p5.4732OGD"> OGD [→<a class="gerlink" href="#p5.4732GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4732PM">P/M</a>]</span></div>
<div class="para tlpdepth4">We cannot give a sign the wrong sense.</div>
<div class="corelinks tlpdepth5"><strong>5.47321</strong><span class="linkarray tlpdepth5" id="p5.47321OGD"> OGD [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span></div>
<div class="para tlpdepth5">Occam’s razor is, of course, not an arbitrary rule nor one justified by its practical success. It simply says that <em>unnecessary</em> elements in a symbolism mean nothing.</div>
<div class="para tlpdepth5">Signs which serve <em>one</em> purpose are logically equivalent, signs
which serve <em>no</em> purpose are logically meaningless.</div>
<div class="corelinks tlpdepth4"><strong>5.4733</strong><span class="linkarray tlpdepth4" id="p5.4733OGD"> OGD [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Frege says: Every legitimately constructed proposition must have a sense; and I say: Every possible proposition is legitimately constructed, and if it has no sense this can only be because we have given no <em>meaning</em> to some of its constituent parts.</div>
<div class="para tlpdepth4">(Even if we believe that we have done so.)</div>
<div class="para tlpdepth4">Thus “Socrates is identical” says nothing, because we have given <em>no</em> meaning to the word “identical” as <em>adjective</em>. For when it occurs as the sign of equality it symbolizes in an entirely different way—the symbolizing relation is another—therefore the symbol is in the two cases entirely different; the two symbols have the sign in common with one another only by accident.</div>
<div class="corelinks tlpdepth3"><strong>5.474</strong><span class="linkarray tlpdepth3" id="p5.474OGD"> OGD [→<a class="gerlink" href="#p5.474GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.474PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The number of necessary fundamental operations depends <em>only</em> on our notation.</div>
<div class="corelinks tlpdepth3"><strong>5.475</strong><span class="linkarray tlpdepth3" id="p5.475OGD"> OGD [→<a class="gerlink" href="#p5.475GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.475PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is only a question of constructing a system of signs of a definite number of dimensions—of a definite mathematical multiplicity.</div>
<div class="corelinks tlpdepth3"><strong>5.476</strong><span class="linkarray tlpdepth3" id="p5.476OGD"> OGD [→<a class="gerlink" href="#p5.476GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.476PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is clear that we are not concerned here with a <em>number of primitive ideas</em> which must be signified but with the expression of a rule.</div>
<div class="corelinks tlpdepth1"><strong>5.5</strong><span class="linkarray tlpdepth1" id="p5.5OGD"> OGD [→<a class="gerlink" href="#p5.5GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Every truth-function is a result of the successive application of the operation <span class="mathmode"><span class="mathop">(−−−−−<span class="mathrm">T</span>)</span> (<var>ξ</var>,&nbsp;.&nbsp;.&nbsp;.&nbsp;.&nbsp;.)</span> to elementary propositions.</div>
<div class="para tlpdepth1">This operation denies all the propositions in the right-hand bracket and I call it the negation of these propositions.</div>
<div class="corelinks tlpdepth3"><strong>5.501</strong><span class="linkarray tlpdepth3" id="p5.501OGD"> OGD [→<a class="gerlink" href="#p5.501GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span></div>
<div class="para tlpdepth3">An expression in brackets whose terms are propositions I indicate—if the order of the terms in the bracket is indifferent—by a sign of the form “<span class="mathmode">(<span class="overlined"><var>ξ</var></span>)</span>”. “<span class="mathmode"><var>ξ</var></span>” is a variable whose values are the terms of the expression in brackets, and the line over the variable indicates that it stands for all its values in the bracket.</div>
<div class="para tlpdepth3">(Thus if <span class="mathmode"><var>ξ</var></span> has the 3 values P, Q, R, then <span class="mathmode">(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span>(<span class="mathrm">P</span>, <span class="mathrm">Q</span>, <span class="mathrm">R</span>)</span>.)</div>
<div class="para tlpdepth3">The values of the variables must be determined.</div>
<div class="para tlpdepth3">The determination is the description of the propositions which the variable stands for.</div>
<div class="para tlpdepth3">How the description of the terms of the expression in brackets takes place is unessential.</div>
<div class="para tlpdepth3">We may distinguish 3 kinds of description: 1. Direct enumeration. In this case we can place simply its constant values instead of the variable. 2. Giving a function <span class="mathmode"><var>fx</var></span>, whose values for all values of <span class="mathmode"><var>x</var></span> are the propositions to be described. 3. Giving a formal law, according to which those propositions are constructed. In this case the terms of the expression in brackets are all the terms of a formal series.</div>
<div class="corelinks tlpdepth3"><strong>5.502</strong><span class="linkarray tlpdepth3" id="p5.502OGD"> OGD [→<a class="gerlink" href="#p5.502GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.502PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Therefore I write instead of “<span class="mathmode"><span class="mathop">(−−−−−<span class="mathrm">T</span>)</span></span> <span class="mathmode">(<var>ξ</var>,&nbsp;.&nbsp;.&nbsp;.&nbsp;.&nbsp;.)</span>”, “<span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)</span>”.</div>
<div class="para tlpdepth3"><span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)</span> is the negation of all the values of the propositional variable <span class="mathmode"><var>ξ</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.503</strong><span class="linkarray tlpdepth3" id="p5.503OGD"> OGD [→<a class="gerlink" href="#p5.503GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.503PM">P/M</a>]</span></div>
<div class="para tlpdepth3">As it is obviously easy to express how propositions can be constructed by means of this operation and how propositions are not to be constructed by means of it, this must be capable of exact expression.</div>
<div class="corelinks tlpdepth2"><strong>5.51</strong><span class="linkarray tlpdepth2" id="p5.51OGD"> OGD [→<a class="gerlink" href="#p5.51GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.51PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If <span class="mathmode"><var>ξ</var></span> has only one value, then <span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><var>p</var></span> (not <span class="mathmode"><var>p</var></span>), if it has two values then <span class="mathmode"><span class="nop">N</span> (<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var></span> (neither <span class="mathmode"><var>p</var></span> nor <span class="mathmode"><var>q</var></span>).</div>
<div class="corelinks tlpdepth3"><strong>5.511</strong><span class="linkarray tlpdepth3" id="p5.511OGD"> OGD [→<a class="gerlink" href="#p5.511GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.511PM">P/M</a>]</span></div>
<div class="para tlpdepth3">How can the all-embracing logic which mirrors the world use such special catches and manipulations? Only because all these are connected into an infinitely fine network, to the great mirror.</div>
<div class="corelinks tlpdepth3"><strong>5.512</strong><span class="linkarray tlpdepth3" id="p5.512OGD"> OGD [→<a class="gerlink" href="#p5.512GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span></div>
<div class="para tlpdepth3">“<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” is true if “<span class="mathmode"><var>p</var></span>” is false. Therefore in the true proposition “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” “<span class="mathmode"><var>p</var></span>” is a false proposition. How then can the stroke “~” bring it into agreement with reality?</div>
<div class="para tlpdepth3">That which denies in “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” is however not “~”, but that which all signs of this notation, which deny <span class="mathmode"><var>p</var></span>, have in common.</div>
<div class="para tlpdepth3">Hence the common rule according to which “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>”, “<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>”, “<span class="mathmode"><span class="mathop">~</span><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>”, “<span class="mathmode"><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var></span>”, etc. etc. (to infinity) are constructed. And this which is common to them all mirrors denial.</div>
<div class="corelinks tlpdepth3"><strong>5.513</strong><span class="linkarray tlpdepth3" id="p5.513OGD"> OGD [→<a class="gerlink" href="#p5.513GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span></div>
<div class="para tlpdepth3">We could say: What is common to all symbols, which assert both <span class="mathmode"><var>p</var></span> and <span class="mathmode"><var>q</var></span>, is the proposition “<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>q</var></span>”. What is common to all symbols, which asserts either <span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>, is the proposition “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>”.</div>
<div class="para tlpdepth3">And similarly we can say: Two propositions are opposed to one another when they have nothing in common with one another; and every proposition has only one negative, because there is only one proposition which lies altogether outside it.</div>
<div class="para tlpdepth3">Thus in Russell’s notation also it appears evident that “<span class="mathmode"><var>q</var><span class="mathrel">:</span><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>” says the same thing as “<span class="mathmode"><var>q</var></span>”; that “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>” says nothing.</div>
<div class="corelinks tlpdepth3"><strong>5.514</strong><span class="linkarray tlpdepth3" id="p5.514OGD"> OGD [→<a class="gerlink" href="#p5.514GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If a notation is fixed, there is in it a rule according to which all the propositions denying <span class="mathmode"><var>p</var></span> are constructed, a rule according to which all the propositions asserting <span class="mathmode"><var>p</var></span> are constructed, a rule according to which all the propositions asserting <span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span> are constructed, and so on. These rules are equivalent to the symbols and in them their sense is mirrored.</div>
<div class="corelinks tlpdepth3"><strong>5.515</strong><span class="linkarray tlpdepth3" id="p5.515OGD"> OGD [→<a class="gerlink" href="#p5.515GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It must be recognized in our symbols that what is connected by “∨”, “.”, etc., must be propositions.</div>
<div class="para tlpdepth3">And this is the case, for the symbols “<span class="mathmode"><var>p</var></span>” and “<span class="mathmode"><var>q</var></span>” presuppose “∨”, “~”, etc. If the sign “<span class="mathmode"><var>p</var></span>” in “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>” does not stand for a complex sign, then by itself it cannot have sense; but then also the signs “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>p</var></span>”, “<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>p</var></span>”, etc. which have the same sense as “<span class="mathmode"><var>p</var></span>” have no sense. If, however, “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>p</var></span>” has no sense, then also “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>” can have no sense.</div>
<div class="corelinks tlpdepth4"><strong>5.5151</strong><span class="linkarray tlpdepth4" id="p5.5151OGD"> OGD [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Must the sign of the negative proposition be constructed by means of the sign of the positive? Why should one not be able to express the negative proposition by means of a negative fact? (Like: if “<span class="mathmode"><var>a</var></span>” does not stand in a certain relation to “<span class="mathmode"><var>b</var></span>”, it could express that <span class="mathmode"><var>aRb</var></span> is not the case.)</div>
<div class="para tlpdepth4">But here also the negative proposition is indirectly constructed with the positive.</div>
<div class="para tlpdepth4">The positive <em>proposition</em> must presuppose the existence of the negative <em>proposition</em> and conversely.</div>
<div class="corelinks tlpdepth2"><strong>5.52</strong><span class="linkarray tlpdepth2" id="p5.52OGD"> OGD [→<a class="gerlink" href="#p5.52GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.52PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If the values of <span class="mathmode"><var>ξ</var></span> are the total values of a function <span class="mathmode"><var>fx</var></span> for all values of <span class="mathmode"><var>x</var></span>, then <span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.521</strong><span class="linkarray tlpdepth3" id="p5.521OGD"> OGD [→<a class="gerlink" href="#p5.521GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span></div>
<div class="para tlpdepth3">I separate the concept <em>all</em> from the truth-function.</div>
<div class="para tlpdepth3">Frege and Russell have introduced generality in connexion with the logical product or the logical sum. Then it would be difficult to understand the propositions “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>” and “<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>” in which both ideas lie concealed.</div>
<div class="corelinks tlpdepth3"><strong>5.522</strong><span class="linkarray tlpdepth3" id="p5.522OGD"> OGD [→<a class="gerlink" href="#p5.522GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.522PM">P/M</a>]</span></div>
<div class="para tlpdepth3">That which is peculiar to the “symbolism of generality” is firstly, that it refers to a logical prototype, and secondly, that it makes constants prominent.</div>
<div class="corelinks tlpdepth3"><strong>5.523</strong><span class="linkarray tlpdepth3" id="p5.523OGD"> OGD [→<a class="gerlink" href="#p5.523GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.523PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The generality symbol occurs as an argument.</div>
<div class="corelinks tlpdepth3"><strong>5.524</strong><span class="linkarray tlpdepth3" id="p5.524OGD"> OGD [→<a class="gerlink" href="#p5.524GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.524PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If the objects are given, therewith are <em>all</em> objects also given.</div>
<div class="para tlpdepth3">If the elementary propositions are given, then therewith <em>all</em> elementary propositions are also given.</div>
<div class="corelinks tlpdepth3"><strong>5.525</strong><span class="linkarray tlpdepth3" id="p5.525OGD"> OGD [→<a class="gerlink" href="#p5.525GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is not correct to render the proposition “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>”—as Russell does—in the words “<span class="mathmode"><var>fx</var></span> is <em>possible</em>”.</div>
<div class="para tlpdepth3">Certainty, possibility or impossibility of a state of affairs are not expressed by a proposition but by the fact that an expression is a tautology, a significant proposition or a contradiction.</div>
<div class="para tlpdepth3">That precedent to which one would always appeal, must be present in the symbol itself.</div>
<div class="corelinks tlpdepth3"><strong>5.526</strong><span class="linkarray tlpdepth3" id="p5.526OGD"> OGD [→<a class="gerlink" href="#p5.526GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span></div>
<div class="para tlpdepth3">One can describe the world completely by completely generalized propositions, <em>i.e.</em> without from the outset co-ordinating any name with a definite object.</div>
<div class="para tlpdepth3">In order then to arrive at the customary way of expression we need simply say after an expression “there is one and only one <span class="mathmode"><var>x</var></span>, which …”: and this <span class="mathmode"><var>x</var></span> is <span class="mathmode"><var>a</var></span>.</div>
<div class="corelinks tlpdepth4"><strong>5.5261</strong><span class="linkarray tlpdepth4" id="p5.5261OGD"> OGD [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span></div>
<div class="para tlpdepth4">A completely generalized proposition is like every other proposition composite. (This is shown by the fact that in “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>, <var>φ</var>).</span><var>φx</var></span>” we must mention “<span class="mathmode"><var>φ</var></span>” and “<span class="mathmode"><var>x</var></span>” separately. Both stand independently in signifying relations to the world as in the ungeneralized proposition.)</div>
<div class="para tlpdepth4">A characteristic of a composite symbol: it has something in common with <em>other</em> symbols.</div>
<div class="corelinks tlpdepth4"><strong>5.5262</strong><span class="linkarray tlpdepth4" id="p5.5262OGD"> OGD [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The truth or falsehood of <em>every</em> proposition alters something in the general structure of the world. And the range which is allowed to its structure by the totality of elementary propositions is exactly that which the completely general propositions delimit.</div>
<div class="para tlpdepth4">(If an elementary proposition is true, then, at any rate, there is one <em>more</em> elementary proposition true.)</div>
<div class="corelinks tlpdepth2"><strong>5.53</strong><span class="linkarray tlpdepth2" id="p5.53OGD"> OGD [→<a class="gerlink" href="#p5.53GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.53PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Identity of the object I express by identity of the sign and not by means of a sign of identity. Difference of the objects by difference of the signs.</div>
<div class="corelinks tlpdepth4"><strong>5.5301</strong><span class="linkarray tlpdepth4" id="p5.5301OGD"> OGD [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span></div>
<div class="para tlpdepth4">That identity is not a relation between objects is obvious. This becomes very clear if, for example, one considers the proposition “<span class="mathmode"><span class="quant">(<var>x</var>):</span><var>fx</var><span class="mathrel">.<span class="symbol">⊃</span>.</span><var>x</var><span class="mathrel">=</span><var>a</var></span>”. What this proposition says is simply that <em>only</em> <span class="mathmode"><var>a</var></span> satisfies the function <span class="mathmode"><var>f</var></span>, and not that only such things satisfy the function <span class="mathmode"><var>f</var></span> which have a certain relation to <span class="mathmode"><var>a</var></span>.</div>
<div class="para tlpdepth4">One could of course say that in fact <em>only</em> <span class="mathmode"><var>a</var></span> has this relation to <span class="mathmode"><var>a</var></span>, but in order to express this we should need the sign of identity itself.</div>
<div class="corelinks tlpdepth4"><strong>5.5302</strong><span class="linkarray tlpdepth4" id="p5.5302OGD"> OGD [→<a class="gerlink" href="#p5.5302GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5302PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Russell’s definition of “=” won’t do; because according to it one cannot say that two objects have all their properties in common. (Even if this proposition is never true, it is nevertheless <em>significant</em>.)</div>
<div class="corelinks tlpdepth4"><strong>5.5303</strong><span class="linkarray tlpdepth4" id="p5.5303OGD"> OGD [→<a class="gerlink" href="#p5.5303GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5303PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Roughly speaking: to say of <em>two</em> things that they are identical is nonsense, and to say of <em>one</em> thing that it is identical with itself is to say nothing.</div>
<div class="corelinks tlpdepth3"><strong>5.531</strong><span class="linkarray tlpdepth3" id="p5.531OGD"> OGD [→<a class="gerlink" href="#p5.531GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.531PM">P/M</a>]</span></div>
<div class="para tlpdepth3">I write therefore not “<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)<span class="mathrel">.</span><var>a</var><span class="mathrel">=</span><var>b</var></span>” but “<span class="mathmode"><var>f</var>(<var>a</var>,<var>a</var>)</span>” (or “<span class="mathmode"><var>f</var>(<var>b</var>,<var>b</var>)</span>”). And not “<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)<span class="mathrel">.</span><span class="mathop">~</span><var>a</var><span class="mathrel">=</span><var>b</var></span>”, but “<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)</span>”.</div>
<div class="corelinks tlpdepth3"><strong>5.532</strong><span class="linkarray tlpdepth3" id="p5.532OGD"> OGD [→<a class="gerlink" href="#p5.532GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.532PM">P/M</a>]</span></div>
<div class="para tlpdepth3">And analogously: not “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>y</var></span>”, but “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>f</var>(<var>x</var>,<var>x</var>)</span>”; and not “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.</span><span class="mathop">~</span><var>x</var><span class="mathrel">=</span><var>y</var></span>”, but “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)</span>”.</div>
<div class="para tlpdepth3">(Therefore instead of Russell’s “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span></span> <span class="mathmode"><var>f</var>(<var>x</var>,<var>y</var>)</span>”: “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.<span class="symbol">∨</span>.</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>f</var>(<var>x</var>,<var>x</var>)</span>”.)</div>
<div class="corelinks tlpdepth4"><strong>5.5321</strong><span class="linkarray tlpdepth4" id="p5.5321OGD"> OGD [→<a class="gerlink" href="#p5.5321GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5321PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Instead of “<span class="mathmode"><span class="quant">(<var>x</var>):</span><var>fx</var><span class="mathrel"><span class="symbol">⊃</span></span><var>x</var><span class="mathrel">=</span><var>a</var></span>” we therefore write <em>e.g.</em> “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.<span class="symbol">⊃</span>.</span><var>fa</var><span class="mathrel">:</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>fx</var><span class="mathrel">.</span><var>fy</var></span>”.</div>
<div class="para tlpdepth4">And if the proposition “<em>only</em> one <span class="mathmode"><var>x</var></span> satisfies <span class="mathmode"><var>f</var>(&nbsp;)</span>” reads: “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">:</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>fx</var><span class="mathrel">.</span><var>fy</var></span>”.</div>
<div class="corelinks tlpdepth3"><strong>5.533</strong><span class="linkarray tlpdepth3" id="p5.533OGD"> OGD [→<a class="gerlink" href="#p5.533GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.533PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The identity sign is therefore not an essential constituent of logical notation.</div>
<div class="corelinks tlpdepth3"><strong>5.534</strong><span class="linkarray tlpdepth3" id="p5.534OGD"> OGD [→<a class="gerlink" href="#p5.534GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.534PM">P/M</a>]</span></div>
<div class="para tlpdepth3">And we see that the apparent propositions like: “<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>”, “<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var><span class="mathrel">.</span><var>b</var><span class="mathrel">=</span><var>c</var><span class="mathrel">.<span class="symbol">⊃</span></span><var>a</var><span class="mathrel">=</span><var>c</var></span>”, “<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>x</var></span>”. “<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>a</var></span>”, etc. cannot be written in a correct logical notation at all.</div>
<div class="corelinks tlpdepth3"><strong>5.535</strong><span class="linkarray tlpdepth3" id="p5.535OGD"> OGD [→<a class="gerlink" href="#p5.535GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span></div>
<div class="para tlpdepth3">So all problems disappear which are connected with such pseudo-propositions.</div>
<div class="para tlpdepth3">This is the place to solve all the problems with arise through Russell’s “Axiom of Infinity”.</div>
<div class="para tlpdepth3">What the axiom of infinity is meant to say would be expressed in language by the fact that there is an infinite number of names with different meanings.</div>
<div class="corelinks tlpdepth4"><strong>5.5351</strong><span class="linkarray tlpdepth4" id="p5.5351OGD"> OGD [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span></div>
<div class="para tlpdepth4">There are certain cases in which one is tempted to use expressions of the form “<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>” or “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span>”. As, for instance, when one would speak of the archetype Proposition, Thing, etc. So Russell in the <em>Principles of Mathematics</em> has rendered the nonsense “<span class="mathmode"><var>p</var></span> is a proposition” in symbols by “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span>” and has put it as hypothesis before certain propositions to show that their places for arguments could only be occupied by propositions.</div>
<div class="para tlpdepth4">(It is nonsense to place the hypothesis <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span> before a proposition in order to ensure that its arguments have the right form, because the hypotheses for a non-proposition as argument becomes not false but meaningless, and because the proposition itself becomes senseless for arguments of the wrong kind, and therefore it survives the wrong arguments no better and no worse than the senseless hypothesis attached for this purpose.)</div>
<div class="corelinks tlpdepth4"><strong>5.5352</strong><span class="linkarray tlpdepth4" id="p5.5352OGD"> OGD [→<a class="gerlink" href="#p5.5352GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5352PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Similarly it was proposed to express “There are no things” by “<span class="mathmode"><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>x</var></span>”. But even if this were a proposition—would it not be true if indeed “There were things”, but these were not identical with themselves?</div>
<div class="corelinks tlpdepth2"><strong>5.54</strong><span class="linkarray tlpdepth2" id="p5.54OGD"> OGD [→<a class="gerlink" href="#p5.54GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.54PM">P/M</a>]</span></div>
<div class="para tlpdepth2">In the general propositional form, propositions occur in a proposition only as bases of the truth-operations.</div>
<div class="corelinks tlpdepth3"><strong>5.541</strong><span class="linkarray tlpdepth3" id="p5.541OGD"> OGD [→<a class="gerlink" href="#p5.541GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span></div>
<div class="para tlpdepth3">At first sight it appears as if there were also a different way in which one proposition could occur in another.</div>
<div class="para tlpdepth3">Especially in certain propositional forms of psychology, like “A thinks, that <span class="mathmode"><var>p</var></span> is the case”, or “A thinks <span class="mathmode"><var>p</var></span>”, etc.</div>
<div class="para tlpdepth3">Here it appears superficially as if the proposition <span class="mathmode"><var>p</var></span> stood to the object A in a kind of relation.</div>
<div class="para tlpdepth3">(And in modern epistemology (Russell, Moore, etc.) those propositions have been conceived in this way.)</div>
<div class="corelinks tlpdepth3"><strong>5.542</strong><span class="linkarray tlpdepth3" id="p5.542OGD"> OGD [→<a class="gerlink" href="#p5.542GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span></div>
<div class="para tlpdepth3">But it is clear that “A believes that <span class="mathmode"><var>p</var></span>”, “A thinks <span class="mathmode"><var>p</var></span>”, “A says <span class="mathmode"><var>p</var></span>”, are of the form “‘<span class="mathmode"><var>p</var></span>’ says <span class="mathmode"><var>p</var></span>”: and here we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination of their objects.</div>
<div class="corelinks tlpdepth4"><strong>5.5421</strong><span class="linkarray tlpdepth4" id="p5.5421OGD"> OGD [→<a class="gerlink" href="#p5.5421GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5421PM">P/M</a>]</span></div>
<div class="para tlpdepth4">This shows that there is no such thing as the soul—the subject, etc.—as it is conceived in superficial psychology.</div>
<div class="para tlpdepth4">A composite soul would not be a soul any longer.</div>
<div class="corelinks tlpdepth4"><strong>5.5422</strong><span class="linkarray tlpdepth4" id="p5.5422OGD"> OGD [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The correct explanation of the form of the proposition “A judges <span class="mathmode"><var>p</var></span>” must show that it is impossible to judge a nonsense. (Russell’s theory does not satisfy this condition.)</div>
<div class="corelinks tlpdepth4"><strong>5.5423</strong><span class="linkarray tlpdepth4" id="p5.5423OGD"> OGD [→<a class="gerlink" href="#p5.5423GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5423PM">P/M</a>]</span></div>
<div class="para tlpdepth4">To perceive a complex means to perceive that its constituents are combined in such and such a way.</div>
<div class="para tlpdepth4">This perhaps explains that the figure </div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/thecube.svg" type="image/svg+xml" class="thecubesvg" ><img src="images/thecube.png" alt="Cube with a face and b face" class="thecubepng" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> can be seen in two ways as a cube; and all similar phenomena. For we really see two different facts.</div>
<div class="para tlpdepth4">(If I fix my eyes first on the corners <span class="mathmode"><var>a</var></span> and only glance at <span class="mathmode"><var>b</var></span>, <span class="mathmode"><var>a</var></span> appears in front and <span class="mathmode"><var>b</var></span> behind, and vice versa.)</div>
<div class="corelinks tlpdepth2"><strong>5.55</strong><span class="linkarray tlpdepth2" id="p5.55OGD"> OGD [→<a class="gerlink" href="#p5.55GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span></div>
<div class="para tlpdepth2">We must now answer a priori the question as to all possible forms of the elementary propositions.</div>
<div class="para tlpdepth2">The elementary proposition consists of names. Since we cannot give the number of names with different meanings, we cannot give the composition of the elementary proposition.</div>
<div class="corelinks tlpdepth3"><strong>5.551</strong><span class="linkarray tlpdepth3" id="p5.551OGD"> OGD [→<a class="gerlink" href="#p5.551GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.551PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Our fundamental principle is that every question which can be decided at all by logic can be decided off-hand.</div>
<div class="para tlpdepth3">(And if we get into a situation where we need to answer such a problem by looking at the world, this shows that we are on a fundamentally wrong track.)</div>
<div class="corelinks tlpdepth3"><strong>5.552</strong><span class="linkarray tlpdepth3" id="p5.552OGD"> OGD [→<a class="gerlink" href="#p5.552GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.552PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The “experience” which we need to understand logic is not that such and such is the case, but that something <em>is</em>; but that is <em>no</em> experience.</div>
<div class="para tlpdepth3">Logic <em>precedes</em> every experience—that something is <em>so</em>.</div>
<div class="para tlpdepth3">It is before the How, not before the What.</div>
<div class="corelinks tlpdepth4"><strong>5.5521</strong><span class="linkarray tlpdepth4" id="p5.5521OGD"> OGD [→<a class="gerlink" href="#p5.5521GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5521PM">P/M</a>]</span></div>
<div class="para tlpdepth4">And if this were not the case, how could we apply logic? We could say: if there were a logic, even if there were no world, how then could there be a logic, since there is a world?</div>
<div class="corelinks tlpdepth3"><strong>5.553</strong><span class="linkarray tlpdepth3" id="p5.553OGD"> OGD [→<a class="gerlink" href="#p5.553GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Russell said that there were simple relations between different numbers of things (individuals). But between what numbers? And how should this be decided—by experience?</div>
<div class="para tlpdepth3">(There is no pre-eminent number.)</div>
<div class="corelinks tlpdepth3"><strong>5.554</strong><span class="linkarray tlpdepth3" id="p5.554OGD"> OGD [→<a class="gerlink" href="#p5.554GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.554PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The enumeration of any special forms would be entirely arbitrary.</div>
<div class="corelinks tlpdepth4"><strong>5.5541</strong><span class="linkarray tlpdepth4" id="p5.5541OGD"> OGD [→<a class="gerlink" href="#p5.5541GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5541PM">P/M</a>]</span></div>
<div class="para tlpdepth4">How could we decide a priori whether, for example, I can get into a situation in which I need to symbolize with a sign of a 27-termed relation?</div>
<div class="corelinks tlpdepth4"><strong>5.5542</strong><span class="linkarray tlpdepth4" id="p5.5542OGD"> OGD [→<a class="gerlink" href="#p5.5542GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5542PM">P/M</a>]</span></div>
<div class="para tlpdepth4">May we then ask this at all? Can we set out a sign form and not know whether anything can correspond to it?</div>
<div class="para tlpdepth4">Has the question sense: what must there <em>be</em> in order that anything can be the case?</div>
<div class="corelinks tlpdepth3"><strong>5.555</strong><span class="linkarray tlpdepth3" id="p5.555OGD"> OGD [→<a class="gerlink" href="#p5.555GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is clear that we have a concept of the elementary proposition apart from its special logical form.</div>
<div class="para tlpdepth3">Where, however, we can build symbols according to a system, there this system is the logically important thing and not the single symbols.</div>
<div class="para tlpdepth3">And how would it be possible that I should have to deal with forms in logic which I can invent: but I must have to deal with that which makes it possible for me to invent them.</div>
<div class="corelinks tlpdepth3"><strong>5.556</strong><span class="linkarray tlpdepth3" id="p5.556OGD"> OGD [→<a class="gerlink" href="#p5.556GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.556PM">P/M</a>]</span></div>
<div class="para tlpdepth3">There cannot be a hierarchy of the forms of the elementary propositions. Only that which we ourselves construct can we foresee.</div>
<div class="corelinks tlpdepth4"><strong>5.5561</strong><span class="linkarray tlpdepth4" id="p5.5561OGD"> OGD [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Empirical reality is limited by the totality of objects. The boundary appears again in the totality of elementary propositions.</div>
<div class="para tlpdepth4">The hierarchies are and must be independent of reality.</div>
<div class="corelinks tlpdepth4"><strong>5.5562</strong><span class="linkarray tlpdepth4" id="p5.5562OGD"> OGD [→<a class="gerlink" href="#p5.5562GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5562PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If we know on purely logical grounds, that there must be elementary propositions, then this must be known by everyone who understands propositions in their unanalysed form.</div>
<div class="corelinks tlpdepth4"><strong>5.5563</strong><span class="linkarray tlpdepth4" id="p5.5563OGD"> OGD [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span></div>
<div class="para tlpdepth4">All propositions of our colloquial language are actually, just as they are, logically completely in order. That simple thing which we ought to give here is not a model of the truth but the complete truth itself.</div>
<div class="para tlpdepth4">(Our problems are not abstract but perhaps the most concrete that there are.)</div>
<div class="corelinks tlpdepth3"><strong>5.557</strong><span class="linkarray tlpdepth3" id="p5.557OGD"> OGD [→<a class="gerlink" href="#p5.557GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.557PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The <em>application</em> of logic decides what elementary propositions there are.</div>
<div class="para tlpdepth3">What lies in its application logic cannot anticipate.</div>
<div class="para tlpdepth3">It is clear that logic may not conflict with its application.</div>
<div class="para tlpdepth3">But logic must have contact with its application.</div>
<div class="para tlpdepth3">Therefore logic and its application may not overlap one another.</div>
<div class="corelinks tlpdepth4"><strong>5.5571</strong><span class="linkarray tlpdepth4" id="p5.5571OGD"> OGD [→<a class="gerlink" href="#p5.5571GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5571PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If I cannot give elementary propositions a priori then it must lead to obvious nonsense to try to give them.</div>
<div class="corelinks tlpdepth1"><strong>5.6</strong><span class="linkarray tlpdepth1" id="p5.6OGD"> OGD [→<a class="gerlink" href="#p5.6GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6PM">P/M</a>]</span></div>
<div class="para tlpdepth1"><em>The limits of my language</em> mean the limits of my world.</div>
<div class="corelinks tlpdepth2"><strong>5.61</strong><span class="linkarray tlpdepth2" id="p5.61OGD"> OGD [→<a class="gerlink" href="#p5.61GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.61PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Logic fills the world: the limits of the world are also its limits.</div>
<div class="para tlpdepth2">We cannot therefore say in logic: This and this there is in the world, that there is not.</div>
<div class="para tlpdepth2">For that would apparently presuppose that we exclude certain possibilities, and this cannot be the case since otherwise logic must get outside the limits of the world: that is, if it could consider these limits from the other side also.</div>
<div class="para tlpdepth2">What we cannot think, that we cannot think: we cannot therefore <em>say</em> what we cannot think.</div>
<div class="corelinks tlpdepth2"><strong>5.62</strong><span class="linkarray tlpdepth2" id="p5.62OGD"> OGD [→<a class="gerlink" href="#p5.62GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span></div>
<div class="para tlpdepth2">This remark provides a key to the question, to what extent solipsism is a truth.</div>
<div class="para tlpdepth2">In fact what solipsism <em>means</em>, is quite correct, only it cannot be <em>said</em>, but it shows itself.</div>
<div class="para tlpdepth2">That the world is <em>my</em> world, shows itself in the fact that the limits of the language (<em>the</em> language which I understand) mean the limits of <em>my</em> world.</div>
<div class="corelinks tlpdepth3"><strong>5.621</strong><span class="linkarray tlpdepth3" id="p5.621OGD"> OGD [→<a class="gerlink" href="#p5.621GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.621PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The world and life are one.</div>
<div class="corelinks tlpdepth2"><strong>5.63</strong><span class="linkarray tlpdepth2" id="p5.63OGD"> OGD [→<a class="gerlink" href="#p5.63GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.63PM">P/M</a>]</span></div>
<div class="para tlpdepth2">I am my world. (The microcosm.)</div>
<div class="corelinks tlpdepth3"><strong>5.631</strong><span class="linkarray tlpdepth3" id="p5.631OGD"> OGD [→<a class="gerlink" href="#p5.631GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The thinking, presenting subject; there is no such thing.</div>
<div class="para tlpdepth3">If I wrote a book “The world as I found it”, I should also have therein to report on my body and say which members obey my will and which do not, etc. This then would be a method of isolating the subject or rather of showing that in an important sense there is no subject: that is to say, of it alone in this book mention could <em>not</em> be made.</div>
<div class="corelinks tlpdepth3"><strong>5.632</strong><span class="linkarray tlpdepth3" id="p5.632OGD"> OGD [→<a class="gerlink" href="#p5.632GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.632PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The subject does not belong to the world but it is a limit of the world.</div>
<div class="corelinks tlpdepth3"><strong>5.633</strong><span class="linkarray tlpdepth3" id="p5.633OGD"> OGD [→<a class="gerlink" href="#p5.633GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.633PM">P/M</a>]</span></div>
<div class="para tlpdepth3"><em>Where in</em> the world is a metaphysical subject to be noted?</div>
<div class="para tlpdepth3">You say that this case is altogether like that of the eye and the field of sight. But you do <em>not</em> really see the eye.</div>
<div class="para tlpdepth3">And from nothing <em>in the field of sight</em> can it be concluded that it is seen from an eye.</div>
<div class="corelinks tlpdepth4"><strong>5.6331</strong><span class="linkarray tlpdepth4" id="p5.6331OGD"> OGD [→<a class="gerlink" href="#p5.6331GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6331PM">P/M</a>]</span></div>
<div class="para tlpdepth4">For the field of sight has not a form like this:</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><span class="sfmiddle"><span class="lowered">Eye —</span><object data="images/theeye.svg" type="image/svg+xml" class="theeyesvg"><img src="images/theeye.png" alt="Eye image" class="theeyepng" /></object></span></div></div>
<div class="corelinks tlpdepth3"><strong>5.634</strong><span class="linkarray tlpdepth3" id="p5.634OGD"> OGD [→<a class="gerlink" href="#p5.634GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.634PM">P/M</a>]</span></div>
<div class="para tlpdepth3">This is connected with the fact that no part of our experience is also a priori.</div>
<div class="para tlpdepth3">Everything we see could also be otherwise.</div>
<div class="para tlpdepth3">Everything we describe at all could also be otherwise.</div>
<div class="para tlpdepth3">There is no order of things a priori.</div>
<div class="corelinks tlpdepth2"><strong>5.64</strong><span class="linkarray tlpdepth2" id="p5.64OGD"> OGD [→<a class="gerlink" href="#p5.64GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.64PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Here we see that solipsism strictly carried out coincides with pure realism. The I in solipsism shrinks to an extensionless point and there remains the reality co-ordinated with it.</div>
<div class="corelinks tlpdepth3"><strong>5.641</strong><span class="linkarray tlpdepth3" id="p5.641OGD"> OGD [→<a class="gerlink" href="#p5.641GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span></div>
<div class="para tlpdepth3">There is therefore really a sense in which the philosophy we can talk of a non-psychological I.</div>
<div class="para tlpdepth3">The I occurs in philosophy through the fact that the “world is my world”.</div>
<div class="para tlpdepth3">The philosophical I is not the man, not the human body or the human soul of which psychology treats, but the metaphysical subject, the limit—not a part of the world.</div>
<div class="corelinks tlpdepth0"><strong>6</strong><span class="linkarray tlpdepth0" id="p6OGD"> OGD [→<a class="gerlink" href="#p6GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6PM">P/M</a>]</span></div>
<div class="para tlpdepth0">The general form of truth-function is: <span class="mathmode">[<span class="overlined"><var>p</var></span>, <span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)]</span>.</div>
<div class="para tlpdepth0">This is the general form of proposition.</div>
<div class="corelinks tlpdepth3"><strong>6.001</strong><span class="linkarray tlpdepth3" id="p6.001OGD"> OGD [→<a class="gerlink" href="#p6.001GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.001PM">P/M</a>]</span></div>
<div class="para tlpdepth3">This says nothing else than that every proposition is the result of successive applications of the operation <span class="mathmode"><span class="mathop"><span class="nop">N</span>’</span>(<span class="overlined"><var>ξ</var></span>)</span> to the elementary propositions.</div>
<div class="corelinks tlpdepth3"><strong>6.002</strong><span class="linkarray tlpdepth3" id="p6.002OGD"> OGD [→<a class="gerlink" href="#p6.002GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.002PM">P/M</a>]</span></div>
<div class="para tlpdepth3">If we are given the general form of the way in which a proposition is constructed, then thereby we are also given the general form of the way in which by an operation out of one proposition another can be created.</div>
<div class="corelinks tlpdepth2"><strong>6.01</strong><span class="linkarray tlpdepth2" id="p6.01OGD"> OGD [→<a class="gerlink" href="#p6.01GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.01PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The general form of the operation <span class="mathmode"><span class="mathop">Ω’</span>(<span class="overlined"><var>η</var></span>)</span> is therefore: <span class="mathmode"><span class="mathop">[<span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)]’</span> (<span class="overlined"><var>η</var></span>) (<span class="mathrel">=</span>[<span class="overlined"><var>η</var></span>, <span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)])</span>.</div>
<div class="para tlpdepth2">This is the most general form of transition from one proposition to another.</div>
<div class="corelinks tlpdepth2"><strong>6.02</strong><span class="linkarray tlpdepth2" id="p6.02OGD"> OGD [→<a class="gerlink" href="#p6.02GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.02PM">P/M</a>]</span></div>
<div class="para tlpdepth2">And thus we come to numbers: I define</div>
<div class="para tlpdepth2"><div class="centered"><table class="alignedmath"><tr><td class="righttight"><span class="mathmode"><var>x</var><span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode"><span class="mathop">Ω<sup>0</sup>’</span><var>x</var></span>&nbsp;&nbsp;Def. and</td></tr><tr><td class="righttight"><span class="mathmode"><span class="mathop">Ω’</span><span class="mathop">Ω<sup><var>ν</var></sup>’</span><var>x</var><span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode"><span class="mathop">Ω<sup><var>ν</var>+1</sup>’</span><var>x</var></span>&nbsp;&nbsp;Def.</td></tr></table></div></div>
<div class="para tlpdepth2">According, then, to these symbolic rules we write the series</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode"><var>x</var>, <span class="mathop">Ω’</span><var>x</var>, <span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var>, <span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var>,<span class="mathrel">…</span></span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">as:</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode"><span class="mathop">Ω<sup>0</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var>,<span class="mathrel">…</span></span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">Therefore I write in place of “<span class="mathmode">[<var>x</var>, <var>ξ</var>,</span> <span class="mathmode"><span class="mathop">Ω’</span><var>ξ</var>]</span>”,</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode">“[<span class="mathop">Ω<sup>0</sup>’</span><var>x</var>, <span class="mathop">Ω<sup><var>ν</var></sup>’</span><var>x</var>, <span class="mathop">Ω<sup><var>ν</var><span class="mathrel">+</span>1</sup>’</span><var>x</var>]”.</span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">And I define:</div>
<div class="para tlpdepth2"><div class="centered"><table class="alignedmath"><tr><td class="lefttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">=</span>1</span>&nbsp;&nbsp;Def.</td></tr><tr><td class="lefttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">=</span>2</span>&nbsp;&nbsp;Def.</td></tr><tr><td class="lefttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">=</span>3</span>&nbsp;&nbsp;Def.</td></tr><tr><td class="lefttight">and so on.</td></tr></table></div></div>
<div class="corelinks tlpdepth3"><strong>6.021</strong><span class="linkarray tlpdepth3" id="p6.021OGD"> OGD [→<a class="gerlink" href="#p6.021GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.021PM">P/M</a>]</span></div>
<div class="para tlpdepth3">A number is the exponent of an operation.</div>
<div class="corelinks tlpdepth3"><strong>6.022</strong><span class="linkarray tlpdepth3" id="p6.022OGD"> OGD [→<a class="gerlink" href="#p6.022GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The concept number is nothing else than that which is common to all numbers, the general form of a number.</div>
<div class="para tlpdepth3">The concept number is the variable number.</div>
<div class="para tlpdepth3">And the concept of equality of numbers is the general form of all special equalities of numbers.</div>
<div class="corelinks tlpdepth2"><strong>6.03</strong><span class="linkarray tlpdepth2" id="p6.03OGD"> OGD [→<a class="gerlink" href="#p6.03GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.03PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The general form of the cardinal number is: <span class="mathmode">[0, <var>ξ</var>, <var>ξ</var><span class="mathrel">+</span>1]</span>.</div>
<div class="corelinks tlpdepth3"><strong>6.031</strong><span class="linkarray tlpdepth3" id="p6.031OGD"> OGD [→<a class="gerlink" href="#p6.031GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.031PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The theory of classes is altogether superfluous in mathematics.</div>
<div class="para tlpdepth3">This is connected with the fact that the generality which we need in mathematics is not the <em>accidental</em> one.</div>
<div class="corelinks tlpdepth1"><strong>6.1</strong><span class="linkarray tlpdepth1" id="p6.1OGD"> OGD [→<a class="gerlink" href="#p6.1GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1PM">P/M</a>]</span></div>
<div class="para tlpdepth1">The propositions of logic are tautologies.</div>
<div class="corelinks tlpdepth2"><strong>6.11</strong><span class="linkarray tlpdepth2" id="p6.11OGD"> OGD [→<a class="gerlink" href="#p6.11GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.11PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The propositions of logic therefore say nothing. (They are the analytical propositions.)</div>
<div class="corelinks tlpdepth3"><strong>6.111</strong><span class="linkarray tlpdepth3" id="p6.111OGD"> OGD [→<a class="gerlink" href="#p6.111GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Theories which make a proposition of logic appear substantial are always false. One could <em>e.g.</em> believe that the words “true” and “false” signify two properties among other properties, and then it would appear as a remarkable fact that every proposition possesses one of these properties. This now by no means appears self-evident, no more so than the proposition “All roses are either yellow or red” would seem even if it were true. Indeed our proposition now gets quite the character of a proposition of natural science and this is a certain symptom of its being falsely understood.</div>
<div class="corelinks tlpdepth3"><strong>6.112</strong><span class="linkarray tlpdepth3" id="p6.112OGD"> OGD [→<a class="gerlink" href="#p6.112GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.112PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The correct explanation of logical propositions must give them a peculiar position among all propositions.</div>
<div class="corelinks tlpdepth3"><strong>6.113</strong><span class="linkarray tlpdepth3" id="p6.113OGD"> OGD [→<a class="gerlink" href="#p6.113GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.113PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is the characteristic mark of logical propositions that one can perceive in the symbol alone that they are true; and this fact contains in itself the whole philosophy of logic. And so also it is one of the most important facts that the truth or falsehood of non-logical propositions can <em>not</em> be recognized from the propositions alone.</div>
<div class="corelinks tlpdepth2"><strong>6.12</strong><span class="linkarray tlpdepth2" id="p6.12OGD"> OGD [→<a class="gerlink" href="#p6.12GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The fact that the propositions of logic are tautologies <em>shows</em> the formal—logical—properties of language, of the world.</div>
<div class="para tlpdepth2">That its constituent parts connected together <em>in this way</em> give a tautology characterizes the logic of its constituent parts.</div>
<div class="para tlpdepth2">In order that propositions connected together in a definite way may give a tautology they must have definite properties of structure. That they give a tautology when <em>so</em> connected shows therefore that they possess these properties of structure.</div>
<div class="corelinks tlpdepth4"><strong>6.1201</strong><span class="linkarray tlpdepth4" id="p6.1201OGD"> OGD [→<a class="gerlink" href="#p6.1201GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1201PM">P/M</a>]</span></div>
<div class="para tlpdepth4">That <em>e.g.</em> the propositions “<span class="mathmode"><var>p</var></span>” and “<span class="mathmode"><span class="mathop">~</span><var>p</var></span>” in the connexion “<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span>” give a tautology shows that they contradict one another. That the propositions “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>”, “<span class="mathmode"><var>p</var></span>” and “<span class="mathmode"><var>q</var></span>” connected together in the form “<span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>)<span class="mathrel">.</span>(<var>p</var>)<span class="mathrel">:<span class="symbol">⊃</span>:</span>(<var>q</var>)</span>” give a tautology shows that <span class="mathmode"><var>q</var></span> follows from <span class="mathmode"><var>p</var></span> and <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>. That “<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var><span class="mathrel">:<span class="symbol">⊃</span>:</span><var>fa</var></span>” is a tautology shows that <span class="mathmode"><var>fa</var></span> follows from <span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>, etc. etc.</div>
<div class="corelinks tlpdepth4"><strong>6.1202</strong><span class="linkarray tlpdepth4" id="p6.1202OGD"> OGD [→<a class="gerlink" href="#p6.1202GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1202PM">P/M</a>]</span></div>
<div class="para tlpdepth4">It is clear that we could have used for this purpose contradictions instead of tautologies.</div>
<div class="corelinks tlpdepth4"><strong>6.1203</strong><span class="linkarray tlpdepth4" id="p6.1203OGD"> OGD [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span></div>
<div class="para tlpdepth4">In order to recognize a tautology as such, we can, in cases in which no sign of generality occurs in the tautology, make use of the following intuitive method: I write instead of “<span class="mathmode"><var>p</var></span>”, “<span class="mathmode"><var>q</var></span>”, “<span class="mathmode"><var>r</var></span>”, etc., “<span class="mathmode"><span class="mathrm">T</span> <var>p</var> <span class="mathrm">F</span></span>”, “<span class="mathmode"><span class="mathrm">T</span> <var>q</var> <span class="mathrm">F</span></span>”, “<span class="mathmode"><span class="mathrm">T</span> <var>r</var> <span class="mathrm">F</span></span>”, etc. The truth-combinations I express by brackets, <em>e.g.</em>:</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigureoneenglish.svg" type="image/svg+xml" width="156" height="69" style="width: 156pt; height: 69pt;"><img src="images/abfigureoneenglish.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> and the co-ordination of the truth or falsity of the whole proposition with the truth-combinations of the truth-arguments by lines in the following way:</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfiguretwoenglish.svg" type="image/svg+xml" width="156" height="124" style="width: 156pt; height: 124pt;"><img src="images/abfiguretwoenglish.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> This sign, for example, would therefore present the proposition <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>. Now I will proceed to inquire whether such a proposition as <span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span> (The Law of Contradiction) is a tautology. The form “<span class="mathmode"><span class="mathop">~</span><var>ξ</var></span>” is written in our notation</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurethreeenglish.svg" type="image/svg+xml" width="47" height="75" style="width: 47pt; height: 75pt;"><img src="images/abfigurethreeenglish.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> the form “<span class="mathmode"><var>ξ</var><span class="mathrel">.</span><var>η</var></span>” thus:—</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurefourenglish.svg" type="image/svg+xml" width="156" height="116" style="width: 156pt; height: 116pt;"><img src="images/abfigurefourenglish.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent -->Hence the proposition <span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>)</span> runs thus:—</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurefiveenglish.svg" type="image/svg+xml" width="129" height="168" style="width: 129pt; height: 168pt;"><img src="images/abfigurefiveenglish.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> If here we put “<span class="mathmode"><var>p</var></span>” instead of “<span class="mathmode"><var>q</var></span>” and examine the combination of the outermost T and F with the innermost, it is seen that the truth of the whole proposition is co-ordinated with <em>all</em> the truth-combinations of its argument, its falsity with none of the truth-combinations.</div>
<div class="corelinks tlpdepth3"><strong>6.121</strong><span class="linkarray tlpdepth3" id="p6.121OGD"> OGD [→<a class="gerlink" href="#p6.121GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The propositions of logic demonstrate the logical properties of propositions, by combining them into propositions which say nothing.</div>
<div class="para tlpdepth3">This method could be called a zero-method. In a logical proposition propositions are brought into equilibrium with one another, and the state of equilibrium then shows how these propositions must be logically constructed.</div>
<div class="corelinks tlpdepth3"><strong>6.122</strong><span class="linkarray tlpdepth3" id="p6.122OGD"> OGD [→<a class="gerlink" href="#p6.122GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.122PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Whence it follows that we can get on without logical propositions, for we can recognize in an adequate notation the formal properties of the propositions by mere inspection.</div>
<div class="corelinks tlpdepth4"><strong>6.1221</strong><span class="linkarray tlpdepth4" id="p6.1221OGD"> OGD [→<a class="gerlink" href="#p6.1221GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1221PM">P/M</a>]</span></div>
<div class="para tlpdepth4">If for example two propositions “<span class="mathmode"><var>p</var></span>” and “<span class="mathmode"><var>q</var></span>” give a tautology in the connexion “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>”, then it is clear that <span class="mathmode"><var>q</var></span> follows from <span class="mathmode"><var>p</var></span>.</div>
<div class="para tlpdepth4"><em>E.g.</em> that “<span class="mathmode"><var>q</var></span>” follows from “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var><span class="mathrel">.</span><var>p</var></span>” we see from these two propositions themselves, but we can also show it by combining them to “<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var><span class="mathrel">.</span><var>p</var><span class="mathrel">:<span class="symbol">⊃</span>:</span><var>q</var></span>” and then showing that this is a tautology.</div>
<div class="corelinks tlpdepth4"><strong>6.1222</strong><span class="linkarray tlpdepth4" id="p6.1222OGD"> OGD [→<a class="gerlink" href="#p6.1222GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1222PM">P/M</a>]</span></div>
<div class="para tlpdepth4">This throws light on the question why logical propositions can no more be empirically confirmed than they can be empirically refuted. Not only must a proposition of logic be incapable of being contradicted by any possible experience, but it must also be incapable of being confirmed by any such.</div>
<div class="corelinks tlpdepth4"><strong>6.1223</strong><span class="linkarray tlpdepth4" id="p6.1223OGD"> OGD [→<a class="gerlink" href="#p6.1223GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1223PM">P/M</a>]</span></div>
<div class="para tlpdepth4">It now becomes clear why we often feel as though “logical truths” must be “<em>postulated</em>” by us. We can in fact postulate them in so far as we can postulate an adequate notation.</div>
<div class="corelinks tlpdepth4"><strong>6.1224</strong><span class="linkarray tlpdepth4" id="p6.1224OGD"> OGD [→<a class="gerlink" href="#p6.1224GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1224PM">P/M</a>]</span></div>
<div class="para tlpdepth4">It also becomes clear why logic has been called the theory of forms and of inference.</div>
<div class="corelinks tlpdepth3"><strong>6.123</strong><span class="linkarray tlpdepth3" id="p6.123OGD"> OGD [→<a class="gerlink" href="#p6.123GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.123PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is clear that the laws of logic cannot themselves obey further logical laws.</div>
<div class="para tlpdepth3">(There is not, as Russell supposed, for every “type” a special law of contradiction; but one is sufficient, since it is not applied to itself.)</div>
<div class="corelinks tlpdepth4"><strong>6.1231</strong><span class="linkarray tlpdepth4" id="p6.1231OGD"> OGD [→<a class="gerlink" href="#p6.1231GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1231PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The mark of logical propositions is not their general validity.</div>
<div class="para tlpdepth4">To be general is only to be accidentally valid for all things. An ungeneralized proposition can be tautologous just as well as a generalized one.</div>
<div class="corelinks tlpdepth4"><strong>6.1232</strong><span class="linkarray tlpdepth4" id="p6.1232OGD"> OGD [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Logical general validity, we could call essential as opposed to accidental general validity, <em>e.g.</em> of the proposition “all men are mortal”. Propositions like Russell’s “axiom of reducibility” are not logical propositions, and this explains our feeling that, if true, they can only be true by a happy chance.</div>
<div class="corelinks tlpdepth4"><strong>6.1233</strong><span class="linkarray tlpdepth4" id="p6.1233OGD"> OGD [→<a class="gerlink" href="#p6.1233GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1233PM">P/M</a>]</span></div>
<div class="para tlpdepth4">We can imagine a world in which the axiom of reducibility is not valid. But it is clear that logic has nothing to do with the question whether our world is really of this kind or not.</div>
<div class="corelinks tlpdepth3"><strong>6.124</strong><span class="linkarray tlpdepth3" id="p6.124OGD"> OGD [→<a class="gerlink" href="#p6.124GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The logical propositions describe the scaffolding of the world, or rather they present it. They “treat” of nothing. They presuppose that names have meaning, and that elementary propositions have sense. And this is their connexion with the world. It is clear that it must show something about the world that certain combinations of symbols—which essentially have a definite character—are tautologies. Herein lies the decisive point. We said that in the symbols which we use something is arbitrary, something not. In logic only this expresses: but this means that in logic it is not <em>we</em> who express, by means of signs, what we want, but in logic the nature of the essentially necessary signs itself asserts. That is to say, if we know the logical syntax of any sign language, then all the propositions of logic are already given.</div>
<div class="corelinks tlpdepth3"><strong>6.125</strong><span class="linkarray tlpdepth3" id="p6.125OGD"> OGD [→<a class="gerlink" href="#p6.125GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.125PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is possible, also with the old conception of logic, to give at the outset a description of all “true” logical propositions.</div>
<div class="corelinks tlpdepth4"><strong>6.1251</strong><span class="linkarray tlpdepth4" id="p6.1251OGD"> OGD [→<a class="gerlink" href="#p6.1251GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1251PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Hence there can <em>never</em> be surprises in logic.</div>
<div class="corelinks tlpdepth3"><strong>6.126</strong><span class="linkarray tlpdepth3" id="p6.126OGD"> OGD [→<a class="gerlink" href="#p6.126GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Whether a proposition belongs to logic can be calculated by calculating the logical properties of the <em>symbol</em>.</div>
<div class="para tlpdepth3">And this we do when we prove a logical proposition. For without troubling ourselves about a sense and a meaning, we form the logical propositions out of others by mere <em>symbolic rules</em>.</div>
<div class="para tlpdepth3">We prove a logical proposition by creating it out of other logical propositions by applying in succession certain operations, which again generate tautologies out of the first. (And from a tautology only tautologies <em>follow</em>.)</div>
<div class="para tlpdepth3">Naturally this way of showing that its propositions are tautologies is quite unessential to logic. Because the propositions, from which the proof starts, must show without proof that they are tautologies.</div>
<div class="corelinks tlpdepth4"><strong>6.1261</strong><span class="linkarray tlpdepth4" id="p6.1261OGD"> OGD [→<a class="gerlink" href="#p6.1261GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1261PM">P/M</a>]</span></div>
<div class="para tlpdepth4">In logic process and result are equivalent. (Therefore no surprises.)</div>
<div class="corelinks tlpdepth4"><strong>6.1262</strong><span class="linkarray tlpdepth4" id="p6.1262OGD"> OGD [→<a class="gerlink" href="#p6.1262GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1262PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Proof in logic is only a mechanical expedient to facilitate the recognition of tautology, where it is complicated.</div>
<div class="corelinks tlpdepth4"><strong>6.1263</strong><span class="linkarray tlpdepth4" id="p6.1263OGD"> OGD [→<a class="gerlink" href="#p6.1263GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1263PM">P/M</a>]</span></div>
<div class="para tlpdepth4">It would be too remarkable, if one could prove a significant proposition <em>logically</em> from another, and a logical proposition <em>also</em>. It is clear from the beginning that the logical proof of a significant proposition and the proof <em>in</em> logic must be two quite different things.</div>
<div class="corelinks tlpdepth4"><strong>6.1264</strong><span class="linkarray tlpdepth4" id="p6.1264OGD"> OGD [→<a class="gerlink" href="#p6.1264GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1264PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The significant proposition asserts something, and its proof shows that it is so; in logic every proposition is the form of a proof.</div>
<div class="para tlpdepth4">Every proposition of logic is a modus ponens presented in signs. (And the modus ponens can not be expressed by a proposition.)</div>
<div class="corelinks tlpdepth4"><strong>6.1265</strong><span class="linkarray tlpdepth4" id="p6.1265OGD"> OGD [→<a class="gerlink" href="#p6.1265GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1265PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Logic can always be conceived to be such that every proposition is its own proof.</div>
<div class="corelinks tlpdepth3"><strong>6.127</strong><span class="linkarray tlpdepth3" id="p6.127OGD"> OGD [→<a class="gerlink" href="#p6.127GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.127PM">P/M</a>]</span></div>
<div class="para tlpdepth3">All propositions of logic are of equal rank; there are not some which are essentially primitive and others deduced from there.</div>
<div class="para tlpdepth3">Every tautology itself shows that it is a tautology.</div>
<div class="corelinks tlpdepth4"><strong>6.1271</strong><span class="linkarray tlpdepth4" id="p6.1271OGD"> OGD [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span></div>
<div class="para tlpdepth4">It is clear that the number of “primitive propositions of logic” is arbitrary, for we could deduce logic from one primitive proposition by simply forming, for example, the logical produce of Frege’s primitive propositions. (Frege would perhaps say that this would no longer be immediately self-evident. But it is remarkable that so exact a thinker as Frege should have appealed to the degree of self-evidence as the criterion of a logical proposition.)</div>
<div class="corelinks tlpdepth2"><strong>6.13</strong><span class="linkarray tlpdepth2" id="p6.13OGD"> OGD [→<a class="gerlink" href="#p6.13GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.13PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Logic is not a theory but a reflexion of the world.</div>
<div class="para tlpdepth2">Logic is transcendental.</div>
<div class="corelinks tlpdepth1"><strong>6.2</strong><span class="linkarray tlpdepth1" id="p6.2OGD"> OGD [→<a class="gerlink" href="#p6.2GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Mathematics is a logical method.</div>
<div class="para tlpdepth1">The propositions of mathematics are equations, and therefore pseudo-propositions.</div>
<div class="corelinks tlpdepth2"><strong>6.21</strong><span class="linkarray tlpdepth2" id="p6.21OGD"> OGD [→<a class="gerlink" href="#p6.21GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.21PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Mathematical propositions express no thoughts.</div>
<div class="corelinks tlpdepth3"><strong>6.211</strong><span class="linkarray tlpdepth3" id="p6.211OGD"> OGD [→<a class="gerlink" href="#p6.211GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.211PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In life it is never a mathematical proposition which we need, but we use mathematical propositions <em>only</em> in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.</div>
<div class="para tlpdepth3">(In philosophy the question “Why do we really use that word, that proposition?” constantly leads to valuable results.)</div>
<div class="corelinks tlpdepth2"><strong>6.22</strong><span class="linkarray tlpdepth2" id="p6.22OGD"> OGD [→<a class="gerlink" href="#p6.22GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.22PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The logic of the world which the propositions of logic show in tautologies, mathematics shows in equations.</div>
<div class="corelinks tlpdepth2"><strong>6.23</strong><span class="linkarray tlpdepth2" id="p6.23OGD"> OGD [→<a class="gerlink" href="#p6.23GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If two expressions are connected by the sign of equality, this means that they can be substituted for one another. But whether this is the case must show itself in the two expressions themselves.</div>
<div class="para tlpdepth2">It characterizes the logical form of two expressions, that they can be substituted for one another.</div>
<div class="corelinks tlpdepth3"><strong>6.231</strong><span class="linkarray tlpdepth3" id="p6.231OGD"> OGD [→<a class="gerlink" href="#p6.231GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.231PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is a property of affirmation that it can be conceived as double denial.</div>
<div class="para tlpdepth3">It is a property of “<span class="mathmode">1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</span>” that it can be conceived as “<span class="mathmode">(1<span class="mathrel">+</span>1)<span class="mathrel">+</span>(1<span class="mathrel">+</span>1)</span>”.</div>
<div class="corelinks tlpdepth3"><strong>6.232</strong><span class="linkarray tlpdepth3" id="p6.232OGD"> OGD [→<a class="gerlink" href="#p6.232GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Frege says that these expressions have the same meaning but different senses.</div>
<div class="para tlpdepth3">But what is essential about equation is that it is not necessary in order to show that both expressions, which are connected by the sign of equality, have the same meaning: for this can be perceived from the two expressions themselves.</div>
<div class="corelinks tlpdepth4"><strong>6.2321</strong><span class="linkarray tlpdepth4" id="p6.2321OGD"> OGD [→<a class="gerlink" href="#p6.2321GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2321PM">P/M</a>]</span></div>
<div class="para tlpdepth4">And, that the propositions of mathematics can be proved means nothing else than that their correctness can be seen without our having to compare what they express with the facts as regards correctness.</div>
<div class="corelinks tlpdepth4"><strong>6.2322</strong><span class="linkarray tlpdepth4" id="p6.2322OGD"> OGD [→<a class="gerlink" href="#p6.2322GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2322PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The identity of the meaning of two expressions cannot be <em>asserted</em>. For in order to be able to assert anything about their meaning, I must know their meaning, and if I know their meaning, I know whether they mean the same or something different.</div>
<div class="corelinks tlpdepth4"><strong>6.2323</strong><span class="linkarray tlpdepth4" id="p6.2323OGD"> OGD [→<a class="gerlink" href="#p6.2323GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2323PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The equation characterizes only the standpoint from which I consider the two expressions, that is to say the standpoint of their equality of meaning.</div>
<div class="corelinks tlpdepth3"><strong>6.233</strong><span class="linkarray tlpdepth3" id="p6.233OGD"> OGD [→<a class="gerlink" href="#p6.233GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.233PM">P/M</a>]</span></div>
<div class="para tlpdepth3">To the question whether we need intuition for the solution of mathematical problems it must be answered that language itself here supplies the necessary intuition.</div>
<div class="corelinks tlpdepth4"><strong>6.2331</strong><span class="linkarray tlpdepth4" id="p6.2331OGD"> OGD [→<a class="gerlink" href="#p6.2331GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2331PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The process of calculation brings about just this intuition.</div>
<div class="para tlpdepth4">Calculation is not an experiment.</div>
<div class="corelinks tlpdepth3"><strong>6.234</strong><span class="linkarray tlpdepth3" id="p6.234OGD"> OGD [→<a class="gerlink" href="#p6.234GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.234PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Mathematics is a method of logic.</div>
<div class="corelinks tlpdepth4"><strong>6.2341</strong><span class="linkarray tlpdepth4" id="p6.2341OGD"> OGD [→<a class="gerlink" href="#p6.2341GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2341PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The essential of mathematical method is working with equations. On this method depends the fact that every proposition of mathematics must be self-evident.</div>
<div class="corelinks tlpdepth2"><strong>6.24</strong><span class="linkarray tlpdepth2" id="p6.24OGD"> OGD [→<a class="gerlink" href="#p6.24GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.24PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The method by which mathematics arrives at its equations is the method of substitution.</div>
<div class="para tlpdepth2">For equations express the substitutability of two expressions, and we proceed from a number of equations to new equations, replacing expressions by others in accordance with the equations.</div>
<div class="corelinks tlpdepth3"><strong>6.241</strong><span class="linkarray tlpdepth3" id="p6.241OGD"> OGD [→<a class="gerlink" href="#p6.241GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.241PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Thus the proof of the proposition <span class="mathmode">2 × 2<span class="mathrel">=</span>4</span> runs:</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode"><span class="mathop">(Ω<sup><var>ν</var></sup>)<sup><var>μ</var></sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup><var>ν</var>× <var>μ</var></sup>’</span><var>x</var></span> Def.<br />
<span class="mathmode"><span class="mathop">Ω<sup>2 × 2</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω<sup>2</sup>)<sup>2</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω<sup>2</sup>)<sup>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>2</sup>’</span><span class="mathop">Ω<sup>2</sup>’</span><var>x</var></span><br />
<span class="mathmode"><span class="mathrel">=</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1</sup>’</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω’Ω)’</span><span class="mathop">(Ω’Ω)’</span> <var>x</var></span><br />
<span class="mathmode"><span class="mathrel">=</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>4</sup>’</span><var>x</var></span>.<br />
</div></div>
<div class="corelinks tlpdepth1"><strong>6.3</strong><span class="linkarray tlpdepth1" id="p6.3OGD"> OGD [→<a class="gerlink" href="#p6.3GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3PM">P/M</a>]</span></div>
<div class="para tlpdepth1">Logical research means the investigation of <em>all regularity</em>. And outside logic all is accident.</div>
<div class="corelinks tlpdepth2"><strong>6.31</strong><span class="linkarray tlpdepth2" id="p6.31OGD"> OGD [→<a class="gerlink" href="#p6.31GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.31PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The so-called law of induction cannot in any case be a logical law, for it is obviously a significant proposition.—And therefore it cannot be a law a priori either.</div>
<div class="corelinks tlpdepth2"><strong>6.32</strong><span class="linkarray tlpdepth2" id="p6.32OGD"> OGD [→<a class="gerlink" href="#p6.32GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.32PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The law of causality is not a law but the form of a law.<a href="#fn2" id="fn2marker">†</a></div>
<div class="corelinks tlpdepth3"><strong>6.321</strong><span class="linkarray tlpdepth3" id="p6.321OGD"> OGD [→<a class="gerlink" href="#p6.321GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span></div>
<div class="para tlpdepth3">“Law of Causality” is a class name. And as in mechanics there are, for instance, minimum-laws, such as that of least actions, so in physics there are causal laws, laws of the causality form.</div>
<div class="corelinks tlpdepth4"><strong>6.3211</strong><span class="linkarray tlpdepth4" id="p6.3211OGD"> OGD [→<a class="gerlink" href="#p6.3211GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3211PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Men had indeed an idea that there must be <em>a</em> “law of least action”, before they knew exactly how it ran. (Here, as always, the a priori certain proves to be something purely logical.)</div>
<div class="corelinks tlpdepth2"><strong>6.33</strong><span class="linkarray tlpdepth2" id="p6.33OGD"> OGD [→<a class="gerlink" href="#p6.33GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.33PM">P/M</a>]</span></div>
<div class="para tlpdepth2">We do not <em>believe</em> a priori in a law of conservation, but we <em>know</em> a priori the possibility of a logical form.</div>
<div class="corelinks tlpdepth2"><strong>6.34</strong><span class="linkarray tlpdepth2" id="p6.34OGD"> OGD [→<a class="gerlink" href="#p6.34GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span></div>
<div class="para tlpdepth2">All propositions, such as the law of causation, the law of continuity in nature, the law of least expenditure in nature, etc. etc., all these are a priori intuitions of possible forms of the propositions of science.</div>
<div class="corelinks tlpdepth3"><strong>6.341</strong><span class="linkarray tlpdepth3" id="p6.341OGD"> OGD [→<a class="gerlink" href="#p6.341GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Newtonian mechanics, for example, brings the description of the universe to a unified form. Let us imagine a white surface with irregular black spots. We now say: Whatever kind of picture these make I can always get as near as I like to its description, if I cover the surface with a sufficiently fine square network and now say of every square that it is white or black. In this way I shall have brought the description of the surface to a unified form. This form is arbitrary, because I could have applied with equal success a net with a triangular or hexagonal mesh. It can happen that the description would have been simpler with the aid of a triangular mesh; that is to say we might have described the surface more accurately with a triangular, and coarser, than with the finer square mesh, or vice versa, and so on. To the different networks correspond different systems of describing the world. Mechanics determine a form of description by saying: All propositions in the description of the world must be obtained in a given way from a number of given propositions—the mechanical axioms. It thus provides the bricks for building the edifice of science, and says: Whatever building thou wouldst erect, thou shalt construct it in some manner with these bricks and these alone.</div>
<div class="para tlpdepth3">(As with the system of numbers one must be able to write down any arbitrary number, so with the system of mechanics one must be able to write down any arbitrary physical proposition.)</div>
<div class="corelinks tlpdepth3"><strong>6.342</strong><span class="linkarray tlpdepth3" id="p6.342OGD"> OGD [→<a class="gerlink" href="#p6.342GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span></div>
<div class="para tlpdepth3">And now we see the relative position of logic and mechanics. (We could construct the network out of figures of different kinds, as out of triangles and hexagons together.) That a picture like that instanced above can be described by a network of a given form asserts <em>nothing</em> about the picture. (For this holds of every picture of this kind.) But <em>this</em> does characterize the picture, the fact, namely, that it can be <em>completely</em> described by a definite net of <em>definite</em> fineness.</div>
<div class="para tlpdepth3">So too the fact that it can be described by Newtonian mechanics asserts nothing about the world; but <em>this</em> asserts something, namely, that it can be described in that particular way in which as a matter of fact it is described. The fact, too, that it can be described more simply by one system of mechanics than by another says something about the world.</div>
<div class="corelinks tlpdepth3"><strong>6.343</strong><span class="linkarray tlpdepth3" id="p6.343OGD"> OGD [→<a class="gerlink" href="#p6.343GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.343PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Mechanics is an attempt to construct according to a single plan all <em>true</em> propositions which we need for the description of the world.</div>
<div class="corelinks tlpdepth4"><strong>6.3431</strong><span class="linkarray tlpdepth4" id="p6.3431OGD"> OGD [→<a class="gerlink" href="#p6.3431GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3431PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Through their whole logical apparatus the physical laws still speak of the objects of the world.</div>
<div class="corelinks tlpdepth4"><strong>6.3432</strong><span class="linkarray tlpdepth4" id="p6.3432OGD"> OGD [→<a class="gerlink" href="#p6.3432GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3432PM">P/M</a>]</span></div>
<div class="para tlpdepth4">We must not forget that the description of the world by mechanics is always quite general. There is, for example, never any mention of <em>particular</em> material points in it, but always only of <em>some points or other</em>.</div>
<div class="corelinks tlpdepth2"><strong>6.35</strong><span class="linkarray tlpdepth2" id="p6.35OGD"> OGD [→<a class="gerlink" href="#p6.35GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Although the spots in our picture are geometrical figures, geometry can obviously say nothing about their actual form and position. But the network is <em>purely</em> geometrical, and all its properties can be given a priori.</div>
<div class="para tlpdepth2">Laws, like the law of causation, etc., treat of the network and not what the network describes.</div>
<div class="corelinks tlpdepth2"><strong>6.36</strong><span class="linkarray tlpdepth2" id="p6.36OGD"> OGD [→<a class="gerlink" href="#p6.36GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If there were a law of causality, it might run: “There are natural laws”.</div>
<div class="para tlpdepth2">But that can clearly not be said: it shows itself.</div>
<div class="corelinks tlpdepth3"><strong>6.361</strong><span class="linkarray tlpdepth3" id="p6.361OGD"> OGD [→<a class="gerlink" href="#p6.361GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.361PM">P/M</a>]</span></div>
<div class="para tlpdepth3">In the terminology of Hertz we might say: Only <em>uniform</em> connections are <em>thinkable</em>.</div>
<div class="corelinks tlpdepth4"><strong>6.3611</strong><span class="linkarray tlpdepth4" id="p6.3611OGD"> OGD [→<a class="gerlink" href="#p6.3611GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3611PM">P/M</a>]</span></div>
<div class="para tlpdepth4">We cannot compare any process with the “passage of time”—there is no such thing—but only with another process (say, with the movement of the chronometer).</div>
<div class="para tlpdepth4">Hence the description of the temporal sequence of events is only possible if we support ourselves on another process.</div>
<div class="para tlpdepth4">It is exactly analogous for space. When, for example, we say that neither of two events (which mutually exclude one another) can occur, because there is <em>no cause</em> why the one should occur rather than the other, it is really a matter of our being unable to describe <em>one</em> of the two events unless there is some sort of asymmetry. And if there <em>is</em> such an asymmetry, we can regard this as the <em>cause</em> of the occurrence of the one and of the non-occurrence of the other.</div>
<div class="corelinks tlpdepth5"><strong>6.36111</strong><span class="linkarray tlpdepth5" id="p6.36111OGD"> OGD [→<a class="gerlink" href="#p6.36111GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36111PM">P/M</a>]</span></div>
<div class="para tlpdepth5">The Kantian problem of the right and left hand which cannot be made to cover one another already exists in the plane, and even in one-dimensional space; where the two congruent figures <span class="mathmode"><var>a</var></span> and <span class="mathmode"><var>b</var></span> cannot be made to cover one another without </div>
<div class="para tlpdepth5 noindent"><!-- noindent --><div class="centeredsqueeze" ><b>–&nbsp;–&nbsp;–&nbsp;<span class="tight"><span class="symbol">○</span>————<span class="nudgedown"><span class="symbol">✕</span></span></span>&nbsp;–&nbsp;–&nbsp;<span class="tight"><span class="nudgedown"><span class="symbol">✕</span></span>————<span class="symbol">○</span></span>&nbsp;–&nbsp;–&nbsp;–</b><br /><var class="smallvar">a</var>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<var class="smallvar">b</var></div></div>
<div class="para tlpdepth5 noindent"><!-- noindent --> moving them out of this space. The right and left hand are in fact completely congruent. And the fact that they cannot be made to cover one another has nothing to do with it.</div>
<div class="para tlpdepth5">A right-hand glove could be put on a left hand if it could be turned round in four-dimensional space.</div>
<div class="corelinks tlpdepth3"><strong>6.362</strong><span class="linkarray tlpdepth3" id="p6.362OGD"> OGD [→<a class="gerlink" href="#p6.362GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.362PM">P/M</a>]</span></div>
<div class="para tlpdepth3">What can be described can happen too, and what is excluded by the law of causality cannot be described.</div>
<div class="corelinks tlpdepth3"><strong>6.363</strong><span class="linkarray tlpdepth3" id="p6.363OGD"> OGD [→<a class="gerlink" href="#p6.363GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.363PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The process of induction is the process of assuming the <em>simplest</em> law that can be made to harmonize with our experience.</div>
<div class="corelinks tlpdepth4"><strong>6.3631</strong><span class="linkarray tlpdepth4" id="p6.3631OGD"> OGD [→<a class="gerlink" href="#p6.3631GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3631PM">P/M</a>]</span></div>
<div class="para tlpdepth4">This process, however, has no logical foundation but only a psychological one.</div>
<div class="para tlpdepth4">It is clear that there are no grounds for believing that the simplest course of events will really happen.</div>
<div class="corelinks tlpdepth5"><strong>6.36311</strong><span class="linkarray tlpdepth5" id="p6.36311OGD"> OGD [→<a class="gerlink" href="#p6.36311GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36311PM">P/M</a>]</span></div>
<div class="para tlpdepth5">That the sun will rise to-morrow, is an hypothesis; and that means that we do not <em>know</em> whether it will rise.</div>
<div class="corelinks tlpdepth2"><strong>6.37</strong><span class="linkarray tlpdepth2" id="p6.37OGD"> OGD [→<a class="gerlink" href="#p6.37GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.37PM">P/M</a>]</span></div>
<div class="para tlpdepth2">A necessity for one thing to happen because another has happened does not exist. There is only <em>logical</em> necessity.</div>
<div class="corelinks tlpdepth3"><strong>6.371</strong><span class="linkarray tlpdepth3" id="p6.371OGD"> OGD [→<a class="gerlink" href="#p6.371GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.371PM">P/M</a>]</span></div>
<div class="para tlpdepth3">At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena.</div>
<div class="corelinks tlpdepth3"><strong>6.372</strong><span class="linkarray tlpdepth3" id="p6.372OGD"> OGD [→<a class="gerlink" href="#p6.372GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.372PM">P/M</a>]</span></div>
<div class="para tlpdepth3">So people stop short at natural laws as something unassailable, as did the ancients at God and Fate.</div>
<div class="para tlpdepth3">And they are both right and wrong. but the ancients were clearer, in so far as they recognized one clear terminus, whereas the modern system makes it appear as though <em>everything</em> were explained.</div>
<div class="corelinks tlpdepth3"><strong>6.373</strong><span class="linkarray tlpdepth3" id="p6.373OGD"> OGD [→<a class="gerlink" href="#p6.373GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.373PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The world is independent of my will.</div>
<div class="corelinks tlpdepth3"><strong>6.374</strong><span class="linkarray tlpdepth3" id="p6.374OGD"> OGD [→<a class="gerlink" href="#p6.374GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Even if everything we wished were to happen, this would only be, so to speak, a favour of fate, for there is no <em>logical</em> connexion between will and world, which would guarantee this, and the assumed physical connexion itself we could not again will.</div>
<div class="corelinks tlpdepth3"><strong>6.375</strong><span class="linkarray tlpdepth3" id="p6.375OGD"> OGD [→<a class="gerlink" href="#p6.375GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.375PM">P/M</a>]</span></div>
<div class="para tlpdepth3">As there is only a <em>logical</em> necessity, so there is only a <em>logical</em> impossibility.</div>
<div class="corelinks tlpdepth4"><strong>6.3751</strong><span class="linkarray tlpdepth4" id="p6.3751OGD"> OGD [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="para tlpdepth4">For two colours, <em>e.g.</em> to be at one place in the visual field, is impossible, logically impossible, for it is excluded by the logical structure of colour.</div>
<div class="para tlpdepth4">Let us consider how this contradiction presents itself in physics. Somewhat as follows: That a particle cannot at the same time have two velocities, <em>i.e.</em> that at the same time it cannot be in two places, <em>i.e.</em> that particles in different places at the same time cannot be identical.</div>
<div class="para tlpdepth4">It is clear that the logical product of two elementary propositions can neither be a tautology nor a contradiction. The assertion that a point in the visual field has two different colours at the same time, is a contradiction.</div>
<div class="corelinks tlpdepth1"><strong>6.4</strong><span class="linkarray tlpdepth1" id="p6.4OGD"> OGD [→<a class="gerlink" href="#p6.4GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4PM">P/M</a>]</span></div>
<div class="para tlpdepth1">All propositions are of equal value.</div>
<div class="corelinks tlpdepth2"><strong>6.41</strong><span class="linkarray tlpdepth2" id="p6.41OGD"> OGD [→<a class="gerlink" href="#p6.41GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.41PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The sense of the world must lie outside the world. In the world everything is as it is and happens as it does happen. <em>In</em> it there is no value—and if there were, it would be of no value.</div>
<div class="para tlpdepth2">If there is a value which is of value, it must lie outside all happening and being-so. For all happening and being-so is accidental.</div>
<div class="para tlpdepth2">What makes it non-accidental cannot lie <em>in</em> the world, for otherwise this would again be accidental.</div>
<div class="para tlpdepth2">It must lie outside the world.</div>
<div class="corelinks tlpdepth2"><strong>6.42</strong><span class="linkarray tlpdepth2" id="p6.42OGD"> OGD [→<a class="gerlink" href="#p6.42GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.42PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Hence also there can be no ethical propositions.</div>
<div class="para tlpdepth2">Propositions cannot express anything higher.</div>
<div class="corelinks tlpdepth3"><strong>6.421</strong><span class="linkarray tlpdepth3" id="p6.421OGD"> OGD [→<a class="gerlink" href="#p6.421GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.421PM">P/M</a>]</span></div>
<div class="para tlpdepth3">It is clear that ethics cannot be expressed.</div>
<div class="para tlpdepth3">Ethics is transcendental.</div>
<div class="para tlpdepth3">(Ethics and æsthetics are one.)</div>
<div class="corelinks tlpdepth3"><strong>6.422</strong><span class="linkarray tlpdepth3" id="p6.422OGD"> OGD [→<a class="gerlink" href="#p6.422GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The first thought in setting up an ethical law of the form “thou shalt …” is: And what if I do not do it? But it is clear that ethics has nothing to do with punishment and reward in the ordinary sense. This question as to the <em>consequences</em> of an action must therefore be irrelevant. At least these consequences will not be events. For there must be something right in that formulation of the question. There must be some sort of ethical reward and ethical punishment, but this must lie in the action itself.</div>
<div class="para tlpdepth3">(And this is clear also that the reward must be something acceptable, and the punishment something unacceptable.)</div>
<div class="corelinks tlpdepth3"><strong>6.423</strong><span class="linkarray tlpdepth3" id="p6.423OGD"> OGD [→<a class="gerlink" href="#p6.423GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.423PM">P/M</a>]</span></div>
<div class="para tlpdepth3">Of the will as the subject of the ethical we cannot speak.</div>
<div class="para tlpdepth3">And the will as a phenomenon is only of interest to psychology.</div>
<div class="corelinks tlpdepth2"><strong>6.43</strong><span class="linkarray tlpdepth2" id="p6.43OGD"> OGD [→<a class="gerlink" href="#p6.43GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.43PM">P/M</a>]</span></div>
<div class="para tlpdepth2">If good or bad willing changes the world, it can only change the limits of the world, not the facts; not the things that can be expressed in language.</div>
<div class="para tlpdepth2">In brief, the world must thereby become quite another, it must so to speak wax or wane as a whole.</div>
<div class="para tlpdepth2">The world of the happy is quite another than that of the unhappy.</div>
<div class="corelinks tlpdepth3"><strong>6.431</strong><span class="linkarray tlpdepth3" id="p6.431OGD"> OGD [→<a class="gerlink" href="#p6.431GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.431PM">P/M</a>]</span></div>
<div class="para tlpdepth3">As in death, too, the world does not change, but ceases.</div>
<div class="corelinks tlpdepth4"><strong>6.4311</strong><span class="linkarray tlpdepth4" id="p6.4311OGD"> OGD [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span></div>
<div class="para tlpdepth4">Death is not an event of life. Death is not lived through.</div>
<div class="para tlpdepth4">If by eternity is understood not endless temporal duration but timelessness, then he lives eternally who lives in the present.</div>
<div class="para tlpdepth4">Our life is endless in the way that our visual field is without limit.</div>
<div class="corelinks tlpdepth4"><strong>6.4312</strong><span class="linkarray tlpdepth4" id="p6.4312OGD"> OGD [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The temporal immortality of the human soul, that is to say, its eternal survival also after death, is not only in no way guaranteed, but this assumption in the first place will not do for us what we always tried to make it do. Is a riddle solved by the fact that I survive for ever? Is this eternal life not as enigmatic as our present one? The solution of the riddle of life in space and time lies <em>outside</em> space and time.</div>
<div class="para tlpdepth4">(It is not problems of natural science which have to be solved.)</div>
<div class="corelinks tlpdepth3"><strong>6.432</strong><span class="linkarray tlpdepth3" id="p6.432OGD"> OGD [→<a class="gerlink" href="#p6.432GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.432PM">P/M</a>]</span></div>
<div class="para tlpdepth3"><em>How</em> the world is, is completely indifferent for what is higher. God does not reveal himself <em>in</em> the world.</div>
<div class="corelinks tlpdepth4"><strong>6.4321</strong><span class="linkarray tlpdepth4" id="p6.4321OGD"> OGD [→<a class="gerlink" href="#p6.4321GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4321PM">P/M</a>]</span></div>
<div class="para tlpdepth4">The facts all belong only to the task and not to its performance.</div>
<div class="corelinks tlpdepth2"><strong>6.44</strong><span class="linkarray tlpdepth2" id="p6.44OGD"> OGD [→<a class="gerlink" href="#p6.44GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.44PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Not <em>how</em> the world is, is the mystical, but <em>that</em> it is.</div>
<div class="corelinks tlpdepth2"><strong>6.45</strong><span class="linkarray tlpdepth2" id="p6.45OGD"> OGD [→<a class="gerlink" href="#p6.45GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.45PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The contemplation of the world <em>sub specie aeterni</em> is its contemplation as a limited whole.</div>
<div class="para tlpdepth2">The feeling that the world is a limited whole is the mystical feeling.</div>
<div class="corelinks tlpdepth1"><strong>6.5</strong><span class="linkarray tlpdepth1" id="p6.5OGD"> OGD [→<a class="gerlink" href="#p6.5GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.5PM">P/M</a>]</span></div>
<div class="para tlpdepth1">For an answer which cannot be expressed the question too cannot be expressed.</div>
<div class="para tlpdepth1"><em>The riddle</em> does not exist.</div>
<div class="para tlpdepth1">If a question can be put at all, then it <em>can</em> also be answered.</div>
<div class="corelinks tlpdepth2"><strong>6.51</strong><span class="linkarray tlpdepth2" id="p6.51OGD"> OGD [→<a class="gerlink" href="#p6.51GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.51PM">P/M</a>]</span></div>
<div class="para tlpdepth2">Scepticism is <em>not</em> irrefutable, but palpably senseless, if it would doubt where a question cannot be asked.</div>
<div class="para tlpdepth2">For doubt can only exist where there is a question; a question only where there is an answer, and this only where something <em>can</em> be <em>said</em>.</div>
<div class="corelinks tlpdepth2"><strong>6.52</strong><span class="linkarray tlpdepth2" id="p6.52OGD"> OGD [→<a class="gerlink" href="#p6.52GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.52PM">P/M</a>]</span></div>
<div class="para tlpdepth2">We feel that even if <em>all possible</em> scientific questions be answered, the problems of life have still not been touched at all. Of course there is then no question left, and just this is the answer.</div>
<div class="corelinks tlpdepth3"><strong>6.521</strong><span class="linkarray tlpdepth3" id="p6.521OGD"> OGD [→<a class="gerlink" href="#p6.521GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.521PM">P/M</a>]</span></div>
<div class="para tlpdepth3">The solution of the problem of life is seen in the vanishing of this problem.</div>
<div class="para tlpdepth3">(Is not this the reason why men to whom after long doubting the sense of life became clear, could not then say wherein this sense consisted?)</div>
<div class="corelinks tlpdepth3"><strong>6.522</strong><span class="linkarray tlpdepth3" id="p6.522OGD"> OGD [→<a class="gerlink" href="#p6.522GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.522PM">P/M</a>]</span></div>
<div class="para tlpdepth3">There is indeed the inexpressible. This <em>shows</em> itself; it is the mystical.</div>
<div class="corelinks tlpdepth2"><strong>6.53</strong><span class="linkarray tlpdepth2" id="p6.53OGD"> OGD [→<a class="gerlink" href="#p6.53GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span></div>
<div class="para tlpdepth2">The right method of philosophy would be this: To say nothing except what can be said, <em>i.e.</em> the propositions of natural science, <em>i.e.</em> something that has nothing to do with philosophy: and then always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other—he would not have the feeling that we were teaching him philosophy—but it would be the only strictly correct method.</div>
<div class="corelinks tlpdepth2"><strong>6.54</strong><span class="linkarray tlpdepth2" id="p6.54OGD"> OGD [→<a class="gerlink" href="#p6.54GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.54PM">P/M</a>]</span></div>
<div class="para tlpdepth2">My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)</div>
<div class="para tlpdepth2">He must surmount these propositions; then he sees the world rightly.</div>
<div class="corelinks tlpdepth0"><strong>7</strong><span class="linkarray tlpdepth0" id="p7OGD"> OGD [→<a class="gerlink" href="#p7GER">GER</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p7PM">P/M</a>]</span></div>
<div class="para tlpdepth0">Whereof one cannot speak, thereof one must be silent.</div>
<div id="footnotesOgden">
<h4 class="tlpdepth2">Footnotes</h4>
<p class="footnote tlpdepth0" id="fn1OGD"><a href="#fn1markerOGD">*</a> <span id="ogdenfootnote1">The decimal figures as numbers of the separate propositions indicate the logical importance of the propositions, the emphasis laid upon them in my exposition. The propositions <var>n</var>.1, <var>n</var>.2, <var>n</var>.3, etc., are comments on proposition No. <var>n</var>; the propositions <var>n</var>.<var>m</var>1, <var>n</var>.<var>m</var>2, etc., are comments on the proposition No. <var>n</var>.<var>m</var>; and so on.</span> <span class="linkarray">[→<a href="#fn1GER" class="gerlink">GER</a><span class="beforepmclink"> | </span><a href="#fn1PM" class="pmclink">P/M</a>]</span></p>
<p class="footnote tlpdepth2" id="fn2"><a href="#fn2marker">†</a> <em>I.e.</em> not the form of one particular law, but of any law of a certain sort (B.&thinsp;R.).</p>
</div>
<hr />
</div>
<div id="coredivPearsMcGuinness" class="versionbigdiv bigdivPearsMcGuinness">
<div id="prefacedivPearsMcGuinness" class="prefacediv">
<h2 class="majordivision" id="prefacePearsMcGuinness">Preface (Pears/McGuinness)</h2>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref1PM"> P/M [→<a class="gerlink" href="#pref1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref1OGD">OGD</a>]</span></div>
<p>Perhaps this book will be understood only by someone who has himself already had the thoughts that are expressed in it—or at least similar thoughts.—So it is not a textbook.—Its purpose would be achieved if it gave pleasure to one person who read and understood it.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref2PM"> P/M [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a>]</span></div>
<p>The book deals with the problems of philosophy, and shows, I believe, that the reason why these problems are posed is that the logic of our language is misunderstood. The whole sense of the book might be summed up in the following words: what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref3PM"> P/M [→<a class="gerlink" href="#pref3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref3OGD">OGD</a>]</span></div>
<p>Thus the aim of the book is to draw a limit to thought, or rather—not to thought, but to the expression of thoughts: for in order to be able to draw a limit to thought, we should have to find both sides of the limit thinkable (i.e. we should have to be able to think what cannot be thought).</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref4PM"> P/M [→<a class="gerlink" href="#pref4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref4OGD">OGD</a>]</span></div>
<p>It will therefore only be in language that the limit can be drawn, and what lies on the other side of the limit will simply be nonsense.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref5PM"> P/M [→<a class="gerlink" href="#pref5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref5OGD">OGD</a>]</span></div>
<p>I do not wish to judge how far my efforts coincide with those of other philosophers. Indeed, what I have written here makes no claim to novelty in detail, and the reason why I give no sources is that it is a matter of indifference to me whether the thoughts that I have had have been anticipated by someone else.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref6PM"> P/M [→<a class="gerlink" href="#pref6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref6OGD">OGD</a>]</span></div>
<p>I will only mention that I am indebted to Frege’s great works and of the writings of my friend Mr. Bertrand Russell for much of the stimulation of my thoughts.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref7PM"> P/M [→<a class="gerlink" href="#pref7GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref7OGD">OGD</a>]</span></div>
<p>If this work has any value, it consists in two things: the first is that thoughts are expressed in it, and on this score the better the thoughts are expressed—the more the nail has been hit on the head—the greater will be its value.—Here I am conscious of having fallen a long way short of what is possible. Simply because my powers are too slight for the accomplishment of the task.—May others come and do it better.</p>
<div class="preflinks"><span class="linkarray tlpdepth1" id="pref8PM"> P/M [→<a class="gerlink" href="#pref8GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref8OGD">OGD</a>]</span></div>
<p>On the other hand the <em>truth</em> of the thoughts that are here communicated seems to me unassailable and definitive. I therefore believe myself to have found, on all essential points, the final solution of the problems. And if I am not mistaken in this belief, then the second thing in which the value of this work consists is that it shows how little is achieved when these problems are solved.</p>
<p>&nbsp; <!-- flushright --> L. W.<br />
<em>Vienna, 1918</em></p>
</div>
<h2 class="majordivision" id="bodytextPearsMcGuinness">Tractatus Logico-Philosophicus (Pears/McGuinness translation)</h2>
<div class="corelinks tlpdepth0"><strong>1</strong><a href="#fn1PM" id="fn1markerPM">*</a><span class="linkarray tlpdepth0" id="p1PM"> P/M [→<a class="gerlink" href="#p1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1OGD">OGD</a>]</span></div>
<div class="para tlpdepth0">The world is all that is the case.</div>
<div class="corelinks tlpdepth1"><strong>1.1</strong><span class="linkarray tlpdepth1" id="p1.1PM"> P/M [→<a class="gerlink" href="#p1.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.1OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">The world is the totality of facts, not of things.</div>
<div class="corelinks tlpdepth2"><strong>1.11</strong><span class="linkarray tlpdepth2" id="p1.11PM"> P/M [→<a class="gerlink" href="#p1.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.11OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The world is determined by the facts, and by their being <em>all</em> the facts.</div>
<div class="corelinks tlpdepth2"><strong>1.12</strong><span class="linkarray tlpdepth2" id="p1.12PM"> P/M [→<a class="gerlink" href="#p1.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.12OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">For the totality of facts determines what is the case, and also whatever is not the case.</div>
<div class="corelinks tlpdepth2"><strong>1.13</strong><span class="linkarray tlpdepth2" id="p1.13PM"> P/M [→<a class="gerlink" href="#p1.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.13OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The facts in logical space are the world.</div>
<div class="corelinks tlpdepth1"><strong>1.2</strong><span class="linkarray tlpdepth1" id="p1.2PM"> P/M [→<a class="gerlink" href="#p1.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.2OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">The world divides into facts.</div>
<div class="corelinks tlpdepth2"><strong>1.21</strong><span class="linkarray tlpdepth2" id="p1.21PM"> P/M [→<a class="gerlink" href="#p1.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.21OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Each item can be the case or not the case while everything else remains the same.</div>
<div class="corelinks tlpdepth0"><strong>2</strong><span class="linkarray tlpdepth0" id="p2PM"> P/M [→<a class="gerlink" href="#p2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2OGD">OGD</a>]</span></div>
<div class="para tlpdepth0">What is the case—a fact—is the existence of states of affairs.</div>
<div class="corelinks tlpdepth2"><strong>2.01</strong><span class="linkarray tlpdepth2" id="p2.01PM"> P/M [→<a class="gerlink" href="#p2.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A state of affairs (a state of things) is a combination of objects (things).</div>
<div class="corelinks tlpdepth3"><strong>2.011</strong><span class="linkarray tlpdepth3" id="p2.011PM"> P/M [→<a class="gerlink" href="#p2.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.011OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is essential to things that they should be possible constituents of states of affairs.</div>
<div class="corelinks tlpdepth3"><strong>2.012</strong><span class="linkarray tlpdepth3" id="p2.012PM"> P/M [→<a class="gerlink" href="#p2.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.012OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In logic nothing is accidental: if a thing <em>can</em> occur in a state of affairs, the possibility of the state of affairs must be written into the thing itself.</div>
<div class="corelinks tlpdepth4"><strong>2.0121</strong><span class="linkarray tlpdepth4" id="p2.0121PM"> P/M [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It would seem to be a sort of accident, if it turned out that a situation would fit a thing that could already exist entirely on its own.</div>
<div class="para tlpdepth4">If things can occur in states of affairs, this possibility must be in them from the beginning.</div>
<div class="para tlpdepth4">(Nothing in the province of logic can be merely possible. Logic deals with every possibility and all possibilities are its facts.)</div>
<div class="para tlpdepth4">Just as we are quite unable to imagine spatial objects outside space or temporal objects outside time, so too there is <em>no</em> object that we can imagine excluded from the possibility of combining with others.</div>
<div class="para tlpdepth4">If I can imagine objects combined in states of affairs, I cannot imagine them excluded from the possibility of such combinations.</div>
<div class="corelinks tlpdepth4"><strong>2.0122</strong><span class="linkarray tlpdepth4" id="p2.0122PM"> P/M [→<a class="gerlink" href="#p2.0122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0122OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Things are independent in so far as they can occur in all <em>possible</em> situations, but this form of independence is a form of connexion with states of affairs, a form of dependence. (It is impossible for words to appear in two different roles: by themselves, and in propositions.)</div>
<div class="corelinks tlpdepth4"><strong>2.0123</strong><span class="linkarray tlpdepth4" id="p2.0123PM"> P/M [→<a class="gerlink" href="#p2.0123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0123OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If I know an object I also know all its possible occurrences in states of affairs.</div>
<div class="para tlpdepth4">(Every one of these possibilities must be part of the nature of the object.)</div>
<div class="para tlpdepth4">A new possibility cannot be discovered later.</div>
<div class="corelinks tlpdepth5"><strong>2.01231</strong><span class="linkarray tlpdepth5" id="p2.01231PM"> P/M [→<a class="gerlink" href="#p2.01231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01231OGD">OGD</a>]</span></div>
<div class="para tlpdepth5">If I am to know an object, though I need not know its external properties, I must know all its internal properties.</div>
<div class="corelinks tlpdepth4"><strong>2.0124</strong><span class="linkarray tlpdepth4" id="p2.0124PM"> P/M [→<a class="gerlink" href="#p2.0124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0124OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If all objects are given, then at the same time all <em>possible</em> states of affairs are also given.</div>
<div class="corelinks tlpdepth3"><strong>2.013</strong><span class="linkarray tlpdepth3" id="p2.013PM"> P/M [→<a class="gerlink" href="#p2.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.013OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Each thing is, as it were, in a space of possible states of affairs. This space I can imagine empty, but I cannot imagine the thing without the space.</div>
<div class="corelinks tlpdepth4"><strong>2.0131</strong><span class="linkarray tlpdepth4" id="p2.0131PM"> P/M [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">A spatial object must be situated in infinite space. (A spatial point is an argument-place.)</div>
<div class="para tlpdepth4">A speck in the visual field, thought it need not be red, must have some colour: it is, so to speak, surrounded by colour-space. Notes must have <em>some</em> pitch, objects of the sense of touch <em>some</em> degree of hardness, and so on.</div>
<div class="corelinks tlpdepth3"><strong>2.014</strong><span class="linkarray tlpdepth3" id="p2.014PM"> P/M [→<a class="gerlink" href="#p2.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.014OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Objects contain the possibility of all situations.</div>
<div class="corelinks tlpdepth4"><strong>2.0141</strong><span class="linkarray tlpdepth4" id="p2.0141PM"> P/M [→<a class="gerlink" href="#p2.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0141OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The possibility of its occurring in states of affairs is the form of an object.</div>
<div class="corelinks tlpdepth2"><strong>2.02</strong><span class="linkarray tlpdepth2" id="p2.02PM"> P/M [→<a class="gerlink" href="#p2.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.02OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Objects are simple.</div>
<div class="corelinks tlpdepth4"><strong>2.0201</strong><span class="linkarray tlpdepth4" id="p2.0201PM"> P/M [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0201OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Every statement about complexes can be resolved into a statement about their constituents and into the propositions that describe the complexes completely.</div>
<div class="corelinks tlpdepth3"><strong>2.021</strong><span class="linkarray tlpdepth3" id="p2.021PM"> P/M [→<a class="gerlink" href="#p2.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.021OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Objects make up the substance of the world. That is why they cannot be composite.</div>
<div class="corelinks tlpdepth4"><strong>2.0211</strong><span class="linkarray tlpdepth4" id="p2.0211PM"> P/M [→<a class="gerlink" href="#p2.0211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0211OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.</div>
<div class="corelinks tlpdepth4"><strong>2.0212</strong><span class="linkarray tlpdepth4" id="p2.0212PM"> P/M [→<a class="gerlink" href="#p2.0212GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0212OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">In that case we could not sketch any picture of the world (true or false).</div>
<div class="corelinks tlpdepth3"><strong>2.022</strong><span class="linkarray tlpdepth3" id="p2.022PM"> P/M [→<a class="gerlink" href="#p2.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.022OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is obvious that an imagined world, however different it may be from the real one, must have <em>something</em>—a form—in common with it.</div>
<div class="corelinks tlpdepth3"><strong>2.023</strong><span class="linkarray tlpdepth3" id="p2.023PM"> P/M [→<a class="gerlink" href="#p2.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.023OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Objects are just what constitute this unalterable form.</div>
<div class="corelinks tlpdepth4"><strong>2.0231</strong><span class="linkarray tlpdepth4" id="p2.0231PM"> P/M [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The substance of the world <em>can</em> only determine a form, and not any material properties. For it is only by means of propositions that material properties are represented—only by the configuration of objects that they are produced.</div>
<div class="corelinks tlpdepth4"><strong>2.0232</strong><span class="linkarray tlpdepth4" id="p2.0232PM"> P/M [→<a class="gerlink" href="#p2.0232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0232OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">In a manner of speaking, objects are colourless.</div>
<div class="corelinks tlpdepth4"><strong>2.0233</strong><span class="linkarray tlpdepth4" id="p2.0233PM"> P/M [→<a class="gerlink" href="#p2.0233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0233OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If two objects have the same logical form, the only distinction between them, apart from their external properties, is that they are different.</div>
<div class="corelinks tlpdepth5"><strong>2.02331</strong><span class="linkarray tlpdepth5" id="p2.02331PM"> P/M [→<a class="gerlink" href="#p2.02331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.02331OGD">OGD</a>]</span></div>
<div class="para tlpdepth5">Either a thing has properties that nothing else has, in which case we can immediately use a description to distinguish it from the others and refer to it; or, on the other hand, there are several things that have the whole set of their properties in common, in which case it is quite impossible to indicate one of them.</div>
<div class="para tlpdepth5">For if there is nothing to distinguish a thing, I cannot distinguish it, since otherwise it would be distinguished after all.</div>
<div class="corelinks tlpdepth3"><strong>2.024</strong><span class="linkarray tlpdepth3" id="p2.024PM"> P/M [→<a class="gerlink" href="#p2.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.024OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The substance is what subsists independently of what is the case.</div>
<div class="corelinks tlpdepth3"><strong>2.025</strong><span class="linkarray tlpdepth3" id="p2.025PM"> P/M [→<a class="gerlink" href="#p2.025GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.025OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is form and content.</div>
<div class="corelinks tlpdepth4"><strong>2.0251</strong><span class="linkarray tlpdepth4" id="p2.0251PM"> P/M [→<a class="gerlink" href="#p2.0251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0251OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Space, time, colour (being coloured) are forms of objects.</div>
<div class="corelinks tlpdepth3"><strong>2.026</strong><span class="linkarray tlpdepth3" id="p2.026PM"> P/M [→<a class="gerlink" href="#p2.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.026OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">There must be objects, if the world is to have unalterable form.</div>
<div class="corelinks tlpdepth3"><strong>2.027</strong><span class="linkarray tlpdepth3" id="p2.027PM"> P/M [→<a class="gerlink" href="#p2.027GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.027OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Objects, the unalterable, and the subsistent are one and the same.</div>
<div class="corelinks tlpdepth4"><strong>2.0271</strong><span class="linkarray tlpdepth4" id="p2.0271PM"> P/M [→<a class="gerlink" href="#p2.0271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0271OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Objects are what is unalterable and subsistent; their configuration is what is changing and unstable.</div>
<div class="corelinks tlpdepth4"><strong>2.0272</strong><span class="linkarray tlpdepth4" id="p2.0272PM"> P/M [→<a class="gerlink" href="#p2.0272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0272OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The configuration of objects produces states of affairs.</div>
<div class="corelinks tlpdepth2"><strong>2.03</strong><span class="linkarray tlpdepth2" id="p2.03PM"> P/M [→<a class="gerlink" href="#p2.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.03OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">In a state of affairs objects fit into one another like the links of a chain.</div>
<div class="corelinks tlpdepth3"><strong>2.031</strong><span class="linkarray tlpdepth3" id="p2.031PM"> P/M [→<a class="gerlink" href="#p2.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.031OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In a state of affairs objects stand in a determinate relation to one another.</div>
<div class="corelinks tlpdepth3"><strong>2.032</strong><span class="linkarray tlpdepth3" id="p2.032PM"> P/M [→<a class="gerlink" href="#p2.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.032OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The determinate way in which objects are connected in a state of affairs is the structure of the state of affairs.</div>
<div class="corelinks tlpdepth3"><strong>2.033</strong><span class="linkarray tlpdepth3" id="p2.033PM"> P/M [→<a class="gerlink" href="#p2.033GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.033OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Form is the possibility of structure.</div>
<div class="corelinks tlpdepth3"><strong>2.034</strong><span class="linkarray tlpdepth3" id="p2.034PM"> P/M [→<a class="gerlink" href="#p2.034GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.034OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The structure of a fact consists of the structures of states of affairs.</div>
<div class="corelinks tlpdepth2"><strong>2.04</strong><span class="linkarray tlpdepth2" id="p2.04PM"> P/M [→<a class="gerlink" href="#p2.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.04OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The totality of existing states of affairs is the world.</div>
<div class="corelinks tlpdepth2"><strong>2.05</strong><span class="linkarray tlpdepth2" id="p2.05PM"> P/M [→<a class="gerlink" href="#p2.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.05OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The totality of existing states of affairs also determines which states of affairs do not exist.</div>
<div class="corelinks tlpdepth2"><strong>2.06</strong><span class="linkarray tlpdepth2" id="p2.06PM"> P/M [→<a class="gerlink" href="#p2.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.06OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The existence and non-existence of states of affairs is reality.</div>
<div class="para tlpdepth2">(We call the existence of states of affairs a positive fact, and their non-existence a negative fact.)</div>
<div class="corelinks tlpdepth3"><strong>2.061</strong><span class="linkarray tlpdepth3" id="p2.061PM"> P/M [→<a class="gerlink" href="#p2.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.061OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">States of affairs are independent of one another.</div>
<div class="corelinks tlpdepth3"><strong>2.062</strong><span class="linkarray tlpdepth3" id="p2.062PM"> P/M [→<a class="gerlink" href="#p2.062GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.062OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">From the existence or non-existence of one state of affairs it is impossible to infer the existence or non-existence of another.</div>
<div class="corelinks tlpdepth3"><strong>2.063</strong><span class="linkarray tlpdepth3" id="p2.063PM"> P/M [→<a class="gerlink" href="#p2.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.063OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The sum-total of reality is the world.</div>
<div class="corelinks tlpdepth1"><strong>2.1</strong><span class="linkarray tlpdepth1" id="p2.1PM"> P/M [→<a class="gerlink" href="#p2.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">We picture facts to ourselves.</div>
<div class="corelinks tlpdepth2"><strong>2.11</strong><span class="linkarray tlpdepth2" id="p2.11PM"> P/M [→<a class="gerlink" href="#p2.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.11OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A picture presents a situation in logical space, the existence and non-existence of states of affairs.</div>
<div class="corelinks tlpdepth2"><strong>2.12</strong><span class="linkarray tlpdepth2" id="p2.12PM"> P/M [→<a class="gerlink" href="#p2.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.12OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A picture is a model of reality.</div>
<div class="corelinks tlpdepth2"><strong>2.13</strong><span class="linkarray tlpdepth2" id="p2.13PM"> P/M [→<a class="gerlink" href="#p2.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.13OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">In a picture objects have the elements of the picture corresponding to them.</div>
<div class="corelinks tlpdepth3"><strong>2.131</strong><span class="linkarray tlpdepth3" id="p2.131PM"> P/M [→<a class="gerlink" href="#p2.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.131OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In a picture the elements of the picture are the representatives of objects.</div>
<div class="corelinks tlpdepth2"><strong>2.14</strong><span class="linkarray tlpdepth2" id="p2.14PM"> P/M [→<a class="gerlink" href="#p2.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.14OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">What constitutes a picture is that its elements are related to one another in a determinate way.</div>
<div class="corelinks tlpdepth3"><strong>2.141</strong><span class="linkarray tlpdepth3" id="p2.141PM"> P/M [→<a class="gerlink" href="#p2.141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.141OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture is a fact.</div>
<div class="corelinks tlpdepth2"><strong>2.15</strong><span class="linkarray tlpdepth2" id="p2.15PM"> P/M [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way.</div>
<div class="para tlpdepth2">Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture.</div>
<div class="corelinks tlpdepth3"><strong>2.151</strong><span class="linkarray tlpdepth3" id="p2.151PM"> P/M [→<a class="gerlink" href="#p2.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.151OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture.</div>
<div class="corelinks tlpdepth4"><strong>2.1511</strong><span class="linkarray tlpdepth4" id="p2.1511PM"> P/M [→<a class="gerlink" href="#p2.1511GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1511OGD">OGD</a>]</span></div>
<div class="para tlpdepth4"><em>That</em> is how a picture is attached to reality; it reaches right out to it.</div>
<div class="corelinks tlpdepth4"><strong>2.1512</strong><span class="linkarray tlpdepth4" id="p2.1512PM"> P/M [→<a class="gerlink" href="#p2.1512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1512OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is laid against reality like a measure.</div>
<div class="corelinks tlpdepth5"><strong>2.15121</strong><span class="linkarray tlpdepth5" id="p2.15121PM"> P/M [→<a class="gerlink" href="#p2.15121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15121OGD">OGD</a>]</span></div>
<div class="para tlpdepth5">Only the end-points of the graduating lines actually <em>touch</em> the object that is to be measured.</div>
<div class="corelinks tlpdepth4"><strong>2.1513</strong><span class="linkarray tlpdepth4" id="p2.1513PM"> P/M [→<a class="gerlink" href="#p2.1513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1513OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">So a picture, conceived in this way, also includes the pictorial relationship, which makes it into a picture.</div>
<div class="corelinks tlpdepth4"><strong>2.1514</strong><span class="linkarray tlpdepth4" id="p2.1514PM"> P/M [→<a class="gerlink" href="#p2.1514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1514OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The pictorial relationship consists of the correlations of the picture’s elements with things.</div>
<div class="corelinks tlpdepth4"><strong>2.1515</strong><span class="linkarray tlpdepth4" id="p2.1515PM"> P/M [→<a class="gerlink" href="#p2.1515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1515OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">These correlations are, as it were, the feelers of the picture’s elements, with which the picture touches reality.</div>
<div class="corelinks tlpdepth2"><strong>2.16</strong><span class="linkarray tlpdepth2" id="p2.16PM"> P/M [→<a class="gerlink" href="#p2.16GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.16OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If a fact is to be a picture, it must have something in common with what it depicts.</div>
<div class="corelinks tlpdepth3"><strong>2.161</strong><span class="linkarray tlpdepth3" id="p2.161PM"> P/M [→<a class="gerlink" href="#p2.161GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.161OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all.</div>
<div class="corelinks tlpdepth2"><strong>2.17</strong><span class="linkarray tlpdepth2" id="p2.17PM"> P/M [→<a class="gerlink" href="#p2.17GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.17OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">What a picture must have in common with reality, in order to be able to depict it—correctly or incorrectly—in the way that it does, is its pictorial form.</div>
<div class="corelinks tlpdepth3"><strong>2.171</strong><span class="linkarray tlpdepth3" id="p2.171PM"> P/M [→<a class="gerlink" href="#p2.171GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.171OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture can depict any reality whose form it has.</div>
<div class="para tlpdepth3">A spatial picture can depict anything spatial, a coloured one anything coloured, etc.</div>
<div class="corelinks tlpdepth3"><strong>2.172</strong><span class="linkarray tlpdepth3" id="p2.172PM"> P/M [→<a class="gerlink" href="#p2.172GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.172OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture cannot, however, depict its pictorial form: it displays it.</div>
<div class="corelinks tlpdepth3"><strong>2.173</strong><span class="linkarray tlpdepth3" id="p2.173PM"> P/M [→<a class="gerlink" href="#p2.173GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.173OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture represents its subject from a position outside it. (Its standpoint is its representational form.) That is why a picture represents its subject correctly or incorrectly.</div>
<div class="corelinks tlpdepth3"><strong>2.174</strong><span class="linkarray tlpdepth3" id="p2.174PM"> P/M [→<a class="gerlink" href="#p2.174GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.174OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture cannot, however, place itself outside its representational form.</div>
<div class="corelinks tlpdepth2"><strong>2.18</strong><span class="linkarray tlpdepth2" id="p2.18PM"> P/M [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">What any picture, of whatever form, must have in common with reality, in order to be able to depict it—correctly or incorrectly—in any way at all, is logical form, i.e. the form of reality.</div>
<div class="corelinks tlpdepth3"><strong>2.181</strong><span class="linkarray tlpdepth3" id="p2.181PM"> P/M [→<a class="gerlink" href="#p2.181GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.181OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture whose pictorial form is logical form is called a logical picture.</div>
<div class="corelinks tlpdepth3"><strong>2.182</strong><span class="linkarray tlpdepth3" id="p2.182PM"> P/M [→<a class="gerlink" href="#p2.182GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.182OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Every picture is <em>at the same time</em> a logical one. (On the other hand, not every picture is, for example, a spatial one.)</div>
<div class="corelinks tlpdepth2"><strong>2.19</strong><span class="linkarray tlpdepth2" id="p2.19PM"> P/M [→<a class="gerlink" href="#p2.19GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.19OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Logical pictures can depict the world.</div>
<div class="corelinks tlpdepth1"><strong>2.2</strong><span class="linkarray tlpdepth1" id="p2.2PM"> P/M [→<a class="gerlink" href="#p2.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.2OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">A picture has logico-pictorial form in common with what it depicts.</div>
<div class="corelinks tlpdepth3"><strong>2.201</strong><span class="linkarray tlpdepth3" id="p2.201PM"> P/M [→<a class="gerlink" href="#p2.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.201OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture depicts reality by representing a possibility of existence and non-existence of states of affairs.</div>
<div class="corelinks tlpdepth3"><strong>2.202</strong><span class="linkarray tlpdepth3" id="p2.202PM"> P/M [→<a class="gerlink" href="#p2.202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.202OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture represents a possible situation in logical space.</div>
<div class="corelinks tlpdepth3"><strong>2.203</strong><span class="linkarray tlpdepth3" id="p2.203PM"> P/M [→<a class="gerlink" href="#p2.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.203OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A picture contains the possibility of the situation that it represents.</div>
<div class="corelinks tlpdepth2"><strong>2.21</strong><span class="linkarray tlpdepth2" id="p2.21PM"> P/M [→<a class="gerlink" href="#p2.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.21OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A picture agrees with reality or fails to agree; it is correct or incorrect, true or false.</div>
<div class="corelinks tlpdepth2"><strong>2.22</strong><span class="linkarray tlpdepth2" id="p2.22PM"> P/M [→<a class="gerlink" href="#p2.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.22OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">What a picture represents it represents independently of its truth or falsity, by means of its pictorial form.</div>
<div class="corelinks tlpdepth3"><strong>2.221</strong><span class="linkarray tlpdepth3" id="p2.221PM"> P/M [→<a class="gerlink" href="#p2.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.221OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What a picture represents is its sense.</div>
<div class="corelinks tlpdepth3"><strong>2.222</strong><span class="linkarray tlpdepth3" id="p2.222PM"> P/M [→<a class="gerlink" href="#p2.222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.222OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The agreement or disagreement of its sense with reality constitutes its truth or falsity.</div>
<div class="corelinks tlpdepth3"><strong>2.223</strong><span class="linkarray tlpdepth3" id="p2.223PM"> P/M [→<a class="gerlink" href="#p2.223GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.223OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In order to tell whether a picture is true or false we must compare it with reality.</div>
<div class="corelinks tlpdepth3"><strong>2.224</strong><span class="linkarray tlpdepth3" id="p2.224PM"> P/M [→<a class="gerlink" href="#p2.224GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.224OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is impossible to tell from the picture alone whether it is true or false.</div>
<div class="corelinks tlpdepth3"><strong>2.225</strong><span class="linkarray tlpdepth3" id="p2.225PM"> P/M [→<a class="gerlink" href="#p2.225GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.225OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">There are no pictures that are true <em>a priori</em>.</div>
<div class="corelinks tlpdepth0"><strong>3</strong><span class="linkarray tlpdepth0" id="p3PM"> P/M [→<a class="gerlink" href="#p3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3OGD">OGD</a>]</span></div>
<div class="para tlpdepth0">A logical picture of facts is a thought.</div>
<div class="corelinks tlpdepth3"><strong>3.001</strong><span class="linkarray tlpdepth3" id="p3.001PM"> P/M [→<a class="gerlink" href="#p3.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.001OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">‘A state of affairs is thinkable’: what this means is that we can picture it to ourselves.</div>
<div class="corelinks tlpdepth2"><strong>3.01</strong><span class="linkarray tlpdepth2" id="p3.01PM"> P/M [→<a class="gerlink" href="#p3.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.01OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The totality of true thoughts is a picture of the world.</div>
<div class="corelinks tlpdepth2"><strong>3.02</strong><span class="linkarray tlpdepth2" id="p3.02PM"> P/M [→<a class="gerlink" href="#p3.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.02OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A thought contains the possibility of the situation of which it is the thought. What is thinkable is possible too.</div>
<div class="corelinks tlpdepth2"><strong>3.03</strong><span class="linkarray tlpdepth2" id="p3.03PM"> P/M [→<a class="gerlink" href="#p3.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.03OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Thought can never be of anything illogical, since, if it were, we should have to think illogically.</div>
<div class="corelinks tlpdepth3"><strong>3.031</strong><span class="linkarray tlpdepth3" id="p3.031PM"> P/M [→<a class="gerlink" href="#p3.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.031OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not <em>say</em> what an ‘illogical’ world would look like.</div>
<div class="corelinks tlpdepth3"><strong>3.032</strong><span class="linkarray tlpdepth3" id="p3.032PM"> P/M [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is as impossible to represent in language anything that ‘contradicts logic’ as it is in geometry to represent by its co-ordinates a figure that contradicts the laws of space, or to give the co-ordinates of a point that does not exist.</div>
<div class="corelinks tlpdepth4"><strong>3.0321</strong><span class="linkarray tlpdepth4" id="p3.0321PM"> P/M [→<a class="gerlink" href="#p3.0321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.0321OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Though a state of affairs that would contravene the laws of physics can be represented by us spatially, one that would contravene the laws of geometry cannot.</div>
<div class="corelinks tlpdepth2"><strong>3.04</strong><span class="linkarray tlpdepth2" id="p3.04PM"> P/M [→<a class="gerlink" href="#p3.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.04OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If a thought were correct <em>a priori</em>, it would be a thought whose possibility ensured its truth.</div>
<div class="corelinks tlpdepth2"><strong>3.05</strong><span class="linkarray tlpdepth2" id="p3.05PM"> P/M [→<a class="gerlink" href="#p3.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.05OGD">OGD</a>]</span></div>
<div class="para tlpdepth2"><em>A priori</em> knowledge that a thought was true would be possible only if its truth were recognizable from the thought itself (without anything to compare it with).</div>
<div class="corelinks tlpdepth1"><strong>3.1</strong><span class="linkarray tlpdepth1" id="p3.1PM"> P/M [→<a class="gerlink" href="#p3.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">In a proposition a thought finds an expression that can be perceived by the senses.</div>
<div class="corelinks tlpdepth2"><strong>3.11</strong><span class="linkarray tlpdepth2" id="p3.11PM"> P/M [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">We use the perceptible sign of a proposition (spoken or written, etc.) as a projection of a possible situation.</div>
<div class="para tlpdepth2">The method of projection is to think of the sense of the proposition.</div>
<div class="corelinks tlpdepth2"><strong>3.12</strong><span class="linkarray tlpdepth2" id="p3.12PM"> P/M [→<a class="gerlink" href="#p3.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.12OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">I call the sign with which we express a thought a propositional sign.—And a proposition is a propositional sign in its projective relation to the world.</div>
<div class="corelinks tlpdepth2"><strong>3.13</strong><span class="linkarray tlpdepth2" id="p3.13PM"> P/M [→<a class="gerlink" href="#p3.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.13OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition includes all that the projection includes, but not what is projected.</div>
<div class="para tlpdepth2">Therefore, though what is projected is not itself included, its possibility is.</div>
<div class="para tlpdepth2">A proposition, therefore, does not actually contain its sense, but does contain the possibility of expressing it.</div>
<div class="para tlpdepth2">(‘The content of a proposition’ means the content of a proposition that has sense.)</div>
<div class="para tlpdepth2">A proposition contains the form, but not the content, of its sense.</div>
<div class="corelinks tlpdepth2"><strong>3.14</strong><span class="linkarray tlpdepth2" id="p3.14PM"> P/M [→<a class="gerlink" href="#p3.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.14OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to one another.</div>
<div class="para tlpdepth2">A propositional sign is a fact.</div>
<div class="corelinks tlpdepth3"><strong>3.141</strong><span class="linkarray tlpdepth3" id="p3.141PM"> P/M [→<a class="gerlink" href="#p3.141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.141OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A proposition is not a blend of words.—(Just as a theme in music is not a blend of notes.)</div>
<div class="para tlpdepth3">A proposition is articulate.</div>
<div class="corelinks tlpdepth3"><strong>3.142</strong><span class="linkarray tlpdepth3" id="p3.142PM"> P/M [→<a class="gerlink" href="#p3.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.142OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Only facts can express a sense, a set of names cannot.</div>
<div class="corelinks tlpdepth3"><strong>3.143</strong><span class="linkarray tlpdepth3" id="p3.143PM"> P/M [→<a class="gerlink" href="#p3.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.143OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Although a propositional sign is a fact, this is obscured by the usual form of expression in writing or print.</div>
<div class="para tlpdepth3">For in a printed proposition, for example, no essential difference is apparent between a propositional sign and a word.</div>
<div class="para tlpdepth3">(That is what made it possible for Frege to call a proposition a composite name.)</div>
<div class="corelinks tlpdepth4"><strong>3.1431</strong><span class="linkarray tlpdepth4" id="p3.1431PM"> P/M [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The essence of a propositional sign is very clearly seen if we imagine one composed of spatial objects (such as tables, chairs, and books) instead of written signs.</div>
<div class="para tlpdepth4">Then the spatial arrangement of these things will express the sense of the proposition.</div>
<div class="corelinks tlpdepth4"><strong>3.1432</strong><span class="linkarray tlpdepth4" id="p3.1432PM"> P/M [→<a class="gerlink" href="#p3.1432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1432OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Instead of, ‘The complex sign “<span class="mathmode"><var>aRb</var></span>” says that <span class="mathmode"><var>a</var></span> stands to <span class="mathmode"><var>b</var></span> in
the relation <span class="mathmode"><var>R</var></span>’, we ought to put, ‘<em>That</em> “<span class="mathmode"><var>a</var></span>” stands to “<span class="mathmode"><var>b</var></span>” in a certain
relation says <em>that</em> <span class="mathmode"><var>aRb</var></span>.’</div>
<div class="corelinks tlpdepth3"><strong>3.144</strong><span class="linkarray tlpdepth3" id="p3.144PM"> P/M [→<a class="gerlink" href="#p3.144GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.144OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Situations can be described but not <em>given names</em>.</div>
<div class="para tlpdepth3">(Names are like points; propositions like arrows—they have sense.)</div>
<div class="corelinks tlpdepth1"><strong>3.2</strong><span class="linkarray tlpdepth1" id="p3.2PM"> P/M [→<a class="gerlink" href="#p3.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.2OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">In a proposition a thought can be expressed in such a way that elements of the propositional sign correspond to the objects of the thought.</div>
<div class="corelinks tlpdepth3"><strong>3.201</strong><span class="linkarray tlpdepth3" id="p3.201PM"> P/M [→<a class="gerlink" href="#p3.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.201OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">I call such elements ‘simple signs’, and such a proposition ‘complete analysed’.</div>
<div class="corelinks tlpdepth3"><strong>3.202</strong><span class="linkarray tlpdepth3" id="p3.202PM"> P/M [→<a class="gerlink" href="#p3.202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.202OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The simple signs employed in propositions are called names.</div>
<div class="corelinks tlpdepth3"><strong>3.203</strong><span class="linkarray tlpdepth3" id="p3.203PM"> P/M [→<a class="gerlink" href="#p3.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.203OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A name means an object. The object is its meaning. (‘<span class="mathmode"><var>A</var></span>’ is the same sign as ‘<span class="mathmode"><var>A</var></span>’.)</div>
<div class="corelinks tlpdepth2"><strong>3.21</strong><span class="linkarray tlpdepth2" id="p3.21PM"> P/M [→<a class="gerlink" href="#p3.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.21OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The configuration of objects in a situation corresponds to the configuration of simple signs in the propositional sign.</div>
<div class="corelinks tlpdepth2"><strong>3.22</strong><span class="linkarray tlpdepth2" id="p3.22PM"> P/M [→<a class="gerlink" href="#p3.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.22OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">In a proposition a name is the representative of an object.</div>
<div class="corelinks tlpdepth3"><strong>3.221</strong><span class="linkarray tlpdepth3" id="p3.221PM"> P/M [→<a class="gerlink" href="#p3.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.221OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Objects can only be <em>named</em>. Signs are their representatives. I can only speak <em>about</em> them: I cannot <em>put them into words</em>. Propositions can only say <em>how</em> things are, not <em>what</em> they are.</div>
<div class="corelinks tlpdepth2"><strong>3.23</strong><span class="linkarray tlpdepth2" id="p3.23PM"> P/M [→<a class="gerlink" href="#p3.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.23OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The requirement that simple signs be possible is the requirement that sense be determinate.</div>
<div class="corelinks tlpdepth2"><strong>3.24</strong><span class="linkarray tlpdepth2" id="p3.24PM"> P/M [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition about a complex stands in an internal relation to a proposition about a constituent of the complex.</div>
<div class="para tlpdepth2">A complex can be given
only by its description, which will be right or wrong. A proposition
that mentions a complex will not be nonsensical, if the complex does
not exist, but simply false.</div>
<div class="para tlpdepth2">When a propositional element signifies a complex, this can be seen from an indeterminateness in the propositions in which it occurs. In such cases we <em>know</em> that the proposition leaves something undetermined. (In fact the notation for generality <em>contains</em> a prototype.)</div>
<div class="para tlpdepth2">The contraction of a symbol for a complex into a simple symbol can be expressed in a definition.</div>
<div class="corelinks tlpdepth2"><strong>3.25</strong><span class="linkarray tlpdepth2" id="p3.25PM"> P/M [→<a class="gerlink" href="#p3.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.25OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition has one and only one complete analysis.</div>
<div class="corelinks tlpdepth3"><strong>3.251</strong><span class="linkarray tlpdepth3" id="p3.251PM"> P/M [→<a class="gerlink" href="#p3.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.251OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What a proposition expresses it expresses in a determinate manner, which can be set out clearly: a proposition is articulated.</div>
<div class="corelinks tlpdepth2"><strong>3.26</strong><span class="linkarray tlpdepth2" id="p3.26PM"> P/M [→<a class="gerlink" href="#p3.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.26OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A name cannot be dissected any further by means of a definition: it is a primitive sign.</div>
<div class="corelinks tlpdepth3"><strong>3.261</strong><span class="linkarray tlpdepth3" id="p3.261PM"> P/M [→<a class="gerlink" href="#p3.261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.261OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Every sign that has a definition signifies <em>via</em> the signs that serve to define it; and the definitions point the way.</div>
<div class="para tlpdepth3">Two signs cannot signify in the same manner if one is primitive and the other is defined by means of primitive signs. Names <em>cannot</em> be anatomized by means of definitions. (Nor can any sign that has a meaning independently and on its own.)</div>
<div class="corelinks tlpdepth3"><strong>3.262</strong><span class="linkarray tlpdepth3" id="p3.262PM"> P/M [→<a class="gerlink" href="#p3.262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.262OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What signs fail to express, their application shows. What signs slur over, their application says clearly.</div>
<div class="corelinks tlpdepth3"><strong>3.263</strong><span class="linkarray tlpdepth3" id="p3.263PM"> P/M [→<a class="gerlink" href="#p3.263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.263OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The meanings of primitive signs can be explained by means of elucidations. Elucidations are propositions that contain the primitive signs. So they can only be understood if the meanings of those signs are already known.</div>
<div class="corelinks tlpdepth1"><strong>3.3</strong><span class="linkarray tlpdepth1" id="p3.3PM"> P/M [→<a class="gerlink" href="#p3.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">Only propositions have sense; only in the nexus of a proposition does a name have meaning.</div>
<div class="corelinks tlpdepth2"><strong>3.31</strong><span class="linkarray tlpdepth2" id="p3.31PM"> P/M [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">I call any part of a proposition that characterizes its sense an expression (or a symbol).</div>
<div class="para tlpdepth2">(A proposition is itself an expression.)</div>
<div class="para tlpdepth2">Everything essential to their sense that propositions can have in common with one another is an expression.</div>
<div class="para tlpdepth2">An expression is the mark of a form and a content.</div>
<div class="corelinks tlpdepth3"><strong>3.311</strong><span class="linkarray tlpdepth3" id="p3.311PM"> P/M [→<a class="gerlink" href="#p3.311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.311OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">An expression presupposes the forms of all the propositions in which it can occur. It is the common characteristic mark of a class of propositions.</div>
<div class="corelinks tlpdepth3"><strong>3.312</strong><span class="linkarray tlpdepth3" id="p3.312PM"> P/M [→<a class="gerlink" href="#p3.312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.312OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is therefore presented by means of the general form of the propositions that it characterizes.</div>
<div class="para tlpdepth3">In fact, in this form the expression will be <em>constant</em> and everything else <em>variable</em>.</div>
<div class="corelinks tlpdepth3"><strong>3.313</strong><span class="linkarray tlpdepth3" id="p3.313PM"> P/M [→<a class="gerlink" href="#p3.313GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.313OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Thus an expression is presented by means of a variable whose values are the propositions that contain the expression.</div>
<div class="para tlpdepth3">(In the limiting case the variable becomes a constant, the expression becomes a proposition.)</div>
<div class="para tlpdepth3">I call such a variable a ‘propositional variable’.</div>
<div class="corelinks tlpdepth3"><strong>3.314</strong><span class="linkarray tlpdepth3" id="p3.314PM"> P/M [→<a class="gerlink" href="#p3.314GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.314OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">An expression has meaning only in a proposition. All variables can be construed as propositional variables.</div>
<div class="para tlpdepth3">(Even variable names.)</div>
<div class="corelinks tlpdepth3"><strong>3.315</strong><span class="linkarray tlpdepth3" id="p3.315PM"> P/M [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If we turn a constituent of a proposition into a variable, there is a class of propositions all of which are values of the resulting variable proposition. In general, this class too will be dependent on the meaning that our arbitrary conventions have given to parts of the original proposition. But if all the signs in it that have arbitrarily determined meanings are turned into variables, we shall still get a class of this kind. This one, however, is not dependent on any convention, but solely on the nature of the proposition. It corresponds to a logical form—a logical prototype.</div>
<div class="corelinks tlpdepth3"><strong>3.316</strong><span class="linkarray tlpdepth3" id="p3.316PM"> P/M [→<a class="gerlink" href="#p3.316GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.316OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What values a propositional variable may take is something that is stipulated.</div>
<div class="para tlpdepth3">The stipulation of values <em>is</em> the variable.</div>
<div class="corelinks tlpdepth3"><strong>3.317</strong><span class="linkarray tlpdepth3" id="p3.317PM"> P/M [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">To stipulate values for a propositional variable is to <em>give the propositions</em> whose common characteristic the variable is.</div>
<div class="para tlpdepth3">The stipulation is a description of those propositions.</div>
<div class="para tlpdepth3">The stipulation will therefore be concerned only with symbols, not with their meaning.</div>
<div class="para tlpdepth3">And the <em>only</em> thing essential to the stipulation is <em>that it is merely a description of symbols and states nothing about what is signified</em>.</div>
<div class="para tlpdepth3">How the description of the propositions is produced is not essential.</div>
<div class="corelinks tlpdepth3"><strong>3.318</strong><span class="linkarray tlpdepth3" id="p3.318PM"> P/M [→<a class="gerlink" href="#p3.318GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.318OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Like Frege and Russell I construe a proposition as a function of the expressions contained in it.</div>
<div class="corelinks tlpdepth2"><strong>3.32</strong><span class="linkarray tlpdepth2" id="p3.32PM"> P/M [→<a class="gerlink" href="#p3.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.32OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A sign is what can be perceived of a symbol.</div>
<div class="corelinks tlpdepth3"><strong>3.321</strong><span class="linkarray tlpdepth3" id="p3.321PM"> P/M [→<a class="gerlink" href="#p3.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.321OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">So one and the same sign (written or spoken, etc.) can be common to two different symbols—in which case they will signify in different ways.</div>
<div class="corelinks tlpdepth3"><strong>3.322</strong><span class="linkarray tlpdepth3" id="p3.322PM"> P/M [→<a class="gerlink" href="#p3.322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.322OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Our use of the same sign to signify two different objects can never indicate a common characteristic of the two, if we use it with two different <em>modes of signification</em>. For the sign, of course, is arbitrary. So we could choose two different signs instead, and then what would be left in common on the signifying side?</div>
<div class="corelinks tlpdepth3"><strong>3.323</strong><span class="linkarray tlpdepth3" id="p3.323PM"> P/M [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In everyday language it very frequently happens that the same word has different modes of signification—and so belongs to different symbols—or that two words that have different modes of signification are employed in propositions in what is superficially the same way.</div>
<div class="para tlpdepth3">Thus the word ‘is’ figures as the copula, as a sign for identity, and as an expression for existence; ‘exist’ figures as an intransitive verb like ‘go’, and ‘identical’ as an adjective; we speak of <em>something</em>, but also of <em>something’s</em> happening.</div>
<div class="para tlpdepth3">(In the proposition, ‘Green is green’—where the first word is the proper name of a person and the last an adjective—these words do not merely have different meanings: they are <em>different symbols</em>.)</div>
<div class="corelinks tlpdepth3"><strong>3.324</strong><span class="linkarray tlpdepth3" id="p3.324PM"> P/M [→<a class="gerlink" href="#p3.324GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.324OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In this way the most fundamental confusions are easily produced (the whole of philosophy is full of them).</div>
<div class="corelinks tlpdepth3"><strong>3.325</strong><span class="linkarray tlpdepth3" id="p3.325PM"> P/M [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In order to avoid such errors we must make use of a sign-language that excludes them by not using the same sign for different symbols and by not using in a superficially similar way signs that have different modes of signification: that is to say, a sign-language that is governed by <em>logical</em> grammar—by logical syntax.</div>
<div class="para tlpdepth3">(The conceptual notation of Frege and Russell is such a language, though, it is true, it fails to exclude all mistakes.)</div>
<div class="corelinks tlpdepth3"><strong>3.326</strong><span class="linkarray tlpdepth3" id="p3.326PM"> P/M [→<a class="gerlink" href="#p3.326GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.326OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In order to recognize a symbol by its sign we must observe how it is used with a sense.</div>
<div class="corelinks tlpdepth3"><strong>3.327</strong><span class="linkarray tlpdepth3" id="p3.327PM"> P/M [→<a class="gerlink" href="#p3.327GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.327OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A sign does not determine a logical form unless it is taken together with its logico-syntactical employment.</div>
<div class="corelinks tlpdepth3"><strong>3.328</strong><span class="linkarray tlpdepth3" id="p3.328PM"> P/M [→<a class="gerlink" href="#p3.328GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.328OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If a sign is <em>useless</em>, it is meaningless. That is the point of Occam’s maxim.</div>
<div class="para tlpdepth3">(If everything behaves as if a sign had meaning, then it does have meaning.)</div>
<div class="corelinks tlpdepth2"><strong>3.33</strong><span class="linkarray tlpdepth2" id="p3.33PM"> P/M [→<a class="gerlink" href="#p3.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.33OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">In logical syntax the meaning of a sign should never play a role. It must be possible to establish logical syntax without mentioning the <em>meaning</em> of a sign: <em>only</em> the description of expressions may be presupposed.</div>
<div class="corelinks tlpdepth3"><strong>3.331</strong><span class="linkarray tlpdepth3" id="p3.331PM"> P/M [→<a class="gerlink" href="#p3.331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.331OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">From this observation we turn to Russell’s ‘theory of types’. It can be seen that Russell must be wrong, because he had to mention the meaning of signs when establishing the rules for them.</div>
<div class="corelinks tlpdepth3"><strong>3.332</strong><span class="linkarray tlpdepth3" id="p3.332PM"> P/M [→<a class="gerlink" href="#p3.332GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.332OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">No proposition can make a statement about itself, because a propositional sign cannot be contained in itself (that is the whole of the ‘theory of types’).</div>
<div class="corelinks tlpdepth3"><strong>3.333</strong><span class="linkarray tlpdepth3" id="p3.333PM"> P/M [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself.</div>
<div class="para tlpdepth3">For let us suppose that the function <span class="mathmode"><var>F</var>(<var>fx</var>)</span> could be its own argument: in that case there would be a proposition ‘<span class="mathmode"><var>F</var>(<var>F</var>(<var>fx</var>))</span>’, in which the outer function <span class="mathmode"><var>F</var></span> and the inner function <span class="mathmode"><var>F</var></span> must have different meanings, since the inner one has the form <span class="mathmode"><var>φ</var>(<var>fx</var>)</span> and the outer one has the form <span class="mathmode"><var>ψ</var>(<var>φ</var>(<var>fx</var>))</span>. Only the letter ‘<span class="mathmode"><var>F</var></span>’ is common to the two functions, but the letter by itself signifies nothing.</div>
<div class="para tlpdepth3">This immediately becomes clear if instead of ‘<span class="mathmode"><var>F</var>(<var>Fu</var>)</span>’ we write ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>φ</var>):</span><var>F</var>(<var>φu</var>)<span class="mathrel">.</span><var>φu</var><span class="mathrel">=</span><var>Fu</var></span>’.</div>
<div class="para tlpdepth3">That disposes of Russell’s paradox.</div>
<div class="corelinks tlpdepth3"><strong>3.334</strong><span class="linkarray tlpdepth3" id="p3.334PM"> P/M [→<a class="gerlink" href="#p3.334GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.334OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The rules of logical syntax must go without saying, once we know how each individual sign signifies.</div>
<div class="corelinks tlpdepth2"><strong>3.34</strong><span class="linkarray tlpdepth2" id="p3.34PM"> P/M [→<a class="gerlink" href="#p3.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.34OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition possesses essential and accidental features.</div>
<div class="para tlpdepth2">Accidental features are those that result from the particular way in which the propositional sign is produced. Essential features are those without which the proposition could not express its sense.</div>
<div class="corelinks tlpdepth3"><strong>3.341</strong><span class="linkarray tlpdepth3" id="p3.341PM"> P/M [→<a class="gerlink" href="#p3.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.341OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">So what is essential in a proposition is what all propositions that can express the same sense have in common.</div>
<div class="para tlpdepth3">And similarly, in general, what is essential in a symbol is what all symbols that can serve the same purpose have in common.</div>
<div class="corelinks tlpdepth4"><strong>3.3411</strong><span class="linkarray tlpdepth4" id="p3.3411PM"> P/M [→<a class="gerlink" href="#p3.3411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3411OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">So one could say that the real name of an object was what all symbols that signified it had in common. Thus, one by one, all kinds of composition would prove to be unessential to a name.</div>
<div class="corelinks tlpdepth3"><strong>3.342</strong><span class="linkarray tlpdepth3" id="p3.342PM"> P/M [→<a class="gerlink" href="#p3.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.342OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Although there is something arbitrary in our notations, <em>this much</em> is not arbitrary—that <em>when</em> we have determined one thing arbitrarily, something else is necessarily the case. (This derives from the <em>essence</em> of notation.)</div>
<div class="corelinks tlpdepth4"><strong>3.3421</strong><span class="linkarray tlpdepth4" id="p3.3421PM"> P/M [→<a class="gerlink" href="#p3.3421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3421OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">A particular mode of signifying may be unimportant but it is always important that it is a <em>possible</em> mode of signifying. And that is generally so in philosophy: again and again the individual case turns out to be unimportant, but the possibility of each individual case discloses something about the essence of the world.</div>
<div class="corelinks tlpdepth3"><strong>3.343</strong><span class="linkarray tlpdepth3" id="p3.343PM"> P/M [→<a class="gerlink" href="#p3.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.343OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Definitions are rules for translating from one language into another. Any correct sign-language must be translatable into any other in accordance with such rules: it is <em>this</em> that they all have in common.</div>
<div class="corelinks tlpdepth3"><strong>3.344</strong><span class="linkarray tlpdepth3" id="p3.344PM"> P/M [→<a class="gerlink" href="#p3.344GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.344OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What signifies in a symbol is what is common to all the symbols that the rules of logical syntax allow us to substitute for it.</div>
<div class="corelinks tlpdepth4"><strong>3.3441</strong><span class="linkarray tlpdepth4" id="p3.3441PM"> P/M [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3441OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">For instance, we can express what is common to all notations for truth-functions in the following way: they have in common that, for example, the notation that uses ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ (‘not <span class="mathmode"><var>p</var></span>’) and ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>’ (‘<span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>’) <em>can be substituted</em> for any of them.</div>
<div class="para tlpdepth4">(This serves to characterize the way in which something general can be disclosed by the possibility of a specific notation.)</div>
<div class="corelinks tlpdepth4"><strong>3.3442</strong><span class="linkarray tlpdepth4" id="p3.3442PM"> P/M [→<a class="gerlink" href="#p3.3442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3442OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Nor does analysis resolve the sign for a complex in an arbitrary way, so that it would have a different resolution every time that it was incorporated in a different proposition.</div>
<div class="corelinks tlpdepth1"><strong>3.4</strong><span class="linkarray tlpdepth1" id="p3.4PM"> P/M [→<a class="gerlink" href="#p3.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.4OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">A proposition determines a place in logical space. The existence of this logical place is guaranteed by the mere existence of the constituents—by the existence of the proposition with a sense.</div>
<div class="corelinks tlpdepth2"><strong>3.41</strong><span class="linkarray tlpdepth2" id="p3.41PM"> P/M [→<a class="gerlink" href="#p3.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.41OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The propositional sign with logical co-ordinates—that is the logical place.</div>
<div class="corelinks tlpdepth3"><strong>3.411</strong><span class="linkarray tlpdepth3" id="p3.411PM"> P/M [→<a class="gerlink" href="#p3.411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.411OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In geometry and logic alike a place is a possibility: something can exist in it.</div>
<div class="corelinks tlpdepth2"><strong>3.42</strong><span class="linkarray tlpdepth2" id="p3.42PM"> P/M [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition can determine only one place in logical space: nevertheless the whole of logical space must already be given by it.</div>
<div class="para tlpdepth2">(Otherwise negation, logical sum, logical product, etc., would introduce more and more new elements—in co-ordination.)</div>
<div class="para tlpdepth2">(The logical scaffolding surrounding a picture determines logical space. The force of a proposition reaches through the whole of logical space.)</div>
<div class="corelinks tlpdepth1"><strong>3.5</strong><span class="linkarray tlpdepth1" id="p3.5PM"> P/M [→<a class="gerlink" href="#p3.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.5OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">A propositional sign, applied and thought out, is a thought.</div>
<div class="corelinks tlpdepth0"><strong>4</strong><span class="linkarray tlpdepth0" id="p4PM"> P/M [→<a class="gerlink" href="#p4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4OGD">OGD</a>]</span></div>
<div class="para tlpdepth0">A thought is a proposition with a sense.</div>
<div class="corelinks tlpdepth3"><strong>4.001</strong><span class="linkarray tlpdepth3" id="p4.001PM"> P/M [→<a class="gerlink" href="#p4.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.001OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The totality of propositions is language.</div>
<div class="corelinks tlpdepth3"><strong>4.002</strong><span class="linkarray tlpdepth3" id="p4.002PM"> P/M [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Man possesses the ability to construct languages capable of expressing every sense, without having any idea how each word has meaning or what its meaning is—just as people speak without knowing how the individual sounds are produced.</div>
<div class="para tlpdepth3">Everyday language is a part of the human organism and is no less complicated than it.</div>
<div class="para tlpdepth3">It is not humanly possible to gather immediately from it what the logic of language is.</div>
<div class="para tlpdepth3">Language disguises thought. So much so, that from the outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes.</div>
<div class="para tlpdepth3">The tacit conventions on which the understanding of everyday language depends are enormously complicated.</div>
<div class="corelinks tlpdepth3"><strong>4.003</strong><span class="linkarray tlpdepth3" id="p4.003PM"> P/M [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Most of the propositions and questions to be found in philosophical works are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical. Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language.</div>
<div class="para tlpdepth3">(They belong to the same class as the question whether the good is more or less identical than the beautiful.)</div>
<div class="para tlpdepth3">And it is not surprising that the deepest problems are in fact <em>not</em> problems at all.</div>
<div class="corelinks tlpdepth4"><strong>4.0031</strong><span class="linkarray tlpdepth4" id="p4.0031PM"> P/M [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">All philosophy is a ‘critique of language’ (though not in Mauthner’s sense). It was Russell who performed the service of showing that the apparent logical form of a proposition need not be its real one.</div>
<div class="corelinks tlpdepth2"><strong>4.01</strong><span class="linkarray tlpdepth2" id="p4.01PM"> P/M [→<a class="gerlink" href="#p4.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.01OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition is a picture of reality.</div>
<div class="para tlpdepth2">A proposition is a model of reality as we imagine it.</div>
<div class="corelinks tlpdepth3"><strong>4.011</strong><span class="linkarray tlpdepth3" id="p4.011PM"> P/M [→<a class="gerlink" href="#p4.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.011OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">At first sight a proposition—one set out on the printed page, for example—does not seem to be a picture of the reality with which it is concerned. But neither do written notes seem at first sight to be a picture of a piece of music, nor our phonetic notation (the alphabet) to be a picture of our speech.</div>
<div class="para tlpdepth3">And yet these sign-languages prove to be pictures, even in the ordinary sense, of what they represent.</div>
<div class="corelinks tlpdepth3"><strong>4.012</strong><span class="linkarray tlpdepth3" id="p4.012PM"> P/M [→<a class="gerlink" href="#p4.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.012OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is obvious that a proposition of the form ‘<span class="mathmode"><var>aRb</var></span>’ strikes us as a picture. In this case the sign is obviously a likeness of what is signified.</div>
<div class="corelinks tlpdepth3"><strong>4.013</strong><span class="linkarray tlpdepth3" id="p4.013PM"> P/M [→<a class="gerlink" href="#p4.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.013OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">And if we penetrate to the essence of this pictorial character, we see that it is <em>not</em> impaired by <em>apparent irregularities</em> (such as the use of <span class="mathmode"><span class="symbol">♯</span></span> and <span class="mathmode"><span class="symbol">♭</span></span> in musical notation).</div>
<div class="para tlpdepth3">For even these irregularities depict what they are intended to express; only they do it in a different way.</div>
<div class="corelinks tlpdepth3"><strong>4.014</strong><span class="linkarray tlpdepth3" id="p4.014PM"> P/M [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A gramophone record, the musical idea, the written notes, and the sound-waves, all stand to one another in the same internal relation of depicting that holds between language and the world.</div>
<div class="para tlpdepth3">They are all constructed according to a common logical pattern.</div>
<div class="para tlpdepth3">(Like the two youths in the fairy-tale, their two horses, and their lilies. They are all in a certain sense one.)</div>
<div class="corelinks tlpdepth4"><strong>4.0141</strong><span class="linkarray tlpdepth4" id="p4.0141PM"> P/M [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">There is a general rule by means of which the musician can obtain the symphony from the score, and which makes it possible to derive the symphony from the groove on the gramophone record, and, using the first rule, to derive the score again. That is what constitutes the inner similarity between these things which seem to be constructed in such entirely different ways. And that rule is the law of projection which projects the symphony into the language of musical notation. It is the rule for translating this language into the language of gramophone records.</div>
<div class="corelinks tlpdepth3"><strong>4.015</strong><span class="linkarray tlpdepth3" id="p4.015PM"> P/M [→<a class="gerlink" href="#p4.015GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.015OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The possibility of all imagery, of all our pictorial modes of expression, is contained in the logic of depiction.</div>
<div class="corelinks tlpdepth3"><strong>4.016</strong><span class="linkarray tlpdepth3" id="p4.016PM"> P/M [→<a class="gerlink" href="#p4.016GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.016OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In order to understand the essential nature of a proposition, we should consider hieroglyphic script, which depicts the facts that it describes.</div>
<div class="para tlpdepth3">And alphabetic script developed out of it without losing what was essential to depiction.</div>
<div class="corelinks tlpdepth2"><strong>4.02</strong><span class="linkarray tlpdepth2" id="p4.02PM"> P/M [→<a class="gerlink" href="#p4.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.02OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">We can see this from the fact that we understand the sense of a propositional sign without its having been explained to us.</div>
<div class="corelinks tlpdepth3"><strong>4.021</strong><span class="linkarray tlpdepth3" id="p4.021PM"> P/M [→<a class="gerlink" href="#p4.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.021OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A proposition is a picture of reality: for if I understand a proposition, I know the situation that it represents. And I understand the proposition without having had its sense explained to me.</div>
<div class="corelinks tlpdepth3"><strong>4.022</strong><span class="linkarray tlpdepth3" id="p4.022PM"> P/M [→<a class="gerlink" href="#p4.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.022OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A proposition <em>shows</em> its sense.</div>
<div class="para tlpdepth3">A proposition <em>shows</em> how things stand <em>if</em> it is true. And it <em>says that</em> they do so stand.</div>
<div class="corelinks tlpdepth3"><strong>4.023</strong><span class="linkarray tlpdepth3" id="p4.023PM"> P/M [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A proposition must restrict reality to two alternatives: yes or no.</div>
<div class="para tlpdepth3">In order to do that, it must describe reality completely.</div>
<div class="para tlpdepth3">A proposition is a description of a state of affairs.</div>
<div class="para tlpdepth3">Just as a description of an object describes it by giving its external properties, so a proposition describes reality by its internal properties.</div>
<div class="para tlpdepth3">A proposition constructs a world with the help of a logical scaffolding, so that one can actually see from the proposition how everything stands logically <em>if</em> it is true. One can <em>draw inferences</em> from a false proposition.</div>
<div class="corelinks tlpdepth3"><strong>4.024</strong><span class="linkarray tlpdepth3" id="p4.024PM"> P/M [→<a class="gerlink" href="#p4.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.024OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">To understand a proposition means to know what is the case if it is true.</div>
<div class="para tlpdepth3">(One can understand it, therefore, without knowing whether it is true.)</div>
<div class="para tlpdepth3">It is understood by anyone who understands its constituents.</div>
<div class="corelinks tlpdepth3"><strong>4.025</strong><span class="linkarray tlpdepth3" id="p4.025PM"> P/M [→<a class="gerlink" href="#p4.025GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.025OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">When translating one language into another, we do not proceed by translating each <em>proposition</em> of the one into a <em>proposition</em> of the other, but merely by translating the constituents of propositions.</div>
<div class="para tlpdepth3">(And the dictionary translates not only substantives, but also verbs, adjectives, and conjunctions, etc.; and it treats them all in the same way.)</div>
<div class="corelinks tlpdepth3"><strong>4.026</strong><span class="linkarray tlpdepth3" id="p4.026PM"> P/M [→<a class="gerlink" href="#p4.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.026OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The meanings of simple signs (words) must be explained to us if we are to understand them.</div>
<div class="para tlpdepth3">With propositions, however, we make ourselves understood.</div>
<div class="corelinks tlpdepth3"><strong>4.027</strong><span class="linkarray tlpdepth3" id="p4.027PM"> P/M [→<a class="gerlink" href="#p4.027GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.027OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It belongs to the essence of a proposition that it should be able to communicate a <em>new</em> sense to us.</div>
<div class="corelinks tlpdepth2"><strong>4.03</strong><span class="linkarray tlpdepth2" id="p4.03PM"> P/M [→<a class="gerlink" href="#p4.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.03OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition must use old expressions to communicate a new sense.</div>
<div class="para tlpdepth2">A proposition communicates a situation to us, and so it must be <em>essentially</em> connected with the situation.</div>
<div class="para tlpdepth2">And the connexion is precisely that it is its logical picture.</div>
<div class="para tlpdepth2">A proposition states something only in so far as it is a picture.</div>
<div class="corelinks tlpdepth3"><strong>4.031</strong><span class="linkarray tlpdepth3" id="p4.031PM"> P/M [→<a class="gerlink" href="#p4.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.031OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In a proposition a situation is, as it were, constructed by way of experiment.</div>
<div class="para tlpdepth3">Instead of, ‘This proposition has such and such a sense’, we can simply say, ‘This proposition represents such and such a situation’.</div>
<div class="corelinks tlpdepth4"><strong>4.0311</strong><span class="linkarray tlpdepth4" id="p4.0311PM"> P/M [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0311OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">One name stands for one thing, another for another thing, and they are combined with one another. In this way the whole group—like a <em>tableau vivant</em>—presents a state of affairs.</div>
<div class="corelinks tlpdepth4"><strong>4.0312</strong><span class="linkarray tlpdepth4" id="p4.0312PM"> P/M [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0312OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The possibility of propositions is based on the principle that objects have signs as their representatives.</div>
<div class="para tlpdepth4">My fundamental idea is that the ‘logical constants’ are not representatives; that there can be no representatives of the <em>logic</em> of facts.</div>
<div class="corelinks tlpdepth3"><strong>4.032</strong><span class="linkarray tlpdepth3" id="p4.032PM"> P/M [→<a class="gerlink" href="#p4.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.032OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is only in so far as a proposition is logically articulated that it is a picture of a situation.</div>
<div class="para tlpdepth3">(Even the proposition, <em>Ambulo</em>, is composite: for its stem with a different ending yields a different sense, and so does its ending with a different stem.)</div>
<div class="corelinks tlpdepth2"><strong>4.04</strong><span class="linkarray tlpdepth2" id="p4.04PM"> P/M [→<a class="gerlink" href="#p4.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.04OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">In a proposition there must be exactly as many distinguishable parts as in the situation that it represents.</div>
<div class="para tlpdepth2">The two must possess the same logical (mathematical) multiplicity. (Compare Hertz’s <em>Mechanics</em> on dynamical models.)</div>
<div class="corelinks tlpdepth3"><strong>4.041</strong><span class="linkarray tlpdepth3" id="p4.041PM"> P/M [→<a class="gerlink" href="#p4.041GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.041OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">This mathematical multiplicity, of course, cannot itself be the subject of depiction. One cannot get away from it when depicting.</div>
<div class="corelinks tlpdepth4"><strong>4.0411</strong><span class="linkarray tlpdepth4" id="p4.0411PM"> P/M [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If, for example, we wanted to express what we now write as ‘<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>’ by putting an affix in front of ‘<span class="mathmode"><var>fx</var></span>’—for instance by writing ‘<span class="mathmode"><span class="mathop"><span class="mathrm">Gen.</span></span> <var>fx</var></span>’—it would not be adequate: we should not know what was being generalized. If we wanted to signalize it with an affix ‘<span class="mathmode"><var>g</var></span>’—for instance by writing ‘<span class="mathmode"><var>f</var>(<var>x</var><sub><var>g</var></sub>)</span>’—that would not be adequate either: we should not know the scope of the generality-sign.</div>
<div class="para tlpdepth4">If we were to try to do it by introducing a mark into the argument-places—for instance by writing ‘<span class="mathmode"><span class="mathop">(<var>G</var>, <var>G</var>).</span> <var>F</var>(<var>G</var>, <var>G</var>)</span>’—it would not be adequate: we should not be able to establish the identity of the variables. And so on.</div>
<div class="para tlpdepth4">All these modes of signifying are inadequate because they lack the necessary mathematical multiplicity.</div>
<div class="corelinks tlpdepth4"><strong>4.0412</strong><span class="linkarray tlpdepth4" id="p4.0412PM"> P/M [→<a class="gerlink" href="#p4.0412GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0412OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">For the same reason the idealist’s appeal to ‘spatial spectacles’ is inadequate to explain the seeing of spatial relations, because it cannot explain the multiplicity of these relations.</div>
<div class="corelinks tlpdepth2"><strong>4.05</strong><span class="linkarray tlpdepth2" id="p4.05PM"> P/M [→<a class="gerlink" href="#p4.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.05OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Reality is compared with propositions.</div>
<div class="corelinks tlpdepth2"><strong>4.06</strong><span class="linkarray tlpdepth2" id="p4.06PM"> P/M [→<a class="gerlink" href="#p4.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.06OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition can be true or false only in virtue of being a picture of reality.</div>
<div class="corelinks tlpdepth3"><strong>4.061</strong><span class="linkarray tlpdepth3" id="p4.061PM"> P/M [→<a class="gerlink" href="#p4.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.061OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It must not be overlooked that a proposition has a sense that is independent of the facts: otherwise one can easily suppose that true and false are relations of equal status between signs and what they signify.</div>
<div class="para tlpdepth3">In that case one could say, for example, that ‘<span class="mathmode"><var>p</var></span>’ signified in the true way what ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ signified in the false way, etc.</div>
<div class="corelinks tlpdepth3"><strong>4.062</strong><span class="linkarray tlpdepth3" id="p4.062PM"> P/M [→<a class="gerlink" href="#p4.062GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.062OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Can we not make ourselves understood with false propositions just as we have done up till now with true ones?—So long as it is known that they are meant to be false.—No! For a proposition is true if we use it to say that things stand in a certain way, and they do; and if by ‘<span class="mathmode"><var>p</var></span>’ we mean <span class="mathmode"><span class="mathop">~</span><var>p</var></span> and things stand as we mean that they do, then, construed in the new way, ‘<span class="mathmode"><var>p</var></span>’ is true and not false.</div>
<div class="corelinks tlpdepth4"><strong>4.0621</strong><span class="linkarray tlpdepth4" id="p4.0621PM"> P/M [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">But it is important that the signs ‘<span class="mathmode"><var>p</var></span>’ and ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ can say the same thing. For it shows that nothing in reality corresponds to the sign ‘~’.</div>
<div class="para tlpdepth4">The occurrence of negation in a proposition is not enough to characterize its sense (<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var><span class="mathrel">=</span><var>p</var></span>).</div>
<div class="para tlpdepth4">The propositions ‘<span class="mathmode"><var>p</var></span>’ and ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ have opposite sense, but there corresponds to them one and the same reality.</div>
<div class="corelinks tlpdepth3"><strong>4.063</strong><span class="linkarray tlpdepth3" id="p4.063PM"> P/M [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">An analogy to illustrate the concept of truth: imagine a black spot on white paper: you can describe the shape of the spot by saying, for each point on the sheet, whether it is black or white. To the fact that a point is black there corresponds a positive fact, and to the fact that a point is white (not black), a negative fact. If I designate a point on the sheet (a truth-value according to Frege), then this corresponds to the supposition that is put forward for judgement, etc. etc.</div>
<div class="para tlpdepth3">But in order to be able to say that a point is black or white, I must first know when a point is called black, and when white: in order to be able to say, ‘“<span class="mathmode"><var>p</var></span>” is true (or false)’, I must have determined in what circumstances I call ‘<span class="mathmode"><var>p</var></span>’ true, and in so doing I determine the sense of the proposition.</div>
<div class="para tlpdepth3">Now the point where the simile breaks down is this: we can indicate a point on the paper even if we do not know what black and white are, but if a proposition has no sense, nothing corresponds to it, since it does not designate a thing (a truth-value) which might have properties called ‘false’ or ‘true’. The verb of a proposition is not ‘is true’ or ‘is false’, as Frege thought: rather, that which ‘is true’ must already contain the verb.</div>
<div class="corelinks tlpdepth3"><strong>4.064</strong><span class="linkarray tlpdepth3" id="p4.064PM"> P/M [→<a class="gerlink" href="#p4.064GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.064OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Every proposition must <em>already</em> have a sense: it cannot be given a sense by affirmation. Indeed its sense is just what is affirmed. And the same applies to negation, etc.</div>
<div class="corelinks tlpdepth4"><strong>4.0641</strong><span class="linkarray tlpdepth4" id="p4.0641PM"> P/M [→<a class="gerlink" href="#p4.0641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0641OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">One could say that negation must be related to the logical place determined by the negated proposition.</div>
<div class="para tlpdepth4">The negating proposition determines a logical place <em>different</em> from that of the negated proposition.</div>
<div class="para tlpdepth4">The negating proposition determines a logical place with the help of the logical place of the negated proposition. For it describes it as lying outside the latter’s logical place.</div>
<div class="para tlpdepth4">The negated proposition can be negated again, and this in itself shows that what is negated is already a proposition, and not merely something that is preliminary to a proposition.</div>
<div class="corelinks tlpdepth1"><strong>4.1</strong><span class="linkarray tlpdepth1" id="p4.1PM"> P/M [→<a class="gerlink" href="#p4.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">Propositions represent the existence and non-existence of states of affairs.</div>
<div class="corelinks tlpdepth2"><strong>4.11</strong><span class="linkarray tlpdepth2" id="p4.11PM"> P/M [→<a class="gerlink" href="#p4.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.11OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The totality of true propositions is the whole of natural science (or the whole corpus of the natural sciences).</div>
<div class="corelinks tlpdepth3"><strong>4.111</strong><span class="linkarray tlpdepth3" id="p4.111PM"> P/M [→<a class="gerlink" href="#p4.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.111OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Philosophy is not one of the natural sciences.</div>
<div class="para tlpdepth3">(The word ‘philosophy’ must mean something whose place is above or below the natural sciences, not beside them.)</div>
<div class="corelinks tlpdepth3"><strong>4.112</strong><span class="linkarray tlpdepth3" id="p4.112PM"> P/M [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Philosophy aims at the logical clarification of thoughts.</div>
<div class="para tlpdepth3">Philosophy is not a body of doctrine but an activity.</div>
<div class="para tlpdepth3">A philosophical work consists essentially of elucidations.</div>
<div class="para tlpdepth3">Philosophy does not result in ‘philosophical propositions’, but rather in the clarification of propositions.</div>
<div class="para tlpdepth3">Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries.</div>
<div class="corelinks tlpdepth4"><strong>4.1121</strong><span class="linkarray tlpdepth4" id="p4.1121PM"> P/M [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Psychology is no more closely related to philosophy than any other natural science.</div>
<div class="para tlpdepth4">Theory of knowledge is the philosophy of psychology.</div>
<div class="para tlpdepth4">Does not my study of sign-language correspond to the study of thought-processes, which philosophers used to consider so essential to the philosophy of logic? Only in most cases they got entangled in unessential psychological investigations, and with my method too there is an analogous risk.</div>
<div class="corelinks tlpdepth4"><strong>4.1122</strong><span class="linkarray tlpdepth4" id="p4.1122PM"> P/M [→<a class="gerlink" href="#p4.1122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1122OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Darwin’s theory has no more to do with philosophy than any other hypothesis in natural science.</div>
<div class="corelinks tlpdepth3"><strong>4.113</strong><span class="linkarray tlpdepth3" id="p4.113PM"> P/M [→<a class="gerlink" href="#p4.113GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.113OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Philosophy sets limits to the much disputed sphere of natural science.</div>
<div class="corelinks tlpdepth3"><strong>4.114</strong><span class="linkarray tlpdepth3" id="p4.114PM"> P/M [→<a class="gerlink" href="#p4.114GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.114OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It must set limits to what can be thought; and, in doing so, to what cannot be thought.</div>
<div class="para tlpdepth3">It must set limits to what cannot be thought by working outwards through what can be thought.</div>
<div class="corelinks tlpdepth3"><strong>4.115</strong><span class="linkarray tlpdepth3" id="p4.115PM"> P/M [→<a class="gerlink" href="#p4.115GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.115OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It will signify what cannot be said, by presenting clearly what can be said.</div>
<div class="corelinks tlpdepth3"><strong>4.116</strong><span class="linkarray tlpdepth3" id="p4.116PM"> P/M [→<a class="gerlink" href="#p4.116GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.116OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Everything that can be thought at all can be thought clearly. Everything that can be put into words can be put clearly.</div>
<div class="corelinks tlpdepth2"><strong>4.12</strong><span class="linkarray tlpdepth2" id="p4.12PM"> P/M [→<a class="gerlink" href="#p4.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it—logical form.</div>
<div class="para tlpdepth2">In order to be able to represent logical form, we should have to be able to station ourselves with propositions somewhere outside logic, that is to say outside the world.</div>
<div class="corelinks tlpdepth3"><strong>4.121</strong><span class="linkarray tlpdepth3" id="p4.121PM"> P/M [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Propositions cannot represent logical form: it is mirrored in them.</div>
<div class="para tlpdepth3">What finds its reflection in language, language cannot represent.</div>
<div class="para tlpdepth3">What expresses <em>itself</em> in language, <em>we</em> cannot express by means of language.</div>
<div class="para tlpdepth3">Propositions <em>show</em> the logical form of reality.</div>
<div class="para tlpdepth3">They display it.</div>
<div class="corelinks tlpdepth4"><strong>4.1211</strong><span class="linkarray tlpdepth4" id="p4.1211PM"> P/M [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1211OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Thus one proposition ‘<span class="mathmode"><var>fa</var></span>’ shows that the object <span class="mathmode"><var>a</var></span> occurs in its sense, two propositions ‘<span class="mathmode"><var>fa</var></span>’ and ‘<span class="mathmode"><var>ga</var></span>’ show that the same object is mentioned in both of them.</div>
<div class="para tlpdepth4">If two propositions contradict one another, then their structure shows it; the same is true if one of them follows from the other. And so on.</div>
<div class="corelinks tlpdepth4"><strong>4.1212</strong><span class="linkarray tlpdepth4" id="p4.1212PM"> P/M [→<a class="gerlink" href="#p4.1212GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1212OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">What <em>can</em> be shown, <em>cannot</em> be said.</div>
<div class="corelinks tlpdepth4"><strong>4.1213</strong><span class="linkarray tlpdepth4" id="p4.1213PM"> P/M [→<a class="gerlink" href="#p4.1213GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1213OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Now, too, we understand our feeling that once we have a sign-language in which everything is all right, we already have a correct logical point of view.</div>
<div class="corelinks tlpdepth3"><strong>4.122</strong><span class="linkarray tlpdepth3" id="p4.122PM"> P/M [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In a certain sense we can talk about formal properties of objects and states of affairs, or, in the case of facts, about structural properties: and in the same sense about formal relations and structural relations.</div>
<div class="para tlpdepth3">(Instead of ‘structural property’ I also say ‘internal property’; instead of ‘structural relation’, ‘internal relation’.</div>
<div class="para tlpdepth3">I introduce these expressions in order to indicate the source of the confusion between internal relations and relations proper (external relations), which is very widespread among philosophers.)</div>
<div class="para tlpdepth3">It is impossible, however, to assert by means of propositions that such internal properties and relations obtain: rather, this makes itself manifest in the propositions that represent the relevant states of affairs and are concerned with the relevant objects.</div>
<div class="corelinks tlpdepth4"><strong>4.1221</strong><span class="linkarray tlpdepth4" id="p4.1221PM"> P/M [→<a class="gerlink" href="#p4.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1221OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">An internal property of a fact can also be called a feature of that fact (in the sense in which we speak of facial features, for example).</div>
<div class="corelinks tlpdepth3"><strong>4.123</strong><span class="linkarray tlpdepth3" id="p4.123PM"> P/M [→<a class="gerlink" href="#p4.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.123OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A property is internal if it is unthinkable that its object should not possess it.</div>
<div class="para tlpdepth3">(This shade of blue and that one stand, <em>eo ipso</em>, in the internal relation of lighter to darker. It is unthinkable that <em>these</em> two objects should not stand in this relation.)</div>
<div class="para tlpdepth3">(Here the shifting use of the word ‘object’ corresponds to the shifting use of the words ‘property’ and ‘relation’.)</div>
<div class="corelinks tlpdepth3"><strong>4.124</strong><span class="linkarray tlpdepth3" id="p4.124PM"> P/M [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The existence of an internal property of a possible situation is not expressed by means of a proposition: rather, it expresses itself in the proposition representing the situation, by means of an internal property of that proposition.</div>
<div class="para tlpdepth3">It would be just as nonsensical to assert that a proposition had a formal property as to deny it.</div>
<div class="corelinks tlpdepth4"><strong>4.1241</strong><span class="linkarray tlpdepth4" id="p4.1241PM"> P/M [→<a class="gerlink" href="#p4.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1241OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is impossible to distinguish forms from one another by saying that one has this property and another that property: for this presupposes that it makes sense to ascribe either property to either form.</div>
<div class="corelinks tlpdepth3"><strong>4.125</strong><span class="linkarray tlpdepth3" id="p4.125PM"> P/M [→<a class="gerlink" href="#p4.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.125OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The existence of an internal relation between possible situations expresses itself in language by means of an internal relation between the propositions representing them.</div>
<div class="corelinks tlpdepth4"><strong>4.1251</strong><span class="linkarray tlpdepth4" id="p4.1251PM"> P/M [→<a class="gerlink" href="#p4.1251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1251OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Here we have the answer to the vexed question ‘whether all relations are internal or external’.</div>
<div class="corelinks tlpdepth4"><strong>4.1252</strong><span class="linkarray tlpdepth4" id="p4.1252PM"> P/M [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1252OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">I call a series that is ordered by an internal relation a series of forms.</div>
<div class="para tlpdepth4">The order of the number-series is not governed by an external relation but by an internal relation.</div>
<div class="para tlpdepth4">The same is true of the series of propositions ‘<span class="mathmode"><var>aRb</var></span>’,</div>
<div class="para tlpdepth4">‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRb</var></span>’,</div>
<div class="para tlpdepth4">‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRy</var><span class="mathrel">.</span><var>yRb</var></span>’, and so forth.</div>
<div class="para tlpdepth4">(If <span class="mathmode"><var>b</var></span> stands in one of these relations to <span class="mathmode"><var>a</var></span>, I call <span class="mathmode"><var>b</var></span> a successor of <span class="mathmode"><var>a</var></span>.)</div>
<div class="corelinks tlpdepth3"><strong>4.126</strong><span class="linkarray tlpdepth3" id="p4.126PM"> P/M [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">We can now talk about formal concepts, in the same sense that we speak of formal properties.</div>
<div class="para tlpdepth3">(I introduce this expression in order to exhibit the source of the confusion between formal concepts and concepts proper, which pervades the whole of traditional logic.)</div>
<div class="para tlpdepth3">When something falls under a formal concept as one of its objects, this cannot be expressed by means of a proposition. Instead it is shown in the very sign for this object. (A name shows that it signifies an object, a sign for a number that it signifies a number, etc.)</div>
<div class="para tlpdepth3">Formal concepts cannot, in fact, be represented by means of a function, as concepts proper can.</div>
<div class="para tlpdepth3">For their characteristics, formal properties, are not expressed by means of functions.</div>
<div class="para tlpdepth3">The expression for a formal property is a feature of certain symbols.</div>
<div class="para tlpdepth3">So the sign for the characteristics of a formal concept is a distinctive feature of all symbols whose meanings fall under the concept.</div>
<div class="para tlpdepth3">So the expression for a formal concept is a propositional variable in which this distinctive feature alone is constant.</div>
<div class="corelinks tlpdepth3"><strong>4.127</strong><span class="linkarray tlpdepth3" id="p4.127PM"> P/M [→<a class="gerlink" href="#p4.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.127OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The propositional variable signifies the formal concept, and its values signify the objects that fall under the concept.</div>
<div class="corelinks tlpdepth4"><strong>4.1271</strong><span class="linkarray tlpdepth4" id="p4.1271PM"> P/M [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1271OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Every variable is the sign for a formal concept.</div>
<div class="para tlpdepth4">For every variable represents a constant form that all its values possess, and this can be regarded as a formal property of those values.</div>
<div class="corelinks tlpdepth4"><strong>4.1272</strong><span class="linkarray tlpdepth4" id="p4.1272PM"> P/M [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Thus the variable name ‘<span class="mathmode"><var>x</var></span>’ is the proper sign for the pseudo-concept <em>object</em>.</div>
<div class="para tlpdepth4">Wherever the word ‘object’ (‘thing’, etc.) is correctly used, it is expressed in conceptual notation by a variable name.</div>
<div class="para tlpdepth4">For example, in the proposition, ‘There are 2 objects which …’, it is expressed by ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>)</span><span class="mathrel">…</span></span>’.</div>
<div class="para tlpdepth4">Wherever it is used in a different way, that is as a proper concept-word, nonsensical pseudo-propositions are the result.</div>
<div class="para tlpdepth4">So one cannot say, for example, ‘There are objects’, as one might say, ‘There are books’. And it is just as impossible to say, ‘There are 100 objects’, or, ‘There are <span class="mathmode"><span class="symbol">ℵ</span><sub>0</sub></span> objects’.</div>
<div class="para tlpdepth4">And it is nonsensical to speak of the <em>total number of objects</em>.</div>
<div class="para tlpdepth4">The same applies to the words ‘complex’, ‘fact’, ‘function’, ‘number’, etc.</div>
<div class="para tlpdepth4">They all signify formal concepts, and are represented in conceptual notation by variables, not by functions or classes (as Frege and Russell believed).</div>
<div class="para tlpdepth4">‘1 is a number’, ‘There is only one zero’, and all similar expressions are nonsensical.</div>
<div class="para tlpdepth4">(It is just as nonsensical to say, ‘There is only one 1’, as it would be to say, ‘<span class="mathmode">2<span class="mathrel">+</span>2</span> at 3 o’clock equals 4’.)</div>
<div class="corelinks tlpdepth5"><strong>4.12721</strong><span class="linkarray tlpdepth5" id="p4.12721PM"> P/M [→<a class="gerlink" href="#p4.12721GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12721OGD">OGD</a>]</span></div>
<div class="para tlpdepth5">A formal concept is given immediately any object falling under it is given. It is not possible, therefore, to introduce as primitive ideas objects belonging to a formal concept <em>and</em> the formal concept itself. So it is impossible, for example, to introduce as primitive ideas both the concept of a function and specific functions, as Russell does; or the concept of a number and particular numbers.</div>
<div class="corelinks tlpdepth4"><strong>4.1273</strong><span class="linkarray tlpdepth4" id="p4.1273PM"> P/M [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If we want to express in conceptual notation the general proposition, ‘<span class="mathmode"><var>b</var></span> is a successor of <span class="mathmode"><var>a</var></span>’, then we require an expression for the general term of the series of forms</div>
<div class="para tlpdepth4"><div class="centered"><span class="mathmode"><var>aRb</var></span>,<br />
<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRb</var></span>,<br />
<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>):</span><var>aRx</var><span class="mathrel">.</span><var>xRy</var><span class="mathrel">.</span><var>yRb</var></span>,<br />
…&nbsp; .</div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> In order to express the general term of a series of forms, we must use a variable, because the concept ‘term of that series of forms’ is a <em>formal</em> concept. (This is what Frege and Russell overlooked: consequently the way in which they want to express general propositions like the one above is incorrect; it contains a vicious circle.)</div>
<div class="para tlpdepth4">We can determine the general term of a series of forms by giving its first term and the general form of the operation that produces the next term out of the proposition that precedes it.</div>
<div class="corelinks tlpdepth4"><strong>4.1274</strong><span class="linkarray tlpdepth4" id="p4.1274PM"> P/M [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1274OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">To ask whether a formal concept exists is nonsensical. For no proposition can be the answer to such a question.</div>
<div class="para tlpdepth4">(So, for example, the question, ‘Are there unanalysable subject-predicate propositions?’ cannot be asked.)</div>
<div class="corelinks tlpdepth3"><strong>4.128</strong><span class="linkarray tlpdepth3" id="p4.128PM"> P/M [→<a class="gerlink" href="#p4.128GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.128OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Logical forms are <em>without</em> number.</div>
<div class="para tlpdepth3">Hence there are no pre-eminent numbers in logic, and hence there is no possibility of philosophical monism or dualism, etc.</div>
<div class="corelinks tlpdepth1"><strong>4.2</strong><span class="linkarray tlpdepth1" id="p4.2PM"> P/M [→<a class="gerlink" href="#p4.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">The sense of a proposition is its agreement and disagreement with possibilities of existence and non-existence of states of affairs.</div>
<div class="corelinks tlpdepth2"><strong>4.21</strong><span class="linkarray tlpdepth2" id="p4.21PM"> P/M [→<a class="gerlink" href="#p4.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.21OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs.</div>
<div class="corelinks tlpdepth3"><strong>4.211</strong><span class="linkarray tlpdepth3" id="p4.211PM"> P/M [→<a class="gerlink" href="#p4.211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.211OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is a sign of a proposition’s being elementary that there can be no elementary proposition contradicting it.</div>
<div class="corelinks tlpdepth2"><strong>4.22</strong><span class="linkarray tlpdepth2" id="p4.22PM"> P/M [→<a class="gerlink" href="#p4.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.22OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">An elementary proposition consists of names. It is a nexus, a concatenation, of names.</div>
<div class="corelinks tlpdepth3"><strong>4.221</strong><span class="linkarray tlpdepth3" id="p4.221PM"> P/M [→<a class="gerlink" href="#p4.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.221OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is obvious that the analysis of propositions must bring us to elementary propositions which consist of names in immediate combination.</div>
<div class="para tlpdepth3">This raises the question how such combination into propositions comes about.</div>
<div class="corelinks tlpdepth4"><strong>4.2211</strong><span class="linkarray tlpdepth4" id="p4.2211PM"> P/M [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2211OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Even if the world is infinitely complex, so that every fact consists of infinitely many states of affairs and every state of affairs is composed of infinitely many objects, there would still have to be objects and states of affairs.</div>
<div class="corelinks tlpdepth2"><strong>4.23</strong><span class="linkarray tlpdepth2" id="p4.23PM"> P/M [→<a class="gerlink" href="#p4.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.23OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">It is only in the nexus of an elementary proposition that a name occurs in a proposition.</div>
<div class="corelinks tlpdepth2"><strong>4.24</strong><span class="linkarray tlpdepth2" id="p4.24PM"> P/M [→<a class="gerlink" href="#p4.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.24OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Names are the simple symbols: I indicate them by single letters (‘<span class="mathmode"><var>x</var></span>’, ‘<span class="mathmode"><var>y</var></span>’, ‘<span class="mathmode"><var>z</var></span>’).</div>
<div class="para tlpdepth2">I write elementary propositions as functions of names, so that they have the form ‘<span class="mathmode"><var>fx</var></span>’, ‘<span class="mathmode"><var>φ</var>(<var>x</var>,<var>y</var>)</span>’, etc.</div>
<div class="para tlpdepth2">Or I indicate them by the letters ‘<span class="mathmode"><var>p</var></span>’, ‘<span class="mathmode"><var>q</var></span>’, ‘<span class="mathmode"><var>r</var></span>’.</div>
<div class="corelinks tlpdepth3"><strong>4.241</strong><span class="linkarray tlpdepth3" id="p4.241PM"> P/M [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">When I use two signs with one and the same meaning, I express this by putting the sign ‘=’ between them.</div>
<div class="para tlpdepth3">So ‘<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span>’ means that the sign ‘<span class="mathmode"><var>b</var></span>’ can be substituted for the sign ‘<span class="mathmode"><var>a</var></span>’.</div>
<div class="para tlpdepth3">(If I use an equation to introduce a new sign ‘<span class="mathmode"><var>b</var></span>’, laying down that it shall serve as a substitute for a sign ‘<span class="mathmode"><var>a</var></span>’ that is already known, then, like Russell, I write the equation—definition—in the form ‘<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span> Def.’ A definition is a rule dealing with signs.)</div>
<div class="corelinks tlpdepth3"><strong>4.242</strong><span class="linkarray tlpdepth3" id="p4.242PM"> P/M [→<a class="gerlink" href="#p4.242GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.242OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Expressions of the form ‘<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var></span>’ are, therefore, mere representational devices. They state nothing about the meaning of the signs ‘<span class="mathmode"><var>a</var></span>’ and ‘<span class="mathmode"><var>b</var></span>’.</div>
<div class="corelinks tlpdepth3"><strong>4.243</strong><span class="linkarray tlpdepth3" id="p4.243PM"> P/M [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Can we understand two names without knowing whether they signify the same thing or two different things?—Can we understand a proposition in which two names occur without knowing whether their meaning is the same or different?</div>
<div class="para tlpdepth3">Suppose I know the meaning of an English word and of a German word that means the same: then it is impossible for me to be unaware that they do mean the same; I must be capable of translating each into the other.</div>
<div class="para tlpdepth3">Expressions like ‘<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>’, and those derived from them, are neither elementary propositions nor is there any other way in which they have sense. (This will become evident later.)</div>
<div class="corelinks tlpdepth2"><strong>4.25</strong><span class="linkarray tlpdepth2" id="p4.25PM"> P/M [→<a class="gerlink" href="#p4.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.25OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If an elementary proposition is true, the state of affairs exists: if an elementary proposition is false, the state of affairs does not exist.</div>
<div class="corelinks tlpdepth2"><strong>4.26</strong><span class="linkarray tlpdepth2" id="p4.26PM"> P/M [→<a class="gerlink" href="#p4.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.26OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If all true elementary propositions are given, the result is a complete description of the world. The world is completely described by giving all elementary propositions, and adding which of them are true and which false.</div>
<div class="corelinks tlpdepth2"><strong>4.27</strong><span class="linkarray tlpdepth2" id="p4.27PM"> P/M [→<a class="gerlink" href="#p4.27GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.27OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">For <span class="mathmode"><var>n</var></span> states of affairs, there are <table class="possibilities"><tr><td rowspan="3" class="middleright"><span class="mathmode">K<sub><var>n</var></sub> = </span></td><td class="summationtop"><span class="mathmode"><var class="smallvar">n</var></span></td><td rowspan="3" class="middleright"><span class="largeparen">(</span></td><td rowspan="3" class="middlecenter"><span class="mathmode"><var>n</var></span><br /><span class="mathmode"><var>ν</var></span></td><td rowspan="3" class="middleleft"><span class="largeparen">)</span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="largeop">∑</span></span></td></tr><tr><td class="summationbottom"><span class="mathmode"><span class="smallvar"><var>ν</var> = 0</span></span></td></tr></table> possibilities of existence and non-existence.</div>
<div class="para tlpdepth2">Of these states of affairs any combination can exist and the remainder not exist.</div>
<div class="corelinks tlpdepth2"><strong>4.28</strong><span class="linkarray tlpdepth2" id="p4.28PM"> P/M [→<a class="gerlink" href="#p4.28GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.28OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">There correspond to these combinations the same number of possibilities of truth—and falsity—for <span class="mathmode"><var>n</var></span> elementary propositions.</div>
<div class="corelinks tlpdepth1"><strong>4.3</strong><span class="linkarray tlpdepth1" id="p4.3PM"> P/M [→<a class="gerlink" href="#p4.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.3OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">Truth-possibilities of elementary propositions mean possibilities of existence and non-existence of states of affairs.</div>
<div class="corelinks tlpdepth2"><strong>4.31</strong><span class="linkarray tlpdepth2" id="p4.31PM"> P/M [→<a class="gerlink" href="#p4.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.31OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">We can represent truth-possibilities by schemata of the following kind (‘T’ means ‘true’, ‘F’ means ‘false’; the rows of ‘T’s’ and ‘F’s’ under the row of elementary propositions symbolize their truth-possibilities in a way that can easily be understood):</div>
<div class="para tlpdepth2"><div class="centered"><table class="truthtable"><tr><th class="l"><span class="mathmode"><var>p</var></span></th><th class="m"><span class="mathmode"><var>q</var></span></th><th class="e"><span class="mathmode"><var>r</var></span></th></tr><tr><td class="l">T</td><td class="m">T</td><td class="e">T</td></tr><tr><td class="l">F</td><td class="m">T</td><td class="e">T</td></tr><tr><td class="l">T</td><td class="m">F</td><td class="e">T</td></tr><tr><td class="l">T</td><td class="m">T</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="m">F</td><td class="e">T</td></tr><tr><td class="l">F</td><td class="m">T</td><td class="e">F</td></tr><tr><td class="l">T</td><td class="m">F</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="m">F</td><td class="e">F</td></tr></table><span class="padrthree"></span><table class="truthtable"><tr><th class="l"><span class="mathmode"><var>p</var></span></th><th class="e"><span class="mathmode"><var>q</var></span></th></tr><tr><td class="l">T</td><td class="e">T</td></tr><tr><td class="l">F</td><td class="e">T</td></tr><tr><td class="l">T</td><td class="e">F</td></tr><tr><td class="l">F</td><td class="e">F</td></tr></table><span class="padrthree"></span><table class="truthtable"><tr><th class="e"><span class="mathmode"><var>p</var></span></th></tr><tr><td class="e">T</td></tr><tr><td class="e">F</td></tr></table></div></div>
<div class="corelinks tlpdepth1"><strong>4.4</strong><span class="linkarray tlpdepth1" id="p4.4PM"> P/M [→<a class="gerlink" href="#p4.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">A proposition is an expression of agreement and disagreement with truth-possibilities of elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>4.41</strong><span class="linkarray tlpdepth2" id="p4.41PM"> P/M [→<a class="gerlink" href="#p4.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.41OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Truth-possibilities of elementary propositions are the conditions of the truth and falsity of propositions.</div>
<div class="corelinks tlpdepth3"><strong>4.411</strong><span class="linkarray tlpdepth3" id="p4.411PM"> P/M [→<a class="gerlink" href="#p4.411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.411OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It immediately strikes one as probable that the introduction of elementary propositions provides the basis for understanding all other kinds of proposition. Indeed the understanding of general propositions <em>palpably</em> depends on the understanding of elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>4.42</strong><span class="linkarray tlpdepth2" id="p4.42PM"> P/M [→<a class="gerlink" href="#p4.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.42OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">For <span class="mathmode"><var>n</var></span> elementary propositions there are <table class="possibilities"><tr><td class="summationtop"><span class="mathmode"><span class="smallvar">K<sub><var>n</var></sub></span></span></td><td class="middleright" rowspan="3"><span class="largeparen">(</span></td><td class="middlecenter" rowspan="3"><span class="mathode">K<sub><var>n</var></sub></span><br /><span class="mathmode"><var>κ</var></span></td><td class="middleright" rowspan="3"><span class="mathomde"><span class="largeparen">)</span> = L<sub><var>n</var></sub></span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="largeop">∑</span></span></td></tr><tr><td class="summationmiddle"><span class="mathmode"><span class="smallvar"><var>κ</var> = 0</span></span></td></tr></table> ways in which a proposition can agree and disagree with their truth possibilities.</div>
<div class="corelinks tlpdepth2"><strong>4.43</strong><span class="linkarray tlpdepth2" id="p4.43PM"> P/M [→<a class="gerlink" href="#p4.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.43OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">We can express agreement with truth-possibilities by correlating the mark ‘T’ (true) with them in the schema.</div>
<div class="para tlpdepth2">The absence of this mark means disagreement.</div>
<div class="corelinks tlpdepth3"><strong>4.431</strong><span class="linkarray tlpdepth3" id="p4.431PM"> P/M [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The expression of agreement and disagreement with the truth possibilities of elementary propositions expresses the truth-conditions of a proposition.</div>
<div class="para tlpdepth3">A proposition is the expression of its truth-conditions.</div>
<div class="para tlpdepth3">(Thus Frege was quite right to use them as a starting point when he explained the signs of his conceptual notation. But the explanation of the concept of truth that Frege gives is mistaken: if ‘the true’ and ‘the false’ were really objects, and were the arguments in <span class="mathmode"><span class="mathop">~</span><var>p</var></span> etc., then Frege’s method of determining the sense of ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ would leave it absolutely undetermined.)</div>
<div class="corelinks tlpdepth2"><strong>4.44</strong><span class="linkarray tlpdepth2" id="p4.44PM"> P/M [→<a class="gerlink" href="#p4.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.44OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The sign that results from correlating the mark ‘T’ with truth-possibilities is a propositional sign.</div>
<div class="corelinks tlpdepth3"><strong>4.441</strong><span class="linkarray tlpdepth3" id="p4.441PM"> P/M [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is clear that a complex of the signs ‘F’ and ‘T’ has no object (or complex of objects) corresponding to it, just as there is none corresponding to the horizontal and vertical lines or to the brackets.—There are no ‘logical objects’.</div>
<div class="para tlpdepth3">Of course the same applies to all signs that express what the schemata of ‘T’s’ and ‘F’s’ express.</div>
<div class="corelinks tlpdepth3"><strong>4.442</strong><span class="linkarray tlpdepth3" id="p4.442PM"> P/M [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">For example, the following is a propositional sign:</div>
<div class="para tlpdepth3 noindent"><!-- noindent --><div class="centered"><table class="truthtable"><tr><th>‘</th><th class="l"><span class="mathmode"><var>p</var></span></th><th class="m"><span class="mathmode"><var>q</var></span></th><th class="e"></th><th>’</th></tr><tr><td></td><td class="l">T</td><td class="m">T</td><td class="e">T</td><td></td></tr><tr><td></td><td class="l">F</td><td class="m">T</td><td class="e">T</td><td></td></tr><tr><td></td><td class="l">T</td><td class="m">F</td><td class="e"></td><td></td></tr><tr><td></td><td class="l">F</td><td class="m">F</td><td class="e">T</td><td></td></tr></table></div></div>
<div class="para tlpdepth3"></div>
<div class="para tlpdepth3">(Frege’s ‘judgement stroke’ ‘<span class="mathmode">⊢</span>’ is logically quite meaningless: in the works of Frege (and Russell) it simply indicates that these authors hold the propositions marked with this sign to be true. Thus ‘<span class="mathmode">⊢</span>’ is no more a component part of a proposition than is, for instance, the proposition’s number. It is quite impossible for a proposition to state that it itself is true.)</div>
<div class="para tlpdepth3">If the order or the truth-possibilities in a schema is fixed once and for all by a combinatory rule, then the last column by itself will be an expression of the truth-conditions. If we now write this column as a row, the propositional sign will become</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode"> “<span class="mathop">(<span class="mathrm">TT–T</span>)</span>&nbsp; (<var>p</var>, <var>q</var>)”, </span></div><span class="mathmode"></span></div>
<div class="para tlpdepth3 noindent"><!-- noindent --> or more explicitly</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode">“<span class="mathop">(<span class="mathrm">TTFT</span>)</span>&nbsp; (<var>p</var>, <var>q</var>)”.</span></div><span class="mathmode"></span></div>
<div class="para tlpdepth3">(The number of places in the left-hand pair of brackets is determined by the number of terms in the right-hand pair.)</div>
<div class="corelinks tlpdepth2"><strong>4.45</strong><span class="linkarray tlpdepth2" id="p4.45PM"> P/M [→<a class="gerlink" href="#p4.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.45OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">For <span class="mathmode"><var>n</var></span> elementary propositions there are <span class="mathmode"><span class="mathrm">L</span><sub><var>n</var></sub></span> possible groups of truth-conditions.</div>
<div class="para tlpdepth2">The groups of truth-conditions that are obtainable from the truth-possibilities of a given number of elementary propositions can be arranged in a series.</div>
<div class="corelinks tlpdepth2"><strong>4.46</strong><span class="linkarray tlpdepth2" id="p4.46PM"> P/M [→<a class="gerlink" href="#p4.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.46OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Among the possible groups of truth-conditions there are two extreme cases.</div>
<div class="para tlpdepth2">In one of these cases the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are <em>tautological</em>.</div>
<div class="para tlpdepth2">In the second case the proposition is false for all the truth-possibilities: the truth-conditions are <em>contradictory</em>.</div>
<div class="para tlpdepth2">In the first case we call the proposition a tautology; in the second, a contradiction.</div>
<div class="corelinks tlpdepth3"><strong>4.461</strong><span class="linkarray tlpdepth3" id="p4.461PM"> P/M [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Propositions show what they say: tautologies and contradictions show that they say nothing.</div>
<div class="para tlpdepth3">A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.</div>
<div class="para tlpdepth3">Tautologies and contradictions lack sense.</div>
<div class="para tlpdepth3">(Like a point from which two arrows go out in opposite directions to one another.)</div>
<div class="para tlpdepth3">(For example, I know nothing about the weather when I know that it is either raining or not raining.)</div>
<div class="corelinks tlpdepth4"><strong>4.4611</strong><span class="linkarray tlpdepth4" id="p4.4611PM"> P/M [→<a class="gerlink" href="#p4.4611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4611OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Tautologies and contradictions are not, however, nonsensical. They are part of the symbolism, much as ‘0’ is part of the symbolism of arithmetic.</div>
<div class="corelinks tlpdepth3"><strong>4.462</strong><span class="linkarray tlpdepth3" id="p4.462PM"> P/M [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Tautologies and contradictions are not pictures of reality. They do not represent any possible situations. For the former admit <em>all</em> possible situations, and latter <em>none</em>.</div>
<div class="para tlpdepth3">In a tautology the conditions of agreement with the world—the representational relations—cancel one another, so that it does not stand in any representational relation to reality.</div>
<div class="corelinks tlpdepth3"><strong>4.463</strong><span class="linkarray tlpdepth3" id="p4.463PM"> P/M [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The truth-conditions of a proposition determine the range that it leaves open to the facts.</div>
<div class="para tlpdepth3">(A proposition, a picture, or a model is, in the negative sense, like a solid body that restricts the freedom of movement of others, and, in the positive sense, like a space bounded by solid substance in which there is room for a body.)</div>
<div class="para tlpdepth3">A tautology leaves open to reality the whole—the infinite whole—of logical space: a contradiction fills the whole of logical space leaving no point of it for reality. Thus neither of them can determine reality in any way.</div>
<div class="corelinks tlpdepth3"><strong>4.464</strong><span class="linkarray tlpdepth3" id="p4.464PM"> P/M [→<a class="gerlink" href="#p4.464GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.464OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A tautology’s truth is certain, a proposition’s possible, a contradiction’s impossible.</div>
<div class="para tlpdepth3">(Certain, possible, impossible: here we have the first indication of the scale that we need in the theory of probability.)</div>
<div class="corelinks tlpdepth3"><strong>4.465</strong><span class="linkarray tlpdepth3" id="p4.465PM"> P/M [→<a class="gerlink" href="#p4.465GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.465OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The logical product of a tautology and a proposition says the same thing as the proposition. This product, therefore, is identical with the proposition. For it is impossible to alter what is essential to a symbol without altering its sense.</div>
<div class="corelinks tlpdepth3"><strong>4.466</strong><span class="linkarray tlpdepth3" id="p4.466PM"> P/M [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What corresponds to a determinate logical combination of signs is a determinate logical combination of their meanings. It is only to the uncombined signs that <em>absolutely any</em> combination corresponds.</div>
<div class="para tlpdepth3">In other words, propositions that are true for every situation cannot be combinations of signs at all, since, if they were, only determinate combinations of objects could correspond to them.</div>
<div class="para tlpdepth3">(And what is not a logical combination has <em>no</em> combination of objects corresponding to it.)</div>
<div class="para tlpdepth3">Tautology and contradiction are the limiting cases—indeed the disintegration—of the combination of signs.</div>
<div class="corelinks tlpdepth4"><strong>4.4661</strong><span class="linkarray tlpdepth4" id="p4.4661PM"> P/M [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Admittedly the signs are still combined with one another even in tautologies and contradictions—i.e. they stand in certain relations to one another: but these relations have no meaning, they are not essential to the <em>symbol</em>.</div>
<div class="corelinks tlpdepth1"><strong>4.5</strong><span class="linkarray tlpdepth1" id="p4.5PM"> P/M [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">It now seems possible to give the most general propositional form: that is, to give a description of the propositions of <em>any</em> sign-language <em>whatsoever</em> in such a way that every possible sense can be expressed by a symbol satisfying the description, and every symbol satisfying the description can express a sense, provided that the meanings of the names are suitably chosen.</div>
<div class="para tlpdepth1">It is clear that <em>only</em> what is essential to the most general propositional form may be included in its description—for otherwise it would not be the most general form.</div>
<div class="para tlpdepth1">The existence of a general propositional form is proved by the fact that there cannot be a proposition whose form could not have been foreseen (i.e. constructed). The general form of a proposition is: This is how things stand.</div>
<div class="corelinks tlpdepth2"><strong>4.51</strong><span class="linkarray tlpdepth2" id="p4.51PM"> P/M [→<a class="gerlink" href="#p4.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.51OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Suppose that I am given <em>all</em> elementary propositions: then I can simply ask what propositions I can construct out of them. And there I have <em>all</em> propositions, and <em>that</em> fixes their limits.</div>
<div class="corelinks tlpdepth2"><strong>4.52</strong><span class="linkarray tlpdepth2" id="p4.52PM"> P/M [→<a class="gerlink" href="#p4.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.52OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Propositions comprise all that follows from the totality of all elementary propositions (and, of course, from its being the <em>totality</em> of them <em>all</em>). (Thus, in a certain sense, it could be said that <em>all</em> propositions were generalizations of elementary propositions.)</div>
<div class="corelinks tlpdepth2"><strong>4.53</strong><span class="linkarray tlpdepth2" id="p4.53PM"> P/M [→<a class="gerlink" href="#p4.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.53OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The general propositional form is a variable.</div>
<div class="corelinks tlpdepth0"><strong>5</strong><span class="linkarray tlpdepth0" id="p5PM"> P/M [→<a class="gerlink" href="#p5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5OGD">OGD</a>]</span></div>
<div class="para tlpdepth0">A proposition is a truth-function of elementary propositions.</div>
<div class="para tlpdepth0">(An elementary proposition is a truth-function of itself.)</div>
<div class="corelinks tlpdepth2"><strong>5.01</strong><span class="linkarray tlpdepth2" id="p5.01PM"> P/M [→<a class="gerlink" href="#p5.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.01OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Elementary propositions are the truth-arguments of propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.02</strong><span class="linkarray tlpdepth2" id="p5.02PM"> P/M [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The arguments of functions are readily confused with the affixes of names. For both arguments and affixes enable me to recognize the meaning of the signs containing them.</div>
<div class="para tlpdepth2">For example, when Russell writes ‘<span class="mathmode"><span class="mathrel">+</span><sub><var>c</var></sub></span>’, the ‘<span class="mathmode"><sub><var>c</var></sub></span>’ is an affix which indicates that the sign as a whole is the addition-sign for cardinal numbers. But the use of this sign is the result of arbitrary convention and it would be quite possible to choose a simple sign instead of ‘<span class="mathmode"><span class="mathrel">+</span><sub><var>c</var></sub></span>’; in ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’, however, ‘<span class="mathmode"><var>p</var></span>’ is not an affix but an argument: the sense of ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ <em>cannot</em> be understood unless the sense of ‘<span class="mathmode"><var>p</var></span>’ has been understood already. (In the name Julius Caesar ‘Julius’ is an affix. An affix is always part of a description of the object to whose name we attach it: e.g. <em>the</em> Caesar of the Julian gens.)</div>
<div class="para tlpdepth2">If I am not mistaken, Frege’s theory about the meaning of propositions and functions is based on the confusion between an argument and an affix. Frege regarded the propositions of logic as names, and their arguments as the affixes of those names.</div>
<div class="corelinks tlpdepth1"><strong>5.1</strong><span class="linkarray tlpdepth1" id="p5.1PM"> P/M [→<a class="gerlink" href="#p5.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">Truth-functions can be arranged in series.</div>
<div class="para tlpdepth1">That is the foundation of the theory of probability.</div>
<div class="corelinks tlpdepth3"><strong>5.101</strong><span class="linkarray tlpdepth3" id="p5.101PM"> P/M [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The truth-functions of a given number of elementary propositions can always be set out in a schema of the following kind:</div>
<div class="para tlpdepth3 noindent"><!-- noindent --><table class="fnlist"> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >Tautology&nbsp;</td><td >(If <span class="mathmode"><var>p</var></span> then <span class="mathmode"><var>p</var></span>; and if <span class="mathmode"><var>q</var></span> then <span class="mathmode"><var>q</var></span>.) &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var><span class="mathrel">.</span><var>q</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >In&nbsp;words:&nbsp;</td><td >Not both <span class="mathmode"><var>p</var></span> and <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><var>q</var>))</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td >If <span class="mathmode"><var>q</var></span> then <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>q</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td >If <span class="mathmode"><var>p</var></span> then <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td ><span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td >Not <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<span class="mathop">~</span><var>q</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td >Not <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<span class="mathop">~</span><var>p</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td ><span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>, but not both. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var><span class="mathrel">:<span class="symbol">∨</span>:</span><var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td >If <span class="mathmode"><var>p</var></span> then <span class="mathmode"><var>q</var></span>, and if <span class="mathmode"><var>q</var></span> then <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">≡</span></span><var>q</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td ><span class="mathmode"><var>p</var></span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td ><span class="mathmode"><var>q</var></span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td >Neither <span class="mathmode"><var>p</var></span> nor <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var></span> or <span class="mathmode"><var>p</var><span class="mathrel">|</span><var>q</var>)</span></td></tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td ><span class="mathmode"><var>p</var></span> and not <span class="mathmode"><var>q</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td ><span class="mathmode"><var>q</var></span> and not <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >T</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" >&nbsp;”&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;”&nbsp;&nbsp;&nbsp;:</td><td ><span class="mathmode"><var>q</var></span> and <span class="mathmode"><var>p</var></span>. &nbsp;&nbsp; <span class="mathmode">(<var>q</var><span class="mathrel">.</span><var>p</var>)</span></td> </tr> <tr><td class="righttight" >(</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="centertight" >F</td><td class="lefttight" >)</td><td class="leftcell" ><span class="mathmode">(<var>p</var>,&nbsp;<var>q</var>)</span>&nbsp;&nbsp;</td><td class="leftcell" colspan="2">Contradiction (<span class="mathmode"><var>p</var></span> and not <span class="mathmode"><var>p</var></span>, and <span class="mathmode"><var>q</var></span> and not <span class="mathmode"><var>q</var></span>.) &nbsp;&nbsp; <span class="mathmode">(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><var>q</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>)</span></td></tr></table></div>
<div class="para tlpdepth3">I will give the name <em>truth-grounds</em> of a proposition to those truth-possibilities of its truth-arguments that make it true.</div>
<div class="corelinks tlpdepth2"><strong>5.11</strong><span class="linkarray tlpdepth2" id="p5.11PM"> P/M [→<a class="gerlink" href="#p5.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.11OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If all the truth-grounds that are common to a number of propositions are at the same time truth-grounds of a certain proposition, then we say that the truth of that proposition follows from the truth of the others.</div>
<div class="corelinks tlpdepth2"><strong>5.12</strong><span class="linkarray tlpdepth2" id="p5.12PM"> P/M [→<a class="gerlink" href="#p5.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.12OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">In particular, the truth of a proposition ‘<span class="mathmode"><var>p</var></span>’ follows from the truth of another proposition ‘<span class="mathmode"><var>q</var></span>’ if all the truth-grounds of the latter are truth-grounds of the former.</div>
<div class="corelinks tlpdepth3"><strong>5.121</strong><span class="linkarray tlpdepth3" id="p5.121PM"> P/M [→<a class="gerlink" href="#p5.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.121OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The truth-grounds of the one are contained in those of the other: <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.122</strong><span class="linkarray tlpdepth3" id="p5.122PM"> P/M [→<a class="gerlink" href="#p5.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.122OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span>, the sense of ‘<span class="mathmode"><var>p</var></span>’ is contained in the sense of ‘<span class="mathmode"><var>q</var></span>’.</div>
<div class="corelinks tlpdepth3"><strong>5.123</strong><span class="linkarray tlpdepth3" id="p5.123PM"> P/M [→<a class="gerlink" href="#p5.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.123OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If a god creates a world in which certain propositions are true, then by that very act he also creates a world in which all the propositions that follow from them come true. And similarly he could not create a world in which the proposition ‘<span class="mathmode"><var>p</var></span>’ was true without creating all its objects.</div>
<div class="corelinks tlpdepth3"><strong>5.124</strong><span class="linkarray tlpdepth3" id="p5.124PM"> P/M [→<a class="gerlink" href="#p5.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.124OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A proposition affirms every proposition that follows from it.</div>
<div class="corelinks tlpdepth4"><strong>5.1241</strong><span class="linkarray tlpdepth4" id="p5.1241PM"> P/M [→<a class="gerlink" href="#p5.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1241OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">‘<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>q</var></span>’ is one of the propositions that affirm ‘<span class="mathmode"><var>p</var></span>’ and at the same time one of the propositions that affirm ‘<span class="mathmode"><var>q</var></span>’.</div>
<div class="para tlpdepth4">Two propositions are opposed to one another if there is no proposition with a sense, that affirms them both.</div>
<div class="para tlpdepth4">Every proposition that contradicts another negates it.</div>
<div class="corelinks tlpdepth2"><strong>5.13</strong><span class="linkarray tlpdepth2" id="p5.13PM"> P/M [→<a class="gerlink" href="#p5.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.13OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">When the truth of one proposition follows from the truth of others, we can see this from the structure of the propositions.</div>
<div class="corelinks tlpdepth3"><strong>5.131</strong><span class="linkarray tlpdepth3" id="p5.131PM"> P/M [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If the truth of one proposition follows from the truth of others, this finds expression in relations in which the forms of the propositions stand to one another: nor is it necessary for us to set up these relations between them, by combining them with one another in a single proposition; on the contrary, the relations are internal, and their existence is an immediate result of the existence of the propositions.</div>
<div class="corelinks tlpdepth4"><strong>5.1311</strong><span class="linkarray tlpdepth4" id="p5.1311PM"> P/M [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">When we infer <span class="mathmode"><var>q</var></span> from <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span> and <span class="mathmode"><span class="mathop">~</span><var>p</var></span>, the relation between the propositional forms of ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>’ and ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ is masked, in this case, by our mode of signifying. But if instead of ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>’ we write, for example, ‘<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>q</var><span class="mathrel">.|.</span><var>p</var><span class="mathrel">|</span><var>q</var></span>’, and instead of ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’, ‘<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>p</var></span>’ (<span class="mathmode"><var>p</var><span class="mathrel">|</span><var>q</var></span> = neither <span class="mathmode"><var>p</var></span> nor <span class="mathmode"><var>q</var></span>), then the inner connexion becomes obvious.</div>
<div class="para tlpdepth4">(The possibility of inference from <span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span> to <span class="mathmode"><var>fa</var></span> shows that the symbol <span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span> itself has generality in it.)</div>
<div class="corelinks tlpdepth3"><strong>5.132</strong><span class="linkarray tlpdepth3" id="p5.132PM"> P/M [→<a class="gerlink" href="#p5.132GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.132OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span>, I can make an inference from <span class="mathmode"><var>q</var></span> to <span class="mathmode"><var>p</var></span>, deduce <span class="mathmode"><var>p</var></span> from <span class="mathmode"><var>q</var></span>.</div>
<div class="para tlpdepth3">The nature of the inference can be gathered only from the two propositions.</div>
<div class="para tlpdepth3">They themselves are the only possible justification of the inference.</div>
<div class="para tlpdepth3">‘Laws of inference’, which are supposed to justify inferences, as in the works of Frege and Russell, have no sense, and would be superfluous.</div>
<div class="corelinks tlpdepth3"><strong>5.133</strong><span class="linkarray tlpdepth3" id="p5.133PM"> P/M [→<a class="gerlink" href="#p5.133GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.133OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">All deductions are made <em>a priori</em>.</div>
<div class="corelinks tlpdepth3"><strong>5.134</strong><span class="linkarray tlpdepth3" id="p5.134PM"> P/M [→<a class="gerlink" href="#p5.134GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.134OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">One elementary proposition cannot be deduced from another.</div>
<div class="corelinks tlpdepth3"><strong>5.135</strong><span class="linkarray tlpdepth3" id="p5.135PM"> P/M [→<a class="gerlink" href="#p5.135GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.135OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">There is no possible way of making an inference from the existence of one situation to the existence of another, entirely different situation.</div>
<div class="corelinks tlpdepth3"><strong>5.136</strong><span class="linkarray tlpdepth3" id="p5.136PM"> P/M [→<a class="gerlink" href="#p5.136GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.136OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">There is no causal nexus to justify such an inference.</div>
<div class="corelinks tlpdepth4"><strong>5.1361</strong><span class="linkarray tlpdepth4" id="p5.1361PM"> P/M [→<a class="gerlink" href="#p5.1361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1361OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">We <em>cannot</em> infer the events of the future from those of the present.</div>
<div class="para tlpdepth4">Belief in the causal nexus is <em>superstition</em>.</div>
<div class="corelinks tlpdepth4"><strong>5.1362</strong><span class="linkarray tlpdepth4" id="p5.1362PM"> P/M [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The freedom of the will consists in the impossibility of knowing actions that still lie in the future. We could know them only if causality were an <em>inner</em> necessity like that of logical inference.—The connexion between knowledge and what is known is that of logical necessity.</div>
<div class="para tlpdepth4">(‘A knows that <span class="mathmode"><var>p</var></span> is the case’, has no sense if <span class="mathmode"><var>p</var></span> is a tautology.)</div>
<div class="corelinks tlpdepth4"><strong>5.1363</strong><span class="linkarray tlpdepth4" id="p5.1363PM"> P/M [→<a class="gerlink" href="#p5.1363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1363OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If the truth of a proposition does not <em>follow</em> from the fact that it is self-evident to us, then its self-evidence in no way justifies our belief in its truth.</div>
<div class="corelinks tlpdepth2"><strong>5.14</strong><span class="linkarray tlpdepth2" id="p5.14PM"> P/M [→<a class="gerlink" href="#p5.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.14OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If one proposition follows from another, then the latter says more than the former, and the former less than the latter.</div>
<div class="corelinks tlpdepth3"><strong>5.141</strong><span class="linkarray tlpdepth3" id="p5.141PM"> P/M [→<a class="gerlink" href="#p5.141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.141OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span> and <span class="mathmode"><var>q</var></span> from <span class="mathmode"><var>p</var></span>, then they are one and the same proposition.</div>
<div class="corelinks tlpdepth3"><strong>5.142</strong><span class="linkarray tlpdepth3" id="p5.142PM"> P/M [→<a class="gerlink" href="#p5.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.142OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A tautology follows from all propositions: it says nothing.</div>
<div class="corelinks tlpdepth3"><strong>5.143</strong><span class="linkarray tlpdepth3" id="p5.143PM"> P/M [→<a class="gerlink" href="#p5.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.143OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Contradiction is that common factor of propositions which <em>no</em> proposition has in common with another. Tautology is the common factor of all propositions that have nothing in common with one another.</div>
<div class="para tlpdepth3">Contradiction, one might say, vanishes outside all propositions: tautology vanishes inside them.</div>
<div class="para tlpdepth3">Contradiction is the outer limit of propositions: tautology is the unsubstantial point at their centre.</div>
<div class="corelinks tlpdepth2"><strong>5.15</strong><span class="linkarray tlpdepth2" id="p5.15PM"> P/M [→<a class="gerlink" href="#p5.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.15OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If <span class="mathmode"><span class="mathrm">T</span><sub><var>r</var></sub></span> is the number of the truth-grounds of a proposition ‘<span class="mathmode"><var>r</var></span>’, and if <span class="mathmode"><span class="mathrm">T</span><sub><var>rs</var></sub></span> is the number of the truth-grounds of a proposition ‘<span class="mathmode"><var>s</var></span>’ that are at the same time truth-grounds of ‘<span class="mathmode"><var>r</var></span>’, then we call the ratio <span class="mathmode"><span class="mathrm">T</span><sub><var>rs</var></sub> : <span class="mathrm">T</span><sub><var>r</var></sub></span> the degree of probability that the proposition ‘<span class="mathmode"><var>r</var></span>’ gives to the proposition ‘<span class="mathmode"><var>s</var></span>’.</div>
<div class="corelinks tlpdepth3"><strong>5.151</strong><span class="linkarray tlpdepth3" id="p5.151PM"> P/M [→<a class="gerlink" href="#p5.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.151OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In a schema like the one above in 5.101, let <span class="mathmode"><span class="mathrm">T</span><sub><var>r</var></sub></span> be the number of ‘T’s’ in the proposition <span class="mathmode"><var>r</var></span>, and let <span class="mathmode"><span class="mathrm">T</span><sub><var>rs</var></sub></span>, be the number of ‘T’s’ in the proposition <span class="mathmode"><var>s</var></span> that stand in columns in which the proposition <span class="mathmode"><var>r</var></span> has ‘T’s’. Then the proposition <span class="mathmode"><var>r</var></span> gives to the proposition <span class="mathmode"><var>s</var></span> the probability <span class="mathmode"><span class="mathrm">T</span><sub><var>rs</var></sub> : <span class="mathrm">T</span><sub><var>r</var></sub></span>.</div>
<div class="corelinks tlpdepth4"><strong>5.1511</strong><span class="linkarray tlpdepth4" id="p5.1511PM"> P/M [→<a class="gerlink" href="#p5.1511GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1511OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">There is no special object peculiar to probability propositions.</div>
<div class="corelinks tlpdepth3"><strong>5.152</strong><span class="linkarray tlpdepth3" id="p5.152PM"> P/M [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">When propositions have no truth-arguments in common with one another, we call them independent of one another.</div>
<div class="para tlpdepth3">Two elementary propositions give one another the probability <span class="mathmode">½</span>.</div>
<div class="para tlpdepth3">If <span class="mathmode"><var>p</var></span> follows from <span class="mathmode"><var>q</var></span>, then the proposition ‘<span class="mathmode"><var>q</var></span>’ gives to the proposition ‘<span class="mathmode"><var>p</var></span>’ the probability 1. The certainty of logical inference is a limiting case of probability.</div>
<div class="para tlpdepth3">(Application of this to tautology and contradiction.)</div>
<div class="corelinks tlpdepth3"><strong>5.153</strong><span class="linkarray tlpdepth3" id="p5.153PM"> P/M [→<a class="gerlink" href="#p5.153GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.153OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In itself, a proposition is neither probable nor improbable. Either an event occurs or it does not: there is no middle way.</div>
<div class="corelinks tlpdepth3"><strong>5.154</strong><span class="linkarray tlpdepth3" id="p5.154PM"> P/M [→<a class="gerlink" href="#p5.154GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.154OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Suppose that an urn contains black and white balls in equal numbers (and none of any other kind). I draw one ball after another, putting them back into the urn. By this experiment I can establish that the number of black balls drawn and the number of white balls drawn approximate to one another as the draw continues.</div>
<div class="para tlpdepth3">So <em>this</em> is not a mathematical truth.</div>
<div class="para tlpdepth3">Now, if I say, ‘The probability of my drawing a white ball is equal to the probability of my drawing a black one’, this means that all the circumstances that I know of (including the laws of nature assumed as hypotheses) give no <em>more</em> probability to the occurrence of the one event than to that of the other. That is to say, they give each the probability <span class="mathmode">½</span>, as can easily be gathered from the above definitions.</div>
<div class="para tlpdepth3">What I confirm by the experiment is that the occurrence of the two events is independent of the circumstances of which I have no more detailed knowledge.</div>
<div class="corelinks tlpdepth3"><strong>5.155</strong><span class="linkarray tlpdepth3" id="p5.155PM"> P/M [→<a class="gerlink" href="#p5.155GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.155OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The minimal unit for a probability proposition is this: The circumstances—of which I have no further knowledge—give such and such a degree of probability to the occurrence of a particular event.</div>
<div class="corelinks tlpdepth3"><strong>5.156</strong><span class="linkarray tlpdepth3" id="p5.156PM"> P/M [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is in this way that probability is a generalization.</div>
<div class="para tlpdepth3">It involves a general description of a propositional form.</div>
<div class="para tlpdepth3">We use probability only in default of certainty—if our knowledge of a fact is not indeed complete, but we do know <em>something</em> about its form.</div>
<div class="para tlpdepth3">(A proposition may well be an incomplete picture of a certain situation, but it is always a complete picture of <em>something</em>.)</div>
<div class="para tlpdepth3">A probability proposition is a sort of excerpt from other propositions.</div>
<div class="corelinks tlpdepth1"><strong>5.2</strong><span class="linkarray tlpdepth1" id="p5.2PM"> P/M [→<a class="gerlink" href="#p5.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">The structures of propositions stand in internal relations to one another.</div>
<div class="corelinks tlpdepth2"><strong>5.21</strong><span class="linkarray tlpdepth2" id="p5.21PM"> P/M [→<a class="gerlink" href="#p5.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.21OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">In order to give prominence to these internal relations we can adopt the following mode of expression: we can represent a proposition as the result of an operation that produces it out of other propositions (which are the bases of the operation).</div>
<div class="corelinks tlpdepth2"><strong>5.22</strong><span class="linkarray tlpdepth2" id="p5.22PM"> P/M [→<a class="gerlink" href="#p5.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.22OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">An operation is the expression of a relation between the structures of its result and of its bases.</div>
<div class="corelinks tlpdepth2"><strong>5.23</strong><span class="linkarray tlpdepth2" id="p5.23PM"> P/M [→<a class="gerlink" href="#p5.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.23OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The operation is what has to be done to the one proposition in order to make the other out of it.</div>
<div class="corelinks tlpdepth3"><strong>5.231</strong><span class="linkarray tlpdepth3" id="p5.231PM"> P/M [→<a class="gerlink" href="#p5.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.231OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">And that will, of course, depend on their formal properties, on the internal similarity of their forms.</div>
<div class="corelinks tlpdepth3"><strong>5.232</strong><span class="linkarray tlpdepth3" id="p5.232PM"> P/M [→<a class="gerlink" href="#p5.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.232OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The internal relation by which a series is ordered is equivalent to the operation that produces one term from another.</div>
<div class="corelinks tlpdepth3"><strong>5.233</strong><span class="linkarray tlpdepth3" id="p5.233PM"> P/M [→<a class="gerlink" href="#p5.233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.233OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Operations cannot make their appearance before the point at which one proposition is generated out of another in a logically meaningful way; i.e. the point at which the logical construction of propositions begins.</div>
<div class="corelinks tlpdepth3"><strong>5.234</strong><span class="linkarray tlpdepth3" id="p5.234PM"> P/M [→<a class="gerlink" href="#p5.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.234OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Truth-functions of elementary propositions are results of operations with elementary propositions as bases. (These operations I call truth-operations.)</div>
<div class="corelinks tlpdepth4"><strong>5.2341</strong><span class="linkarray tlpdepth4" id="p5.2341PM"> P/M [→<a class="gerlink" href="#p5.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2341OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The sense of a truth-function of <span class="mathmode"><var>p</var></span> is a function of the sense of <span class="mathmode"><var>p</var></span>.</div>
<div class="para tlpdepth4">Negation, logical addition, logical multiplication, etc. etc. are operations.</div>
<div class="para tlpdepth4">(Negation reverses the sense of a proposition.)</div>
<div class="corelinks tlpdepth2"><strong>5.24</strong><span class="linkarray tlpdepth2" id="p5.24PM"> P/M [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">An operation manifests itself in a variable; it shows how we can get from one form of proposition to another.</div>
<div class="para tlpdepth2">It gives expression to the difference between the forms.</div>
<div class="para tlpdepth2">(And what the bases of an operation and its result have in common is just the bases themselves.)</div>
<div class="corelinks tlpdepth3"><strong>5.241</strong><span class="linkarray tlpdepth3" id="p5.241PM"> P/M [→<a class="gerlink" href="#p5.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.241OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">An operation is not the mark of a form, but only of a difference between forms.</div>
<div class="corelinks tlpdepth3"><strong>5.242</strong><span class="linkarray tlpdepth3" id="p5.242PM"> P/M [→<a class="gerlink" href="#p5.242GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.242OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The operation that produces ‘<span class="mathmode"><var>q</var></span>’ from ‘<span class="mathmode"><var>p</var></span>’ also produces ‘<span class="mathmode"><var>r</var></span>’ from ‘<span class="mathmode"><var>q</var></span>’, and so on. There is only one way of expressing this: ‘<span class="mathmode"><var>p</var></span>’, ‘<span class="mathmode"><var>q</var></span>’, ‘<span class="mathmode"><var>r</var></span>’, etc. have to be variables that give expression in a general way to certain formal relations.</div>
<div class="corelinks tlpdepth2"><strong>5.25</strong><span class="linkarray tlpdepth2" id="p5.25PM"> P/M [→<a class="gerlink" href="#p5.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.25OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The occurrence of an operation does not characterize the sense of a proposition.</div>
<div class="para tlpdepth2">Indeed, no statement is made by an operation, but only by its result, and this depends on the bases of the operation.</div>
<div class="para tlpdepth2">(Operations and functions must not be confused with each other.)</div>
<div class="corelinks tlpdepth3"><strong>5.251</strong><span class="linkarray tlpdepth3" id="p5.251PM"> P/M [→<a class="gerlink" href="#p5.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.251OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A function cannot be its own argument, whereas an operation can take one of its own results as its base.</div>
<div class="corelinks tlpdepth3"><strong>5.252</strong><span class="linkarray tlpdepth3" id="p5.252PM"> P/M [→<a class="gerlink" href="#p5.252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.252OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is only in this way that the step from one term of a series of forms to another is possible (from one type to another in the hierarchies of Russell and Whitehead). (Russell and Whitehead did not admit the possibility of such steps, but repeatedly availed themselves of it.)</div>
<div class="corelinks tlpdepth4"><strong>5.2521</strong><span class="linkarray tlpdepth4" id="p5.2521PM"> P/M [→<a class="gerlink" href="#p5.2521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2521OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If an operation is applied repeatedly to its own results, I speak of successive applications of it. (‘<span class="mathmode"><span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><var>a</var></span>’ is the result of three successive applications of the operation ‘<span class="mathmode"><span class="mathop"><span class="mathrm">O</span>’</span><var>ξ</var></span>’ to ‘<span class="mathmode"><var>a</var></span>’.)</div>
<div class="para tlpdepth4">In a similar sense I speak of successive applications of <em>more than one</em> operation to a number of propositions.</div>
<div class="corelinks tlpdepth4"><strong>5.2522</strong><span class="linkarray tlpdepth4" id="p5.2522PM"> P/M [→<a class="gerlink" href="#p5.2522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2522OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Accordingly I use the sign ‘<span class="mathmode">[<var>a</var>, <var>x</var>, <span class="mathop"><span class="mathrm">O</span>’</span><var>x</var>]</span>’ for the general term of the series of forms <span class="mathmode"><var>a</var>, <span class="mathop"><span class="mathrm">O</span>’</span><var>a</var>, <span class="mathop"><span class="mathrm">O</span>’</span><span class="mathop"><span class="mathrm">O</span>’</span><var>a</var>,<span class="mathrel">…</span></span>. This bracketed expression is a variable: the first term of the bracketed expression is the beginning of the series of forms, the second is the form of a term <span class="mathmode"><var>x</var></span> arbitrarily selected from the series, and the third is the form of the term that immediately follows <span class="mathmode"><var>x</var></span> in the series.</div>
<div class="corelinks tlpdepth4"><strong>5.2523</strong><span class="linkarray tlpdepth4" id="p5.2523PM"> P/M [→<a class="gerlink" href="#p5.2523GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2523OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The concept of successive applications of an operation is equivalent to the concept ‘and so on’.</div>
<div class="corelinks tlpdepth3"><strong>5.253</strong><span class="linkarray tlpdepth3" id="p5.253PM"> P/M [→<a class="gerlink" href="#p5.253GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.253OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">One operation can counteract the effect of another. Operations can cancel one another.</div>
<div class="corelinks tlpdepth3"><strong>5.254</strong><span class="linkarray tlpdepth3" id="p5.254PM"> P/M [→<a class="gerlink" href="#p5.254GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.254OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">An operation can vanish (e.g. negation in ‘<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>’: <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var><span class="mathrel">=</span><var>p</var></span>).</div>
<div class="corelinks tlpdepth1"><strong>5.3</strong><span class="linkarray tlpdepth1" id="p5.3PM"> P/M [→<a class="gerlink" href="#p5.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.3OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">All propositions are results of truth-operations on elementary propositions.</div>
<div class="para tlpdepth1">A truth-operation is the way in which a truth-function is produced out of elementary propositions.</div>
<div class="para tlpdepth1">It is of the essence of truth-operations that, just as elementary propositions yield a truth-function of themselves, so too in the same way truth-functions yield a further truth-function. When a truth-operation is applied to truth-functions of elementary propositions, it always generates another truth-function of elementary propositions, another proposition. When a truth-operation is applied to the results of truth-operations on elementary propositions, there is always a <em>single</em> operation on elementary propositions that has the same result.</div>
<div class="para tlpdepth1">Every proposition is the result of truth-operations on elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.31</strong><span class="linkarray tlpdepth2" id="p5.31PM"> P/M [→<a class="gerlink" href="#p5.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.31OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The schemata in 4.31 have a meaning even when ‘<span class="mathmode"><var>p</var></span>’, ‘<span class="mathmode"><var>q</var></span>’, ‘<span class="mathmode"><var>r</var></span>’, etc. are not elementary propositions.</div>
<div class="para tlpdepth2">And it is easy to see that the propositional sign in 4.442 expresses a single truth-function of elementary propositions even when ‘<span class="mathmode"><var>p</var></span>’ and ‘<span class="mathmode"><var>q</var></span>’ are truth-functions of elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.32</strong><span class="linkarray tlpdepth2" id="p5.32PM"> P/M [→<a class="gerlink" href="#p5.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.32OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">All truth-functions are results of successive applications to elementary propositions of a finite number of truth-operations.</div>
<div class="corelinks tlpdepth1"><strong>5.4</strong><span class="linkarray tlpdepth1" id="p5.4PM"> P/M [→<a class="gerlink" href="#p5.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">At this point it becomes manifest that there are no ‘logical objects’ or ‘logical constants’ (in Frege’s and Russell’s sense).</div>
<div class="corelinks tlpdepth2"><strong>5.41</strong><span class="linkarray tlpdepth2" id="p5.41PM"> P/M [→<a class="gerlink" href="#p5.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.41OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The reason is that the results of truth-operations on truth-functions are always identical whenever they are one and the same truth-function of elementary propositions.</div>
<div class="corelinks tlpdepth2"><strong>5.42</strong><span class="linkarray tlpdepth2" id="p5.42PM"> P/M [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">It is self-evident that ∨, ⊃, etc. are not relations in the sense in which right and left etc. are relations.</div>
<div class="para tlpdepth2">The interdefinability of Frege’s and Russell’s ‘primitive signs’ of logic is enough to show that they are not primitive signs, still less signs for relations.</div>
<div class="para tlpdepth2">And it is obvious that the ‘⊃’ defined by means of ‘~’ and ‘∨’ is identical with the one that figures with ‘~’ in the definition of ‘∨’; and that the second ‘∨’ is identical with the first one; and so on.</div>
<div class="corelinks tlpdepth2"><strong>5.43</strong><span class="linkarray tlpdepth2" id="p5.43PM"> P/M [→<a class="gerlink" href="#p5.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.43OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Even at first sight it seems scarcely credible that there should follow from one fact <span class="mathmode"><var>p</var></span> infinitely many <em>others</em>, namely <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>, <span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>, etc. And it is no less remarkable that the infinite number of propositions of logic (mathematics) follow from half a dozen ‘primitive propositions’.</div>
<div class="para tlpdepth2">But in fact all the propositions of logic say the same thing, to wit nothing.</div>
<div class="corelinks tlpdepth2"><strong>5.44</strong><span class="linkarray tlpdepth2" id="p5.44PM"> P/M [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Truth-functions are not material functions.</div>
<div class="para tlpdepth2">For example, an affirmation can be produced by double negation: in such a case does it follow that in some sense negation is contained in affirmation? Does ‘<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>’ negate <span class="mathmode"><span class="mathop">~</span><var>p</var></span>, or does it affirm <span class="mathmode"><var>p</var></span>—or both?</div>
<div class="para tlpdepth2">The proposition ‘<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>’ is not about negation, as if negation were an object: on the other hand, the possibility of negation is already written into affirmation.</div>
<div class="para tlpdepth2">And if there were an object called ‘~’, it would follow that ‘<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>’ said something different from what ‘<span class="mathmode"><var>p</var></span>’ said, just because the one proposition would then be about ~ and the other would not.</div>
<div class="corelinks tlpdepth3"><strong>5.441</strong><span class="linkarray tlpdepth3" id="p5.441PM"> P/M [→<a class="gerlink" href="#p5.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.441OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">This vanishing of the apparent logical constants also occurs in the case of ‘<span class="mathmode"><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><span class="mathop">~</span><var>fx</var></span>’, which says the same as ‘<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>’, and in the case of ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>a</var></span>’, which says the same as ‘<span class="mathmode"><var>fa</var></span>’.</div>
<div class="corelinks tlpdepth3"><strong>5.442</strong><span class="linkarray tlpdepth3" id="p5.442PM"> P/M [→<a class="gerlink" href="#p5.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.442OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If we are given a proposition, then <em>with it</em> we are also given the results of all truth-operations that have it as their base.</div>
<div class="corelinks tlpdepth2"><strong>5.45</strong><span class="linkarray tlpdepth2" id="p5.45PM"> P/M [→<a class="gerlink" href="#p5.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.45OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If there are primitive logical signs, then any logic that fails to show clearly how they are placed relatively to one another and to justify their existence will be incorrect. The construction of logic <em>out of</em> its primitive signs must be made clear.</div>
<div class="corelinks tlpdepth3"><strong>5.451</strong><span class="linkarray tlpdepth3" id="p5.451PM"> P/M [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If logic has primitive ideas, they must be independent of one another. If a primitive idea has been introduced, it must have been introduced in all the combinations in which it ever occurs. It cannot, therefore, be introduced first for <em>one</em> combination and later reintroduced for another. For example, once negation has been introduced, we must understand it both in propositions of the form ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ and in propositions like ‘<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var>)</span>’, ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><span class="mathop">~</span><var>fx</var></span>’, etc. We must not introduce it first for the one class of cases and then for the other, since it would then be left in doubt whether its meaning were the same in both cases, and no reason would have been given for combining the signs in the same way in both cases.</div>
<div class="para tlpdepth3">(In short, Frege’s remarks about introducing signs by means of definitions (in <em>The Fundamental Laws of Arithmetic</em>) also apply, <em>mutatis mutandis</em>, to the introduction of primitive signs.)</div>
<div class="corelinks tlpdepth3"><strong>5.452</strong><span class="linkarray tlpdepth3" id="p5.452PM"> P/M [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The introduction of any new device into the symbolism of logic is necessarily a momentous event. In logic a new device should not be introduced in brackets or in a footnote with what one might call a completely innocent air.</div>
<div class="para tlpdepth3">(Thus in Russell and Whitehead’s <em>Principia Mathematica</em> there occur definitions and primitive propositions expressed in words. Why this sudden appearance of words? It would require a justification, but none is given, or could be given, since the procedure is in fact illicit.)</div>
<div class="para tlpdepth3">But if the introduction of a new device has proved necessary at a certain point, we must immediately ask ourselves, ‘At what points is the employment of this device now <em>unavoidable</em>?’ and its place in logic must be made clear.</div>
<div class="corelinks tlpdepth3"><strong>5.453</strong><span class="linkarray tlpdepth3" id="p5.453PM"> P/M [→<a class="gerlink" href="#p5.453GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.453OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">All numbers in logic stand in need of justification.</div>
<div class="para tlpdepth3">Or rather, it must become evident that there are no numbers in logic.</div>
<div class="para tlpdepth3">There are no privileged numbers.</div>
<div class="corelinks tlpdepth3"><strong>5.454</strong><span class="linkarray tlpdepth3" id="p5.454PM"> P/M [→<a class="gerlink" href="#p5.454GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.454OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">In logic there is no co-ordinate status, and there can be no classification.</div>
<div class="para tlpdepth3">In logic there can be no distinction between the general and the specific.</div>
<div class="corelinks tlpdepth4"><strong>5.4541</strong><span class="linkarray tlpdepth4" id="p5.4541PM"> P/M [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4541OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The solutions of the problems of logic must be simple, since they set the standard of simplicity.</div>
<div class="para tlpdepth4">Men have always had a presentiment that there must be a realm in which the answers to questions are symmetrically combined—<em>a priori</em>—to form a self-contained system.</div>
<div class="para tlpdepth4">A realm subject to the law: <em>Simplex sigillum veri</em>.</div>
<div class="corelinks tlpdepth2"><strong>5.46</strong><span class="linkarray tlpdepth2" id="p5.46PM"> P/M [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If we introduced logical signs properly, then we should also have introduced at the same time the sense of all combinations of them; i.e. not only ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>’ but ‘<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>q</var>)</span>’ as well, etc. etc. We should also have introduced at the same time the effect of all possible combinations of brackets. And thus it would have been made clear that the real general primitive signs are not ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>’, ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>’, etc. but the most general form of their combinations.</div>
<div class="corelinks tlpdepth3"><strong>5.461</strong><span class="linkarray tlpdepth3" id="p5.461PM"> P/M [→<a class="gerlink" href="#p5.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.461OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Though it seems unimportant, it is in fact significant that the pseudo-relations of logic, such as ∨ and ⊃, need brackets—unlike real relations.</div>
<div class="para tlpdepth3">Indeed, the use of brackets with these apparently primitive signs is itself an indication that they are not primitive signs. And surely no one is going to believe brackets have an independent meaning.</div>
<div class="corelinks tlpdepth4"><strong>5.4611</strong><span class="linkarray tlpdepth4" id="p5.4611PM"> P/M [→<a class="gerlink" href="#p5.4611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4611OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Signs for logical operations are punctuation-marks.</div>
<div class="corelinks tlpdepth2"><strong>5.47</strong><span class="linkarray tlpdepth2" id="p5.47PM"> P/M [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">It is clear that whatever we can say <em>in advance</em> about the form of all propositions, we must be able to say <em>all at once</em>.</div>
<div class="para tlpdepth2">An elementary proposition really contains all logical operations in itself. For ‘<span class="mathmode"><var>fa</var></span>’ says the same thing as</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode">‘<span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>a</var>’.</span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">Wherever there is compositeness, argument and function are present, and where these are present, we already have all the logical constants.</div>
<div class="para tlpdepth2">One could say that the sole logical constant was what <em>all</em> propositions, by their very nature, had in common with one another.</div>
<div class="para tlpdepth2">But that is the general propositional form.</div>
<div class="corelinks tlpdepth3"><strong>5.471</strong><span class="linkarray tlpdepth3" id="p5.471PM"> P/M [→<a class="gerlink" href="#p5.471GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.471OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The general propositional form is the essence of a proposition.</div>
<div class="corelinks tlpdepth4"><strong>5.4711</strong><span class="linkarray tlpdepth4" id="p5.4711PM"> P/M [→<a class="gerlink" href="#p5.4711GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4711OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">To give the essence of a proposition means to give the essence of all description, and thus the essence of the world.</div>
<div class="corelinks tlpdepth3"><strong>5.472</strong><span class="linkarray tlpdepth3" id="p5.472PM"> P/M [→<a class="gerlink" href="#p5.472GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.472OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The description of the most general propositional form is the description of the one and only general primitive sign in logic.</div>
<div class="corelinks tlpdepth3"><strong>5.473</strong><span class="linkarray tlpdepth3" id="p5.473PM"> P/M [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Logic must look after itself.</div>
<div class="para tlpdepth3">If a sign is <em>possible</em>, then it is also capable of signifying. Whatever is possible in logic is also permitted. (The reason why ‘Socrates is identical’ means nothing is that there is no property called ‘identical’. The proposition is nonsensical because we have failed to make an arbitrary determination, and not because the symbol, in itself, would be illegitimate.)</div>
<div class="para tlpdepth3">In a certain sense, we cannot make mistakes in logic.</div>
<div class="corelinks tlpdepth4"><strong>5.4731</strong><span class="linkarray tlpdepth4" id="p5.4731PM"> P/M [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4731OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Self-evidence, which Russell talked about so much, can become dispensable in logic, only because language itself prevents every logical mistake.—What makes logic <em>a priori</em> is the <em>impossibility</em> of illogical thought.</div>
<div class="corelinks tlpdepth4"><strong>5.4732</strong><span class="linkarray tlpdepth4" id="p5.4732PM"> P/M [→<a class="gerlink" href="#p5.4732GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4732OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">We cannot give a sign the wrong sense.</div>
<div class="corelinks tlpdepth5"><strong>5.47321</strong><span class="linkarray tlpdepth5" id="p5.47321PM"> P/M [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a>]</span></div>
<div class="para tlpdepth5">Occam’s maxim is, of course, not an arbitrary rule, nor one that is justified by its success in practice: its point is that <em>unnecessary</em> units in a sign-language mean nothing.</div>
<div class="para tlpdepth5">Signs that serve <em>one</em> purpose are logically equivalent, and signs that serve <em>none</em> are logically meaningless.</div>
<div class="corelinks tlpdepth4"><strong>5.4733</strong><span class="linkarray tlpdepth4" id="p5.4733PM"> P/M [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Frege says that any legitimately constructed proposition must have a sense. And I say that any possible proposition is legitimately constructed, and, if it has no sense, that can only be because we have failed to give a <em>meaning</em> to some of its constituents.</div>
<div class="para tlpdepth4">(Even if we think that we have done so.)</div>
<div class="para tlpdepth4">Thus the reason why ‘Socrates is identical’ says nothing is that we have <em>not</em> given any <em>adjectival</em> meaning to the word ‘identical’. For when it appears as a sign for identity, it symbolizes in an entirely different way—the signifying relation is a different one—therefore the symbols also are entirely different in the two cases: the two symbols have only the sign in common, and that is an accident.</div>
<div class="corelinks tlpdepth3"><strong>5.474</strong><span class="linkarray tlpdepth3" id="p5.474PM"> P/M [→<a class="gerlink" href="#p5.474GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.474OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The number of fundamental operations that are necessary depends <em>solely</em> on our notation.</div>
<div class="corelinks tlpdepth3"><strong>5.475</strong><span class="linkarray tlpdepth3" id="p5.475PM"> P/M [→<a class="gerlink" href="#p5.475GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.475OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">All that is required is that we should construct a system of signs with a particular number of dimensions—with a particular mathematical multiplicity.</div>
<div class="corelinks tlpdepth3"><strong>5.476</strong><span class="linkarray tlpdepth3" id="p5.476PM"> P/M [→<a class="gerlink" href="#p5.476GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.476OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is clear that this is not a question of a <em>number of primitive ideas</em> that have to be signified, but rather of the expression of a rule.</div>
<div class="corelinks tlpdepth1"><strong>5.5</strong><span class="linkarray tlpdepth1" id="p5.5PM"> P/M [→<a class="gerlink" href="#p5.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">Every truth-function is a result of successive applications to elementary propositions of the operation ‘<span class="mathmode"><span class="mathop">(−−−−−<span class="mathrm">T</span>)</span></span> <span class="mathmode">(<var>ξ</var>,&nbsp;.&nbsp;.&nbsp;.&nbsp;.&nbsp;.)</span>’.</div>
<div class="para tlpdepth1">This operation negates all the propositions in the right-hand pair of brackets, and I call it the negation of those propositions.</div>
<div class="corelinks tlpdepth3"><strong>5.501</strong><span class="linkarray tlpdepth3" id="p5.501PM"> P/M [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">When a bracketed expression has propositions as its terms—and the order of the terms inside the brackets is indifferent—then I indicate it by a sign of the form ‘<span class="mathmode">(<span class="overlined"><var>ξ</var></span>)</span>’. ‘<span class="mathmode"><var>ξ</var></span>’ is a variable whose values are terms of the bracketed expression and the bar over the variable indicates that it is the representative of all its values in the brackets.</div>
<div class="para tlpdepth3">(E.g. if <span class="mathmode"><var>ξ</var></span> has the three values P, Q, R, then <span class="mathmode">(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span>(<span class="mathrm">P</span>, <span class="mathrm">Q</span>, <span class="mathrm">R</span>)</span>. )</div>
<div class="para tlpdepth3">What the values of the variable are is something that is stipulated.</div>
<div class="para tlpdepth3">The stipulation is a description of the propositions that have the variable as their representative.</div>
<div class="para tlpdepth3">How the description of the terms of the bracketed expression is produced is not essential.</div>
<div class="para tlpdepth3">We <em>can</em> distinguish three kinds of description: 1. direct enumeration, in which case we can simply substitute for the variable the constants that are its values; 2. giving a function <span class="mathmode"><var>fx</var></span> whose values for all values of <span class="mathmode"><var>x</var></span> are the propositions to be described; 3. giving a formal law that governs the construction of the propositions, in which case the bracketed expression has as its members all the terms of a series of forms.</div>
<div class="corelinks tlpdepth3"><strong>5.502</strong><span class="linkarray tlpdepth3" id="p5.502PM"> P/M [→<a class="gerlink" href="#p5.502GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.502OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">So instead of ‘<span class="mathmode"><span class="mathop">(−−−−−<span class="mathrm">T</span>)</span></span> <span class="mathmode">(<var>ξ</var>,&nbsp;.&nbsp;.&nbsp;.&nbsp;.&nbsp;.)</span>’, I write ‘<span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)</span>’.</div>
<div class="para tlpdepth3"><span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)</span> is the negation of all the values of the propositional variable <span class="mathmode"><var>ξ</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.503</strong><span class="linkarray tlpdepth3" id="p5.503PM"> P/M [→<a class="gerlink" href="#p5.503GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.503OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is obvious that we can easily express how propositions may be constructed with this operation, and how they may not be constructed with it; so it must be possible to find an exact expression for this.</div>
<div class="corelinks tlpdepth2"><strong>5.51</strong><span class="linkarray tlpdepth2" id="p5.51PM"> P/M [→<a class="gerlink" href="#p5.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.51OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If <span class="mathmode"><var>ξ</var></span> has only one value, then <span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><var>p</var></span> (not <span class="mathmode"><var>p</var></span>); if it has two values, then <span class="mathmode"><span class="nop">N</span> (<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var></span> (neither <span class="mathmode"><var>p</var></span> nor <span class="mathmode"><var>q</var></span>).</div>
<div class="corelinks tlpdepth3"><strong>5.511</strong><span class="linkarray tlpdepth3" id="p5.511PM"> P/M [→<a class="gerlink" href="#p5.511GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.511OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">How can logic—all-embracing logic, which mirrors the world—use such peculiar crotchets and contrivances? Only because they are all connected with one another in an infinitely fine network, the great mirror.</div>
<div class="corelinks tlpdepth3"><strong>5.512</strong><span class="linkarray tlpdepth3" id="p5.512PM"> P/M [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ is true if ‘<span class="mathmode"><var>p</var></span>’ is false. Therefore, in the proposition ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’, when it is true, ‘<span class="mathmode"><var>p</var></span>’ is a false proposition. How then can the stroke ‘~’ make it agree with reality?</div>
<div class="para tlpdepth3">But in ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ it is not ‘~’ that negates, it is rather what is common to all the signs of this notation that negate <span class="mathmode"><var>p</var></span>.</div>
<div class="para tlpdepth3">That is to say the common rule that governs the construction of ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’, ‘<span class="mathmode"><span class="mathop">~</span><span class="mathop">~</span><span class="mathop">~</span><var>p</var></span>’, ‘<span class="mathmode"><span class="mathop">~</span><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>’, ‘<span class="mathmode"><span class="mathop">~</span><var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var></span>’, etc. etc. (ad inf.). And this common factor mirrors negation.</div>
<div class="corelinks tlpdepth3"><strong>5.513</strong><span class="linkarray tlpdepth3" id="p5.513PM"> P/M [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">We might say that what is common to all symbols that affirm both <span class="mathmode"><var>p</var></span> and <span class="mathmode"><var>q</var></span> is the proposition ‘<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>q</var></span>’; and that what is common to all symbols that affirm either <span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span> is the proposition ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>’.</div>
<div class="para tlpdepth3">And similarly we can say that two propositions are opposed to one another if they have nothing in common with one another, and that every proposition has only one negative, since there is only one proposition that lies completely outside it.</div>
<div class="para tlpdepth3">Thus in Russell’s notation too it is manifest that ‘<span class="mathmode"><var>q</var><span class="mathrel">:</span><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>’ says the same thing as ‘<span class="mathmode"><var>q</var></span>’, that ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><span class="mathop">~</span><var>p</var></span>’ says nothing.</div>
<div class="corelinks tlpdepth3"><strong>5.514</strong><span class="linkarray tlpdepth3" id="p5.514PM"> P/M [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Once a notation has been established, there will be in it a rule governing the construction of all propositions that negate <span class="mathmode"><var>p</var></span>, a rule governing the construction of all propositions that affirm <span class="mathmode"><var>p</var></span>, and a rule governing the construction of all propositions that affirm <span class="mathmode"><var>p</var></span> or <span class="mathmode"><var>q</var></span>; and so on. These rules are equivalent to the symbols; and in them their sense is mirrored.</div>
<div class="corelinks tlpdepth3"><strong>5.515</strong><span class="linkarray tlpdepth3" id="p5.515PM"> P/M [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It must be manifest in our symbols that it can only be propositions that are combined with one another by ‘∨’, ‘.’, etc.</div>
<div class="para tlpdepth3">And this is indeed the case, since the symbol in ‘<span class="mathmode"><var>p</var></span>’ and ‘<span class="mathmode"><var>q</var></span>’ itself presupposes ‘∨’, ‘~’, etc. If the sign ‘<span class="mathmode"><var>p</var></span>’ in ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>’ does not stand for a complex sign, then it cannot have sense by itself: but in that case the signs ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>p</var></span>’, ‘<span class="mathmode"><var>p</var><span class="mathrel">.</span><var>p</var></span>’, etc., which have the same sense as <span class="mathmode"><var>p</var></span>, must also lack sense. But if ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>p</var></span>’ has no sense, then ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">∨</span></span><var>q</var></span>’ cannot have a sense either.</div>
<div class="corelinks tlpdepth4"><strong>5.5151</strong><span class="linkarray tlpdepth4" id="p5.5151PM"> P/M [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Must the sign of a negative proposition be constructed with that of the positive proposition? Why should it not be possible to express a negative proposition by means of a negative fact? (E.g. suppose that ‘<span class="mathmode"><var>a</var></span>’ does not stand in a certain relation to ‘<span class="mathmode"><var>b</var></span>’; then this might be used to say that <span class="mathmode"><var>aRb</var></span> was not the case.)</div>
<div class="para tlpdepth4">But really even in this case the negative proposition is constructed by an indirect use of the positive.</div>
<div class="para tlpdepth4">The positive <em>proposition</em> necessarily presupposes the existence of the negative <em>proposition</em> and <em>vice versa</em>.</div>
<div class="corelinks tlpdepth2"><strong>5.52</strong><span class="linkarray tlpdepth2" id="p5.52PM"> P/M [→<a class="gerlink" href="#p5.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.52OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If <span class="mathmode"><var>ξ</var></span> has as its values all the values of a function <span class="mathmode"><var>fx</var></span> for all values of <span class="mathmode"><var>x</var></span>, then <span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)<span class="mathrel">=</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>.</div>
<div class="corelinks tlpdepth3"><strong>5.521</strong><span class="linkarray tlpdepth3" id="p5.521PM"> P/M [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">I dissociate the concept <em>all</em> from truth-functions.</div>
<div class="para tlpdepth3">Frege and Russell introduced generality in association with logical product or logical sum. This made it difficult to understand the propositions ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>’ and ‘<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>’, in which both ideas are embedded.</div>
<div class="corelinks tlpdepth3"><strong>5.522</strong><span class="linkarray tlpdepth3" id="p5.522PM"> P/M [→<a class="gerlink" href="#p5.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.522OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What is peculiar to the generality-sign is first, that it indicates a logical prototype, and secondly, that it gives prominence to constants.</div>
<div class="corelinks tlpdepth3"><strong>5.523</strong><span class="linkarray tlpdepth3" id="p5.523PM"> P/M [→<a class="gerlink" href="#p5.523GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.523OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The generality-sign occurs as an argument.</div>
<div class="corelinks tlpdepth3"><strong>5.524</strong><span class="linkarray tlpdepth3" id="p5.524PM"> P/M [→<a class="gerlink" href="#p5.524GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.524OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If objects are given, then at the same time we are given <em>all</em> objects.</div>
<div class="para tlpdepth3">If elementary propositions are given, then at the same time <em>all</em> elementary propositions are given.</div>
<div class="corelinks tlpdepth3"><strong>5.525</strong><span class="linkarray tlpdepth3" id="p5.525PM"> P/M [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is incorrect to render the proposition ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var></span>’ in the words, ‘<span class="mathmode"><var>fx</var></span> is <em>possible</em>’ as Russell does.</div>
<div class="para tlpdepth3">The certainty, possibility, or impossibility of a situation is not expressed by a proposition, but by an expression’s being a tautology, a proposition with a sense, or a contradiction.</div>
<div class="para tlpdepth3">The precedent to which we are constantly inclined to appeal must reside in the symbol itself.</div>
<div class="corelinks tlpdepth3"><strong>5.526</strong><span class="linkarray tlpdepth3" id="p5.526PM"> P/M [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">We can describe the world completely by means of fully generalized propositions, i.e. without first correlating any name with a particular object.</div>
<div class="para tlpdepth3">Then, in order to arrive at the customary mode of expression, we simply need to add, after an expression like, ‘There is one and only one <span class="mathmode"><var>x</var></span> such that …’, the words, ‘and that <span class="mathmode"><var>x</var></span> is <span class="mathmode"><var>a</var></span>’.</div>
<div class="corelinks tlpdepth4"><strong>5.5261</strong><span class="linkarray tlpdepth4" id="p5.5261PM"> P/M [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">A fully generalized proposition, like every other proposition, is composite. (This is shown by the fact that in ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>, <var>φ</var>).</span><var>φx</var></span>’ we have to mention ‘<span class="mathmode"><var>φ</var></span>’ and ‘<span class="mathmode"><var>x</var></span>’ separately. They both, independently, stand in signifying relations to the world, just as is the case in ungeneralized propositions.)</div>
<div class="para tlpdepth4">It is a mark of a composite symbol that it has something in common with <em>other</em> symbols.</div>
<div class="corelinks tlpdepth4"><strong>5.5262</strong><span class="linkarray tlpdepth4" id="p5.5262PM"> P/M [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The truth or falsity of <em>every</em> proposition does make some alteration in the general construction of the world. And the range that the totality of elementary propositions leaves open for its construction is exactly the same as that which is delimited by entirely general propositions.</div>
<div class="para tlpdepth4">(If an elementary proposition is true, that means, at any rate, one <em>more</em> true elementary proposition.)</div>
<div class="corelinks tlpdepth2"><strong>5.53</strong><span class="linkarray tlpdepth2" id="p5.53PM"> P/M [→<a class="gerlink" href="#p5.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.53OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Identity of object I express by identity of sign, and not by using a sign for identity. Difference of objects I express by difference of signs.</div>
<div class="corelinks tlpdepth4"><strong>5.5301</strong><span class="linkarray tlpdepth4" id="p5.5301PM"> P/M [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5301OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is self-evident that identity is not a relation between objects. This becomes very clear if one considers, for example, the proposition ‘<span class="mathmode"><span class="quant">(<var>x</var>):</span><var>fx</var><span class="mathrel">.<span class="symbol">⊃</span>.</span><var>x</var><span class="mathrel">=</span><var>a</var></span>’. What this proposition says is simply that <em>only</em> <span class="mathmode"><var>a</var></span> satisfies the function <span class="mathmode"><var>f</var></span>, and not that only things that have a certain relation to <span class="mathmode"><var>a</var></span> satisfy the function <span class="mathmode"><var>f</var></span>.</div>
<div class="para tlpdepth4">Of course, it might then be said that <em>only</em> <span class="mathmode"><var>a</var></span> did have this relation to <span class="mathmode"><var>a</var></span>; but in order to express that, we should need the identity-sign itself.</div>
<div class="corelinks tlpdepth4"><strong>5.5302</strong><span class="linkarray tlpdepth4" id="p5.5302PM"> P/M [→<a class="gerlink" href="#p5.5302GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5302OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Russell’s definition of ‘=’ is inadequate, because according to it we cannot say that two objects have all their properties in common. (Even if this proposition is never correct, it still has <em>sense</em>.)</div>
<div class="corelinks tlpdepth4"><strong>5.5303</strong><span class="linkarray tlpdepth4" id="p5.5303PM"> P/M [→<a class="gerlink" href="#p5.5303GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5303OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Roughly speaking, to say of <em>two</em> things that they are identical is nonsense, and to say of <em>one</em> thing that it is identical with itself is to say nothing at all.</div>
<div class="corelinks tlpdepth3"><strong>5.531</strong><span class="linkarray tlpdepth3" id="p5.531PM"> P/M [→<a class="gerlink" href="#p5.531GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.531OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Thus I do not write ‘<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)<span class="mathrel">.</span><var>a</var><span class="mathrel">=</span><var>b</var></span>’, but ‘<span class="mathmode"><var>f</var>(<var>a</var>,<var>a</var>)</span>’ (or ‘<span class="mathmode"><var>f</var>(<var>b</var>,<var>b</var>)</span>’); and not ‘<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)<span class="mathrel">.</span><span class="mathop">~</span><var>a</var><span class="mathrel">=</span><var>b</var></span>’, but ‘<span class="mathmode"><var>f</var>(<var>a</var>,<var>b</var>)</span>’.</div>
<div class="corelinks tlpdepth3"><strong>5.532</strong><span class="linkarray tlpdepth3" id="p5.532PM"> P/M [→<a class="gerlink" href="#p5.532GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.532OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">And analogously I do not write ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.</span><var>x</var><span class="mathrel">=</span><var>y</var></span>’, but ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>f</var>(<var>x</var>,<var>x</var>)</span>’; and not ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.</span><span class="mathop">~</span><var>x</var><span class="mathrel">=</span><var>y</var></span>’, but ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)</span>’.</div>
<div class="para tlpdepth3">(So Russell’s ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)</span>’ becomes ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>f</var>(<var>x</var>,<var>y</var>)<span class="mathrel">.<span class="symbol">∨</span>.</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>f</var>(<var>x</var>,<var>x</var>)</span>’.)</div>
<div class="corelinks tlpdepth4"><strong>5.5321</strong><span class="linkarray tlpdepth4" id="p5.5321PM"> P/M [→<a class="gerlink" href="#p5.5321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5321OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Thus, for example, instead of ‘<span class="mathmode"><span class="quant">(<var>x</var>):</span><var>fx</var><span class="mathrel"><span class="symbol">⊃</span></span><var>x</var><span class="mathrel">=</span><var>a</var></span>’ we write ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">.<span class="symbol">⊃</span>.</span><var>fa</var><span class="mathrel">:</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>fx</var><span class="mathrel">.</span><var>fy</var></span>’.</div>
<div class="para tlpdepth4">And the proposition, ‘<em>Only one</em> <span class="mathmode"><var>x</var></span> satisfies <span class="mathmode"><var>f</var>(&nbsp;)</span>’, will read ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>fx</var><span class="mathrel">:</span><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>,<var>y</var>).</span><var>fx</var><span class="mathrel">.</span><var>fy</var></span>’.</div>
<div class="corelinks tlpdepth3"><strong>5.533</strong><span class="linkarray tlpdepth3" id="p5.533PM"> P/M [→<a class="gerlink" href="#p5.533GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.533OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The identity-sign, therefore, is not an essential constituent of conceptual notation.</div>
<div class="corelinks tlpdepth3"><strong>5.534</strong><span class="linkarray tlpdepth3" id="p5.534PM"> P/M [→<a class="gerlink" href="#p5.534GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.534OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">And now we see that in a correct conceptual notation pseudo-propositions like ‘<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>’, ‘<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>b</var><span class="mathrel">.</span><var>b</var><span class="mathrel">=</span><var>c</var><span class="mathrel">.<span class="symbol">⊃</span></span><var>a</var><span class="mathrel">=</span><var>c</var></span>’, ‘<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>x</var></span>’, ‘<span class="mathmode"><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>a</var></span>’, etc. cannot even be written down.</div>
<div class="corelinks tlpdepth3"><strong>5.535</strong><span class="linkarray tlpdepth3" id="p5.535PM"> P/M [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">This also disposes of all the problems that were connected with such pseudo-propositions.</div>
<div class="para tlpdepth3">All the problems that Russell’s ‘axiom of infinity’ brings with it can be solved at this point.</div>
<div class="para tlpdepth3">What the axiom of infinity is intended to say would express itself in language through the existence of infinitely many names with different meanings.</div>
<div class="corelinks tlpdepth4"><strong>5.5351</strong><span class="linkarray tlpdepth4" id="p5.5351PM"> P/M [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">There are certain cases in which one is tempted to use expressions of the form ‘<span class="mathmode"><var>a</var><span class="mathrel">=</span><var>a</var></span>’ or ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span>’ and the like. In fact, this happens when one wants to talk about prototypes, e.g. about proposition, thing, etc. Thus in Russell’s <em>Principles of Mathematics</em> ‘<span class="mathmode"><var>p</var></span> is a proposition’—which is nonsense—was given the symbolic rendering ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span>’ and placed as an hypothesis in front of certain propositions in order to exclude from their argument-places everything but propositions.</div>
<div class="para tlpdepth4">(It is nonsense to place the hypothesis ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>p</var></span>’ in front of a proposition, in order to ensure that its arguments shall have the right form, if only because with a non-proposition as argument the hypothesis becomes not false but nonsensical, and because arguments of the wrong kind make the proposition itself nonsensical, so that it preserves itself from wrong arguments just as well, or as badly, as the hypothesis without sense that was appended for that purpose.)</div>
<div class="corelinks tlpdepth4"><strong>5.5352</strong><span class="linkarray tlpdepth4" id="p5.5352PM"> P/M [→<a class="gerlink" href="#p5.5352GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5352OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">In the same way people have wanted to express, ‘There are no <em>things</em>’, by writing ‘<span class="mathmode"><span class="mathop">~</span><span class="quant">(<span class="symbol">∃</span><var>x</var>).</span><var>x</var><span class="mathrel">=</span><var>x</var></span>’. But even if this were a proposition, would it not be equally true if in fact ‘there were things’ but they were not identical with themselves?</div>
<div class="corelinks tlpdepth2"><strong>5.54</strong><span class="linkarray tlpdepth2" id="p5.54PM"> P/M [→<a class="gerlink" href="#p5.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.54OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">In the general propositional form propositions occur in other propositions only as bases of truth-operations.</div>
<div class="corelinks tlpdepth3"><strong>5.541</strong><span class="linkarray tlpdepth3" id="p5.541PM"> P/M [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">At first sight it looks as if it were also possible for one proposition to occur in another in a different way.</div>
<div class="para tlpdepth3">Particularly with certain forms of proposition in psychology, such as ‘A believes that <span class="mathmode"><var>p</var></span> is the case’ and A has the thought <span class="mathmode"><var>p</var></span>’, etc.</div>
<div class="para tlpdepth3">For if these are considered superficially, it looks as if the proposition <span class="mathmode"><var>p</var></span> stood in some kind of relation to an object A.</div>
<div class="para tlpdepth3">(And in modern theory of knowledge (Russell, Moore, etc.) these propositions have actually been construed in this way.)</div>
<div class="corelinks tlpdepth3"><strong>5.542</strong><span class="linkarray tlpdepth3" id="p5.542PM"> P/M [→<a class="gerlink" href="#p5.542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.542OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is clear, however, that ‘A believes that <span class="mathmode"><var>p</var></span>’, ‘A has the thought <span class="mathmode"><var>p</var></span>’, and ‘A says <span class="mathmode"><var>p</var></span>’ are of the form ‘“<span class="mathmode"><var>p</var></span>” says <span class="mathmode"><var>p</var></span>’: and this does not involve a correlation of a fact with an object, but rather the correlation of facts by means of the correlation of their objects.</div>
<div class="corelinks tlpdepth4"><strong>5.5421</strong><span class="linkarray tlpdepth4" id="p5.5421PM"> P/M [→<a class="gerlink" href="#p5.5421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5421OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">This shows too that there is no such thing as the soul—the subject, etc.—as it is conceived in the superficial psychology of the present day.</div>
<div class="para tlpdepth4">Indeed a composite soul would no longer be a soul.</div>
<div class="corelinks tlpdepth4"><strong>5.5422</strong><span class="linkarray tlpdepth4" id="p5.5422PM"> P/M [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The correct explanation of the form of the proposition, ‘A makes the judgement <span class="mathmode"><var>p</var></span>’, must show that it is impossible for a judgement to be a piece of nonsense. (Russell’s theory does not satisfy this requirement.)</div>
<div class="corelinks tlpdepth4"><strong>5.5423</strong><span class="linkarray tlpdepth4" id="p5.5423PM"> P/M [→<a class="gerlink" href="#p5.5423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5423OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">To perceive a complex means to perceive that its constituents are related to one another in such and such a way.</div>
<div class="para tlpdepth4">This no doubt also explains why there are two possible ways of seeing the figure </div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/thecube.svg" type="image/svg+xml" class="thecubesvg" ><img src="images/thecube.png" alt="Cube with a face and b face" class="thecubepng" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> as a cube; and all similar phenomena. For we really see two different facts.</div>
<div class="para tlpdepth4">(If I look in the first place at the corners marked <span class="mathmode"><var>a</var></span> and only glance at the <span class="mathmode"><var>b</var></span>’s, then the <span class="mathmode"><var>a</var></span>’s appear to be in front, and <em>vice versa</em>).</div>
<div class="corelinks tlpdepth2"><strong>5.55</strong><span class="linkarray tlpdepth2" id="p5.55PM"> P/M [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">We now have to answer <em>a priori</em> the question about all the possible forms of elementary propositions.</div>
<div class="para tlpdepth2">Elementary propositions consist of names. Since, however, we are unable to give the number of names with different meanings, we are also unable to give the composition of elementary propositions.</div>
<div class="corelinks tlpdepth3"><strong>5.551</strong><span class="linkarray tlpdepth3" id="p5.551PM"> P/M [→<a class="gerlink" href="#p5.551GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.551OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Our fundamental principle is that whenever a question can be decided by logic at all it must be possible to decide it without more ado.</div>
<div class="para tlpdepth3">(And if we get into a position where we have to look at the world for an answer to such a problem, that shows that we are on a completely wrong track.)</div>
<div class="corelinks tlpdepth3"><strong>5.552</strong><span class="linkarray tlpdepth3" id="p5.552PM"> P/M [→<a class="gerlink" href="#p5.552GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.552OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The ‘experience’ that we need in order to understand logic is not that something or other is the state of things, but that something <em>is</em>: that, however, is <em>not</em> an experience.</div>
<div class="para tlpdepth3">Logic is <em>prior</em> to every experience—that something <em>is so</em>.</div>
<div class="para tlpdepth3">It is prior to the question ‘How?’, not prior to the question ‘What?’</div>
<div class="corelinks tlpdepth4"><strong>5.5521</strong><span class="linkarray tlpdepth4" id="p5.5521PM"> P/M [→<a class="gerlink" href="#p5.5521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5521OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">And if this were not so, how could we apply logic? We might put it in this way: if there would be a logic even if there were no world, how then could there be a logic given that there is a world?</div>
<div class="corelinks tlpdepth3"><strong>5.553</strong><span class="linkarray tlpdepth3" id="p5.553PM"> P/M [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Russell said that there were simple relations between different numbers of things (individuals). But between what numbers? And how is this supposed to be decided?—By experience?</div>
<div class="para tlpdepth3">(There is no privileged number.)</div>
<div class="corelinks tlpdepth3"><strong>5.554</strong><span class="linkarray tlpdepth3" id="p5.554PM"> P/M [→<a class="gerlink" href="#p5.554GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.554OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It would be completely arbitrary to give any specific form.</div>
<div class="corelinks tlpdepth4"><strong>5.5541</strong><span class="linkarray tlpdepth4" id="p5.5541PM"> P/M [→<a class="gerlink" href="#p5.5541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5541OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is supposed to be possible to answer <em>a priori</em> the question whether I can get into a position in which I need the sign for a 27-termed relation in order to signify something.</div>
<div class="corelinks tlpdepth4"><strong>5.5542</strong><span class="linkarray tlpdepth4" id="p5.5542PM"> P/M [→<a class="gerlink" href="#p5.5542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5542OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">But is it really legitimate even to ask such a question? Can we set up a form of sign without knowing whether anything can correspond to it?</div>
<div class="para tlpdepth4">Does it make sense to ask what there must <em>be</em> in order that something can be the case?</div>
<div class="corelinks tlpdepth3"><strong>5.555</strong><span class="linkarray tlpdepth3" id="p5.555PM"> P/M [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Clearly we have some concept of elementary propositions quite apart from their particular logical forms.</div>
<div class="para tlpdepth3">But when there is a system by which we can create symbols, the system is what is important for logic and not the individual symbols.</div>
<div class="para tlpdepth3">And anyway, is it really possible that in logic I should have to deal with forms that I can invent? What I have to deal with must be that which makes it possible for me to invent them.</div>
<div class="corelinks tlpdepth3"><strong>5.556</strong><span class="linkarray tlpdepth3" id="p5.556PM"> P/M [→<a class="gerlink" href="#p5.556GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.556OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">There cannot be a hierarchy of the forms of elementary propositions. We can foresee only what we ourselves construct.</div>
<div class="corelinks tlpdepth4"><strong>5.5561</strong><span class="linkarray tlpdepth4" id="p5.5561PM"> P/M [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Empirical reality is limited by the totality of objects. The limit also makes itself manifest in the totality of elementary propositions.</div>
<div class="para tlpdepth4">Hierarchies are and must be independent of reality.</div>
<div class="corelinks tlpdepth4"><strong>5.5562</strong><span class="linkarray tlpdepth4" id="p5.5562PM"> P/M [→<a class="gerlink" href="#p5.5562GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5562OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If we know on purely logical grounds that there must be elementary propositions, then everyone who understands propositions in their unanalyzed form must know it.</div>
<div class="corelinks tlpdepth4"><strong>5.5563</strong><span class="linkarray tlpdepth4" id="p5.5563PM"> P/M [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">In fact, all the propositions of our everyday language, just as they stand, are in perfect logical order.—That utterly simple thing, which we have to formulate here, is not an image of the truth, but the truth itself in its entirety.</div>
<div class="para tlpdepth4">(Our problems are not abstract, but perhaps the most concrete that there are.)</div>
<div class="corelinks tlpdepth3"><strong>5.557</strong><span class="linkarray tlpdepth3" id="p5.557PM"> P/M [→<a class="gerlink" href="#p5.557GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.557OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The <em>application</em> of logic decides what elementary propositions there are.</div>
<div class="para tlpdepth3">What belongs to its application, logic cannot anticipate.</div>
<div class="para tlpdepth3">It is clear that logic must not clash with its application.</div>
<div class="para tlpdepth3">But logic has to be in contact with its application.</div>
<div class="para tlpdepth3">Therefore logic and its application must not overlap.</div>
<div class="corelinks tlpdepth4"><strong>5.5571</strong><span class="linkarray tlpdepth4" id="p5.5571PM"> P/M [→<a class="gerlink" href="#p5.5571GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5571OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If I cannot say <em>a priori</em> what elementary propositions there are, then the attempt to do so must lead to obvious nonsense.</div>
<div class="corelinks tlpdepth1"><strong>5.6</strong><span class="linkarray tlpdepth1" id="p5.6PM"> P/M [→<a class="gerlink" href="#p5.6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.6OGD">OGD</a>]</span></div>
<div class="para tlpdepth1"><em>The limits of my language</em> mean the limits of my world.</div>
<div class="corelinks tlpdepth2"><strong>5.61</strong><span class="linkarray tlpdepth2" id="p5.61PM"> P/M [→<a class="gerlink" href="#p5.61GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.61OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Logic pervades the world: the limits of the world are also its limits.</div>
<div class="para tlpdepth2">So we cannot say in logic, ‘The world has this in it, and this, but not that.’</div>
<div class="para tlpdepth2">For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well.</div>
<div class="para tlpdepth2">We cannot think what we cannot think; so what we cannot think we cannot <em>say</em> either.</div>
<div class="corelinks tlpdepth2"><strong>5.62</strong><span class="linkarray tlpdepth2" id="p5.62PM"> P/M [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">This remark provides the key to the problem, how much truth there is in solipsism.</div>
<div class="para tlpdepth2">For what the solipsist <em>means</em> is quite correct; only it cannot be <em>said</em>, but makes itself manifest.</div>
<div class="para tlpdepth2">The world is <em>my</em> world: this is manifest in the fact that the limits of <em>language</em> (of that language which alone I understand) mean the limits of <em>my</em> world.</div>
<div class="corelinks tlpdepth3"><strong>5.621</strong><span class="linkarray tlpdepth3" id="p5.621PM"> P/M [→<a class="gerlink" href="#p5.621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.621OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The world and life are one.</div>
<div class="corelinks tlpdepth2"><strong>5.63</strong><span class="linkarray tlpdepth2" id="p5.63PM"> P/M [→<a class="gerlink" href="#p5.63GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.63OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">I am my world. (The microcosm.)</div>
<div class="corelinks tlpdepth3"><strong>5.631</strong><span class="linkarray tlpdepth3" id="p5.631PM"> P/M [→<a class="gerlink" href="#p5.631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.631OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">There is no such thing as the subject that thinks or entertains ideas.</div>
<div class="para tlpdepth3">If I wrote a book called <em>The World as I found it</em>, I should have to include a report on my body, and should have to say which parts were subordinate to my will, and which were not, etc., this being a method of isolating the subject, or rather of showing that in an important sense there is no subject; for it alone could <em>not</em> be mentioned in that book.—</div>
<div class="corelinks tlpdepth3"><strong>5.632</strong><span class="linkarray tlpdepth3" id="p5.632PM"> P/M [→<a class="gerlink" href="#p5.632GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.632OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The subject does not belong to the world: rather, it is a limit of the world.</div>
<div class="corelinks tlpdepth3"><strong>5.633</strong><span class="linkarray tlpdepth3" id="p5.633PM"> P/M [→<a class="gerlink" href="#p5.633GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.633OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Where <em>in</em> the world is a metaphysical subject to be found?</div>
<div class="para tlpdepth3">You will say that this is exactly like the case of the eye and the visual field. But really you do <em>not</em> see the eye.</div>
<div class="para tlpdepth3">And nothing <em>in the visual field</em> allows you to infer that it is seen by an eye.</div>
<div class="corelinks tlpdepth4"><strong>5.6331</strong><span class="linkarray tlpdepth4" id="p5.6331PM"> P/M [→<a class="gerlink" href="#p5.6331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.6331OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">For the form of the visual field is surely not like this</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><span class="sfmiddle"><span class="lowered">Eye —</span><object data="images/theeye.svg" type="image/svg+xml" class="theeyesvg"><img src="images/theeye.png" alt="Eye image" class="theeyepng" /></object></span></div></div>
<div class="corelinks tlpdepth3"><strong>5.634</strong><span class="linkarray tlpdepth3" id="p5.634PM"> P/M [→<a class="gerlink" href="#p5.634GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.634OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">This is connected with the fact that no part of our experience is at the same time <em>a priori</em>.</div>
<div class="para tlpdepth3">Whatever we see could be other than it is.</div>
<div class="para tlpdepth3">Whatever we can describe at all could be other than it is.</div>
<div class="para tlpdepth3">There is no <em>a priori</em> order of things.</div>
<div class="corelinks tlpdepth2"><strong>5.64</strong><span class="linkarray tlpdepth2" id="p5.64PM"> P/M [→<a class="gerlink" href="#p5.64GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.64OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Here it can be seen that solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without extension, and there remains the reality co-ordinated with it.</div>
<div class="corelinks tlpdepth3"><strong>5.641</strong><span class="linkarray tlpdepth3" id="p5.641PM"> P/M [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Thus there really is a sense in which philosophy can talk about the self in a non-psychological way.</div>
<div class="para tlpdepth3">What brings the self into philosophy is the fact that ‘the world is my world’.</div>
<div class="para tlpdepth3">The philosophical self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the world—not a part of it.</div>
<div class="corelinks tlpdepth0"><strong>6</strong><span class="linkarray tlpdepth0" id="p6PM"> P/M [→<a class="gerlink" href="#p6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6OGD">OGD</a>]</span></div>
<div class="para tlpdepth0">The general form of a truth-function is <span class="mathmode">[<span class="overlined"><var>p</var></span>, <span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)]</span>.</div>
<div class="para tlpdepth0">This is the general form of a proposition.</div>
<div class="corelinks tlpdepth3"><strong>6.001</strong><span class="linkarray tlpdepth3" id="p6.001PM"> P/M [→<a class="gerlink" href="#p6.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.001OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What this says is just that every proposition is a result of successive applications to elementary propositions of the operation <span class="mathmode"><span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)</span>.</div>
<div class="corelinks tlpdepth3"><strong>6.002</strong><span class="linkarray tlpdepth3" id="p6.002PM"> P/M [→<a class="gerlink" href="#p6.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.002OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">If we are given the general form according to which propositions are constructed, then with it we are also given the general form according to which one proposition can be generated out of another by means of an operation.</div>
<div class="corelinks tlpdepth2"><strong>6.01</strong><span class="linkarray tlpdepth2" id="p6.01PM"> P/M [→<a class="gerlink" href="#p6.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.01OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Therefore the general form of an operation <span class="mathmode"><span class="mathop">Ω’</span>(<span class="overlined"><var>η</var></span>)</span> is <span class="mathmode"><span class="mathop">[<span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)]’</span> (<span class="overlined"><var>η</var></span>) (<span class="mathrel">=</span>[<span class="overlined"><var>η</var></span>, <span class="overlined"><var>ξ</var></span>, <span class="nop">N</span>(<span class="overlined"><var>ξ</var></span>)])</span>.</div>
<div class="para tlpdepth2">This is the most general form of transition from one proposition to another.</div>
<div class="corelinks tlpdepth2"><strong>6.02</strong><span class="linkarray tlpdepth2" id="p6.02PM"> P/M [→<a class="gerlink" href="#p6.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.02OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">And <em>this</em> is how we arrive at numbers. I give the following definitions</div>
<div class="para tlpdepth2"><div class="centered"><table class="alignedmath"><tr><td class="righttight"><span class="mathmode"><var>x</var><span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode"><span class="mathop">Ω<sup>0</sup>’</span><var>x</var></span>&nbsp;&nbsp;Def.,</td></tr><tr><td class="righttight"><span class="mathmode"><span class="mathop">Ω’</span><span class="mathop">Ω<sup><var>ν</var></sup>’</span><var>x</var><span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode"><span class="mathop">Ω<sup><var>ν</var>+1</sup>’</span><var>x</var></span>&nbsp;&nbsp;Def.</td></tr></table></div></div>
<div class="para tlpdepth2">So, in accordance with these rules, which deal with signs, we write the series</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode"><var>x</var>, <span class="mathop">Ω’</span><var>x</var>, <span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var>, <span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var>,<span class="mathrel">…</span></span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">in the following way</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode"><span class="mathop">Ω<sup>0</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var>, <span class="mathop">Ω<sup>0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var>,<span class="mathrel">…</span></span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">Therefore, instead of ‘<span class="mathmode">[<var>x</var>, <var>ξ</var>, <span class="mathop">Ω’</span><var>ξ</var>]</span>’,</div>
<div class="para tlpdepth2"><div class="centered"><span class="mathmode"><span class="mathrm">I write</span> &nbsp; ‘[<span class="mathop">Ω<sup>0</sup>’</span><var>x</var>, <span class="mathop">Ω<sup><var>ν</var></sup>’</span><var>x</var>, <span class="mathop">Ω<sup><var>ν</var><span class="mathrel">+</span>1</sup>’</span><var>x</var>]’.</span></div><span class="mathmode"></span></div>
<div class="para tlpdepth2">And I give the following definitions</div>
<div class="para tlpdepth2"><div class="centered"><table class="alignedmath"><tr><td class="righttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode">1</span>&nbsp;&nbsp;Def.,</td></tr><tr><td class="righttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode">2</span>&nbsp;&nbsp;Def.,</td></tr><tr><td class="righttight"><span class="mathmode">0<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">=</span></span></td><td class="lefttight"><span class="mathmode">3</span>&nbsp;&nbsp;Def.,</td></tr><tr><td class="centertight" colspan="2">(and so on).</td></tr></table></div></div>
<div class="corelinks tlpdepth3"><strong>6.021</strong><span class="linkarray tlpdepth3" id="p6.021PM"> P/M [→<a class="gerlink" href="#p6.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.021OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">A number is the exponent of an operation.</div>
<div class="corelinks tlpdepth3"><strong>6.022</strong><span class="linkarray tlpdepth3" id="p6.022PM"> P/M [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The concept of number is simply what is common to all numbers, the general form of a number.</div>
<div class="para tlpdepth3">The concept of number is the variable number.</div>
<div class="para tlpdepth3">And the concept of numerical equality is the general form of all particular cases of numerical equality.</div>
<div class="corelinks tlpdepth2"><strong>6.03</strong><span class="linkarray tlpdepth2" id="p6.03PM"> P/M [→<a class="gerlink" href="#p6.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.03OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The general form of an integer is <span class="mathmode">[0, <var>ξ</var>, <var>ξ</var><span class="mathrel">+</span>1]</span>.</div>
<div class="corelinks tlpdepth3"><strong>6.031</strong><span class="linkarray tlpdepth3" id="p6.031PM"> P/M [→<a class="gerlink" href="#p6.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.031OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The theory of classes is completely superfluous in mathematics.</div>
<div class="para tlpdepth3">This is connected with the fact that the generality required in mathematics is not <em>accidental</em> generality.</div>
<div class="corelinks tlpdepth1"><strong>6.1</strong><span class="linkarray tlpdepth1" id="p6.1PM"> P/M [→<a class="gerlink" href="#p6.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">The propositions of logic are tautologies.</div>
<div class="corelinks tlpdepth2"><strong>6.11</strong><span class="linkarray tlpdepth2" id="p6.11PM"> P/M [→<a class="gerlink" href="#p6.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.11OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Therefore the propositions of logic say nothing. (They are the analytic propositions.)</div>
<div class="corelinks tlpdepth3"><strong>6.111</strong><span class="linkarray tlpdepth3" id="p6.111PM"> P/M [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">All theories that make a proposition of logic appear to have content are false. One might think, for example, that the words ‘true’ and ‘false’ signified two properties among other properties, and then it would seem to be a remarkable fact that every proposition possessed one of these properties. On this theory it seems to be anything but obvious, just as, for instance, the proposition, ‘All roses are either yellow or red’, would not sound obvious even if it were true. Indeed, the logical proposition acquires all the characteristics of a proposition of natural science and this is the sure sign that it has been construed wrongly.</div>
<div class="corelinks tlpdepth3"><strong>6.112</strong><span class="linkarray tlpdepth3" id="p6.112PM"> P/M [→<a class="gerlink" href="#p6.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.112OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The correct explanation of the propositions of logic must assign to them a unique status among all propositions.</div>
<div class="corelinks tlpdepth3"><strong>6.113</strong><span class="linkarray tlpdepth3" id="p6.113PM"> P/M [→<a class="gerlink" href="#p6.113GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.113OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is the peculiar mark of logical propositions that one can recognize that they are true from the symbol alone, and this fact contains in itself the whole philosophy of logic. And so too it is a very important fact that the truth or falsity of non-logical propositions <em>cannot</em> be recognized from the propositions alone.</div>
<div class="corelinks tlpdepth2"><strong>6.12</strong><span class="linkarray tlpdepth2" id="p6.12PM"> P/M [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The fact that the propositions of logic are tautologies <em>shows</em> the formal—logical—properties of language and the world.</div>
<div class="para tlpdepth2">The fact that a tautology is yielded by <em>this particular way</em> of connecting its constituents characterizes the logic of its constituents.</div>
<div class="para tlpdepth2">If propositions are to yield a tautology when they are connected in a certain way, they must have certain structural properties. So their yielding a tautology when combined <em>in this way</em> shows that they possess these structural properties.</div>
<div class="corelinks tlpdepth4"><strong>6.1201</strong><span class="linkarray tlpdepth4" id="p6.1201PM"> P/M [→<a class="gerlink" href="#p6.1201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1201OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">For example, the fact that the propositions ‘<span class="mathmode"><var>p</var></span>’ and ‘<span class="mathmode"><span class="mathop">~</span><var>p</var></span>’ in the combination ‘<span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span>’ yield a tautology shows that they contradict one another. The fact that the propositions ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>’, ‘<span class="mathmode"><var>p</var></span>’, and ‘<span class="mathmode"><var>q</var></span>’, combined with one another in the form ‘<span class="mathmode">(<var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var>)<span class="mathrel">.</span>(<var>p</var>)<span class="mathrel">:<span class="symbol">⊃</span>:</span>(<var>q</var>)</span>’, yield a tautology shows that <span class="mathmode"><var>q</var></span> follows from <span class="mathmode"><var>p</var></span> and <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>. The fact that ‘<span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var><span class="mathrel">:<span class="symbol">⊃</span>:</span><var>fa</var></span>’ is a tautology shows that <span class="mathmode"><var>fa</var></span> follows from <span class="mathmode"><span class="quant">(<var>x</var>).</span><var>fx</var></span>. Etc. etc.</div>
<div class="corelinks tlpdepth4"><strong>6.1202</strong><span class="linkarray tlpdepth4" id="p6.1202PM"> P/M [→<a class="gerlink" href="#p6.1202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1202OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is clear that one could achieve the same purpose by using contradictions instead of tautologies.</div>
<div class="corelinks tlpdepth4"><strong>6.1203</strong><span class="linkarray tlpdepth4" id="p6.1203PM"> P/M [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">In order to recognize an expression as a tautology, in cases where no generality-sign occurs in it, one can employ the following intuitive method: instead of ‘<span class="mathmode"><var>p</var></span>’, ‘<span class="mathmode"><var>q</var></span>’, ‘<span class="mathmode"><var>r</var></span>’, etc. I write ‘<span class="mathmode"><span class="mathrm">T</span> <var>p</var> <span class="mathrm">F</span></span>’, ‘<span class="mathmode"><span class="mathrm">T</span> <var>q</var> <span class="mathrm">F</span></span>’, ‘<span class="mathmode"><span class="mathrm">T</span> <var>r</var> <span class="mathrm">F</span></span>’, etc. Truth-combinations I express by means of brackets, e.g.</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigureoneenglishpmc.svg" type="image/svg+xml" width="157" height="69" style="width: 157pt; height: 69pt;"><img src="images/abfigureoneenglishpmc.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> and I use lines to express the correlation of the truth or falsity of the whole proposition with the truth-combinations of its truth-arguments, in the following way</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfiguretwoenglishpmc.svg" type="image/svg+xml" width="157" height="124" style="width: 157pt; height: 124pt;"><img src="images/abfiguretwoenglishpmc.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> So this sign, for instance, would represent the proposition <span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>. Now, by way of example, I wish to examine the proposition <span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>p</var>)</span> (the law of contradiction) in order to determine whether it is a tautology. In our notation the form ‘<span class="mathmode"><span class="mathop">~</span><var>ξ</var></span>’ is written as</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurethreeenglishpmc.svg" type="image/svg+xml" width="46" height="75" style="width: 46pt; height: 75pt;"><img src="images/abfigurethreeenglishpmc.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> and the form ‘<span class="mathmode"><var>ξ</var><span class="mathrel">.</span><var>η</var></span>’ as</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurefourenglishpmc.svg" type="image/svg+xml" width="157" height="116" style="width: 157pt; height: 116pt;"><img src="images/abfigurefourenglishpmc.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> Hence the proposition <span class="mathmode"><span class="mathop">~</span>(<var>p</var><span class="mathrel">.</span><span class="mathop">~</span><var>q</var>)</span> reads as follows</div>
<div class="para tlpdepth4 noindent"><!-- noindent --><div class="centered"><object data="images/abfigurefiveenglishpmc.svg" type="image/svg+xml" width="129" height="168" style="width: 129pt; height: 168pt;"><img src="images/abfigurefiveenglishpmc.png" alt="[TF figure]" /></object></div></div>
<div class="para tlpdepth4 noindent"><!-- noindent --> If we here substitute ‘<span class="mathmode"><var>p</var></span>’ for ‘<span class="mathmode"><var>q</var></span>’ and examine how the outermost T and F are connected with the innermost ones, the result will be that the truth of the whole proposition is correlated with <em>all</em> the truth-combinations of its argument, and its falsity with none of the truth-combinations.</div>
<div class="corelinks tlpdepth3"><strong>6.121</strong><span class="linkarray tlpdepth3" id="p6.121PM"> P/M [→<a class="gerlink" href="#p6.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.121OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The propositions of logic demonstrate the logical properties of propositions by combining them so as to form propositions that say nothing.</div>
<div class="para tlpdepth3">This method could also be called a zero-method. In a logical proposition, propositions are brought into equilibrium with one another, and the state of equilibrium then indicates what the logical constitution of these propositions must be.</div>
<div class="corelinks tlpdepth3"><strong>6.122</strong><span class="linkarray tlpdepth3" id="p6.122PM"> P/M [→<a class="gerlink" href="#p6.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.122OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It follows from this that we can actually do without logical propositions; for in a suitable notation we can in fact recognize the formal properties of propositions by mere inspection of the propositions themselves.</div>
<div class="corelinks tlpdepth4"><strong>6.1221</strong><span class="linkarray tlpdepth4" id="p6.1221PM"> P/M [→<a class="gerlink" href="#p6.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1221OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">If, for example, two propositions ‘<span class="mathmode"><var>p</var></span>’ and ‘<span class="mathmode"><var>q</var></span>’ in the combination ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var></span>’ yield a tautology, then it is clear that <span class="mathmode"><var>q</var></span> follows from <span class="mathmode"><var>p</var></span>.</div>
<div class="para tlpdepth4">For example, we see from the two propositions themselves that ‘<span class="mathmode"><var>q</var></span>’ follows from ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var><span class="mathrel">.</span><var>p</var></span>’, but it is also possible to show it in <em>this</em> way: we combine them to form ‘<span class="mathmode"><var>p</var><span class="mathrel"><span class="symbol">⊃</span></span><var>q</var><span class="mathrel">.</span><var>p</var><span class="mathrel">:<span class="symbol">⊃</span>:</span><var>q</var></span>’, and then show that this is a tautology.</div>
<div class="corelinks tlpdepth4"><strong>6.1222</strong><span class="linkarray tlpdepth4" id="p6.1222PM"> P/M [→<a class="gerlink" href="#p6.1222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1222OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">This throws some light on the question why logical propositions cannot be confirmed by experience any more than they can be refuted by it. Not only must a proposition of logic be irrefutable by any possible experience, but it must also be unconfirmable by any possible experience.</div>
<div class="corelinks tlpdepth4"><strong>6.1223</strong><span class="linkarray tlpdepth4" id="p6.1223PM"> P/M [→<a class="gerlink" href="#p6.1223GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1223OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Now it becomes clear why people have often felt as if it were for us to ‘<em>postulate</em>’ the ‘truths of logic’. The reason is that we can postulate them in so far as we can postulate an adequate notation.</div>
<div class="corelinks tlpdepth4"><strong>6.1224</strong><span class="linkarray tlpdepth4" id="p6.1224PM"> P/M [→<a class="gerlink" href="#p6.1224GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1224OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It also becomes clear now why logic was called the theory of forms and of inference.</div>
<div class="corelinks tlpdepth3"><strong>6.123</strong><span class="linkarray tlpdepth3" id="p6.123PM"> P/M [→<a class="gerlink" href="#p6.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.123OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Clearly the laws of logic cannot in their turn be subject to laws of logic.</div>
<div class="para tlpdepth3">(There is not, as Russell thought, a special law of contradiction for each ‘type’; one law is enough, since it is not applied to itself.)</div>
<div class="corelinks tlpdepth4"><strong>6.1231</strong><span class="linkarray tlpdepth4" id="p6.1231PM"> P/M [→<a class="gerlink" href="#p6.1231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1231OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The mark of a logical proposition is <em>not</em> general validity.</div>
<div class="para tlpdepth4">To be general means no more than to be accidentally valid for all things. An ungeneralized proposition can be tautological just as well as a generalized one.</div>
<div class="corelinks tlpdepth4"><strong>6.1232</strong><span class="linkarray tlpdepth4" id="p6.1232PM"> P/M [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1232OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The general validity of logic might be called essential, in contrast with the accidental general validity of such propositions as ‘All men are mortal’. Propositions like Russell’s ‘axiom of reducibility’ are not logical propositions, and this explains our feeling that, even if they were true, their truth could only be the result of a fortunate accident.</div>
<div class="corelinks tlpdepth4"><strong>6.1233</strong><span class="linkarray tlpdepth4" id="p6.1233PM"> P/M [→<a class="gerlink" href="#p6.1233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1233OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is possible to imagine a world in which the axiom of reducibility is not valid. It is clear, however, that logic has nothing to do with the question whether our world really is like that or not.</div>
<div class="corelinks tlpdepth3"><strong>6.124</strong><span class="linkarray tlpdepth3" id="p6.124PM"> P/M [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The propositions of logic describe the scaffolding of the world, or rather they represent it. They have no ‘subject-matter’. They presuppose that names have meaning and elementary propositions sense; and that is their connexion with the world. It is clear that something about the world must be indicated by the fact that certain combinations of symbols—whose essence involves the possession of a determinate character—are tautologies. This contains the decisive point. We have said that some things are arbitrary in the symbols that we use and that some things are not. In logic it is only the latter that express: but that means that logic is not a field in which <em>we</em> express what we wish with the help of signs, but rather one in which the nature of the natural and inevitable signs speaks for itself. If we know the logical syntax of any sign-language, then we have already been given all the propositions of logic.</div>
<div class="corelinks tlpdepth3"><strong>6.125</strong><span class="linkarray tlpdepth3" id="p6.125PM"> P/M [→<a class="gerlink" href="#p6.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.125OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is possible—indeed possible even according to the old conception of logic—to give in advance a description of all ‘true’ logical propositions.</div>
<div class="corelinks tlpdepth4"><strong>6.1251</strong><span class="linkarray tlpdepth4" id="p6.1251PM"> P/M [→<a class="gerlink" href="#p6.1251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1251OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Hence there can <em>never</em> be surprises in logic.</div>
<div class="corelinks tlpdepth3"><strong>6.126</strong><span class="linkarray tlpdepth3" id="p6.126PM"> P/M [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">One can calculate whether a proposition belongs to logic, by calculating the logical properties of the <em>symbol</em>.</div>
<div class="para tlpdepth3">And this is what we do when we ‘prove’ a logical proposition. For, without bothering about sense or meaning, we construct the logical proposition out of others using only <em>rules that deal with signs</em>.</div>
<div class="para tlpdepth3">The proof of logical propositions consists in the following process: we produce them out of other logical propositions by successively applying certain operations that always generate further tautologies out of the initial ones. (And in fact only tautologies <em>follow</em> from a tautology.)</div>
<div class="para tlpdepth3">Of course this way of showing that the propositions of logic are tautologies is not at all essential to logic, if only because the propositions from which the proof starts must show without any proof that they are tautologies.</div>
<div class="corelinks tlpdepth4"><strong>6.1261</strong><span class="linkarray tlpdepth4" id="p6.1261PM"> P/M [→<a class="gerlink" href="#p6.1261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1261OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">In logic process and result are equivalent. (Hence the absence of surprise.)</div>
<div class="corelinks tlpdepth4"><strong>6.1262</strong><span class="linkarray tlpdepth4" id="p6.1262PM"> P/M [→<a class="gerlink" href="#p6.1262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1262OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Proof in logic is merely a mechanical expedient to facilitate the recognition of tautologies in complicated cases.</div>
<div class="corelinks tlpdepth4"><strong>6.1263</strong><span class="linkarray tlpdepth4" id="p6.1263PM"> P/M [→<a class="gerlink" href="#p6.1263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1263OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Indeed, it would be altogether too remarkable if a proposition that had sense could be proved <em>logically</em> from others, and <em>so too</em> could a logical proposition. It is clear from the start that a logical proof of a proposition that has sense and a proof <em>in</em> logic must be two entirely different things.</div>
<div class="corelinks tlpdepth4"><strong>6.1264</strong><span class="linkarray tlpdepth4" id="p6.1264PM"> P/M [→<a class="gerlink" href="#p6.1264GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1264OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">A proposition that has sense states something, which is shown by its proof to be so. In logic every proposition is the form of a proof.</div>
<div class="para tlpdepth4">Every proposition of logic is a <em>modus ponens</em> represented in signs. (And one cannot express the <em>modus ponens</em> by means of a proposition.)</div>
<div class="corelinks tlpdepth4"><strong>6.1265</strong><span class="linkarray tlpdepth4" id="p6.1265PM"> P/M [→<a class="gerlink" href="#p6.1265GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1265OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is always possible to construe logic in such a way that every proposition is its own proof.</div>
<div class="corelinks tlpdepth3"><strong>6.127</strong><span class="linkarray tlpdepth3" id="p6.127PM"> P/M [→<a class="gerlink" href="#p6.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.127OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">All the propositions of logic are of equal status: it is not the case that some of them are essentially derived propositions.</div>
<div class="para tlpdepth3">Every tautology itself shows that it is a tautology.</div>
<div class="corelinks tlpdepth4"><strong>6.1271</strong><span class="linkarray tlpdepth4" id="p6.1271PM"> P/M [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is clear that the number of the ‘primitive propositions of logic’ is arbitrary, since one could derive logic from a single primitive proposition, e.g. by simply constructing the logical product of Frege’s primitive propositions. (Frege would perhaps say that we should then no longer have an immediately self-evident primitive proposition. But it is remarkable that a thinker as rigorous as Frege appealed to the degree of self-evidence as the criterion of a logical proposition.)</div>
<div class="corelinks tlpdepth2"><strong>6.13</strong><span class="linkarray tlpdepth2" id="p6.13PM"> P/M [→<a class="gerlink" href="#p6.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.13OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Logic is not a body of doctrine, but a mirror-image of the world.</div>
<div class="para tlpdepth2">Logic is transcendental.</div>
<div class="corelinks tlpdepth1"><strong>6.2</strong><span class="linkarray tlpdepth1" id="p6.2PM"> P/M [→<a class="gerlink" href="#p6.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">Mathematics is a logical method.</div>
<div class="para tlpdepth1">The propositions of mathematics are equations, and therefore pseudo-propositions.</div>
<div class="corelinks tlpdepth2"><strong>6.21</strong><span class="linkarray tlpdepth2" id="p6.21PM"> P/M [→<a class="gerlink" href="#p6.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.21OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">A proposition of mathematics does not express a thought.</div>
<div class="corelinks tlpdepth3"><strong>6.211</strong><span class="linkarray tlpdepth3" id="p6.211PM"> P/M [→<a class="gerlink" href="#p6.211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.211OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Indeed in real life a mathematical proposition is never what we want. Rather, we make use of mathematical propositions <em>only</em> in inferences from propositions that do not belong to mathematics to others that likewise do not belong to mathematics.</div>
<div class="para tlpdepth3">(In philosophy the question, ‘What do we actually use this word or this proposition for?’ repeatedly leads to valuable insights.)</div>
<div class="corelinks tlpdepth2"><strong>6.22</strong><span class="linkarray tlpdepth2" id="p6.22PM"> P/M [→<a class="gerlink" href="#p6.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.22OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics.</div>
<div class="corelinks tlpdepth2"><strong>6.23</strong><span class="linkarray tlpdepth2" id="p6.23PM"> P/M [→<a class="gerlink" href="#p6.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.23OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If two expressions are combined by means of the sign of equality, that means that they can be substituted for one another. But it must be manifest in the two expressions themselves whether this is the case or not.</div>
<div class="para tlpdepth2">When two expressions can be substituted for one another, that characterizes their logical form.</div>
<div class="corelinks tlpdepth3"><strong>6.231</strong><span class="linkarray tlpdepth3" id="p6.231PM"> P/M [→<a class="gerlink" href="#p6.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.231OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is a property of affirmation that it can be construed as double negation.</div>
<div class="para tlpdepth3">It is a property of ‘<span class="mathmode">1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</span>’ that it can be construed as ‘<span class="mathmode">(1<span class="mathrel">+</span>1)<span class="mathrel">+</span>(1<span class="mathrel">+</span>1)</span>’.</div>
<div class="corelinks tlpdepth3"><strong>6.232</strong><span class="linkarray tlpdepth3" id="p6.232PM"> P/M [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Frege says that the two expressions have the same meaning but different senses.</div>
<div class="para tlpdepth3">But the essential point about an equation is that it is not necessary in order to show that the two expressions connected by the sign of equality have the same meaning, since this can be seen from the two expressions themselves.</div>
<div class="corelinks tlpdepth4"><strong>6.2321</strong><span class="linkarray tlpdepth4" id="p6.2321PM"> P/M [→<a class="gerlink" href="#p6.2321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2321OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">And the possibility of proving the propositions of mathematics means simply that their correctness can be perceived without its being necessary that what they express should itself be compared with the facts in order to determine its correctness.</div>
<div class="corelinks tlpdepth4"><strong>6.2322</strong><span class="linkarray tlpdepth4" id="p6.2322PM"> P/M [→<a class="gerlink" href="#p6.2322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2322OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is impossible to <em>assert</em> the identity of meaning of two expressions. For in order to be able to assert anything about their meaning, I must know their meaning, and I cannot know their meaning without knowing whether what they mean is the same or different.</div>
<div class="corelinks tlpdepth4"><strong>6.2323</strong><span class="linkarray tlpdepth4" id="p6.2323PM"> P/M [→<a class="gerlink" href="#p6.2323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2323OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">An equation merely marks the point of view from which I consider the two expressions: it marks their equivalence in meaning.</div>
<div class="corelinks tlpdepth3"><strong>6.233</strong><span class="linkarray tlpdepth3" id="p6.233PM"> P/M [→<a class="gerlink" href="#p6.233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.233OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The question whether intuition is needed for the solution of mathematical problems must be given the answer that in this case language itself provides the necessary intuition.</div>
<div class="corelinks tlpdepth4"><strong>6.2331</strong><span class="linkarray tlpdepth4" id="p6.2331PM"> P/M [→<a class="gerlink" href="#p6.2331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2331OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The process of <em>calculating</em> serves to bring about that intuition.</div>
<div class="para tlpdepth4">Calculation is not an experiment.</div>
<div class="corelinks tlpdepth3"><strong>6.234</strong><span class="linkarray tlpdepth3" id="p6.234PM"> P/M [→<a class="gerlink" href="#p6.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.234OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Mathematics is a method of logic.</div>
<div class="corelinks tlpdepth4"><strong>6.2341</strong><span class="linkarray tlpdepth4" id="p6.2341PM"> P/M [→<a class="gerlink" href="#p6.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2341OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">It is the essential characteristic of mathematical method that it employs equations. For it is because of this method that every proposition of mathematics must go without saying.</div>
<div class="corelinks tlpdepth2"><strong>6.24</strong><span class="linkarray tlpdepth2" id="p6.24PM"> P/M [→<a class="gerlink" href="#p6.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.24OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The method by which mathematics arrives at its equations is the method of substitution.</div>
<div class="para tlpdepth2">For equations express the substitutability of two expressions and, starting from a number of equations, we advance to new equations by substituting different expressions in accordance with the equations.</div>
<div class="corelinks tlpdepth3"><strong>6.241</strong><span class="linkarray tlpdepth3" id="p6.241PM"> P/M [→<a class="gerlink" href="#p6.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.241OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Thus the proof of the proposition <span class="mathmode">2 × 2<span class="mathrel">=</span>4</span> runs as follows:</div>
<div class="para tlpdepth3"><div class="centered"><span class="mathmode"><span class="mathop">(Ω<sup><var>ν</var></sup>)<sup><var>μ</var></sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup><var>ν</var>× <var>μ</var></sup>’</span><var>x</var></span> Def.<br />
<span class="mathmode"><span class="mathop">Ω<sup>2 × 2</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω<sup>2</sup>)<sup>2</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω<sup>2</sup>)<sup>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>2</sup>’</span><span class="mathop">Ω<sup>2</sup>’</span><var>x</var></span><br />
<span class="mathmode"><span class="mathrel">=</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1</sup>’</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">(Ω’Ω)’</span><span class="mathop">(Ω’Ω)’</span> <var>x</var></span><br />
<span class="mathmode"><span class="mathrel">=</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><span class="mathop">Ω’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1<span class="mathrel">+</span>1</sup>’</span><var>x</var><span class="mathrel">=</span><span class="mathop">Ω<sup>4</sup>’</span><var>x</var></span>.<br />
</div></div>
<div class="corelinks tlpdepth1"><strong>6.3</strong><span class="linkarray tlpdepth1" id="p6.3PM"> P/M [→<a class="gerlink" href="#p6.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">The exploration of logic means the exploration of <em>everything that is subject to law</em>. And outside logic everything is accidental.</div>
<div class="corelinks tlpdepth2"><strong>6.31</strong><span class="linkarray tlpdepth2" id="p6.31PM"> P/M [→<a class="gerlink" href="#p6.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.31OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The so-called law of induction cannot possibly be a law of logic, since it is obviously a proposition with sense.—Nor, therefore, can it be an <em>a priori</em> law.</div>
<div class="corelinks tlpdepth2"><strong>6.32</strong><span class="linkarray tlpdepth2" id="p6.32PM"> P/M [→<a class="gerlink" href="#p6.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.32OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The law of causality is not a law but the form of a law.</div>
<div class="corelinks tlpdepth3"><strong>6.321</strong><span class="linkarray tlpdepth3" id="p6.321PM"> P/M [→<a class="gerlink" href="#p6.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.321OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">‘Law of causality’—that is a general name. And just as in mechanics, for example, there are ‘minimum-principles’, such as the law of least action, so too in physics there are causal laws, laws of the causal form.</div>
<div class="corelinks tlpdepth4"><strong>6.3211</strong><span class="linkarray tlpdepth4" id="p6.3211PM"> P/M [→<a class="gerlink" href="#p6.3211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3211OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Indeed people even surmised that there must be a ‘law of least action’ before they knew exactly how it went. (Here, as always, what is certain <em>a priori</em> proves to be something purely logical.)</div>
<div class="corelinks tlpdepth2"><strong>6.33</strong><span class="linkarray tlpdepth2" id="p6.33PM"> P/M [→<a class="gerlink" href="#p6.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.33OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">We do not have an <em>a priori belief</em> in a law of conservation, but rather <em>a priori knowledge</em> of the possibility of a logical form.</div>
<div class="corelinks tlpdepth2"><strong>6.34</strong><span class="linkarray tlpdepth2" id="p6.34PM"> P/M [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">All such propositions, including the principle of sufficient reason, the laws of continuity in nature and of least effort in nature, etc. etc.—all these are <em>a priori</em> insights about the forms in which the propositions of science can be cast.</div>
<div class="corelinks tlpdepth3"><strong>6.341</strong><span class="linkarray tlpdepth3" id="p6.341PM"> P/M [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Newtonian mechanics, for example, imposes a unified form on the description of the world. Let us imagine a white surface with irregular black spots on it. We then say that whatever kind of picture these make, I can always approximate as closely as I wish to the description of it by covering the surface with a sufficiently fine square mesh, and then saying of every square whether it is black or white. In this way I shall have imposed a unified form on the description of the surface. The form is optional, since I could have achieved the same result by using a net with a triangular or hexagonal mesh. Possibly the use of a triangular mesh would have made the description simpler: that is to say, it might be that we could describe the surface more accurately with a coarse triangular mesh than with a fine square mesh (or conversely), and so on. The different nets correspond to different systems for describing the world. Mechanics determines one form of description of the world by saying that all propositions used in the description of the world must be obtained in a given way from a given set of propositions—the axioms of mechanics. It thus supplies the bricks for building the edifice of science, and it says, ‘Any building that you want to erect, whatever it may be, must somehow be constructed with these bricks, and with these alone.’</div>
<div class="para tlpdepth3">(Just as with the number-system we must be able to write down any number we wish, so with the system of mechanics we must be able to write down any proposition of physics that we wish.)</div>
<div class="corelinks tlpdepth3"><strong>6.342</strong><span class="linkarray tlpdepth3" id="p6.342PM"> P/M [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">And now we can see the relative position of logic and mechanics. (The net might also consist of more than one kind of mesh: e.g. we could use both triangles and hexagons.) The possibility of describing a picture like the one mentioned above with a net of a given form tells us <em>nothing</em> about the picture. (For that is true of all such pictures.) But what <em>does</em> characterize the picture is that it can be described <em>completely</em> by a particular net with a <em>particular</em> size of mesh.</div>
<div class="para tlpdepth3">Similarly the possibility of describing the world by means of Newtonian mechanics tells us nothing about the world: but what does tell us something about it is the precise <em>way</em> in which it is possible to describe it by these means. We are also told something about the world by the fact that it can be described more simply with one system of mechanics than with another.</div>
<div class="corelinks tlpdepth3"><strong>6.343</strong><span class="linkarray tlpdepth3" id="p6.343PM"> P/M [→<a class="gerlink" href="#p6.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.343OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Mechanics is an attempt to construct according to a single plan all the <em>true</em> propositions that we need for the description of the world.</div>
<div class="corelinks tlpdepth4"><strong>6.3431</strong><span class="linkarray tlpdepth4" id="p6.3431PM"> P/M [→<a class="gerlink" href="#p6.3431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3431OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The laws of physics, with all their logical apparatus, still speak, however indirectly, about the objects of the world.</div>
<div class="corelinks tlpdepth4"><strong>6.3432</strong><span class="linkarray tlpdepth4" id="p6.3432PM"> P/M [→<a class="gerlink" href="#p6.3432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3432OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">We ought not to forget that any description of the world by means of mechanics will be of the completely general kind. For example, it will never mention <em>particular</em> point-masses: it will only talk about <em>any point-masses whatsoever</em>.</div>
<div class="corelinks tlpdepth2"><strong>6.35</strong><span class="linkarray tlpdepth2" id="p6.35PM"> P/M [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Although the spots in our picture are geometrical figures, nevertheless geometry can obviously say nothing at all about their actual form and position. The network, however, is <em>purely</em> geometrical; all its properties can be given <em>a priori</em>.</div>
<div class="para tlpdepth2">Laws like the principle of sufficient reason, etc. are about the net and not about what the net describes.</div>
<div class="corelinks tlpdepth2"><strong>6.36</strong><span class="linkarray tlpdepth2" id="p6.36PM"> P/M [→<a class="gerlink" href="#p6.36GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If there were a law of causality, it might be put in the following way: There are laws of nature.</div>
<div class="para tlpdepth2">But of course that cannot be said: it makes itself manifest.</div>
<div class="corelinks tlpdepth3"><strong>6.361</strong><span class="linkarray tlpdepth3" id="p6.361PM"> P/M [→<a class="gerlink" href="#p6.361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.361OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">One might say, using Hertz’s terminology, that only connexions that are <em>subject to law</em> are <em>thinkable</em>.</div>
<div class="corelinks tlpdepth4"><strong>6.3611</strong><span class="linkarray tlpdepth4" id="p6.3611PM"> P/M [→<a class="gerlink" href="#p6.3611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3611OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">We cannot compare a process with ‘the passage of time’—there is no such thing—but only with another process (such as the working of a chronometer).</div>
<div class="para tlpdepth4">Hence we can describe the lapse of time only by relying on some other process.</div>
<div class="para tlpdepth4">Something exactly analogous applies to space: e.g. when people say that neither of two events (which exclude one another) can occur, because there is <em>nothing to cause</em> the one to occur rather than the other, it is really a matter of our being unable to describe <em>one</em> of the two events unless there is some sort of asymmetry to be found. And <em>if</em> such an asymmetry <em>is</em> to be found, we can regard it as the <em>cause</em> of the occurrence of the one and the non-occurrence of the other.</div>
<div class="corelinks tlpdepth5"><strong>6.36111</strong><span class="linkarray tlpdepth5" id="p6.36111PM"> P/M [→<a class="gerlink" href="#p6.36111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36111OGD">OGD</a>]</span></div>
<div class="para tlpdepth5">Kant’s problem about the right hand and the left hand, which cannot be made to coincide, exists even in two dimensions. Indeed, it exists in one-dimensional space</div>
<div class="para tlpdepth5 noindent"><!-- noindent --><div class="centeredsqueeze" ><b>–&nbsp;–&nbsp;–&nbsp;<span class="tight"><span class="symbol">○</span>————<span class="nudgedown"><span class="symbol">✕</span></span></span>&nbsp;–&nbsp;–&nbsp;<span class="tight"><span class="nudgedown"><span class="symbol">✕</span></span>————<span class="symbol">○</span></span>&nbsp;–&nbsp;–&nbsp;–</b><br /><var class="smallvar">a</var>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<var class="smallvar">b</var></div></div>
<div class="para tlpdepth5 noindent"><!-- noindent --> in which the two congruent figures, <span class="mathmode"><var>a</var></span> and <span class="mathmode"><var>b</var></span>, cannot be made to coincide unless they are moved out of this space. The right hand and the left hand are in fact completely congruent. It is quite irrelevant that they cannot be made to coincide.</div>
<div class="para tlpdepth5">A right-hand glove could be put on the left hand, if it could be turned round in four-dimensional space.</div>
<div class="corelinks tlpdepth3"><strong>6.362</strong><span class="linkarray tlpdepth3" id="p6.362PM"> P/M [→<a class="gerlink" href="#p6.362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.362OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">What can be described can happen too: and what the law of causality is meant to exclude cannot even be described.</div>
<div class="corelinks tlpdepth3"><strong>6.363</strong><span class="linkarray tlpdepth3" id="p6.363PM"> P/M [→<a class="gerlink" href="#p6.363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.363OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The procedure of induction consists in accepting as true the <em>simplest</em> law that can be reconciled with our experiences.</div>
<div class="corelinks tlpdepth4"><strong>6.3631</strong><span class="linkarray tlpdepth4" id="p6.3631PM"> P/M [→<a class="gerlink" href="#p6.3631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3631OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">This procedure, however, has no logical justification but only a psychological one.</div>
<div class="para tlpdepth4">It is clear that there are no grounds for believing that the simplest eventuality will in fact be realized.</div>
<div class="corelinks tlpdepth5"><strong>6.36311</strong><span class="linkarray tlpdepth5" id="p6.36311PM"> P/M [→<a class="gerlink" href="#p6.36311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36311OGD">OGD</a>]</span></div>
<div class="para tlpdepth5">It is an hypothesis that the sun will rise tomorrow: and this means that we do not <em>know</em> whether it will rise.</div>
<div class="corelinks tlpdepth2"><strong>6.37</strong><span class="linkarray tlpdepth2" id="p6.37PM"> P/M [→<a class="gerlink" href="#p6.37GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.37OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">There is no compulsion making one thing happen because another has happened. The only necessity that exists is <em>logical</em> necessity</div>
<div class="corelinks tlpdepth3"><strong>6.371</strong><span class="linkarray tlpdepth3" id="p6.371PM"> P/M [→<a class="gerlink" href="#p6.371GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.371OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The whole modern conception of the world is founded on the illusion that the so-called laws of nature are the explanations of natural phenomena.</div>
<div class="corelinks tlpdepth3"><strong>6.372</strong><span class="linkarray tlpdepth3" id="p6.372PM"> P/M [→<a class="gerlink" href="#p6.372GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.372OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Thus people today stop at the laws of nature, treating them as something inviolable, just as God and Fate were treated in past ages.</div>
<div class="para tlpdepth3">And in fact both are right and both wrong: though the view of the ancients is clearer in so far as they have a clear and acknowledged terminus, while the modern system tries to make it look as if <em>everything</em> were explained.</div>
<div class="corelinks tlpdepth3"><strong>6.373</strong><span class="linkarray tlpdepth3" id="p6.373PM"> P/M [→<a class="gerlink" href="#p6.373GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.373OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The world is independent of my will.</div>
<div class="corelinks tlpdepth3"><strong>6.374</strong><span class="linkarray tlpdepth3" id="p6.374PM"> P/M [→<a class="gerlink" href="#p6.374GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.374OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Even if all that we wish for were to happen, still this would only be a favour granted by fate, so to speak: for there is no <em>logical</em> connexion between the will and the world, which would guarantee it, and the supposed physical connexion itself is surely not something that we could will.</div>
<div class="corelinks tlpdepth3"><strong>6.375</strong><span class="linkarray tlpdepth3" id="p6.375PM"> P/M [→<a class="gerlink" href="#p6.375GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.375OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">Just as the only necessity that exists is <em>logical</em> necessity, so too the only impossibility that exists is <em>logical</em> impossibility.</div>
<div class="corelinks tlpdepth4"><strong>6.3751</strong><span class="linkarray tlpdepth4" id="p6.3751PM"> P/M [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">For example, the simultaneous presence of two colours at the same place in the visual field is impossible, in fact logically impossible, since it is ruled out by the logical structure of colour.</div>
<div class="para tlpdepth4">Let us think how this contradiction appears in physics: more or less as follows—a particle cannot have two velocities at the same time; that is to say, it cannot be in two places at the same time; that is to say, particles that are in different places at the same time cannot be identical.</div>
<div class="para tlpdepth4">(It is clear that the logical product of two elementary propositions can neither be a tautology nor a contradiction. The statement that a point in the visual field has two different colours at the same time is a contradiction.)</div>
<div class="corelinks tlpdepth1"><strong>6.4</strong><span class="linkarray tlpdepth1" id="p6.4PM"> P/M [→<a class="gerlink" href="#p6.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">All propositions are of equal value.</div>
<div class="corelinks tlpdepth2"><strong>6.41</strong><span class="linkarray tlpdepth2" id="p6.41PM"> P/M [→<a class="gerlink" href="#p6.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.41OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The sense of the world must lie outside the world. In the world everything is as it is, and everything happens as it does happen: <em>in</em> it no value exists—and if it did exist, it would have no value.</div>
<div class="para tlpdepth2">If there is any value that does have value, it must lie outside the whole sphere of what happens and is the case. For all that happens and is the case is accidental.</div>
<div class="para tlpdepth2">What makes it non-accidental cannot lie <em>within</em> the world, since if it did it would itself be accidental.</div>
<div class="para tlpdepth2">It must lie outside the world.</div>
<div class="corelinks tlpdepth2"><strong>6.42</strong><span class="linkarray tlpdepth2" id="p6.42PM"> P/M [→<a class="gerlink" href="#p6.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.42OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">So too it is impossible for there to be propositions of ethics.</div>
<div class="para tlpdepth2">Propositions can express nothing that is higher.</div>
<div class="corelinks tlpdepth3"><strong>6.421</strong><span class="linkarray tlpdepth3" id="p6.421PM"> P/M [→<a class="gerlink" href="#p6.421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.421OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is clear that ethics cannot be put into words.</div>
<div class="para tlpdepth3">Ethics is transcendental.</div>
<div class="para tlpdepth3">(Ethics and aesthetics are one and the same.)</div>
<div class="corelinks tlpdepth3"><strong>6.422</strong><span class="linkarray tlpdepth3" id="p6.422PM"> P/M [→<a class="gerlink" href="#p6.422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.422OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">When an ethical law of the form, ‘Thou shalt …’ is laid down, one’s first thought is, ‘And what if I do not do it?’ It is clear, however, that ethics has nothing to do with punishment and reward in the usual sense of the terms. So our question about the <em>consequences</em> of an action must be unimportant.—At least those consequences should not be events. For there must be something right about the question we posed. There must indeed be some kind of ethical reward and ethical punishment, but they must reside in the action itself.</div>
<div class="para tlpdepth3">(And it is also clear that the reward must be something pleasant and the punishment something unpleasant.)</div>
<div class="corelinks tlpdepth3"><strong>6.423</strong><span class="linkarray tlpdepth3" id="p6.423PM"> P/M [→<a class="gerlink" href="#p6.423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.423OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">It is impossible to speak about the will in so far as it is the subject of ethical attributes.</div>
<div class="para tlpdepth3">And the will as a phenomenon is of interest only to psychology.</div>
<div class="corelinks tlpdepth2"><strong>6.43</strong><span class="linkarray tlpdepth2" id="p6.43PM"> P/M [→<a class="gerlink" href="#p6.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.43OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">If the good or bad exercise of the will does alter the world, it can alter only the limits of the world, not the facts—not what can be expressed by means of language.</div>
<div class="para tlpdepth2">In short the effect must be that it becomes an altogether different world. It must, so to speak, wax and wane as a whole.</div>
<div class="para tlpdepth2">The world of the happy man is a different one from that of the unhappy man.</div>
<div class="corelinks tlpdepth3"><strong>6.431</strong><span class="linkarray tlpdepth3" id="p6.431PM"> P/M [→<a class="gerlink" href="#p6.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.431OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">So too at death the world does not alter, but comes to an end.</div>
<div class="corelinks tlpdepth4"><strong>6.4311</strong><span class="linkarray tlpdepth4" id="p6.4311PM"> P/M [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4311OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Death is not an event in life: we do not live to experience death.</div>
<div class="para tlpdepth4">If we take eternity to mean not infinite temporal duration but timelessness, then eternal life belongs to those who live in the present.</div>
<div class="para tlpdepth4">Our life has no end in just the way in which our visual field has no limits.</div>
<div class="corelinks tlpdepth4"><strong>6.4312</strong><span class="linkarray tlpdepth4" id="p6.4312PM"> P/M [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">Not only is there no guarantee of the temporal immortality of the human soul, that is to say of its eternal survival after death; but, in any case, this assumption completely fails to accomplish the purpose for which it has always been intended. Or is some riddle solved by my surviving for ever? Is not this eternal life itself as much of a riddle as our present life? The solution of the riddle of life in space and time lies <em>outside</em> space and time.</div>
<div class="para tlpdepth4">(It is certainly not the solution of any problems of natural science that is required.)</div>
<div class="corelinks tlpdepth3"><strong>6.432</strong><span class="linkarray tlpdepth3" id="p6.432PM"> P/M [→<a class="gerlink" href="#p6.432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.432OGD">OGD</a>]</span></div>
<div class="para tlpdepth3"><em>How</em> things are in the world is a matter of complete indifference for what is higher. God does not reveal himself <em>in</em> the world.</div>
<div class="corelinks tlpdepth4"><strong>6.4321</strong><span class="linkarray tlpdepth4" id="p6.4321PM"> P/M [→<a class="gerlink" href="#p6.4321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4321OGD">OGD</a>]</span></div>
<div class="para tlpdepth4">The facts all contribute only to setting the problem, not to its solution.</div>
<div class="corelinks tlpdepth2"><strong>6.44</strong><span class="linkarray tlpdepth2" id="p6.44PM"> P/M [→<a class="gerlink" href="#p6.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.44OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">It is not <em>how</em> things are in the world that is mystical, but <em>that</em> it exists.</div>
<div class="corelinks tlpdepth2"><strong>6.45</strong><span class="linkarray tlpdepth2" id="p6.45PM"> P/M [→<a class="gerlink" href="#p6.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.45OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">To view the world sub specie aeterni is to view it as a whole—a limited whole.</div>
<div class="para tlpdepth2">Feeling the world as a limited whole—it is this that is mystical.</div>
<div class="corelinks tlpdepth1"><strong>6.5</strong><span class="linkarray tlpdepth1" id="p6.5PM"> P/M [→<a class="gerlink" href="#p6.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.5OGD">OGD</a>]</span></div>
<div class="para tlpdepth1">When the answer cannot be put into words, neither can the question be put into words.</div>
<div class="para tlpdepth1"><em>The riddle</em> does not exist.</div>
<div class="para tlpdepth1">If a question can be framed at all, it is also <em>possible</em> to answer it.</div>
<div class="corelinks tlpdepth2"><strong>6.51</strong><span class="linkarray tlpdepth2" id="p6.51PM"> P/M [→<a class="gerlink" href="#p6.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.51OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">Scepticism is <em>not</em> irrefutable, but obviously nonsensical, when it tries to raise doubts where no questions can be asked.</div>
<div class="para tlpdepth2">For doubt can exist only where a question exists, a question only where an answer exists, and an answer only where something <em>can be said</em>.</div>
<div class="corelinks tlpdepth2"><strong>6.52</strong><span class="linkarray tlpdepth2" id="p6.52PM"> P/M [→<a class="gerlink" href="#p6.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.52OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">We feel that even when <em>all possible</em> scientific questions have been answered, the problems of life remain completely untouched. Of course there are then no questions left, and this itself is the answer.</div>
<div class="corelinks tlpdepth3"><strong>6.521</strong><span class="linkarray tlpdepth3" id="p6.521PM"> P/M [→<a class="gerlink" href="#p6.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.521OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">The solution of the problem of life is seen in the vanishing of the problem.</div>
<div class="para tlpdepth3">(Is not this the reason why those who have found after a long period of doubt that the sense of life became clear to them have then been unable to say what constituted that sense?)</div>
<div class="corelinks tlpdepth3"><strong>6.522</strong><span class="linkarray tlpdepth3" id="p6.522PM"> P/M [→<a class="gerlink" href="#p6.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.522OGD">OGD</a>]</span></div>
<div class="para tlpdepth3">There are, indeed, things that cannot be put into words. They <em>make themselves manifest</em>. They are what is mystical.</div>
<div class="corelinks tlpdepth2"><strong>6.53</strong><span class="linkarray tlpdepth2" id="p6.53PM"> P/M [→<a class="gerlink" href="#p6.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.53OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">The correct method in philosophy would really be the following: to say nothing except what can be said, i.e. propositions of natural science—i.e. something that has nothing to do with philosophy—and then, whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions. Although it would not be satisfying to the other person—he would not have the feeling that we were teaching him philosophy—<em>this</em> method would be the only strictly correct one.</div>
<div class="corelinks tlpdepth2"><strong>6.54</strong><span class="linkarray tlpdepth2" id="p6.54PM"> P/M [→<a class="gerlink" href="#p6.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.54OGD">OGD</a>]</span></div>
<div class="para tlpdepth2">My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)</div>
<div class="para tlpdepth2">He must transcend these propositions, and then he will see the world aright.</div>
<div class="corelinks tlpdepth0"><strong>7</strong><span class="linkarray tlpdepth0" id="p7PM"> P/M [→<a class="gerlink" href="#p7GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p7OGD">OGD</a>]</span></div>
<div class="para tlpdepth0">What we cannot speak about we must pass over in silence.</div>
<div id="footnotesPearsMcGuinness">
<h4 class="tlpdepth0">Footnote</h4>
<p class="footnote tlpdepth0" id="fn1PM"><a href="#fn1markerPM">*</a> <span id="pmcfootnote1">The decimal numbers assigned to the individual propositions indicate the logical importance of the propositions, the stress laid on them in my exposition. The propositions <var>n</var>.1, <var>n</var>.2, <var>n</var>.3, etc. are comments on proposition no. <var>n</var>; the propositions <var>n</var>.<var>m</var>1, <var>n</var>.<var>m</var>2, etc. are comments on proposition no. <var>n</var>.<var>m</var>; and so on.</span> <span class="linkarray">[→<a href="#fn1GER" class="gerlink">GER</a><span class="aftergerlink"> | </span><a href="#fn1OGD" class="ogdlink">OGD</a>]</span></p>
</div>
<hr />
</div>
<div id="indexdiv" class="indexdiv">
<h2 class="majordivision" id="index">Index (Pears/McGuinness)</h2>
<div class="centered">
<span class="kckaddition">[Original note by Pears and McGuinness.]</span>
</div>
<p class="openingpar">The translators’ aim has been to include all the more interesting words, and, in each case, either to give all the occurrences of a word, or else to omit only a few unimportant ones. Paragraphs in the preface are referred to as P1, P2, etc. Propositions are indicated by numbers without points <span class="kckaddition">[—the points have been restored for the side-by-side-by-side edition—]</span>; more than two consecutive propositions, by two numbers joined by an en-rule, as 202–2021.</p>
<p>In the translation it has sometimes been necessary to use different English expressions for the same German expression or the same English expression for different German expressions. The index contains various devices designed to make it an informative guide to the German terminology and, in particular, to draw attention to some important connexions between ideas that are more difficult to bring out in English than in German.</p>
<p>First, when a German expression is of any interest in itself, it is given in brackets after the English expression that translates it, e.g. <strong>situation</strong> [<em>Sachlage</em>]; also, whenever an English expression is used to translate more than one German expression, each of the German expressions is given separately in numbered brackets, and is followed by the list of passages in which it is translated by the English expression, e.g. <strong>reality</strong> 1. [<em>Realität</em>], 55561, etc. 2. [<em>Wirklichkeit</em>], 206, etc.</p>
<p>Secondly, the German expressions given in this way sometimes have two or more English translations in the text; and when this is so, if the alternative English translations are of interest, they follow the German expression inside the brackets, e.g. <strong>proposition</strong> [<em>Satz</em>: law; principle].</p>
<p>The alternative translations recorded by these two devices are sometimes given in an abbreviated way. For a German expression need not actually be translated by the English expressions that it follows or precedes, as it is in the examples above. The relationship may be more complicated. For instance, the German expression may be only part of a phrase that is translated by the English expression, e.g. <strong>stand in a relation to one another</strong>; <strong>are related</strong>
[<em>sich verhalten</em>: stand, how things; state of things].</p>
<p>Thirdly, cross-references have been used to draw attention to other important connexions between ideas, e.g. <strong>true</strong>, cf. correct; right: and <strong><em>a priori</em></strong>, cf. advance, in.</p>
<p>In subordinate entries and cross-references the catchword is indicated by <span class="mathmode">~</span>, unless the catchword contains /, in which case the part preceding / is so indicated, e.g. <strong>accident</strong>; <span class="mathmode">~</span><strong>al</strong> for <strong>accident</strong>; <strong>accidental</strong>, and <strong>state of /affairs</strong>; <span class="mathmode">~</span> <strong>things</strong> for <strong>state of affairs</strong>; <strong>state of things</strong>. Cross-references relate to the last preceding entry or numbered bracket. When references are given both for a word in its own right and for a phrase containing it, occurrences of the latter are generally not also counted as occurrences of the former, so that both entries should be consulted.</p><div id="indexentries">
<div class="indexletterblock">
<div class="indexentry">about [<em>von etwas handeln</em>: concerned with; deal with; subject-matter], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span>; cf. mention; speak; talk. </div>
<div class="indexentry">abstract, 5.5563<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span></div>
<div class="indexentry">accident; <span class="mathmode">~</span>al [<em>Zufall</em>], 2.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.012PM">P/M</a>]</span>, 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 3.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.34PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 6.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.031PM">P/M</a>]</span>, 6.1231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1231PM">P/M</a>]</span>, 6.1232<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span>, 6.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3PM">P/M</a>]</span>, 6.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.41PM">P/M</a>]</span></div>
<div class="indexentry">action, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 6.422<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span></div>
<div class="indexentry">activity, 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span></div>
<div class="indexentry">addition, cf. logical.</div>
<div class="indexentry">adjectiv/e; <span class="mathmode">~</span>al, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span></div>
<div class="indexentry">advance, in [<em>von vornherein</em>], 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 6.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.125PM">P/M</a>]</span>; cf. <em>a priori</em>. </div>
<div class="indexentry">aesthetics, 6.421<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.421PM">P/M</a>]</span></div>
<div class="indexentry">affirmation [<em>Bejahung</em>], 4.064<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.064GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.064OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.064PM">P/M</a>]</span>, 5.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.124PM">P/M</a>]</span>, 5.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1241PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 5.513<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span>, 5.514<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span>, 6.231<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.231PM">P/M</a>]</span></div>
<div class="indexentry">affix, [<em>Index</em>], 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span></div>
<div class="indexentry">agreement</div>
<div class="indexsubentry">1. [<em>stimmmen</em>: right; true], 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Übereinstimmmung</em>], 2.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.21PM">P/M</a>]</span>, 2.222<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.222PM">P/M</a>]</span>, 4.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2PM">P/M</a>]</span>, 4.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4PM">P/M</a>]</span>, 4.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.42PM">P/M</a>]</span>–4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span></div>
<div class="indexentry">analysis [<em>Analyse</em>], 3.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.201PM">P/M</a>]</span>, 3.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.25PM">P/M</a>]</span>, 3.3442<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3442PM">P/M</a>]</span>, 4.1274<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1274OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span>, 4.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.221PM">P/M</a>]</span>, 5.5562<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5562GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5562OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5562PM">P/M</a>]</span>; cf. anatomize; dissect; resolve. </div>
<div class="indexentry">analytic, 6.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.11PM">P/M</a>]</span></div>
<div class="indexentry">anatomize [<em>auseinanderlegen</em>], 3.261<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span>; cf. analysis. </div>
<div class="indexentry">answer, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 4.1274<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1274OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span>, 5.4541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.551<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.551GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.551OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.551PM">P/M</a>]</span>, 6.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.5PM">P/M</a>]</span>–6.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.52PM">P/M</a>]</span></div>
<div class="indexentry">apparent, 4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span>, 5.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.441PM">P/M</a>]</span>, 5.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span>; cf. pseudo-. </div>
<div class="indexentry">application [<em>Anwendung</em>: employment], 3.262<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.262PM">P/M</a>]</span>, 3.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.5PM">P/M</a>]</span>, 5.2521<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2521PM">P/M</a>]</span>, 5.2523<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2523GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2523OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2523PM">P/M</a>]</span>, 5.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.32PM">P/M</a>]</span>, 5.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5PM">P/M</a>]</span>, 5.5521<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5521PM">P/M</a>]</span>, 5.557<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.557GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.557OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.557PM">P/M</a>]</span>, 6.001<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.001PM">P/M</a>]</span>, 6.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.123PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span></div>
<div class="indexentry"><em>a priori</em>, 2.225<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.225GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.225OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.225PM">P/M</a>]</span>, 3.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.04PM">P/M</a>]</span>, 3.05<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.05PM">P/M</a>]</span>, 5.133<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.133GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.133OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.133PM">P/M</a>]</span>, 5.4541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span>, 5.4731<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4731OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.5541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5541PM">P/M</a>]</span>, 5.5571<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5571GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5571OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5571PM">P/M</a>]</span>, 5.634<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.634GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.634OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.634PM">P/M</a>]</span>, 6.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.31PM">P/M</a>]</span>, 6.3211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3211PM">P/M</a>]</span>, 6.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.33PM">P/M</a>]</span>, 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span>; cf. advance, in. </div>
<div class="indexentry">arbitrary, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 3.322<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span>, 3.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.342PM">P/M</a>]</span>, 3.3442<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3442PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span>, 5.554<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.554GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.554OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.554PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span></div>
<div class="indexentry">argument, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.251<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.251PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.523<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.523GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.523OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.523PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>; cf. truth-argument. </div>
<div class="indexsubentry"><span class="mathmode">~</span>-place, 2.0131<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span>, 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span></div>
<div class="indexentry">arithmetic, 4.4611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4611PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span></div>
<div class="indexentry">arrow, 3.144<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.144GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.144OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.144PM">P/M</a>]</span>, 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span></div>
<div class="indexentry">articulated [<em>artikuliert</em>], 3.141<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.141PM">P/M</a>]</span>, 3.251<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.251PM">P/M</a>]</span>; cf. segmented. </div>
<div class="indexentry">ascribe [<em>aussagen</em>: speak; state; statement; tell], 4.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1241PM">P/M</a>]</span></div>
<div class="indexentry">assert</div>
<div class="indexsubentry">1. [<em>behaupten</em>], 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.21PM">P/M</a>]</span>, 6.2322<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2322PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>zusprechen</em>], 4.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span></div>
<div class="indexentry">asymmetry, 6.3611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3611PM">P/M</a>]</span></div>
<div class="indexentry">axiom, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> of infinity, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> of reducibility, 6.1232<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span>, 6.1233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1233PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">bad, 6.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.43PM">P/M</a>]</span></div>
<div class="indexentry">basis, 5.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.21PM">P/M</a>]</span>, 5.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.22PM">P/M</a>]</span>, 5.234<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.234PM">P/M</a>]</span>, 5.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span>, 5.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.25PM">P/M</a>]</span>, 5.251<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.251PM">P/M</a>]</span>, 5.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.442PM">P/M</a>]</span>, 5.54<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.54PM">P/M</a>]</span></div>
<div class="indexentry">beautiful, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span></div>
<div class="indexentry">belief, 5.1361<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1361PM">P/M</a>]</span>, 5.1363<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1363PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>, 5.542<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span>, 6.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.33PM">P/M</a>]</span>, 6.3631<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3631PM">P/M</a>]</span></div>
<div class="indexentry">bound; <span class="mathmode">~</span>ary [<em>Grenze</em>: delimit; limit], 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span></div>
<div class="indexentry">brackets, 4.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>, 5.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span></div>
<div class="indexentry">build [<em>Bau</em>: construction], 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">calculation, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.2331<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2331PM">P/M</a>]</span></div>
<div class="indexentry">cardinal, cf. number.</div>
<div class="indexentry">case, be the</div>
<div class="indexsubentry">1. [<em>der Fall sein</em>], 1<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1PM">P/M</a>]</span>, 1.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p1.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.12PM">P/M</a>]</span>, 1.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p1.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.21PM">P/M</a>]</span>, 2<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2PM">P/M</a>]</span>, 2.024<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.024PM">P/M</a>]</span>, 3.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.342PM">P/M</a>]</span>, 4.024<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.024PM">P/M</a>]</span>, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>, 5.5542<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5542PM">P/M</a>]</span>, 6.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>So-Sein</em>], 6.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.41PM">P/M</a>]</span></div>
<div class="indexentry">causality, 5.136<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.136GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.136OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.136PM">P/M</a>]</span>–5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 6.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.32PM">P/M</a>]</span>, 6.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span>, 6.36<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.36GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36PM">P/M</a>]</span>, 6.3611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3611PM">P/M</a>]</span>, 6.362<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.362PM">P/M</a>]</span>; cf. law. </div>
<div class="indexentry">certainty [<em>Gewissheit</em>], 4.464<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.464GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.464OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.464PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span>, 6.3211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3211PM">P/M</a>]</span></div>
<div class="indexentry">chain, 2.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.03PM">P/M</a>]</span>; cf. concatenation. </div>
<div class="indexentry">clarification, 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span></div>
<div class="indexentry">class [<em>Klasse</em>: set], 3.311<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.311PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 6.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.031PM">P/M</a>]</span></div>
<div class="indexentry">clear, P2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span>, 3.251<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.251PM">P/M</a>]</span>, 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span>, 4.115<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.115GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.115OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.115PM">P/M</a>]</span>, 4.116<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.116GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.116OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.116PM">P/M</a>]</span></div>
<div class="indexsubentry">make <span class="mathmode">~</span> [<em>erklären</em>: definition; explanation], 5.452<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span></div>
<div class="indexentry">colour, 2.0131<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span>, 2.0232<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0232PM">P/M</a>]</span>, 2.0251<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0251PM">P/M</a>]</span>, 2.171<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.171GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.171OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.171PM">P/M</a>]</span>, 4.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.123PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>-space, 2.0131<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span></div>
<div class="indexentry">combination</div>
<div class="indexsubentry">1. [<em>Kombination</em>], 4.27<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.27GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.27OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.27PM">P/M</a>]</span>, 4.28<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.28GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.28OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.28PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>; cf. rule, combinatory; truth-<span class="mathmode">~</span>. </div>
<div class="indexsubentry">2. [<em>Verbindung</em>: connexion], 2.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01PM">P/M</a>]</span>, 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 4.0311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span>, 4.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.221PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 4.4661<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span>, 5.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>, 6.1201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1201PM">P/M</a>]</span>, 6.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span>, 6.1221<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1221PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span>; cf. sign. </div>
<div class="indexentry">common, 2.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.022PM">P/M</a>]</span>, 2.16<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.16GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.16OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.16PM">P/M</a>]</span>, 2.17<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.17GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.17OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.17PM">P/M</a>]</span>, 2.18<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span>, 2.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p2.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.2PM">P/M</a>]</span>, 3.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span>, 3.311<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.311PM">P/M</a>]</span>, 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 3.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.321PM">P/M</a>]</span>, 3.322<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span>, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 3.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.341PM">P/M</a>]</span>, 3.3411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3411PM">P/M</a>]</span>, 3.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.343PM">P/M</a>]</span>–3.3441<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 4.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12PM">P/M</a>]</span>, 5.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.11PM">P/M</a>]</span>, 5.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.143PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>, 5.513<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span>, 5.5261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span>, 6.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span></div>
<div class="indexentry">comparison, 2.223<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.223GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.223OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.223PM">P/M</a>]</span>, 3.05<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.05PM">P/M</a>]</span>, 4.05<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.05PM">P/M</a>]</span>, 6.2321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2321PM">P/M</a>]</span>, 6.3611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3611PM">P/M</a>]</span></div>
<div class="indexentry">complete</div>
<div class="indexsubentry">1. [<em>vollkommen</em>: folly], 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>vollstädig</em>], 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>; </div>
<div class="indexsubentry">analyse <span class="mathmode">~</span>ly, 3.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.201PM">P/M</a>]</span>, 3.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.25PM">P/M</a>]</span>; </div>
<div class="indexsubentry">describe <span class="mathmode">~</span>ly, 2.0201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.26PM">P/M</a>]</span>, 5.526<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span>, 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span></div>
<div class="indexentry">complex, 2.0201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span>, 3.1432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1432PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.3442<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3442PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.2211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span>, 4.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span>, 5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span>, 5.5423<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5423PM">P/M</a>]</span></div>
<div class="indexentry">composite [<em>zummmengesetzt</em>], 2.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.021PM">P/M</a>]</span>, 3.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span>, 3.1431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span>, 3.3411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3411PM">P/M</a>]</span>, 4.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.032PM">P/M</a>]</span>, 4.2211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.5261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span>, 5.5421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5421PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span></div>
<div class="indexentry">compulsion, 6.37<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.37GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.37OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.37PM">P/M</a>]</span></div>
<div class="indexentry">concatenation [<em>Verkettung</em>], 4.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.022PM">P/M</a>]</span>; cf. chain. </div>
<div class="indexentry">concept [<em>Begriff</em>: primitive idea], 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>–4.1274<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1274OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 5.2523<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2523GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2523OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2523PM">P/M</a>]</span>, 5.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span>, 5.555<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span>, 6.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span>; cf. formal <span class="mathmode">~</span>; pseudo-<span class="mathmode">~</span>. </div>
<div class="indexsubentry"><span class="mathmode">~</span>ual notation [<em>Begriffsschrift</em>], 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 5.533<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.533GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.533OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.533PM">P/M</a>]</span>, 5.534<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.534GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.534OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.534PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>-word, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span></div>
<div class="indexentry">concerned with [<em>von etwas handeln</em>: about; deal with; subject-matter], 4.011<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.011PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span></div>
<div class="indexentry">concrete, 5.5563<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span></div>
<div class="indexentry">condition, 4.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.41PM">P/M</a>]</span>, 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span>; cf. truth-<span class="mathmode">~</span>. </div>
<div class="indexentry">configuration, 2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 2.0271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0271PM">P/M</a>]</span>, 2.0272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0272PM">P/M</a>]</span>, 3.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.21PM">P/M</a>]</span></div>
<div class="indexentry">connexion</div>
<div class="indexsubentry">1. [<em>Verbindung</em>: combination], 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Zusammenhang</em>: nexus], 2.0122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0122PM">P/M</a>]</span>, 2.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.032PM">P/M</a>]</span>, 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 4.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span>, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 6.361<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.361PM">P/M</a>]</span>, 6.374<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.374GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.374OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span></div>
<div class="indexentry">consequences, 6.422<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span></div>
<div class="indexentry">conservation, cf. law.</div>
<div class="indexentry">constant, 3.312<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.312PM">P/M</a>]</span>, 3.313<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.313GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.313OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.313PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 5.522<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.522PM">P/M</a>]</span>; cf. logical <span class="mathmode">~</span>. </div>
<div class="indexentry">constituent [<em>Bestandteil</em>], 2.011<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.011PM">P/M</a>]</span>, 2.0201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 3.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.4PM">P/M</a>]</span>, 4.024<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.024PM">P/M</a>]</span>, 4.025<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.025GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.025OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.025PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.533<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.533GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.533OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.533PM">P/M</a>]</span>, 5.5423<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5423PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span></div>
<div class="indexentry">construct [<em>bilden</em>], 4.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.51PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.475<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.475GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.475OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.475PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 5.503<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.503GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.503OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.503PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>, 5.514<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span></div>
<div class="indexentry">construction</div>
<div class="indexsubentry">1. [<em>Bau</em>: build], 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 5.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.45PM">P/M</a>]</span>, 5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span>, 6.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.002PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Konstruktion</em>], 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.233<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.233PM">P/M</a>]</span>, 5.556<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.556GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.556OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.556PM">P/M</a>]</span>, 6.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.343PM">P/M</a>]</span></div>
<div class="indexentry">contain [<em>enthalten</em>], 2.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.014PM">P/M</a>]</span>, 2.203<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.203PM">P/M</a>]</span>, 3.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.02PM">P/M</a>]</span>, 3.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.332<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.332GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.332OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.332PM">P/M</a>]</span>, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 5.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.121PM">P/M</a>]</span>, 5.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.122PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span></div>
<div class="indexentry">content</div>
<div class="indexsubentry">1. [<em>Gehalt</em>], 6.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Inhalt</em>], 2.025<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.025GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.025OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.025PM">P/M</a>]</span>, 3.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span>, 3.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span></div>
<div class="indexentry">continuity, cf. law.</div>
<div class="indexentry">contradiction</div>
<div class="indexsubentry">1. [<em>Kontradiktion</em>], 4.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span>–4.4661<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span>, 5.101<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span>, 5.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.143PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span>, 6.1202<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1202PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Widerspruch</em>], 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>, 4.1211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span>, 4.211<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.211PM">P/M</a>]</span>, 5.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1241PM">P/M</a>]</span>, 6.1201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1201PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span>; cf. law of <span class="mathmode">~</span>. </div>
<div class="indexentry">convention</div>
<div class="indexsubentry">1. [<em>Abmachung</em>], 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Übereinkunft</em>], 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span></div>
<div class="indexentry">co-ordinate, 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>, 3.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.41PM">P/M</a>]</span>, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 5.64<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.64GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.64OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.64PM">P/M</a>]</span></div>
<div class="indexentry">copula, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span></div>
<div class="indexentry">correct [<em>richtig</em>], 2.17<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.17GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.17OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.17PM">P/M</a>]</span>, 2.173<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.173GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.173OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.173PM">P/M</a>]</span>, 2.18<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span>, 2.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.21PM">P/M</a>]</span>, 3.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.04PM">P/M</a>]</span>, 5.5302<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5302GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5302OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5302PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 6.2321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2321PM">P/M</a>]</span>; cf. incorrect; true. </div>
<div class="indexentry">correlate [<em>zuordnen</em>], 2.1514<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1514PM">P/M</a>]</span>, 2.1515<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1515PM">P/M</a>]</span>, 4.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.43PM">P/M</a>]</span>, 4.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.44PM">P/M</a>]</span>, 5.526<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span>, 5.542<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span></div>
<div class="indexentry">correspond [<em>entsprechen</em>], 2.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.13PM">P/M</a>]</span>, 3.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.2PM">P/M</a>]</span>, 3.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.21PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 4.0621<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.28<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.28GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.28OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.28PM">P/M</a>]</span>, 4.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 5.5542<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5542PM">P/M</a>]</span></div>
<div class="indexentry">creation, 3.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.031PM">P/M</a>]</span>, 5.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.123PM">P/M</a>]</span></div>
<div class="indexentry">critique of language, 4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span></div>
<div class="indexentry">cube, 5.5423<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5423PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">Darwin, 4.1122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1122PM">P/M</a>]</span></div>
<div class="indexentry">deal with [<em>von etwas handeln</em>: about; concerned with; subject-matter], 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span></div>
<div class="indexentry">death, 6.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.431PM">P/M</a>]</span>–6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span></div>
<div class="indexentry">deduce [<em>folgern</em>], 5.132<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.132GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.132OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.132PM">P/M</a>]</span>–5.134<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.134GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.134OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.134PM">P/M</a>]</span>; cf. infer. </div>
<div class="indexentry">definition</div>
<div class="indexsubentry">1. [<em>Definition</em>], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.26PM">P/M</a>]</span>–3.262<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.262PM">P/M</a>]</span>, 3.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.343PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.452<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span>, 5.5302<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5302GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5302OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5302PM">P/M</a>]</span>, 6.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.02PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Erklärung</em>: clear, make; explanation], 5.154<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.154GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.154OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.154PM">P/M</a>]</span></div>
<div class="indexentry">delimit [<em>begrenzen</em>: bound; limit], 5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span></div>
<div class="indexentry">depiction [<em>Abbildung</em>: form, logico-pictorial; form, pictorial; pictorial], 2.16<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.16GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.16OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.16PM">P/M</a>]</span>–2.172<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.172GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.172OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.172PM">P/M</a>]</span>, 2.18<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span>, 2.19<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.19GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.19OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.19PM">P/M</a>]</span>, 2.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p2.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.2PM">P/M</a>]</span>, 2.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.201PM">P/M</a>]</span>, 4.013<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.013PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 4.015<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.015GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.015OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.015PM">P/M</a>]</span>, 4.016<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.016GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.016OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.016PM">P/M</a>]</span>, 4.041<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.041GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.041OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.041PM">P/M</a>]</span></div>
<div class="indexentry">derive [<em>ableiten</em>], 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 6.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.127PM">P/M</a>]</span>, 6.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span>; cf. infer. </div>
<div class="indexentry">description [<em>Beschreibung</em>], 2.0201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span>, 2.02331<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.02331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.02331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02331PM">P/M</a>]</span>, 3.144<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.144GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.144OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.144PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 3.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.33PM">P/M</a>]</span>, 4.016<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.016GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.016OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.016PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.0641<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0641PM">P/M</a>]</span>, 4.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.26PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> of the world [<em>Weltb.</em>], 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>, 6.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.343PM">P/M</a>]</span>, 6.3432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3432PM">P/M</a>]</span></div>
<div class="indexentry">designate [<em>bezeichnen</em>: sign; signify], 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span></div>
<div class="indexentry">determin/ate [<em>bestimmt</em>], 2.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.031PM">P/M</a>]</span>, 2.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.032PM">P/M</a>]</span>, 2.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.14PM">P/M</a>]</span>, 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 3.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.14PM">P/M</a>]</span>, 3.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.23PM">P/M</a>]</span>, 3.251<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.251PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>; cf. indeterminateness; undetermined. </div>
<div class="indexsubentry"><span class="mathmode">~</span>e, 1.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p1.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.11PM">P/M</a>]</span>, 1.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p1.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.12PM">P/M</a>]</span>, 2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 2.05<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.05PM">P/M</a>]</span>, 3.327<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.327GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.327OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.327PM">P/M</a>]</span>, 3.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.4PM">P/M</a>]</span>, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.0641<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0641PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span></div>
<div class="indexentry">difference [<em>Verschiedenheit</em>], 2.0233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0233PM">P/M</a>]</span>, 5.135<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.135GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.135OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.135PM">P/M</a>]</span>, 5.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.53PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexentry">display [<em>aufweisen</em>], 2.172<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.172GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.172OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.172PM">P/M</a>]</span>, 4.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span>; cf. show. </div>
<div class="indexentry">dissect [<em>zerlegen</em>], 3.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.26PM">P/M</a>]</span>; cf. analysis. </div>
<div class="indexentry">doctrine [<em>Lehre</em>: theory], 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span>, 6.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.13PM">P/M</a>]</span></div>
<div class="indexentry">doubt, 6.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.51PM">P/M</a>]</span>, 6.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.521PM">P/M</a>]</span></div>
<div class="indexentry">dualism, 4.128<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.128GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.128OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span></div>
<div class="indexentry">duration, 6.4311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span></div>
<div class="indexentry">dynamical model, 4.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">effort, least, cf. law.</div>
<div class="indexentry">element, 2.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.13PM">P/M</a>]</span>–2.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.14PM">P/M</a>]</span>, 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 2.151<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.151PM">P/M</a>]</span>, 2.1514<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1514PM">P/M</a>]</span>, 2.1515<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1515PM">P/M</a>]</span>, 3.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.14PM">P/M</a>]</span>, 3.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.2PM">P/M</a>]</span>, 3.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.201PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>ary proposition [<em>Elementarsatz</em>], 4.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.21PM">P/M</a>]</span>–4.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.221PM">P/M</a>]</span>, 4.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.23PM">P/M</a>]</span>, 4.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.24PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>–4.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.26PM">P/M</a>]</span>, 4.28<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.28GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.28OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.28PM">P/M</a>]</span>–4.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.42PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.45PM">P/M</a>]</span>, 4.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span>, 4.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.51PM">P/M</a>]</span>, 4.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.52PM">P/M</a>]</span>, 5<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5PM">P/M</a>]</span>, 5.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.01PM">P/M</a>]</span>, 5.101<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span>, 5.134<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.134GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.134OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.134PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.234<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.234PM">P/M</a>]</span>, 5.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.3PM">P/M</a>]</span>–5.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.32PM">P/M</a>]</span>, 5.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.41PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5PM">P/M</a>]</span>, 5.524<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.524GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.524OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.524PM">P/M</a>]</span>, 5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.555<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span>–5.5571<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5571GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5571OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5571PM">P/M</a>]</span>, 6.001<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.001PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexentry">elucidation [<em>Erläuterung</em>], 3.263<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span>, 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span>, 6.54<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.54PM">P/M</a>]</span></div>
<div class="indexentry">empirical, 5.5561<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span></div>
<div class="indexentry">employment</div>
<div class="indexsubentry">1. [<em>Anwendung</em>: application], 3.202<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.202PM">P/M</a>]</span>, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 5.452<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Verwendung</em>: use], 3.327<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.327GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.327OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.327PM">P/M</a>]</span></div>
<div class="indexentry">enumeration, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span></div>
<div class="indexentry">equal value, of [<em>gleichwertig</em>], 6.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4PM">P/M</a>]</span></div>
<div class="indexentry">equality/, numerical [<em>Zahlengleichheit</em>], 6.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span></div>
<div class="indexsubentry">sign of <span class="mathmode">~</span> [<em>Gleichheitszeichen</em>: identity, sign for], 6.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span></div>
<div class="indexentry">equation [<em>Gleichung</em>], 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>, 6.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2PM">P/M</a>]</span>, 6.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.22PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span>, 6.2323<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2323PM">P/M</a>]</span>, 6.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2341PM">P/M</a>]</span>, 6.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.24PM">P/M</a>]</span></div>
<div class="indexentry">equivalent, cf. meaning, <span class="mathmode">~</span> n. [<em>äquivalent</em>], 5.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.232PM">P/M</a>]</span>, 5.2523<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2523GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2523OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2523PM">P/M</a>]</span>, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span>, 5.514<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span>, 6.1261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1261PM">P/M</a>]</span></div>
<div class="indexentry">essence [<em>Wesen</em>], 2.011<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.011PM">P/M</a>]</span>, 3.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span>, 3.1431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span>, 3.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span>, 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 3.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.34PM">P/M</a>]</span>–3.3421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3421PM">P/M</a>]</span>, 4.013<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.013PM">P/M</a>]</span>, 4.016<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.016GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.016OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.016PM">P/M</a>]</span>, 4.027<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.027GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.027OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.027PM">P/M</a>]</span>, 4.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span>, 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span>, 4.1121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span>, 4.465<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.465GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.465OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.465PM">P/M</a>]</span>, 4.4661<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.3PM">P/M</a>]</span>, 5.471<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.471GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.471OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.471PM">P/M</a>]</span>, 5.4711<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4711GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4711OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4711PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 5.533<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.533GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.533OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.533PM">P/M</a>]</span>, 6.1232<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.127PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span>, 6.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2341PM">P/M</a>]</span></div>
<div class="indexentry">eternity, 6.4311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span>, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span>; cf. <em>sub specie aeterni</em>. </div>
<div class="indexentry">ethics, 6.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.42PM">P/M</a>]</span>–6.423<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.423PM">P/M</a>]</span></div>
<div class="indexentry">everyday language [<em>Umgangssprache</em>], 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 5.5563<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span></div>
<div class="indexentry">existence</div>
<div class="indexsubentry">1. [<em>Bestehen</em>: hold; subsist], 2<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2PM">P/M</a>]</span>, 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 2.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.04PM">P/M</a>]</span>–2.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.06PM">P/M</a>]</span>, 2.062<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.062GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.062OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.062PM">P/M</a>]</span>, 2.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.11PM">P/M</a>]</span>, 2.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.201PM">P/M</a>]</span>, 4.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span>, 4.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span>, 4.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2PM">P/M</a>]</span>, 4.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.21PM">P/M</a>]</span>, 4.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.25PM">P/M</a>]</span>, 4.27<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.27GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.27OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.27PM">P/M</a>]</span>, 4.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.3PM">P/M</a>]</span>, 5.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span>, 5.135<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.135GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.135OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.135PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Existenz</em>], 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 3.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.4PM">P/M</a>]</span>, 3.411<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.411PM">P/M</a>]</span>, 4.1274<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1274OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span></div>
<div class="indexentry">experience [<em>Erfahrung</em>], 5.552<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.552GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.552OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.552PM">P/M</a>]</span>, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span>, 5.634<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.634GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.634OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.634PM">P/M</a>]</span>, 6.1222<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1222PM">P/M</a>]</span>, 6.363<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.363PM">P/M</a>]</span></div>
<div class="indexentry">explanation [<em>Erklärung</em>: clear, make; definition], 3.263<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span>, 4.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.02PM">P/M</a>]</span>, 4.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span>, 4.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span>, 6.371<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.371GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.371OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.371PM">P/M</a>]</span>, 6.372<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.372GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.372OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.372PM">P/M</a>]</span></div>
<div class="indexentry">exponent, 6.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.021PM">P/M</a>]</span></div>
<div class="indexentry">expression [<em>Ausdruck</em>: say], P3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref3PM">P/M</a>]</span>, 3.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1PM">P/M</a>]</span>, 3.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.12PM">P/M</a>]</span>, 3.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span>, 3.142<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.142PM">P/M</a>]</span>, 3.1431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span>, 3.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.2PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.251<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.251PM">P/M</a>]</span>, 3.262<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.262PM">P/M</a>]</span>, 3.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span>–3.314<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.314GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.314OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.314PM">P/M</a>]</span>, 3.318<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.318GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.318OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.318PM">P/M</a>]</span>, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 3.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.33PM">P/M</a>]</span>, 3.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.34PM">P/M</a>]</span>, 3.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.341PM">P/M</a>]</span>, 3.3441<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span>, 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 4.013<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.013PM">P/M</a>]</span>, 4.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span>, 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 4.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span>, 4.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span>, 4.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>, 4.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4PM">P/M</a>]</span>, 4.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.43PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span>, 5.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.22PM">P/M</a>]</span>, 5.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span>, 5.242<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.242GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.242OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.242PM">P/M</a>]</span>, 5.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.31PM">P/M</a>]</span>, 5.476<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.476GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.476OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.476PM">P/M</a>]</span>, 5.503<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.503GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.503OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.503PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span>, 5.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.53PM">P/M</a>]</span>, 5.5301<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5301OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 5.5352<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5352GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5352OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5352PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.1264<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1264GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1264OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1264PM">P/M</a>]</span>, 6.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.21PM">P/M</a>]</span>, 6.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span>–6.2323<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2323PM">P/M</a>]</span>, 6.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.24PM">P/M</a>]</span></div>
<div class="indexsubentry">mode of <span class="mathmode">~</span> [<em>Ausdrucksweise</em>], 4.015<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.015GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.015OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.015PM">P/M</a>]</span>, 5.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.21PM">P/M</a>]</span>, 5.526<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span></div>
<div class="indexentry">external, 2.01231<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.01231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01231PM">P/M</a>]</span>, 2.0233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0233PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.1251<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1251PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">fact [<em>Tatsache</em>], 1.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p1.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.1PM">P/M</a>]</span>–1.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p1.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.2PM">P/M</a>]</span>, 2<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2PM">P/M</a>]</span>, 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 2.034<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.034GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.034OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.034PM">P/M</a>]</span>, 2.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.06PM">P/M</a>]</span>, 2.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p2.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1PM">P/M</a>]</span>, 2.141<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.141PM">P/M</a>]</span>, 2.16<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.16GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.16OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.16PM">P/M</a>]</span>, 3<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3PM">P/M</a>]</span>, 3.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.14PM">P/M</a>]</span>, 3.142<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.142PM">P/M</a>]</span>, 3.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span>, 4.016<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.016GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.016OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.016PM">P/M</a>]</span>, 4.0312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span>, 4.061<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.061PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.1221<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1221PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.2211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 5.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span>, 5.542<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span>, 5.5423<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5423PM">P/M</a>]</span>, 6.2321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2321PM">P/M</a>]</span>, 6.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.43PM">P/M</a>]</span>, 6.4321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4321PM">P/M</a>]</span>; cf. negative <span class="mathmode">~</span>. </div>
<div class="indexentry">fairy tale, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span></div>
<div class="indexentry">false [<em>falsch</em>: incorrect], 2.0212<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0212GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0212OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0212PM">P/M</a>]</span>, 2.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.21PM">P/M</a>]</span>, 2.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.22PM">P/M</a>]</span>, 2.222<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.222PM">P/M</a>]</span>–2.224<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.224GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.224OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.224PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.06PM">P/M</a>]</span>–4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.25PM">P/M</a>]</span>, 4.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.26PM">P/M</a>]</span>, 4.28<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.28GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.28OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.28PM">P/M</a>]</span>, 4.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.31PM">P/M</a>]</span>, 4.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.41PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>, 5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>, 6.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span>, 6.113<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.113GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.113OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.113PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span>; cf. wrong. </div>
<div class="indexentry">fate, 6.372<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.372GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.372OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.372PM">P/M</a>]</span>, 6.374<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.374GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.374OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span></div>
<div class="indexentry">feature [<em>Zug</em>], 3.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.34PM">P/M</a>]</span>, 4.1221<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1221PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span></div>
<div class="indexentry">feeling, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 6.1232<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span>, 6.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.45PM">P/M</a>]</span></div>
<div class="indexentry">finite, 5.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.32PM">P/M</a>]</span></div>
<div class="indexentry">follow, 4.1211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span>, 4.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.52PM">P/M</a>]</span>, 5.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.11PM">P/M</a>]</span>–5.132<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.132GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.132OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.132PM">P/M</a>]</span>, 5.1363<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1363PM">P/M</a>]</span>–5.142<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.142PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span>, 6.1201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1201PM">P/M</a>]</span>, 6.1221<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1221PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span></div>
<div class="indexentry">foresee, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.556<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.556GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.556OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.556PM">P/M</a>]</span></div>
<div class="indexentry">form [<em>Form</em>], 2.0122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0122PM">P/M</a>]</span>, 2.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0141PM">P/M</a>]</span>, 2.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.022PM">P/M</a>]</span>–2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 2.025<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.025GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.025OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.025PM">P/M</a>]</span>–2.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.026PM">P/M</a>]</span>, 2.033<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.033GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.033OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.033PM">P/M</a>]</span>, 2.18<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span>, 3.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span>, 3.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span>, 3.312<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.312PM">P/M</a>]</span>, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span>, 4.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.012PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1241PM">P/M</a>]</span>, 4.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>, 4.242<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.242GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.242OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.242PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 5.231<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.231PM">P/M</a>]</span>, 5.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span>, 5.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.241PM">P/M</a>]</span>, 5.2522<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2522PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>, 5.542<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.554<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.554GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.554OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.554PM">P/M</a>]</span>, 5.5542<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5542PM">P/M</a>]</span>, 5.555<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span>, 5.556<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.556GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.556OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.556PM">P/M</a>]</span>, 5.6331<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.6331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.6331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6331PM">P/M</a>]</span>, 6<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6PM">P/M</a>]</span>, 6.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.002PM">P/M</a>]</span>, 6.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.01PM">P/M</a>]</span>, 6.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span>, 6.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.03PM">P/M</a>]</span>, 6.1201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1201PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span>, 6.1224<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1224GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1224OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1224PM">P/M</a>]</span>, 6.1264<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1264GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1264OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1264PM">P/M</a>]</span>, 6.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.32PM">P/M</a>]</span>, 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span>–6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span>, 6.422<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span>; cf. <span class="mathmode">~</span>al; general <span class="mathmode">~</span>; propositional <span class="mathmode">~</span>; series of <span class="mathmode">~</span>s. </div>
<div class="indexsubentry">logical <span class="mathmode">~</span>, 2.0233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0233PM">P/M</a>]</span>, 2.18<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span>, 2.181<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.181GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.181OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.181PM">P/M</a>]</span>, 2.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p2.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.2PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 3.327<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.327GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.327OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.327PM">P/M</a>]</span>, 4.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12PM">P/M</a>]</span>, 4.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span>, 4.128<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.128GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.128OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span>, 5.555<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span>, 6.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span>, 6.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.33PM">P/M</a>]</span></div>
<div class="indexsubentry">logico-pictorial <span class="mathmode">~</span> [<em>logische Form der Abbildung</em>], 2.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p2.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.2PM">P/M</a>]</span></div>
<div class="indexsubentry">pictorial <span class="mathmode">~</span> [<em>Form der Abbildung</em>: depiction; pictorial], 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 2.151<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.151PM">P/M</a>]</span>, 2.17<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.17GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.17OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.17PM">P/M</a>]</span>, 2.172<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.172GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.172OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.172PM">P/M</a>]</span>, 2.181<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.181GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.181OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.181PM">P/M</a>]</span>, 2.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.22PM">P/M</a>]</span></div>
<div class="indexsubentry">representational <span class="mathmode">~</span> [<em>Form der Darstellung</em>: present; represent], 2.173<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.173GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.173OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.173PM">P/M</a>]</span>, 2.174<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.174GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.174OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.174PM">P/M</a>]</span></div>
<div class="indexentry">formal [<em>formal</em>], 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> concept, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>–4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> property, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span>, 5.231<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.231PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>, 6.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.122PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> relation [<em>Relation</em>], 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 5.242<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.242GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.242OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.242PM">P/M</a>]</span></div>
<div class="indexentry">formulate [<em>angeben</em>: give; say], 5.5563<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span></div>
<div class="indexentry">free will, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span></div>
<div class="indexentry">Frege, P6<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref6PM">P/M</a>]</span>, 3.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span>, 3.318<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.318GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.318OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.318PM">P/M</a>]</span>, 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.132<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.132GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.132OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.132PM">P/M</a>]</span>, 5.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span>, 6.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span></div>
<div class="indexentry">fully [<em>vollkommen</em>: complete], <span class="mathmode">~</span> generalized, 5.526<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span>, 5.5261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span></div>
<div class="indexentry">function [<em>Funktion</em>], 3.318<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.318GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.318OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.318PM">P/M</a>]</span>, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.12721<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p4.12721GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12721OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12721PM">P/M</a>]</span>, 4.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.24PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2341PM">P/M</a>]</span>, 5.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.25PM">P/M</a>]</span>, 5.251<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.251PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 5.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.52PM">P/M</a>]</span>, 5.5301<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5301OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span>; cf. truth-<span class="mathmode">~</span>. </div>
<div class="indexentry"><em>Fundamental Laws of Arithmetic</em> [<em>Grundgesetze der Arithmetik</em>], 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>; cf. primitive proposition. </div>
<div class="indexentry">future, 5.1361<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1361PM">P/M</a>]</span>, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">general [<em>allgemein</em>], 3.3441<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span>, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span>, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 4.411<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.411PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 5.242<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.242GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.242OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.242PM">P/M</a>]</span>, 5.2522<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2522PM">P/M</a>]</span>, 5.454<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.454GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.454OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.454PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>, 5.472<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.472GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.472OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.472PM">P/M</a>]</span>, 5.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span>, 5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span>, 6.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.031PM">P/M</a>]</span>, 6.1231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1231PM">P/M</a>]</span>, 6.3432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3432PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> form, 3.312<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.312PM">P/M</a>]</span>, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 4.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.53PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.471<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.471GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.471OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.471PM">P/M</a>]</span>, 5.472<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.472GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.472OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.472PM">P/M</a>]</span>, 5.54<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.54PM">P/M</a>]</span>, 6<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6PM">P/M</a>]</span>, 6.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.002PM">P/M</a>]</span>, 6.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.01PM">P/M</a>]</span>, 6.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span>, 6.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.03PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>-ity-sign, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 5.522<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.522PM">P/M</a>]</span>, 5.523<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.523GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.523OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.523PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> validity, 6.1231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1231PM">P/M</a>]</span>, 6.1232<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span></div>
<div class="indexentry">generalization [<em>verallgemeinerung</em>], 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 4.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.52PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 5.526<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span>, 5.5261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span>, 6.1231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1231PM">P/M</a>]</span>; cf. fully. </div>
<div class="indexentry">geometry, 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>, 3.0321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.0321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.0321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.0321PM">P/M</a>]</span>, 3.411<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.411PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span></div>
<div class="indexentry">give [<em>angeben</em>: formulate; say], 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.4711<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4711GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4711OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4711PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.554<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.554GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.554OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.554PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span></div>
<div class="indexentry">given [<em>gegeben</em>], 2.0124<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0124PM">P/M</a>]</span>, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.12721<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p4.12721GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12721OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12721PM">P/M</a>]</span>, 4.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.51PM">P/M</a>]</span>, 5.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.442PM">P/M</a>]</span>, 5.524<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.524GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.524OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.524PM">P/M</a>]</span>, 6.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.002PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="indexentry">God, 3.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.031PM">P/M</a>]</span>, 5.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.123PM">P/M</a>]</span>, 6.372<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.372GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.372OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.372PM">P/M</a>]</span>, 6.432<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.432PM">P/M</a>]</span></div>
<div class="indexentry">good, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 6.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.43PM">P/M</a>]</span></div>
<div class="indexentry">grammar, cf. logical.</div>
</div>
<div class="indexletterblock">
<div class="indexentry">happy, 6.374<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.374GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.374OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span></div>
<div class="indexentry">Hertz, 4.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span>, 6.361<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.361PM">P/M</a>]</span></div>
<div class="indexentry">hierarchy, 5.252<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span>, 5.556<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.556GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.556OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.556PM">P/M</a>]</span>, 5.5561<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span></div>
<div class="indexentry">hieroglyphic script, 4.016<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.016GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.016OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.016PM">P/M</a>]</span></div>
<div class="indexentry">higher, 6.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.42PM">P/M</a>]</span>, 6.432<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.432PM">P/M</a>]</span></div>
<div class="indexentry">hold [<em>bestehen</em>: existence; subsist], 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span></div>
<div class="indexentry">how [<em>wie</em>], 6.432<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.432PM">P/M</a>]</span>, 6.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.44PM">P/M</a>]</span>; cf. stand, <span class="mathmode">~</span> things. </div>
<div class="indexsubentry"><span class="mathmode">~</span>) (what, 3.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span>, 5.552<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.552GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.552OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.552PM">P/M</a>]</span></div>
<div class="indexentry">hypothesis, 4.1122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1122PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>, 6.36311<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p6.36311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36311PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">idea, cf. primitive <span class="mathmode">~</span>.</div>
<div class="indexsubentry">1. [<em>Gedanke</em>: thought], musical <span class="mathmode">~</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Vorstellung</em>: present; represent], 5.631<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span></div>
<div class="indexentry">idealist, 4.0412<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0412GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0412OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0412PM">P/M</a>]</span></div>
<div class="indexentry">identical [<em>identisch</em>], 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.5303<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5303GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5303OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5303PM">P/M</a>]</span>, 5.5352<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5352GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5352OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5352PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span>; cf. difference. </div>
<div class="indexentry">identity [<em>Gleichheit</em>], 5.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.53PM">P/M</a>]</span></div>
<div class="indexsubentry">sign for <span class="mathmode">~</span> [<em>Gleichheitszeiche</em>n: equality, sign of], 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.53PM">P/M</a>]</span>, 5.5301<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5301OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span>, 5.533<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.533GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.533OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.533PM">P/M</a>]</span>; cf. equation. </div>
<div class="indexentry">illogical [<em>unlogisch</em>], 3.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.03PM">P/M</a>]</span>, 3.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.031PM">P/M</a>]</span>, 5.4731<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4731OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span></div>
<div class="indexentry">imagine [<em>sich etwas denken</em>: think], 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 2.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.022PM">P/M</a>]</span>, 4.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.01PM">P/M</a>]</span>, 6.1233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1233PM">P/M</a>]</span></div>
<div class="indexentry">immortality, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span></div>
<div class="indexentry">impossibility [<em>Unmöglichkeit</em>], 4.464<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.464GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.464OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.464PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span>, 6.375<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.375GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.375OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.375PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexentry">incorrect</div>
<div class="indexsubentry">1. [<em>falsch</em>: false], 2.17<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.17GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.17OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.17PM">P/M</a>]</span>, 2.173<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.173GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.173OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.173PM">P/M</a>]</span>, 2.18<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>unrichtig</em>], 2.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.21PM">P/M</a>]</span></div>
<div class="indexentry">independence [<em>Selbständigkeit</em>], 2.0122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0122PM">P/M</a>]</span>, 3.261<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span></div>
<div class="indexentry">independent [<em>unabhängig</em>], 2.024<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.024PM">P/M</a>]</span>, 2.061<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.061PM">P/M</a>]</span>, 2.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.22PM">P/M</a>]</span>, 4.061<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.061PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.154<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.154GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.154OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.154PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.5261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span>, 5.5561<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span>, 6.373<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.373GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.373OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.373PM">P/M</a>]</span></div>
<div class="indexentry">indeterminateness [<em>Unbestimmtheit</em>], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span></div>
<div class="indexentry">indicate</div>
<div class="indexsubentry">1. [<em>anzeigen</em>], 3.322<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span>, 6.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>auf etwas zeigen</em>: manifest; show], 2.02331<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.02331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.02331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02331PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span></div>
<div class="indexentry">individuals, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span></div>
<div class="indexentry">induction, 6.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.31PM">P/M</a>]</span>, 6.363<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.363PM">P/M</a>]</span></div>
<div class="indexentry">infer [<em>schließen</em>], 2.062<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.062GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.062OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.062PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span>, 5.132<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.132GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.132OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.132PM">P/M</a>]</span>, 5.135<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.135GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.135OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.135PM">P/M</a>]</span>, 5.1361<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1361PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.633<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.633GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.633OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.633PM">P/M</a>]</span>, 6.1224<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1224GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1224OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1224PM">P/M</a>]</span>, 6.211<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.211PM">P/M</a>]</span>; cf. deduce; derive. </div>
<div class="indexentry">infinite, 2.0131<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span>, 4.2211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>, 5.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 6.4311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span></div>
<div class="indexentry">infinity, cf. axiom.</div>
<div class="indexentry">inner, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span>, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span></div>
<div class="indexentry">internal, 2.01231<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.01231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01231PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>–4.1252<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span>, 5.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span>, 5.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2PM">P/M</a>]</span>, 5.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.21PM">P/M</a>]</span>, 5.231<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.231PM">P/M</a>]</span>, 5.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.232PM">P/M</a>]</span></div>
<div class="indexentry">intuition [<em>Anschauung</em>], 6.233<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.233PM">P/M</a>]</span>, 6.2331<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2331PM">P/M</a>]</span></div>
<div class="indexentry">intuitive [<em>anschaulich</em>], 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">judgement [<em>Urteil</em>], 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>-stroke [<em>Urteilstrich</em>], 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span></div>
<div class="indexentry">Julius Caesar, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">Kant, 6.36111<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p6.36111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36111PM">P/M</a>]</span></div>
<div class="indexentry">know</div>
<div class="indexsubentry">1. [<em>kennen</em>], 2.0123<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0123PM">P/M</a>]</span>, 2.01231<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.01231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01231PM">P/M</a>]</span>, 3.263<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span>, 4.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 6.2322<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2322PM">P/M</a>]</span>; cf. theory of knowledge. </div>
<div class="indexsubentry">2. [<em>wissen</em>], 3.05<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.05PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 4.024<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.024PM">P/M</a>]</span>, 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 5.5562<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5562GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5562OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5562PM">P/M</a>]</span> <span class="kckaddition">[—the previous entry was mistakenly listed as 5.562 in Pears and McGuinness’s original index—]</span>, 6.3211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3211PM">P/M</a>]</span>, 6.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.33PM">P/M</a>]</span>, 6.36311<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p6.36311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36311PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">language [<em>Sprache</em>], P2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span>, P4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref4PM">P/M</a>]</span>, 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>, 3.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.343PM">P/M</a>]</span>, 4.001<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.001PM">P/M</a>]</span>–4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span>, 4.025<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.025GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.025OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.025PM">P/M</a>]</span>, 4.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span>, 4.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span>, 5.4731<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4731OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 5.6<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>, 6.233<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.233PM">P/M</a>]</span>, 6.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.43PM">P/M</a>]</span>; cf. critique of <span class="mathmode">~</span>; everyday <span class="mathmode">~</span>; sign-<span class="mathmode">~</span>. </div>
<div class="indexentry">law</div>
<div class="indexsubentry">1. [<em>Gesetz</em>: minimum-principle; primitive proposition], 3.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.031PM">P/M</a>]</span>, 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>, 3.0321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.0321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.0321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.0321PM">P/M</a>]</span>, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 6.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.123PM">P/M</a>]</span>, 6.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3PM">P/M</a>]</span>–6.3211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3211PM">P/M</a>]</span>, 6.3431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3431PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span>, 6.361<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.361PM">P/M</a>]</span>, 6.363<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.363PM">P/M</a>]</span>, 6.422<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of causality [<em>Kausalitätsg.</em>], 6.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.32PM">P/M</a>]</span>, 6.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of conservation [<em>Erhaltungsg.</em>], 6.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.33PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of contradiction [<em>G. des Widerspruchs</em>], 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span>, 6.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.123PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of least action [<em>G. der kleinsten Wirkung</em>], 6.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span>, 6.3211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3211PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of nature [<em>Naturg.</em>], 5.154<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.154GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.154OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.154PM">P/M</a>]</span>, 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span>, 6.36<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.36GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36PM">P/M</a>]</span>, 6.371<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.371GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.371OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.371PM">P/M</a>]</span>, 6.372<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.372GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.372OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.372PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Satz</em>: principle of sufficient reason; proposition], 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of continuity [<em>S. von der Kontinuität</em>], 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of least effort [<em>S. von kleinsten Aufwande</em>], 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span></div>
<div class="indexentry">life, 5.621<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.621PM">P/M</a>]</span>, 6.4311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span>, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span>, 6.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.52PM">P/M</a>]</span>, 6.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.521PM">P/M</a>]</span></div>
<div class="indexentry">limit [<em>Grenze</em>: bound; delimit], P3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref3PM">P/M</a>]</span>, P4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref4PM">P/M</a>]</span>, 4.113<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.113GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.113OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.113PM">P/M</a>]</span>, 4.114<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.114GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.114OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.114PM">P/M</a>]</span>, 4.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.51PM">P/M</a>]</span>, 5.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.143PM">P/M</a>]</span>, 5.5561<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span>, 5.6<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6PM">P/M</a>]</span>–5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 5.632<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.632GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.632OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.632PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>, 6.4311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span>, 6.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.45PM">P/M</a>]</span></div>
<div class="indexentry">logic; <span class="mathmode">~</span>al, 2.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.012PM">P/M</a>]</span>, 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 3.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.031PM">P/M</a>]</span>, 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 3.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.41PM">P/M</a>]</span>, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 4.015<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.015GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.015OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.015PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.0312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span>, 4.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.032PM">P/M</a>]</span>, 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span>, 4.1121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span>, 4.1213<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1213GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1213OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1213PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.128<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.128GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.128OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.233<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.233PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span>, 5.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.45PM">P/M</a>]</span>–5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.472<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.472GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.472OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.472PM">P/M</a>]</span>–5.4731<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4731OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span>, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span>, 5.522<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.522PM">P/M</a>]</span>, 5.551<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.551GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.551OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.551PM">P/M</a>]</span>–5.5521<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5521PM">P/M</a>]</span>, 5.555<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span>, 5.5562<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5562GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5562OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5562PM">P/M</a>]</span>–5.557<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.557GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.557OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.557PM">P/M</a>]</span>, 5.61<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.61GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.61OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.61PM">P/M</a>]</span>, 6.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1PM">P/M</a>]</span>–6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>, 6.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span>, 6.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.122PM">P/M</a>]</span>, 6.1222<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1222PM">P/M</a>]</span>–6.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2PM">P/M</a>]</span>, 6.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.22PM">P/M</a>]</span>, 6.234<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.234PM">P/M</a>]</span>, 6.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3PM">P/M</a>]</span>, 6.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.31PM">P/M</a>]</span>, 6.3211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3211PM">P/M</a>]</span>, 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span>, 6.3431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3431PM">P/M</a>]</span>, 6.3631<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3631PM">P/M</a>]</span>, 6.37<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.37GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.37OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.37PM">P/M</a>]</span>, 6.374<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.374GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.374OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span>–6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span>; cf. form, <span class="mathmode">~</span>al; illogical. </div>
<div class="indexsubentry"><span class="mathmode">~</span>al addition, 5.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2341PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al constant, 4.0312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span>, 5.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span>, 5.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.441PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al grammar, 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al multiplication, 5.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2341PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al object, 4.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span>, 5.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al picture, 2.18<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span>–2.19<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.19GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.19OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.19PM">P/M</a>]</span>, 3<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3PM">P/M</a>]</span>, 4.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al place, 3.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.41PM">P/M</a>]</span>–3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.0641<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0641PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al product, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.465<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.465GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.465OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.465PM">P/M</a>]</span>, 5.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span>, 6.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al space, 1.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p1.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.13PM">P/M</a>]</span>, 2.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.11PM">P/M</a>]</span>, 2.202<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.202PM">P/M</a>]</span>, 3.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.4PM">P/M</a>]</span>, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al sum, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 5.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al syntax, 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>, 3.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.33PM">P/M</a>]</span>, 3.334<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.334GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.334OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.334PM">P/M</a>]</span>, 3.344<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.344GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.344OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.344PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>o-pictorial, cf. form.</div>
<div class="indexsubentry"><span class="mathmode">~</span>o-syntactical, 3.327<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.327GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.327OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.327PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">manifest [<em>sich zeigen</em>: indicate; show], 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 5.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span>, 5.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span>, 5.513<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span>, 5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span>, 5.5561<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 6.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span>, 6.36<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.36GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36PM">P/M</a>]</span>, 6.522<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.522PM">P/M</a>]</span></div>
<div class="indexentry">material, 2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span></div>
<div class="indexentry">mathematics, 4.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span>–4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 5.154<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.154GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.154OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.154PM">P/M</a>]</span>, 5.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span>, 5.475<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.475GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.475OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.475PM">P/M</a>]</span>, 6.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.031PM">P/M</a>]</span>, 6.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2PM">P/M</a>]</span>–6.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.22PM">P/M</a>]</span>, 6.2321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2321PM">P/M</a>]</span>, 6.233<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.233PM">P/M</a>]</span>, 6.234<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.234PM">P/M</a>]</span>–6.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.24PM">P/M</a>]</span></div>
<div class="indexentry">Mauthner, 4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span></div>
<div class="indexentry">mean [<em>meinen</em>], 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 4.062<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.062GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.062OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.062PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span></div>
<div class="indexentry">meaning [<em>Bedeutung</em>: signify], 3.203<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.203PM">P/M</a>]</span>, 3.261<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span>, 3.263<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span>, 3.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3PM">P/M</a>]</span>, 3.314<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.314GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.314OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.314PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 3.328<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.328GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.328OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.328PM">P/M</a>]</span>–3.331<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.331PM">P/M</a>]</span>, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 4.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>–4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.31PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span>, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.6<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span>, 6.2322<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2322PM">P/M</a>]</span>, 6.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span></div>
<div class="indexsubentry">equivalent in <span class="mathmode">~</span> [<em>Bedeutungsgleichheit</em>], 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 6.2323<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2323PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>ful [<em>bedeutungsvoll</em>], 5.233<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.233PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>less [<em>bedeutungslos</em>], 3.328<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.328GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.328OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.328PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 4.4661<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span>, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span></div>
<div class="indexentry">mechanics, 4.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span>, 6.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span>, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>–6.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.343PM">P/M</a>]</span>, 6.3432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3432PM">P/M</a>]</span></div>
<div class="indexentry">mention [<em>von etwas reden</em>: talk about], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.33PM">P/M</a>]</span>, 4.1211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span>, 5.631<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span>, 6.3432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3432PM">P/M</a>]</span>; cf. about. </div>
<div class="indexentry">metaphysical, 5.633<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.633GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.633OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.633PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>, 6.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span></div>
<div class="indexentry">method, 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span>, 4.1121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span>, 6.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span>, 6.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2PM">P/M</a>]</span>, 6.234<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.234PM">P/M</a>]</span>–6.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.24PM">P/M</a>]</span>, 6.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span>; cf. projection, <span class="mathmode">~</span> of; zero-<span class="mathmode">~</span>. </div>
<div class="indexentry">microcosm, 5.63<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.63GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.63OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.63PM">P/M</a>]</span></div>
<div class="indexentry">minimum-principle [<em>Minimum-Gesetz</em>: law], 6.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span></div>
<div class="indexentry">mirror, 4.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span>, 5.511<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.511GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.511OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.511PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>, 5.514<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span>, 6.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.13PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>-image [<em>Spiegelbild</em>: picture], 6.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.13PM">P/M</a>]</span></div>
<div class="indexentry">misunderstanding, P2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span></div>
<div class="indexentry">mode, cf. expression; signification.</div>
<div class="indexentry">model, 2.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.12PM">P/M</a>]</span>, 4.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.01PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>; cf. dynamical <span class="mathmode">~</span>. </div>
<div class="indexentry"><em>modus ponens</em>, 6.1264<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1264GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1264OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1264PM">P/M</a>]</span></div>
<div class="indexentry">monism, 4.128<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.128GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.128OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span></div>
<div class="indexentry">Moore, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span></div>
<div class="indexentry">multiplicity, 4.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span>–4.0412<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0412GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0412OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0412PM">P/M</a>]</span>, 5.475<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.475GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.475OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.475PM">P/M</a>]</span></div>
<div class="indexentry">music, 3.141<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.141PM">P/M</a>]</span>, 4.011<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.011PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span></div>
<div class="indexentry">mystical, 6.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.44PM">P/M</a>]</span>, 6.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.45PM">P/M</a>]</span>, 6.522<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.522PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">name</div>
<div class="indexsubentry">1. [<em>Name</em>], 3.142<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.142PM">P/M</a>]</span>, 3.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span>, 3.144<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.144GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.144OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.144PM">P/M</a>]</span>, 3.202<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.202PM">P/M</a>]</span>, 3.203<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.203PM">P/M</a>]</span>, 3.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.22PM">P/M</a>]</span>, 3.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.26PM">P/M</a>]</span>, 3.261<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span>, 3.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3PM">P/M</a>]</span>, 3.314<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.314GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.314OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.314PM">P/M</a>]</span>, 3.3411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3411PM">P/M</a>]</span>, 4.0311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.22PM">P/M</a>]</span>, 4.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.221PM">P/M</a>]</span>, 4.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.23PM">P/M</a>]</span>, 4.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.24PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.526<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>; cf. variable <span class="mathmode">~</span>. </div>
<div class="indexsubsubentry">general <span class="mathmode">~</span> [<em>Gattungsn.</em>], 6.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span></div>
<div class="indexsubsubentry">proper <span class="mathmode">~</span> of a person [<em>Personenn.</em>], 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>benennen</em>; <em>nennen</em>], 3.144<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.144GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.144OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.144PM">P/M</a>]</span>, 3.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span></div>
<div class="indexentry">natur/e, 2.0123<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0123PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>; cf. law of <span class="mathmode">~</span>e. </div>
<div class="indexsubsubentry"><span class="mathmode">~</span>al phenomena, 6.371<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.371GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.371OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.371PM">P/M</a>]</span></div>
<div class="indexsubsubentry"><span class="mathmode">~</span>al science, 4.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.11PM">P/M</a>]</span>, 4.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.111PM">P/M</a>]</span>, 4.1121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span>–4.113<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.113GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.113OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.113PM">P/M</a>]</span>, 6.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span>, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span>, 6.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span></div>
<div class="indexentry">necessary, 4.041<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.041GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.041OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.041PM">P/M</a>]</span>, 5.452<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span>, 5.474<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.474GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.474OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.474PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>; cf. unnecessary. </div>
<div class="indexentry">negation</div>
<div class="indexsubentry">1. [<em>Negation</em>], 5.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5PM">P/M</a>]</span>, 5.502<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.502GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.502OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.502PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Verneinung</em>], 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.0621<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span>, 4.064<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.064GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.064OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.064PM">P/M</a>]</span>, 4.0641<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0641PM">P/M</a>]</span>, 5.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1241PM">P/M</a>]</span>, 5.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2341PM">P/M</a>]</span>, 5.254<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.254GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.254OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.254PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>, 5.514<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span>, 6.231<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.231PM">P/M</a>]</span></div>
<div class="indexentry">negative [<em>negativ</em>], 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>, 5.513<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> fact, 2.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.06PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span></div>
<div class="indexentry">network, 5.511<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.511GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.511OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.511PM">P/M</a>]</span>, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>, 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span></div>
<div class="indexentry">Newton, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>, 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span></div>
<div class="indexentry">nexus</div>
<div class="indexsubentry">1. [<em>Nexus</em>], 5.136<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.136GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.136OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.136PM">P/M</a>]</span>, 5.1361<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1361PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Zusammenhang</em>: connexion], 3.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3PM">P/M</a>]</span>, 4.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.22PM">P/M</a>]</span>, 4.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.23PM">P/M</a>]</span></div>
<div class="indexentry">non-proposition, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span></div>
<div class="indexentry">nonsense [<em>Unsinn</em>], P4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref4PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 4.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.1274<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1274OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span>, 4.4611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4611PM">P/M</a>]</span>, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.5303<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5303GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5303OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5303PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span>, 5.5571<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5571GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5571OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5571PM">P/M</a>]</span>, 6.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.51PM">P/M</a>]</span>, 6.54<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.54PM">P/M</a>]</span>; cf. sense, have no. </div>
<div class="indexentry">notation, 3.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.342PM">P/M</a>]</span>, 3.3441<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span>, 5.474<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.474GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.474OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.474PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>–5.514<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span>, 6.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.122PM">P/M</a>]</span>, 6.1223<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1223GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1223OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1223PM">P/M</a>]</span>; cf. conceptual <span class="mathmode">~</span>. </div>
<div class="indexentry">number</div>
<div class="indexsubentry">1. [<em>Anzahl</em>], 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 5.474<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.474GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.474OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.474PM">P/M</a>]</span>–5.476<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.476GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.476OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.476PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span>, 6.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Zahl</em>: integer], 4.1252<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.12721<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p4.12721GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12721OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12721PM">P/M</a>]</span>, 4.128<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.128GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.128OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span>, 5.453<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.453GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.453OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.453PM">P/M</a>]</span>, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span>, 6.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.02PM">P/M</a>]</span>, 6.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span>; cf. equality, numerical; privileged <span class="mathmode">~</span>s; series of <span class="mathmode">~</span>s; variable <span class="mathmode">~</span>. </div>
<div class="indexsubsubentry">cardinal <span class="mathmode">~</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span>-system, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">object [<em>Gegenstand</em>], 2.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01PM">P/M</a>]</span>, 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 2.0123<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0123PM">P/M</a>]</span>–2.0124<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0124PM">P/M</a>]</span>, 2.0131<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span>–2.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02PM">P/M</a>]</span>, 2.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.021PM">P/M</a>]</span>, 2.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.023PM">P/M</a>]</span>–2.0233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0233PM">P/M</a>]</span>, 2.0251<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0251PM">P/M</a>]</span>–2.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.032PM">P/M</a>]</span>, 2.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.13PM">P/M</a>]</span>, 2.15121<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.15121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15121PM">P/M</a>]</span>, 3.1431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span>, 3.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.2PM">P/M</a>]</span>, 3.203<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.203PM">P/M</a>]</span>–3.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span>, 3.322<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span>, 3.3411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3411PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.0312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span>, 4.1211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.123PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.127PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.12721<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p4.12721GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12721OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12721PM">P/M</a>]</span>, 4.2211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.123PM">P/M</a>]</span>, 5.1511<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1511GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1511OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1511PM">P/M</a>]</span>, 5.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 5.524<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.524GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.524OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.524PM">P/M</a>]</span>, 5.526<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span>, 5.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.53PM">P/M</a>]</span>–5.5302<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5302GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5302OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5302PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>, 5.542<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span>, 5.5561<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span>, 6.3431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3431PM">P/M</a>]</span>; cf. thing. </div>
<div class="indexentry">obvious [<em>sich von selbst verstehen</em>: say; understand], 6.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span>; cf. self-evidence. </div>
<div class="indexentry">Occam, 3.328<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.328GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.328OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.328PM">P/M</a>]</span>, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span></div>
<div class="indexentry">occur [<em>vorkommen</em>], 2.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.012PM">P/M</a>]</span>–2.0123<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0123PM">P/M</a>]</span>, 2.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0141PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.311<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.311PM">P/M</a>]</span>, 4.0621<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span>, 4.1211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span>, 4.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.23PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 5.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.25PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.54<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.54PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span></div>
<div class="indexentry">operation, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 5.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.21PM">P/M</a>]</span>–5.254<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.254GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.254OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.254PM">P/M</a>]</span>, 5.4611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4611PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5PM">P/M</a>]</span>, 5.503<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.503GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.503OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.503PM">P/M</a>]</span>, 6.001<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.001PM">P/M</a>]</span>–6.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.01PM">P/M</a>]</span>, 6.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.021PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>; cf. sign for a logical <span class="mathmode">~</span>; truth-<span class="mathmode">~</span>. </div>
<div class="indexentry">oppos/ed; <span class="mathmode">~</span>ite [<em>entgegengesetzt</em>], 4.0621<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span>, 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 5.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1241PM">P/M</a>]</span>, 5.513<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span></div>
<div class="indexentry">order, 4.1252<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span>, 5.5563<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span>, 5.634<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.634GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.634OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.634PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">paradox, Russell’s, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span></div>
<div class="indexentry">particle, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexentry">perceive, 3.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1PM">P/M</a>]</span>, 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span>, 3.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.32PM">P/M</a>]</span>, 5.5423<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5423PM">P/M</a>]</span></div>
<div class="indexentry">phenomenon, 6.423<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.423PM">P/M</a>]</span>; cf. natural <span class="mathmode">~</span>. </div>
<div class="indexentry">philosophy, P2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span>, P5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref5PM">P/M</a>]</span>, 3.324<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.324GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.324OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.324PM">P/M</a>]</span>, 3.3421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3421PM">P/M</a>]</span>, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span>, 4.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.111PM">P/M</a>]</span>–4.115<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.115GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.115OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.115PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.128<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.128GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.128OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>, 6.113<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.113GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.113OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.113PM">P/M</a>]</span>, 6.211<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.211PM">P/M</a>]</span>, 6.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span></div>
<div class="indexentry">physics, 3.0321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.0321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.0321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.0321PM">P/M</a>]</span>, 6.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.321PM">P/M</a>]</span>, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexentry">pictorial</div>
<div class="indexsubentry">1. [<em>abbilden</em>: depict; form, logico-<span class="mathmode">~</span>], 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 2.151<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.151PM">P/M</a>]</span>, 2.1513<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1513PM">P/M</a>]</span>, 2.1514<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1514PM">P/M</a>]</span>, 2.17<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.17GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.17OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.17PM">P/M</a>]</span>, 2.172<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.172GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.172OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.172PM">P/M</a>]</span>, 2.181<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.181GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.181OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.181PM">P/M</a>]</span>, 2.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.22PM">P/M</a>]</span>; cf. form, <span class="mathmode">~</span>. </div>
<div class="indexsubentry">2. [<em>bildhaftig</em>], 4.013<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.013PM">P/M</a>]</span>, 4.015<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.015GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.015OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.015PM">P/M</a>]</span></div>
<div class="indexentry">picture [<em>Bild</em>: mirror-image; <em>tableau vivant</em>], 2.0212<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0212GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0212OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0212PM">P/M</a>]</span>, 2.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p2.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1PM">P/M</a>]</span>–2.1512<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1512PM">P/M</a>]</span>, 2.1513<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1513PM">P/M</a>]</span>–3.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.01PM">P/M</a>]</span>, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.01PM">P/M</a>]</span>–4.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.012PM">P/M</a>]</span>, 4.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span>, 4.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span>, 4.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.032PM">P/M</a>]</span>, 4.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.06PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>, 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span>; cf. logical <span class="mathmode">~</span>; prototype. </div>
<div class="indexentry">place [<em>Ort</em>], 3.411<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.411PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span>; cf. logical <span class="mathmode">~</span>. </div>
<div class="indexentry">point-mass [<em>materieller Punkt</em>], 6.3432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3432PM">P/M</a>]</span></div>
<div class="indexentry">positive, 2.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.06PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span></div>
<div class="indexentry">possible, 2.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.012PM">P/M</a>]</span>, 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 2.0123<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0123PM">P/M</a>]</span>–2.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0141PM">P/M</a>]</span>, 2.033<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.033GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.033OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.033PM">P/M</a>]</span>, 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 2.151<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.151PM">P/M</a>]</span>, 2.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.201PM">P/M</a>]</span>–2.203<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.203PM">P/M</a>]</span>, 3.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.02PM">P/M</a>]</span>, 3.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.04PM">P/M</a>]</span>, 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span>, 3.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span>, 3.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.23PM">P/M</a>]</span>, 3.3421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3421PM">P/M</a>]</span>, 3.3441<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span>, 3.411<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.411PM">P/M</a>]</span>, 4.015<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.015GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.015OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.015PM">P/M</a>]</span>, 4.0312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span>, 4.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span>, 4.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span>, 4.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2PM">P/M</a>]</span>, 4.27<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.27GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.27OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.27PM">P/M</a>]</span>–4.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.3PM">P/M</a>]</span>, 4.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.42PM">P/M</a>]</span>, 4.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.45PM">P/M</a>]</span>, 4.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span>, 4.464<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.464GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.464OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.464PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.252<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.61<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.61GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.61OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.61PM">P/M</a>]</span>, 6.1222<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1222PM">P/M</a>]</span>, 6.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.33PM">P/M</a>]</span>, 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span>, 6.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.52PM">P/M</a>]</span>; cf. impossibility; truth-possibility. </div>
<div class="indexentry">postulate [<em>Forderung</em>: requirement], 6.1223<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1223GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1223OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1223PM">P/M</a>]</span></div>
<div class="indexentry">predicate, cf. subject.</div>
<div class="indexentry">present</div>
<div class="indexsubentry">1. [<em>darstellen</em>: represent], 3.312<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.312PM">P/M</a>]</span>, 3.313<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.313GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.313OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.313PM">P/M</a>]</span>, 4.115<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.115GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.115OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.115PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>vorstellen</em>: Idea; represent], 2.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.11PM">P/M</a>]</span>, 4.0311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span></div>
<div class="indexentry">presuppose [<em>voraussetzen</em>], 3.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span>, 3.33<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.33GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.33OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.33PM">P/M</a>]</span>, 4.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1241PM">P/M</a>]</span>, 5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span>, 5.61<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.61GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.61OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.61PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="indexentry">primitive idea [<em>Grundbegriff</em>], 4.12721<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p4.12721GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12721OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12721PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.476<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.476GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.476OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.476PM">P/M</a>]</span></div>
<div class="indexentry">primitive proposition [<em>Grundgesetz</em>], 5.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span>, 5.452<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span>, 6.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.127PM">P/M</a>]</span>, 6.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span>; cf. <em>Fundamental Laws of Arithmetic</em>; law. </div>
<div class="indexentry">primitive sign [<em>Urzeichen</em>], 3.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.26PM">P/M</a>]</span>, 3.261<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span>, 3.263<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.45PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>, 5.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span>, 5.472<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.472GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.472OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.472PM">P/M</a>]</span></div>
<div class="indexentry"><em>Principia Mathematica</em>, 5.452<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span></div>
<div class="indexentry">principle of sufficient reason [<em>Satz vom Grunde</em>: law; proposition], 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span></div>
<div class="indexentry"><em>Principles of Mathematics</em>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span></div>
<div class="indexentry">privileged [<em>ausgezeichnet</em>], <span class="mathmode">~</span> numbers, 4.128<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.128GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.128OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.128PM">P/M</a>]</span>, 5.453<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.453GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.453OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.453PM">P/M</a>]</span>, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span></div>
<div class="indexentry">probability, 4.464<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.464GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.464OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.464PM">P/M</a>]</span>, 5.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.15PM">P/M</a>]</span>–5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span></div>
<div class="indexentry">problem</div>
<div class="indexsubentry">1. [<em>Fragestellung</em>: question], P2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Problem</em>], P2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span>, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 5.4541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 5.551<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.551GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.551OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.551PM">P/M</a>]</span>, 5.5563<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span>, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span>, 6.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.521PM">P/M</a>]</span></div>
<div class="indexentry">product, cf. logical.</div>
<div class="indexentry">project/ion; <span class="mathmode">~</span>ive, 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span>–3.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span>, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span></div>
<div class="indexsubentry">method of <span class="mathmode">~</span>ion, 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span></div>
<div class="indexentry">proof [<em>Beweis</em>], 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.1262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1262PM">P/M</a>]</span>, 6.1263<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1263PM">P/M</a>]</span>–6.1265<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1265GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1265OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1265PM">P/M</a>]</span>, 6.2321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2321PM">P/M</a>]</span>, 6.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.241PM">P/M</a>]</span></div>
<div class="indexentry">proper, cf. name.</div>
<div class="indexentry">property [<em>Eigenschaft</em>], 2.01231<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.01231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01231PM">P/M</a>]</span>, 2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 2.0233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0233PM">P/M</a>]</span>, 2.02331<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.02331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.02331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02331PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>–4.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1241PM">P/M</a>]</span>, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.5302<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5302GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5302OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5302PM">P/M</a>]</span>, 6.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>, 6.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.231<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.231PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span>; cf. formal <span class="mathmode">~</span>. </div>
<div class="indexentry">proposition [<em>Satz</em>: law; principle], 2.0122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0122PM">P/M</a>]</span>, 2.0201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span>, 2.0211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0211PM">P/M</a>]</span>, 2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 3.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1PM">P/M</a>]</span> (&amp; passim thereafter); cf. non-<span class="mathmode">~</span>; primitive <span class="mathmode">~</span>; pseudo-<span class="mathmode">~</span>; variable, <span class="mathmode">~</span>al; variable <span class="mathmode">~</span>. </div>
<div class="indexsubentry"><span class="mathmode">~</span>al form, 3.312<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.312PM">P/M</a>]</span>, 4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span>, 4.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.012PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 4.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.53PM">P/M</a>]</span>, 5.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 5.231<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.231PM">P/M</a>]</span>, 5.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span>, 5.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.241PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.47<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.47GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47PM">P/M</a>]</span>, 5.471<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.471GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.471OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.471PM">P/M</a>]</span>, 5.472<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.472GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.472OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.472PM">P/M</a>]</span>, 5.54<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.54PM">P/M</a>]</span>–5.542<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.554<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.554GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.554OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.554PM">P/M</a>]</span>, 5.555<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span>, 5.556<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.556GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.556OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.556PM">P/M</a>]</span>, 6<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6PM">P/M</a>]</span>, 6.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.002PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>al sign, 3.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.12PM">P/M</a>]</span>, 3.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.14PM">P/M</a>]</span>, 3.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span>, 3.1431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span>, 3.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.2PM">P/M</a>]</span>, 3.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.21PM">P/M</a>]</span>, 3.332<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.332GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.332OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.332PM">P/M</a>]</span>, 3.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.34PM">P/M</a>]</span>, 3.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.41PM">P/M</a>]</span>, 3.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.5PM">P/M</a>]</span>, 4.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.02PM">P/M</a>]</span>, 4.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.44PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 5.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.31PM">P/M</a>]</span></div>
<div class="indexentry">prototype [<em>Urbild</em>], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 5.522<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.522PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>; cf. picture. </div>
<div class="indexentry">pseudo-, cf. apparent.</div>
<div class="indexsubentry"><span class="mathmode">~</span>-concept, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>-proposition, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 5.534<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.534GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.534OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.534PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 6.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>relation, 5.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span></div>
<div class="indexentry">psychology, 4.1121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>, 5.5421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5421PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>, 6.3631<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3631PM">P/M</a>]</span>, 6.423<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.423PM">P/M</a>]</span></div>
<div class="indexentry">punishment, 6.422<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">question [<em>Frage</em>: problem], 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 4.1274<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1274OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span>, 5.4541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span>, 5.55<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.55GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.55OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.55PM">P/M</a>]</span>, 5.551<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.551GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.551OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.551PM">P/M</a>]</span>, 5.5542<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5542PM">P/M</a>]</span>, 6.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.5PM">P/M</a>]</span>–6.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.52PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">range [<em>Spielraum</em>], 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>, 5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span>; cf. space. </div>
<div class="indexentry">real [<em>wirklich</em>], 2.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.022PM">P/M</a>]</span>, 4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span>, 5.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span></div>
<div class="indexentry">realism, 5.64<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.64GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.64OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.64PM">P/M</a>]</span></div>
<div class="indexentry">reality</div>
<div class="indexsubentry">1. [<em>Realität</em>], 5.5561<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span>, 5.64<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.64GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.64OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.64PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Wirklichkeit</em>], 2.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.06PM">P/M</a>]</span>, 2.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.063PM">P/M</a>]</span>, 2.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.12PM">P/M</a>]</span>, 2.1511<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1511GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1511OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1511PM">P/M</a>]</span>, 2.1512<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1512PM">P/M</a>]</span>, 2.1515<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1515PM">P/M</a>]</span>, 2.17<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.17GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.17OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.17PM">P/M</a>]</span>, 2.171<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.171GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.171OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.171PM">P/M</a>]</span>, 2.18<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.18GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.18OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.18PM">P/M</a>]</span>, 2.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.201PM">P/M</a>]</span>, 2.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.21PM">P/M</a>]</span>, 2.222<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.222PM">P/M</a>]</span>, 2.223<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.223GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.223OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.223PM">P/M</a>]</span>, 4.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.01PM">P/M</a>]</span>, 4.011<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.011PM">P/M</a>]</span>, 4.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.05<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.05PM">P/M</a>]</span>, 4.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.06PM">P/M</a>]</span>, 4.0621<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span>, 4.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12PM">P/M</a>]</span>, 4.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span></div>
<div class="indexentry">reducibility, cf. axiom.</div>
<div class="indexentry">relation</div>
<div class="indexsubentry">1. [<em>Beziehung</em>], 2.1513<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1513PM">P/M</a>]</span>, 2.1514<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1514PM">P/M</a>]</span>, 3.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.12PM">P/M</a>]</span>, 3.1432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1432PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 4.0412<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0412GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0412OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0412PM">P/M</a>]</span>, 4.061<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.061PM">P/M</a>]</span>, 4.0641<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0641PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span>, 4.4661<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span>, 5.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span>, 5.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2PM">P/M</a>]</span>–5.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.22PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.461PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span>, 5.5261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span>, 5.5301<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5301OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span>; cf. pseudo-. </div>
<div class="indexsubentry">2. [<em>Relation</em>], 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.123PM">P/M</a>]</span>, 4.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span>, 4.1251<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1251PM">P/M</a>]</span>, 5.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.232PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.5301<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5301OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span>, 5.5541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5541PM">P/M</a>]</span>; cf. formal. </div>
<div class="indexsubentry">3. stand in a <span class="mathmode">~</span> to one another; are related [<em>sich verhalten</em>: stand, how things; state of things], 2.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.03PM">P/M</a>]</span>, 2.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.14PM">P/M</a>]</span>, 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 2.151<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.151PM">P/M</a>]</span>, 3.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.14PM">P/M</a>]</span>, 5.5423<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5423PM">P/M</a>]</span></div>
<div class="indexentry">represent</div>
<div class="indexsubentry">1. [<em>darstellen</em>: present], 2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 2.173<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.173GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.173OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.173PM">P/M</a>]</span>, 2.174<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.174GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.174OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.174PM">P/M</a>]</span>, 2.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.201PM">P/M</a>]</span>–2.203<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.203PM">P/M</a>]</span>, 2.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.22PM">P/M</a>]</span>, 2.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.221PM">P/M</a>]</span>, 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>, 3.0321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.0321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.0321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.0321PM">P/M</a>]</span>, 4.011<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.011PM">P/M</a>]</span>, 4.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span>, 4.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.031PM">P/M</a>]</span>, 4.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span>, 4.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1PM">P/M</a>]</span>, 4.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12PM">P/M</a>]</span>, 4.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span>, 4.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.24PM">P/M</a>]</span>, 4.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.31PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span>, 5.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.21PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.1264<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1264GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1264OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1264PM">P/M</a>]</span>; cf. form, <span class="mathmode">~</span>ational. </div>
<div class="indexsubentry">2. [<em>vorstellen</em>: idea; present], 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span></div>
<div class="indexentry">representative, be the <span class="mathmode">~</span> of [<em>vertreten</em>], 2.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.131PM">P/M</a>]</span>, 3.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.22PM">P/M</a>]</span>, 3.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span>, 4.0312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span></div>
<div class="indexentry">requirement [<em>Forderung</em>: postulate], 3.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.23PM">P/M</a>]</span></div>
<div class="indexentry">resolve, cf. analysis.</div>
<div class="indexsubentry">1. [<em>auflösen</em>], 3.3442<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3442PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>zerlegen</em>], 2.0201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span></div>
<div class="indexentry">reward, 6.422<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span></div>
<div class="indexentry">riddle, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span>, 6.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.5PM">P/M</a>]</span></div>
<div class="indexentry">right [<em>stimmen</em>: agreement; true], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span></div>
<div class="indexentry">rule [<em>Regel</em>], 3.334<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.334GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.334OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.334PM">P/M</a>]</span>, 3.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.343PM">P/M</a>]</span>, 3.344<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.344GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.344OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.344PM">P/M</a>]</span>, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span>, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span>, 5.476<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.476GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.476OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.476PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>, 5.514<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span></div>
<div class="indexsubentry">combinatory <span class="mathmode">~</span> [<em>Kombinationsr.</em>], 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> dealing with signs [<em>Zeichenr.</em>], 3.331<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.331PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>, 6.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.02PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span></div>
<div class="indexentry">Russell, P6<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref6PM">P/M</a>]</span>, 3.318<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.318GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.318OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.318PM">P/M</a>]</span>, 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>, 3.331<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.331PM">P/M</a>]</span>, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 4.0031<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0031PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>–4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.132<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.132GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.132OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.132PM">P/M</a>]</span>, 5.252<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span>, 5.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.452<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span>, 5.4731<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4731OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span>, 5.513<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span>, 5.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span>, 5.5302<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5302GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5302OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5302PM">P/M</a>]</span>, 5.532<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.532GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.532OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.532PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span>, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span>, 6.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.123PM">P/M</a>]</span>, 6.1232<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">say</div>
<div class="indexsubentry">1. [<em>angeben</em>: give], 5.5571<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5571GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5571OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5571PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>audrücksen</em>: expression], 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span></div>
<div class="indexsubentry">3. [<em>aussprechen</em>: words, put into], <span class="mathmode">~</span> clearly, 3.262<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.262PM">P/M</a>]</span></div>
<div class="indexsubentry">4. [<em>sagen</em>], can be said, P3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref3PM">P/M</a>]</span>, 3.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.031PM">P/M</a>]</span>, 4.115<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.115GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.115OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.115PM">P/M</a>]</span>, 4.1212<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1212GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1212OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1212PM">P/M</a>]</span>, 5.61<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.61GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.61OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.61PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 6.36<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.36GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36PM">P/M</a>]</span>, 6.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.51PM">P/M</a>]</span>, 6.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry">said) (shown, 4.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.022PM">P/M</a>]</span>, 4.1212<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1212GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1212OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1212PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 6.36<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.36GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> nothing, 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 5.142<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.142PM">P/M</a>]</span>, 5.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.43PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.513<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span>, 5.5303<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5303GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5303OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5303PM">P/M</a>]</span>, 6.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.11PM">P/M</a>]</span>, 6.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span>, 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span>, 6.35<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.35GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.35OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.35PM">P/M</a>]</span></div>
<div class="indexsubentry">5. [<em>sich von selbst verstehen</em>: obvious; understand], <span class="mathmode">~</span>ing, go without, 3.334<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.334GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.334OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.334PM">P/M</a>]</span>, 6.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.2341PM">P/M</a>]</span></div>
<div class="indexentry">scaffolding, 3.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.42PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="indexentry">scepticism, 6.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.51PM">P/M</a>]</span></div>
<div class="indexentry">schema, 4.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.31PM">P/M</a>]</span>, 4.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.43PM">P/M</a>]</span>, 4.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 5.101<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span>, 5.151<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.151PM">P/M</a>]</span>, 5.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.31PM">P/M</a>]</span></div>
<div class="indexentry">science, 6.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.34PM">P/M</a>]</span>, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>, 6.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.52PM">P/M</a>]</span>; cf. natural <span class="mathmode">~</span>. </div>
<div class="indexentry">scope, 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span></div>
<div class="indexentry">segmented [<em>gegliedert</em>], 4.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.032PM">P/M</a>]</span>; cf. articulated. </div>
<div class="indexentry">self, the [<em>das Ich</em>], 5.64<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.64GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.64OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.64PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span></div>
<div class="indexentry">self-evidence [<em>Einleuchten</em>], 5.1363<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1363PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.4731<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4731OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span>, 5.5301<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5301OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span>, 6.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1271PM">P/M</a>]</span>; cf. obvious. </div>
<div class="indexentry">sense [<em>Sinn</em>; <em>sinnvoll</em>], P2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span>, 2.0211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0211PM">P/M</a>]</span>, 2.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.221PM">P/M</a>]</span>, 2.222<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.222PM">P/M</a>]</span>, 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span>, 3.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.13PM">P/M</a>]</span>, 3.142<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.142PM">P/M</a>]</span>, 3.1431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span>, 3.144<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.144GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.144OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.144PM">P/M</a>]</span>, 3.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.23PM">P/M</a>]</span>, 3.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3PM">P/M</a>]</span>, 3.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span>, 3.326<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.326GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.326OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.326PM">P/M</a>]</span>, 3.34<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.34GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.34OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.34PM">P/M</a>]</span>, 3.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.341PM">P/M</a>]</span>, 3.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.4PM">P/M</a>]</span>, 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 4.011<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.011PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 4.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.02PM">P/M</a>]</span>–4.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.022PM">P/M</a>]</span>, 4.027<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.027GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.027OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.027PM">P/M</a>]</span>–4.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.031PM">P/M</a>]</span>, 4.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.032PM">P/M</a>]</span>, 4.061<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.061PM">P/M</a>]</span>, 4.0621<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span>–4.064<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.064GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.064OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.064PM">P/M</a>]</span>, 4.1211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.1221<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1221PM">P/M</a>]</span>, 4.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1241PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.465<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.465GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.465OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.465PM">P/M</a>]</span>, 4.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.52PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.122PM">P/M</a>]</span>, 5.1241<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1241PM">P/M</a>]</span>, 5.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2341PM">P/M</a>]</span>, 5.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.25PM">P/M</a>]</span>, 5.2521<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2521PM">P/M</a>]</span>, 5.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>, 5.4732<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4732GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4732OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4732PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.514<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.514PM">P/M</a>]</span>, 5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span>, 5.5302<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5302GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5302OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5302PM">P/M</a>]</span>, 5.5542<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5542PM">P/M</a>]</span>, 5.631<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span>, 6.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.41PM">P/M</a>]</span>, 6.422<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.422PM">P/M</a>]</span>, 6.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.521PM">P/M</a>]</span></div>
<div class="indexsubentry">have the same <span class="mathmode">~</span> [<em>gleichsinnig</em>], 5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span></div>
<div class="indexsubentry">have no <span class="mathmode">~</span>; lack <span class="mathmode">~</span>; without <span class="mathmode">~</span> [<em>sinnlos</em>], 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 5.132<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.132GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.132OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.132PM">P/M</a>]</span>, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>; cf. nonsense. </div>
<div class="indexsubentry"><span class="mathmode">~</span> of touch [<em>Tastsinn</em>], 2.0131<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span></div>
<div class="indexentry">series [<em>Reihe</em>], 4.1252<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span>, 4.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.45PM">P/M</a>]</span>, 5.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1PM">P/M</a>]</span>, 5.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.232PM">P/M</a>]</span>, 6.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.02PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> of forms [<em>Formenr</em>.], 4.1252<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span>, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 5.252<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span>, 5.2522<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2522PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> of numbers [<em>Zahlenr</em>.], 4.1252<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span></div>
<div class="indexentry">set [<em>Klasse</em>: class], 3.142<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.142PM">P/M</a>]</span></div>
<div class="indexentry">show [<em>zeigen</em>: indicate; manifest], 3.262<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.262PM">P/M</a>]</span>, 4.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.022PM">P/M</a>]</span>, 4.0621<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span>, 4.0641<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0641PM">P/M</a>]</span>, 4.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.121PM">P/M</a>]</span>–4.1212<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1212GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1212OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1212PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span>, 5.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span>, 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span>, 5.5261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span>, 5.5421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5421PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span>, 5.631<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>, 6.1201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1201PM">P/M</a>]</span>, 6.1221<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1221PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.127PM">P/M</a>]</span>, 6.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.22PM">P/M</a>]</span>, 6.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.232PM">P/M</a>]</span>; cf. display; say. </div>
<div class="indexentry">sign [<em>Zeichen</em>], 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span>, 3.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.12PM">P/M</a>]</span>, 3.1432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1432PM">P/M</a>]</span>, 3.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.201PM">P/M</a>]</span>–3.203<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.203PM">P/M</a>]</span>, 3.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.21PM">P/M</a>]</span>, 3.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span>, 3.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.23PM">P/M</a>]</span>, 3.261<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span>–3.263<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>, 3.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.32PM">P/M</a>]</span>–3.322<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span>, 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>–3.334<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.334GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.334OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.334PM">P/M</a>]</span>, 3.3442<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3442PM">P/M</a>]</span>, 4.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.012PM">P/M</a>]</span>, 4.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span>, 4.0312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0312PM">P/M</a>]</span>, 4.061<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.061PM">P/M</a>]</span>, 4.0621<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0621GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0621OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0621PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>–4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>–4.441<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.441PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 4.4661<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.46PM">P/M</a>]</span>, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.4732<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4732GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4732OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4732PM">P/M</a>]</span>–5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.475<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.475GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.475OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.475PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>, 5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span>, 5.5151<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5151PM">P/M</a>]</span>, 5.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.53PM">P/M</a>]</span>, 5.5541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5541PM">P/M</a>]</span>, 5.5542<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5542PM">P/M</a>]</span>, 6.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.02PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.1264<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1264GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1264OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1264PM">P/M</a>]</span>, 6.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.53PM">P/M</a>]</span>; cf. primitive <span class="mathmode">~</span>; propositional <span class="mathmode">~</span>; rule dealing with <span class="mathmode">~</span>s; simple <span class="mathmode">~</span>. </div>
<div class="indexsubentry">be a <span class="mathmode">~</span> for [<em>bezeichnen</em>: designate; signify], 5.42<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.42GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.42OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.42PM">P/M</a>]</span></div>
<div class="indexsubentry">combination of <span class="mathmode">~</span>s [<em>Zeichenverbindung</em>], 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> for a logical operation [<em>logisches Operationsz</em>.], 5.4611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4611PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>-language [<em>Zeichensprache</em>], 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>, 3.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.343PM">P/M</a>]</span>, 4.011<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.011GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.011OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.011PM">P/M</a>]</span>, 4.1121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span>, 4.1213<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1213GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1213OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1213PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="indexentry">signif/y</div>
<div class="indexsubentry">1. [<em>bedeuten</em>: meaning], 4.115<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.115GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.115OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.115PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>bezeichnen</em>: designate: sign], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.261<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.261PM">P/M</a>]</span>, 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 3.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.321PM">P/M</a>]</span>, 3.322<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span>, 3.333<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.333GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.333OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.333PM">P/M</a>]</span>, 3.334<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.334GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.334OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.334PM">P/M</a>]</span>, 3.3411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3411PM">P/M</a>]</span>, 3.344<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.344GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.344OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.344PM">P/M</a>]</span>, 4.012<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.012GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.012OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.012PM">P/M</a>]</span>, 4.061<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.061GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.061OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.061PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.127PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.476<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.476GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.476OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.476PM">P/M</a>]</span>, 5.5261<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5261GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5261OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5261PM">P/M</a>]</span>, 5.5541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5541PM">P/M</a>]</span>, 6.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry">mode of <span class="mathmode">~</span>ication [<em>Bezeichnungsweise</em>], 3.322<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.322GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.322OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.322PM">P/M</a>]</span>, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>, 3.3421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3421PM">P/M</a>]</span>, 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span></div>
<div class="indexentry">similarity, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span>, 5.231<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.231PM">P/M</a>]</span></div>
<div class="indexentry">simple, 2.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02PM">P/M</a>]</span>, 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 4.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.21PM">P/M</a>]</span>, 4.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.24PM">P/M</a>]</span>, 4.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.51PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.4541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span>, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span>, 5.5563<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span>, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>, 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span>, 6.363<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.363PM">P/M</a>]</span>, 6.3631<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3631PM">P/M</a>]</span>; </div>
<div class="indexsubentry"><span class="mathmode">~</span> sign, 3.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.201PM">P/M</a>]</span>, 3.202<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.202PM">P/M</a>]</span>, 3.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.21PM">P/M</a>]</span>, 3.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.23PM">P/M</a>]</span>, 4.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span></div>
<div class="indexentry"><em>simplex sigillum veri</em>, 5.4541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span></div>
<div class="indexentry">situation [<em>Sachlage</em>], 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 2.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.014PM">P/M</a>]</span>, 2.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.11PM">P/M</a>]</span>, 2.202<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.202PM">P/M</a>]</span>, 2.203<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.203PM">P/M</a>]</span>, 3.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.02PM">P/M</a>]</span>, 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span>, 3.144<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.144GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.144OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.144PM">P/M</a>]</span>, 3.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.21PM">P/M</a>]</span>, 4.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span>, 4.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span>, 4.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.031PM">P/M</a>]</span>, 4.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.032PM">P/M</a>]</span>, 4.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.04PM">P/M</a>]</span>, 4.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.124PM">P/M</a>]</span>, 4.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.125PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 5.135<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.135GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.135OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.135PM">P/M</a>]</span>, 5.156<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.156GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.156OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.156PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span></div>
<div class="indexentry">Socrates, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span></div>
<div class="indexentry">solipsism, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 5.64<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.64GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.64OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.64PM">P/M</a>]</span></div>
<div class="indexentry">solution, P8<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref8GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref8OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref8PM">P/M</a>]</span>, 5.4541<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4541PM">P/M</a>]</span>, 5.535<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.535GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.535OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.535PM">P/M</a>]</span>, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span>, 6.4321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4321PM">P/M</a>]</span>, 6.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.521PM">P/M</a>]</span></div>
<div class="indexentry">soul, 5.5421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5421PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span></div>
<div class="indexentry">space [<em>Raum</em>], 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 2.013<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.013PM">P/M</a>]</span>, 2.0131<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span>, 2.0251<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0251PM">P/M</a>]</span>, 2.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.11PM">P/M</a>]</span>, 2.171<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.171GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.171OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.171PM">P/M</a>]</span>, 2.182<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.182GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.182OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.182PM">P/M</a>]</span>, 2.202<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.202PM">P/M</a>]</span>, 3.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.032PM">P/M</a>]</span>–3.0321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.0321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.0321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.0321PM">P/M</a>]</span>, 3.1431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span>, 4.0412<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0412GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0412OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0412PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span>, 6.3611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3611PM">P/M</a>]</span>, 6.36111<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p6.36111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.36111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.36111PM">P/M</a>]</span>, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span>; cf. colour-<span class="mathmode">~</span>; logical <span class="mathmode">~</span>; range. </div>
<div class="indexentry">speak/ about [<em>von etwas sprechen</em>], 3.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span>, 6.3431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3431PM">P/M</a>]</span>, 6.423<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.423PM">P/M</a>]</span>, 7<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p7GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p7OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p7PM">P/M</a>]</span>; cf. about. </div>
<div class="indexsubentry"><span class="mathmode">~</span> for itself [<em>aussagen</em>: ascribe; state; statement; tell], 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="indexentry">stand/, how things [<em>sich verhalten</em>: relation; state of things], 4.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.022PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.062<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.062GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.062OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.062PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> for [<em>für etwas stehen</em>], 4.0311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span>, 5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span></div>
<div class="indexentry">state [<em>aussagen</em>: ascribe; speak; statement; tell], 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 4.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.03PM">P/M</a>]</span>, 4.242<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.242GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.242OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.242PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 6.1264<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1264GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1264OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1264PM">P/M</a>]</span></div>
<div class="indexentry">statement [<em>Aussage</em>], 2.0201<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0201PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexsubentry">make a <span class="mathmode">~</span> [<em>aussagen</em>: ascribe; speak; state; tell], 3.332<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.332GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.332OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.332PM">P/M</a>]</span>, 5.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.25PM">P/M</a>]</span></div>
<div class="indexentry">state of/ affairs [<em>Sachverhalt</em>: <span class="mathmode">~</span> things], 2<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2PM">P/M</a>]</span>–2.013<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.013PM">P/M</a>]</span>, 2.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.014PM">P/M</a>]</span>, 2.0272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0272PM">P/M</a>]</span>–2.062<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.062GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.062OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.062PM">P/M</a>]</span>, 2.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.11PM">P/M</a>]</span>, 2.201<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.201GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.201OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.201PM">P/M</a>]</span>, 3.001<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.001PM">P/M</a>]</span>, 3.0321<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.0321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.0321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.0321PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.0311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span>, 4.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 4.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2PM">P/M</a>]</span>, 4.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.21PM">P/M</a>]</span>, 4.2211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span>, 4.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.25PM">P/M</a>]</span>, 4.27<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.27GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.27OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.27PM">P/M</a>]</span>, 4.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.3PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> things</div>
<div class="indexsubsubentry">1. [<em>Sachverhalt</em>: <span class="mathmode">~</span> affairs], 2.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01PM">P/M</a>]</span></div>
<div class="indexsubsubentry">2. [<em>sich verhalten</em>: relation; stand, how things], 5.552<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.552GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.552OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.552PM">P/M</a>]</span></div>
<div class="indexentry">stipulate [<em>festsetzen</em>], 3.316<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.316GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.316OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.316PM">P/M</a>]</span>, 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span></div>
<div class="indexentry">structure [<em>Struktur</em>], 2.032<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.032GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.032OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.032PM">P/M</a>]</span>–2.034<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.034GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.034OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.034PM">P/M</a>]</span>, 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 4.1211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1211PM">P/M</a>]</span>, 4.122<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.122PM">P/M</a>]</span>, 5.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.13PM">P/M</a>]</span>, 5.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2PM">P/M</a>]</span>, 5.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.22PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexentry">subject</div>
<div class="indexsubentry">1. [<em>Subjekt</em>], 5.5421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5421PM">P/M</a>]</span>, 5.631<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span>–5.633<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.633GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.633OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.633PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span>-predicate propositions, 4.1274<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1274GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1274OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1274PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Träger</em>], 6.423<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.423PM">P/M</a>]</span></div>
<div class="indexsubentry">3. <span class="mathmode">~</span>-matter [<em>von etwas handeln</em>: about; concerned with; deal with], 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span></div>
<div class="indexentry">subsistent [<em>bestehen</em>: existence; hold], 2.024<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.024PM">P/M</a>]</span>, 2.027<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.027GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.027OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.027PM">P/M</a>]</span>, 2.0271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0271PM">P/M</a>]</span></div>
<div class="indexentry"><em>sub specie aeterni</em>, 6.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.45PM">P/M</a>]</span>; cf. eternity. </div>
<div class="indexentry">substance [<em>Substanz</em>], 2.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.021PM">P/M</a>]</span>, 2.0211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0211PM">P/M</a>]</span>, 2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 2.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.04PM">P/M</a>]</span></div>
<div class="indexentry">substitut/e, 3.344<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.344GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.344OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.344PM">P/M</a>]</span>, 3.3441<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>, 6.23<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.23GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.23OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.23PM">P/M</a>]</span>, 6.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.24PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>ion, method of, 6.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.24PM">P/M</a>]</span></div>
<div class="indexentry">successor [<em>Nachfolger</em>], 4.1252<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1252PM">P/M</a>]</span>, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span></div>
<div class="indexentry">sum, cf. logical.</div>
<div class="indexentry">sum-total [<em>gesamt</em>: totality; whole], 2.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.063PM">P/M</a>]</span></div>
<div class="indexentry">superstition, 5.1361<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1361PM">P/M</a>]</span></div>
<div class="indexentry">supposition [<em>Annahme</em>], 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span></div>
<div class="indexentry">survival [<em>Fortleben</em>], 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span></div>
<div class="indexentry">symbol [<em>Symbol</em>], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 3.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.31PM">P/M</a>]</span>, 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 3.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.32PM">P/M</a>]</span>, 3.321<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.321PM">P/M</a>]</span>, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>, 3.326<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.326GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.326OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.326PM">P/M</a>]</span>, 3.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.341PM">P/M</a>]</span>, 3.3411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3411PM">P/M</a>]</span>, 3.344<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.344GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.344OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.344PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.24PM">P/M</a>]</span>, 4.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.31PM">P/M</a>]</span>, 4.465<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.465GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.465OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.465PM">P/M</a>]</span>, 4.4661<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span>, 4.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.5PM">P/M</a>]</span>, 5.1311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1311PM">P/M</a>]</span>, 5.473<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.473GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.473OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.473PM">P/M</a>]</span>, 5.4733<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4733GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4733OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4733PM">P/M</a>]</span>, 5.513<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.513GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.513OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.513PM">P/M</a>]</span>–5.515<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.515GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.515OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.515PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>, 5.555<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span>, 6.113<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.113GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.113OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.113PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>ism [<em>Symbolismus</em>], 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span></div>
<div class="indexentry">syntax, cf. logical.</div>
<div class="indexentry">system, 5.475<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.475GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.475OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.475PM">P/M</a>]</span>, 5.555<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.555GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.555OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.555PM">P/M</a>]</span>, 6.341<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.341PM">P/M</a>]</span>, 6.372<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.372GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.372OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.372PM">P/M</a>]</span>; cf. number-<span class="mathmode">~</span>. </div>
</div>
<div class="indexletterblock">
<div class="indexentry"><em>tableau vivant</em> [<em>lebendes Bild</em>: picture], 4.0311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span></div>
<div class="indexentry">talk about [<em>von etwas reden</em>: mention], P2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref2PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>, 6.3432<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3432PM">P/M</a>]</span>; cf. about. </div>
<div class="indexentry">tautology, 4.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span>–4.4661<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.4661GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.4661OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.4661PM">P/M</a>]</span>, 5.101<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span>, 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 5.142<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.142GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.142OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.142PM">P/M</a>]</span>, 5.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.143PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 5.525<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.525GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.525OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.525PM">P/M</a>]</span>, 6.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>–6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span>, 6.1221<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1221PM">P/M</a>]</span>, 6.1231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1231PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.126PM">P/M</a>]</span>, 6.1262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1262PM">P/M</a>]</span>, 6.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.127PM">P/M</a>]</span>, 6.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.22PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span></div>
<div class="indexentry">tell [<em>aussagen</em>: ascribe; speak; state; statement], 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span></div>
<div class="indexentry">term [<em>Glied</em>], 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 5.232<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.232PM">P/M</a>]</span>, 5.252<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span>, 5.2522<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2522PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span></div>
<div class="indexentry">theory</div>
<div class="indexsubentry">1. [<em>Lehre</em>: doctrine], 6.1224<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1224GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1224OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1224PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of probability, 4.464<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.464GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.464OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.464PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Theorie</em>], 4.1122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1122PM">P/M</a>]</span>, 5.5422<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5422GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5422OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5422PM">P/M</a>]</span>, 6.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of classes, 6.031<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.031GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.031OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.031PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of knowledge, 4.1121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span> of types, 3.331<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.331PM">P/M</a>]</span>, 3.332<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.332GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.332OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.332PM">P/M</a>]</span></div>
<div class="indexentry">thing, cf. object; state of affairs; state of <span class="mathmode">~</span>s.</div>
<div class="indexsubentry">1. [<em>Ding</em>], 1.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p1.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.1PM">P/M</a>]</span>, 2.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01PM">P/M</a>]</span>–2.0122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0122PM">P/M</a>]</span>, 2.013<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.013PM">P/M</a>]</span>, 2.02331<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p2.02331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.02331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.02331PM">P/M</a>]</span>, 2.151<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.151GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.151OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.151PM">P/M</a>]</span>, 3.1431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.1431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1431PM">P/M</a>]</span>, 4.0311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0311PM">P/M</a>]</span>, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 5.5301<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5301GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5301OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5301PM">P/M</a>]</span>, 5.5303<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5303GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5303OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5303PM">P/M</a>]</span>, 5.5351<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5351GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5351OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5351PM">P/M</a>]</span>, 5.5352<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5352GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5352OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5352PM">P/M</a>]</span>, 5.553<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.553GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.553OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.553PM">P/M</a>]</span>, 5.634<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.634GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.634OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.634PM">P/M</a>]</span>, 6.1231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1231PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Sache</em>], 2.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.01PM">P/M</a>]</span>, 2.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.15PM">P/M</a>]</span>, 2.1514<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.1514GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.1514OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.1514PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span></div>
<div class="indexentry">think [<em>denken</em>: imagine], P3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref3PM">P/M</a>]</span>, 3.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.02PM">P/M</a>]</span>, 3.03<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.03GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.03OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.03PM">P/M</a>]</span>, 3.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.11PM">P/M</a>]</span>, 3.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.5PM">P/M</a>]</span>, 4.114<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.114GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.114OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.114PM">P/M</a>]</span>, 4.116<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.116GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.116OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.116PM">P/M</a>]</span>, 5.4731<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4731GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4731OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4731PM">P/M</a>]</span>, 5.541<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.541GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.541OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.541PM">P/M</a>]</span>, 5.542<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.542GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.542OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.542PM">P/M</a>]</span>, 5.61<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.61GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.61OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.61PM">P/M</a>]</span>, 5.631<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>able [<em>denkbar</em>], P3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref3PM">P/M</a>]</span>, 3.001<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.001PM">P/M</a>]</span>, 3.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.02PM">P/M</a>]</span>, 6.361<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.361GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.361OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.361PM">P/M</a>]</span>; cf. unthinkable. </div>
<div class="indexentry">thought [<em>Gedanke</em>: idea], P3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#pref3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#pref3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#pref3PM">P/M</a>]</span>, 3<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3PM">P/M</a>]</span>, 3.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.01PM">P/M</a>]</span>, 3.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.02PM">P/M</a>]</span>, 3.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.04PM">P/M</a>]</span>–3.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.1PM">P/M</a>]</span>, 3.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.12PM">P/M</a>]</span>, 3.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.2PM">P/M</a>]</span>, 3.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p3.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.5PM">P/M</a>]</span>, 4<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4PM">P/M</a>]</span>, 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 4.112<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.112GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.112OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.112PM">P/M</a>]</span>, 6.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.21PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>-process [<em>Denkprozess</em>], 4.1121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1121PM">P/M</a>]</span></div>
<div class="indexentry">time, 2.0121<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0121PM">P/M</a>]</span>, 2.0251<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0251GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0251OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0251PM">P/M</a>]</span>, 6.3611<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3611GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3611OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3611PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span>, 6.4311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span>, 6.4312<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4312PM">P/M</a>]</span></div>
<div class="indexentry">totality [<em>Gesamtheit</em>: sum-total; whole], 1.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p1.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.1PM">P/M</a>]</span>, 1.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p1.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.12PM">P/M</a>]</span>, 2.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.04PM">P/M</a>]</span>, 2.05<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.05PM">P/M</a>]</span>, 3.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.01PM">P/M</a>]</span>, 4.001<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.001GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.001OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.001PM">P/M</a>]</span>, 4.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.11PM">P/M</a>]</span>, 4.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.52PM">P/M</a>]</span>, 5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span>, 5.5561<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5561GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5561OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5561PM">P/M</a>]</span></div>
<div class="indexentry">transcendental, 6.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.13PM">P/M</a>]</span>, 6.421<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.421PM">P/M</a>]</span></div>
<div class="indexentry">translation, 3.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.343PM">P/M</a>]</span>, 4.0141<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0141GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0141OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0141PM">P/M</a>]</span>, 4.025<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.025GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.025OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.025PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span></div>
<div class="indexentry">tru/e</div>
<div class="indexsubentry">1. [<em>Faktum</em>], 5.154<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.154GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.154OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.154PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>wahr</em>], 2.0211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0211PM">P/M</a>]</span>, 2.0212<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0212GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0212OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0212PM">P/M</a>]</span>, 2.21<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.21GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.21OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.21PM">P/M</a>]</span>, 2.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p2.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.22PM">P/M</a>]</span>, 2.222<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.222GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.222OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.222PM">P/M</a>]</span>–2.225<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.225GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.225OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.225PM">P/M</a>]</span>, 3.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.01PM">P/M</a>]</span>, 3.04<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.04GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.04OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.04PM">P/M</a>]</span>, 3.05<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.05GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.05OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.05PM">P/M</a>]</span>, 4.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.022PM">P/M</a>]</span>–4.024<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.024PM">P/M</a>]</span>, 4.06<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.06GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.06OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.06PM">P/M</a>]</span>–4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span>, 4.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.11PM">P/M</a>]</span>, 4.25<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.25GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.25OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.25PM">P/M</a>]</span>, 4.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.26PM">P/M</a>]</span>, 4.28<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.28GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.28OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.28PM">P/M</a>]</span>, 4.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.31PM">P/M</a>]</span>, 4.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.41PM">P/M</a>]</span>, 4.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.43PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 4.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span>, 4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 4.464<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.464GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.464OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.464PM">P/M</a>]</span>, 4.466<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.466GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.466OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.466PM">P/M</a>]</span>, 5.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.11PM">P/M</a>]</span>, 5.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.12PM">P/M</a>]</span>, 5.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.123PM">P/M</a>]</span>, 5.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.13PM">P/M</a>]</span>, 5.131<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.131PM">P/M</a>]</span>, 5.1363<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1363GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1363OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1363PM">P/M</a>]</span>, 5.512<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.512GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.512OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.512PM">P/M</a>]</span>, 5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span>, 5.5352<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5352GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5352OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5352PM">P/M</a>]</span>, 5.5563<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5563GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5563OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5563PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>, 6.111<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.111GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.111OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.111PM">P/M</a>]</span>, 6.113<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.113GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.113OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.113PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span>, 6.1223<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1223GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1223OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1223PM">P/M</a>]</span>, 6.1232<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1232GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1232OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1232PM">P/M</a>]</span>, 6.125<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.125GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.125OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.125PM">P/M</a>]</span>, 6.343<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.343GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.343OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.343PM">P/M</a>]</span>; cf. correct; right. </div>
<div class="indexsubentry">come <span class="mathmode">~</span>e [<em>stimmmen</em>: agreement; right], 5.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.123PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>th-argument, 5.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.01PM">P/M</a>]</span>, 5.101<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span>, 5.152<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.152GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.152OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.152PM">P/M</a>]</span>, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>th-combination, 6.1203<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1203GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1203OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1203PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>th-condition, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 4.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.45PM">P/M</a>]</span>–4.461<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.461GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.461OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.461PM">P/M</a>]</span>, 4.463<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.463GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.463OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.463PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>th-function, 3.3441<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3441GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3441OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3441PM">P/M</a>]</span>, 5<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5PM">P/M</a>]</span>, 5.1<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1PM">P/M</a>]</span>, 5.101<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span>, 5.234<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.234PM">P/M</a>]</span>, 5.2341<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2341GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2341OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2341PM">P/M</a>]</span>, 5.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.3PM">P/M</a>]</span>, 5.31<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.31GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.31OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.31PM">P/M</a>]</span>, 5.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.41PM">P/M</a>]</span>, 5.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.44PM">P/M</a>]</span>, 5.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5PM">P/M</a>]</span>, 5.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span>, 6<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>th-ground, 5.101<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span>–5.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.121PM">P/M</a>]</span>, 5.15<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.15GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.15OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.15PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>th-operation, 5.234<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.234GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.234OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.234PM">P/M</a>]</span>, 5.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.3PM">P/M</a>]</span>, 5.32<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.32GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.32OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.32PM">P/M</a>]</span>, 5.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.41PM">P/M</a>]</span>, 5.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.442PM">P/M</a>]</span>, 5.54<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.54PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>th-possibility, 4.3<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p4.3GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.3OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.3PM">P/M</a>]</span>–4.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.44PM">P/M</a>]</span>, 4.442<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.442GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.442OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.442PM">P/M</a>]</span>, 4.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.45PM">P/M</a>]</span>, 4.46<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.46GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.46OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.46PM">P/M</a>]</span>, 5.101<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.101GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.101OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.101PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span>th-value, 4.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.063PM">P/M</a>]</span></div>
<div class="indexentry">type, 3.331<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.331PM">P/M</a>]</span>, 3.332<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.332GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.332OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.332PM">P/M</a>]</span>, 5.252<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span>, 6.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.123PM">P/M</a>]</span>; cf. prototype. </div>
</div>
<div class="indexletterblock">
<div class="indexentry">unalterable [<em>fest</em>], 2.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.023PM">P/M</a>]</span>, 2.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.026PM">P/M</a>]</span>–2.0271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0271PM">P/M</a>]</span></div>
<div class="indexentry">understand [<em>verstehen</em>: obvious; say], 3.263<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.263GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.263OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.263PM">P/M</a>]</span>, 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 4.003<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.003GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.003OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.003PM">P/M</a>]</span>, 4.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.02PM">P/M</a>]</span>, 4.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.021PM">P/M</a>]</span>, 4.024<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.024GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.024OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.024PM">P/M</a>]</span>, 4.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 4.411<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.411PM">P/M</a>]</span>, 5.02<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.02GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.02OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.02PM">P/M</a>]</span>, 5.451<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.451GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.451OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.451PM">P/M</a>]</span>, 5.521<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.521PM">P/M</a>]</span>, 5.552<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.552GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.552OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.552PM">P/M</a>]</span>, 5.5562<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5562GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5562OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5562PM">P/M</a>]</span>, 5.62<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.62GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.62OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.62PM">P/M</a>]</span>; cf. misunderstanding. </div>
<div class="indexsubentry">make oneself understood [<em>sich verständigen</em>], 4.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span>, 4.062<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.062GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.062OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.062PM">P/M</a>]</span></div>
<div class="indexentry">undetermined [<em>nicht bestimmt</em>], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>, 4.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.431PM">P/M</a>]</span></div>
<div class="indexentry">unit, 5.155<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.155GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.155OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.155PM">P/M</a>]</span>, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span></div>
<div class="indexentry">unnecessary, 5.47321<span class="linkarray tlpdepth5"> [→<a class="gerlink" href="#p5.47321GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.47321OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.47321PM">P/M</a>]</span></div>
<div class="indexentry">unthinkable, 4.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.123PM">P/M</a>]</span></div>
<div class="indexentry">use</div>
<div class="indexsubentry">1. [<em>Gebrauch</em>], 3.326<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.326GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.326OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.326PM">P/M</a>]</span>, 4.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.123PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.241<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.241GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.241OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.241PM">P/M</a>]</span>, 6.211<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.211PM">P/M</a>]</span>; </div>
<div class="indexsubsubentry"><span class="mathmode">~</span>less [<em>nicht gebraucht</em>], 3.328<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.328GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.328OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.328PM">P/M</a>]</span></div>
<div class="indexsubentry">2. [<em>Verwendung</em>: employment], 3.325<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.325GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.325OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.325PM">P/M</a>]</span>, 4.013<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.013GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.013OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.013PM">P/M</a>]</span>, 6.1202<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1202GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1202OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1202PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">validity, 6.1233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1233PM">P/M</a>]</span>; cf. general <span class="mathmode">~</span>. </div>
<div class="indexentry">value [<em>Wert</em>], 6.4<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.4GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4PM">P/M</a>]</span>, 6.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.41PM">P/M</a>]</span>; cf. truth-<span class="mathmode">~</span>. </div>
<div class="indexsubentry"><span class="mathmode">~</span> of a variable, 3.313<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.313GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.313OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.313PM">P/M</a>]</span>, 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span>–3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 4.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.127PM">P/M</a>]</span>, 4.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 5.51<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.51GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.51OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.51PM">P/M</a>]</span>, 5.52<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.52GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.52OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.52PM">P/M</a>]</span></div>
<div class="indexentry">variable, 3.312<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.312GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.312OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.312PM">P/M</a>]</span>–3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 4.0411<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.0411GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.0411OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.0411PM">P/M</a>]</span>, 4.1271<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1271GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1271OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1271PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span>, 4.1273<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1273GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1273OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1273PM">P/M</a>]</span>, 4.53<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.53GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.53OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.53PM">P/M</a>]</span>, 5.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p5.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.24PM">P/M</a>]</span>, 5.242<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.242GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.242OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.242PM">P/M</a>]</span>, 5.2522<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.2522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.2522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.2522PM">P/M</a>]</span>, 5.501<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.501GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.501OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.501PM">P/M</a>]</span>, 6.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span></div>
<div class="indexsubentry">propositional <span class="mathmode">~</span> [<em>Satzvariable</em>], 3.313<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.313GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.313OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.313PM">P/M</a>]</span>, 3.317<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.317GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.317OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.317PM">P/M</a>]</span>, 4.126<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.126GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.126OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.126PM">P/M</a>]</span>, 4.127<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.127GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.127OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.127PM">P/M</a>]</span>, 5.502<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.502GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.502OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.502PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> name, 3.314<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.314GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.314OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.314PM">P/M</a>]</span>, 4.1272<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.1272GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.1272OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.1272PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> number, 6.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.022PM">P/M</a>]</span></div>
<div class="indexsubentry"><span class="mathmode">~</span> proposition [<em>variabler Satz</em>], 3.315<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.315GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.315OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.315PM">P/M</a>]</span></div>
<div class="indexentry">visual field, 2.0131<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0131GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0131OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0131PM">P/M</a>]</span>, 5.633<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.633GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.633OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.633PM">P/M</a>]</span>, 5.6331<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.6331GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.6331OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6331PM">P/M</a>]</span>, 6.3751<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3751GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3751OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3751PM">P/M</a>]</span>, 6.4311<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.4311GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.4311OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.4311PM">P/M</a>]</span></div>
</div>
<div class="indexletterblock">
<div class="indexentry">Whitehead, 5.252<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.252GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.252OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.252PM">P/M</a>]</span>, 5.452<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.452GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.452OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.452PM">P/M</a>]</span></div>
<div class="indexentry">whole [<em>gesamt</em>: sum-total; totality], 4.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.11PM">P/M</a>]</span>, 4.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12PM">P/M</a>]</span></div>
<div class="indexentry">will [<em>Wille</em>; <em>wollen</em>], 5.1362<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.1362GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.1362OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.1362PM">P/M</a>]</span>, 5.631<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.631GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.631OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.631PM">P/M</a>]</span>, 6.373<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.373GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.373OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.373PM">P/M</a>]</span>, 6.374<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.374GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.374OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span>, 6.423<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.423GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.423OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.423PM">P/M</a>]</span>, 6.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.43PM">P/M</a>]</span></div>
<div class="indexentry">wish [<em>wünschen</em>], 6.374<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.374GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.374OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span></div>
<div class="indexentry">word [<em>Wort</em>], 2.0122<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0122GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0122OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0122PM">P/M</a>]</span>, 3.14<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.14GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.14OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.14PM">P/M</a>]</span>, 3.143<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.143GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.143OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.143PM">P/M</a>]</span>, 3.323<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.323GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.323OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.323PM">P/M</a>]</span>, 4.002<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.002GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.002OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.002PM">P/M</a>]</span>, 4.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.026PM">P/M</a>]</span>, 4.243<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.243GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.243OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.243PM">P/M</a>]</span>, 6.211<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.211PM">P/M</a>]</span>; cf. concept-<span class="mathmode">~</span>. </div>
<div class="indexsubentry">put into <span class="mathmode">~</span>s [<em>aussprechen</em>; <em>unausprechlich</em>: say], 3.221<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p3.221GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.221OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.221PM">P/M</a>]</span>, 4.116<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.116GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.116OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.116PM">P/M</a>]</span>, 6.421<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.421PM">P/M</a>]</span>, 6.5<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p6.5GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.5OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.5PM">P/M</a>]</span>, 6.522<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.522GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.522OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.522PM">P/M</a>]</span></div>
<div class="indexentry">world, 1<span class="linkarray tlpdepth0"> [→<a class="gerlink" href="#p1GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1PM">P/M</a>]</span>–1.11<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p1.11GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.11OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.11PM">P/M</a>]</span>, 1.13<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p1.13GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.13OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.13PM">P/M</a>]</span>, 1.2<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p1.2GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p1.2OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p1.2PM">P/M</a>]</span>, 2.021<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.021GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.021OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.021PM">P/M</a>]</span>–2.022<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.022GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.022OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.022PM">P/M</a>]</span>, 2.0231<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p2.0231GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.0231OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.0231PM">P/M</a>]</span>, 2.026<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.026GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.026OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.026PM">P/M</a>]</span>, 2.063<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p2.063GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p2.063OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p2.063PM">P/M</a>]</span>, 3.01<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.01GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.01OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.01PM">P/M</a>]</span>, 3.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.12PM">P/M</a>]</span>, 3.3421<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p3.3421GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.3421OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.3421PM">P/M</a>]</span>, 4.014<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.014GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.014OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.014PM">P/M</a>]</span>, 4.023<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.023GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.023OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.023PM">P/M</a>]</span>, 4.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.12PM">P/M</a>]</span>, 4.2211<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p4.2211GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.2211OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.2211PM">P/M</a>]</span>, 4.26<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p4.26GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.26OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.26PM">P/M</a>]</span>, 4.462<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p4.462GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p4.462OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p4.462PM">P/M</a>]</span>, 5.123<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.123GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.123OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.123PM">P/M</a>]</span>, 5.4711<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.4711GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.4711OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.4711PM">P/M</a>]</span>, 5.511<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.511GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.511OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.511PM">P/M</a>]</span>, 5.526<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.526GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.526OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.526PM">P/M</a>]</span>–5.5262<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5262GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5262OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5262PM">P/M</a>]</span>, 5.551<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.551GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.551OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.551PM">P/M</a>]</span>, 5.5521<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p5.5521GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.5521OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.5521PM">P/M</a>]</span>, 5.6<span class="linkarray tlpdepth1"> [→<a class="gerlink" href="#p5.6GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.6OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.6PM">P/M</a>]</span>–5.633<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.633GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.633OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.633PM">P/M</a>]</span>, 5.641<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p5.641GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p5.641OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p5.641PM">P/M</a>]</span>, 6.12<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.12GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.12OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.12PM">P/M</a>]</span>, 6.1233<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.1233GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.1233OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.1233PM">P/M</a>]</span>, 6.124<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.124GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.124OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.124PM">P/M</a>]</span>, 6.22<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.22GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.22OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.22PM">P/M</a>]</span>, 6.342<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.342GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.342OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.342PM">P/M</a>]</span>, 6.3431<span class="linkarray tlpdepth4"> [→<a class="gerlink" href="#p6.3431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.3431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.3431PM">P/M</a>]</span>, 6.371<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.371GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.371OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.371PM">P/M</a>]</span>, 6.373<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.373GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.373OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.373PM">P/M</a>]</span>, 6.374<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.374GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.374OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.374PM">P/M</a>]</span>, 6.41<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.41GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.41OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.41PM">P/M</a>]</span>, 6.43<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.43GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.43OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.43PM">P/M</a>]</span>, 6.431<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.431GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.431OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.431PM">P/M</a>]</span>, 6.432<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.432GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.432OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.432PM">P/M</a>]</span>, 6.44<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.44GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.44OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.44PM">P/M</a>]</span>, 6.45<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.45GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.45OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.45PM">P/M</a>]</span>, 6.54<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p6.54GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.54OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.54PM">P/M</a>]</span>; cf. description of the <span class="mathmode">~</span>. </div>
<div class="indexentry">wrong [<em>nicht stimmen</em>: agreement; true], 3.24<span class="linkarray tlpdepth2"> [→<a class="gerlink" href="#p3.24GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p3.24OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p3.24PM">P/M</a>]</span>; cf. false. </div>
</div>
<div class="indexletterblock">
<div class="indexentry">zero-method, 6.121<span class="linkarray tlpdepth3"> [→<a class="gerlink" href="#p6.121GER">GER</a><span class="aftergerlink"> | </span><a class="ogdlink" href="#p6.121OGD">OGD</a><span class="beforepmclink"> | </span><a class="pmclink" href="#p6.121PM">P/M</a>]</span></div>
</div>
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<span class="ccicongroup"><object data="images/pd.svg" type="image/svg+xml" class="ccicon"><img src="images/pd.png" alt="[PD]" class="ccicon" /></object></span> <span class="sflabel">Ludwig Wittgenstein’s <i>Tractatus Logico-Philosophicus</i> is in the Public Domain.</span></p>
<p class="licensep"><span class="ccicongroup"><object data="images/cc.svg" type="image/svg+xml" class="ccicon"><img src="images/cc.png" alt="[CC]" class="ccicon" /></object> <object data="images/by.svg" type="image/svg+xml" class="ccicon"><img src="images/by.png" alt="[BY]" class="ccicon" /></object> <object data="images/sa.svg" type="image/svg+xml" class="ccicon"><img src="images/sa.png" alt="[SA]" class="ccicon" /></object></span> <span class="sflabel">The layout of the side-by-side-by-side edition, including HTML mark-up and related content, by Kevin C. Klement, is licensed under a <a href="http://creativecommons.org/licenses/by-sa/3.0/us/">Creative Commons Attribution—Share Alike 3.0 United States License</a>.</span></p>
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