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# Frank P. Ramsey — Review of Tractatus Logico-Philosophicus
*Critical Notice, Mind*, New Series, Vol. 32, No. 128 (October 1923), pp. 465–478.
Quelle: `resources/1923-ramsey zur Anhabdlung.pdf` (JSTOR-PDF).
Konvertierung: pdftotext mit minimaler Aufräumung (Page-Numbers, Running Heads, JSTOR-Footer entfernt). Originalfehler im OCR (z. B. „THISis", „WIT'TGENSTEIN", „extraordinaryinterest", „macdeearlier") sind erhalten — bei präzisem Zitat mit dem Mind-Original abgleichen.
---
VI.-CRITICAL
NOTICES.
'Tractatus Logico-Philosophicus. BY LUDWIGWITTGENSTEIN, with
an Introduction by BERTRAND RUSSELL.
(International
Library of Psychology, Philosophy and Scientific Method.)
London: Kegan Paul, Trench, Trubner & Co. Ltd., 1922.
Pp. 189. lOs. 6d.
THISis a most important book containing original ideas on a large
range of topics, forming a coherent system, which whether or not
it be, as the author claims, in essentials the final solution of the
problems dealt with, is of extraordinaryinterest and deserves the
attention of all philosophers. And even if the system be altogether
unsound the book contains a large numberof profound obiter dicta
and criticisms of other theories. It is, however, very difficult to
understand, in spite of the fact that it is printed with the German
text and an English translation on opposite pages. Mr. Wittgenstein writes, not consecutive prose, but short propositions numbered
so as to show the emphasis laid upon them in his exposition.
This gives his work an attractive epigrammatic flavour, and perhaps makes it more accurate in detail, as each sentence must have
received separate consideration; but it seems to have prevented
him from giving adequate explanations of many of his technical
terms and theories, perhaps because explanations require some
,sacrificeof accuracy.
This deficiency is partly made up by Mr. Russell's introduction;
but it is possible that he is not an infallible guide to Mr. Wittgenstein's meaning. "In order to understand Mr. Wittgenstein's
book, says Mr. Russell, "it is necessary to realise 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
that would have to be fulfilled by a logically perfect language."
This seems to be a very doubtful generalisation; there are, indeed,
passages in which Mr. Wittgenstein is explicitly concerned with a
logically perfect, and not with any language, e.g., the discussion of
"logical syntax " in 3 325 if.; but in general he seems to maintain
th?athis doctrines apply to Qrdinarylanguages in spite of the appearance of the contrary(see especially 4002 Sf.).' This is obviously
an important point, for this wider application greatly increases the
interest and diminishes the plausibility of any thesis suc,h as that
which Mr. Russell declares to be perhaps the most fundamental in
Mr. Wittgenstein's theory; that " In order that a certain sentence
should assert a certain fact there must, however the language may
466
be constructed, be something in common between the structure of
the sentence and the structure of the fact".
This doctrine appears to depend on the difficult notions of a,
"picture " and its " form of representation,"which I shall now try
to explain and criticise.
A picture is a fact, the fact that its elements are combinedwith
one another in a definite way. These elements are co-ordinated
with certain objects (the constituents of the fact of which the
picture is a picture). These co-ordinations constitute the representing relation which makes the picture a picture. This representing relation "belongs to the picture" (2 1513); this I think
means'that whenever we talk of a picture we 'have in mind some
representing relation in virtue of which it is a picture. Under
these circusnstances we say that the picture represents that the
objects are so combined with another as are the elements of the
picture, and this is the sense of the picture. And I think this must
be taken to be the definition of "represents " and of " sense";
that is to say, that when we say that a picture represents that
certain objects are combined in a certain way, we mean merely
that the elements of the picture are combined in that way, and are
co-ordinated with the objects by the representing relation which
belongs to the picture. (That this is a definition, follows, I think,
from 5 542.)
Light may be thrown on the "form of representation" by the
following remarks macdeearlier in the book on the structureand
form of facts. "The way in which objects hang together in the
atomic fact is the structure of the atomic fact. The form is the
possibility of the structure. The structureof the fact consists of
the structures of the atomic facts" (2'032, 2-033, 2 034). The only
point which I can see in the distinction between structureand form,
is that the insertion of '' possibility" may include the case, in
which the alleged fact whose form we are consideringis not a fact,
whether or no
so that we can talk of the form of the fact alb,abb
is true, provided it is logically possible. It is to be regretted that,
the above definitions do not make it clear whether two facts can
ever have the same structure or the same form; it looks as if two
atomic facts might well have the same structure,because objects
hung together in the same way in each of them. But it seems
from remarks later in the book that the structure of the fact is not
merely the way in which the objects hang together but depends
also on what objects they are, so that two differentfacts never have
the same structure.
A picture is a fact and as such has a structure and a form; we
are, however, given the following new definitionsof its " structure"
and its " form of tepresentation" in 2-15, 2-151. "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.
This connexion of the elements of the picture is called its structure,
and the possibility of this structure is called the form of representa-
LUDWIG
Tractatus Logico-Philosophicus.
tion of the picture. The form of representationis the possibility
that, the things are so combined with one another as are the
elements of the picture." This passage is puzzling; firstly, because
we have here two differentdefinitions of the form of representation,
and secondly, because it is not obvious how to interpret " this connexion" in the first of the two definitions; it may refer to the
definite way in which the elements are combined, or to the whole
of the preceding sentence, i.e., "this coinexion of the elements"
may be that their combinationrepresents a similar combination of
the things. On neither interpretationdoes the first definitionseem
to coincide with the second. We can only hope to decide between
these possible meanings of "form of representation" by considering
the things which Mr. Wittgenstein says about it. Its chief property, which makes it of fundamental importance in his theory, is
that asserted in 2-17: " What the picture must have in common
with reality in order to be able to represent it after its mannerrightly or falsely-is its form of representation". Further, " what
every picture, of whateverform, 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. If the form of representation is the logical form, then the picture is called a logical picture.
Every picture is also a logical picture. (On the other hand, for
example, not every picture is spatial.)" (2-18, 2-181, 24182). It
appears, then, that a picture may have several forms of representation, but one of these must be thelogical form; and that it is not
asserted that the picture must have the same logical form as what,
it pictures, but that all pictures must have the,logical form. This
a,lso makes more plausible the deduction that the logical form of
representationcannot be represented; for, that it was common ta
one picture and reality, could afford no ground for supposing that
it could not be representedin another picture.
Now it is easy to seeI a sense in which a picture may have the
spatial and must also have the logical form, namely, by taking the
form to be the (possibility of the) way in which the elements of the
picture are combined. (One of the interpretations of the first.
definition given above.) This may be logical, as when the colour
of a patch on a map represents the height above sea level of the
corresponding patch of country; the elements of the picture are
combined as predicate and subject and this represents that the
corresponding things are also combined as predicate and subject.
On the other hand the form may be spatial as when one dot being
between two others represents that a certain town is between two
others; but in this case we can also regard betweenness not as the
way in which the dots are combined but as another element in the
picture, which corresponds with itself. Then since betweenness
and the dots are combined, not spatially, but as triple relation and
its relata, that is logically, the form is logical. Here then we have
something which may be spatial and must also be logical; but it
does not follow that this is the form of representation,for the form
468
of representation may be some more complicated entity involving
this and so derivatively spatial or logical. If. indeed, the above
were what were meant by the form of representation,then in saying
that a picture must have the logical form Mr. Wittgenstein would
be saying no more than that it must be a fact; and in saying that we
-cannotrepresent or speak about the logical form of representation,
no more than that we crnnot talk about what makes a fact a fact,
nor ultimately about facts at all, because every statement apparently
about facts is really about their constituents. These things he
certainly believes, but it seems to me unlikely that his complicated
propositions about the form of representation amount to no more
than this. Probably he is confused and does not use the term consistently; and if we revert to the second of the definitions given
above, " The form of representationis the possibility that the things
are so combined with one another as are the elements of the
picture," we may discover another sense in which the picture has
the form of representationin common with the pictured, namely,
that the things with which its elements are co-ordinated by the
representing relation are of such types that they can be combined
in the same way as the elements of the picture; and so we arrive
at the important principle that " The picture contains the possibility of the state of affairswhich it represents " (2 203). It seems
to me, for reasons explained later, that the independent acceptance
of this principle will justify almost all the non-mystical deductions
which Mr. Wittgenstein makes from the necessity of something in
common between the picture and the world, which cannot itself
be represented; and that these deductions can so be given a firmer
basis than is provided by the nature of this elusive entity, the form
of representation, which is intrinsically impossible to discuss.
In order to obtain any further comprehension of what Mr.
Wittgenstein thinks a sentence must have in common with the
fact which it asserts, or, indeed, of most of his book,it is necessary
to understand his use of the word " proposition". This is, I think,
made easier by the introduction of two words used by C. S. Peirce.
A word, in the sense in which there are a dozen words ' the' on a
page, he called a token; and these dozen tokens are all instances
of one type, the word 'the'. Besides " word" there are other
words which have this type-token ambiguity; thus a sensation, a
thought, an emotion or an idea, may be either a type or a token.
And in Mr. Wittgenstein's usage, in contrast, for instance, to Mr.
Russell's in the Principles of Mathematics," proposition" also has
type-token ambiguity.
A propositionialsign is a sentence; but this statement must be
qualified,for by " sentence " may be meant something of the same
nature as the words of which it is composed. But a propositional
sign differs essentially from a word because it is not an object or
class of objects, but a fact, " the fact that its elements, the words,
are combined in it in a definiteway " (3'14). Thus " propositional
sign" has type-token ambiguity; the tokens (like those of any
LIUDWIG WITTGENSTEIN,
Tractatus Logico-Philosophicus.
sign) are grouped into types by physical similarity (and by conventions associating certain noises with certain shapes) just as are
the instancesof a word. But a propositionis a type whose instances.
consist of all propositional sign tokens which have in common, not.
a certain appearance,but a certain sense.
As to the relation between a proposition and a thought Mr.
Wittgenstein is rather obscure; but I think his meaning is that
a thought is a type whose tokens have in common a certain sense,,
and include the tokens of the correspondingproposition,but include
also other non-verbal tokens; these, however, are not relevantly
differentfrom the verbal ones, so that it is sufficient to consider the
latter. He says "It is clear that 'A believes that p,' 'A thinks
p, 'A says p,' are of the form 'p ' says p'" (5'542), and so explicitly reduces the question as to the analysis of judgment, to
which Mr. Russell has at various times given different answers, to
the question " What is it for a propositiontoken to have a certain
sense?" This reduction seems to me an important advance, and
as the question to which it leads is of fundamental importance,I
propose to examine carefully what Mr. Wittgenstein says by way
of answering it.
First it may be remarkedthat if we can answer our question we.
incidentally solve the problem of truth; or rather it is already evident that there is no such problem. For if a thought or proposition
token " p " says p, then it is called true if p, and false if p. We
can say that it is true if its sense agrees with reality, or if the possible state of affairs which it representsis the actual one, but these
formulations only express the above definition in other words.
According to Mr. Wittgeiistein a proposition token is a logical
picture; and so its sense should be given by the definition of the
sense of a picture; accordiriglythe sense of a proposition is that
the things meant by its elements (the words) are combined with
one another in the same way, as are the elements themselves, that
is, logically. But it is evident that, to say the least, this definition
is very incomplete; it can be applied literally only in one case,
that of the completely analysed*-elementary proposition. (It
may be explained that an elementary proposition is one which
asserts the existence of an atomic fact, and that a proposition
token is completelyanalysed if there is an element in it corresponding, to each object occurring in its sense.) Thus if " a " means a,
"b " b, and "R," or more accurately the relation we establish between " a " and " b" by writing " aRb,"means R, then that " a "
stands in this relation to " b" says that aRb,and this is its sense.
But this simple scheme must evidently be modified,if, for example,
one word is used for " having R to b " so that the propositionis not,
completely analysed; or if we have to deal with a-morecomplicated
propositionwhich contains logical constants such as " not " or " if,"
which do not represent objects as names do. Mr. Wittgenstein
does not make it quite clear how he proposes to deal with either of
these difficulties. As regards the first, which he almost ignores, he
470
may reasonablyplead that it results from the enormous complication of colloquial language, which cannot be disentangled a priori;
for in- a perfect language all propositions would be completely
analysed except when we defined ,a sign to take the place of a string
of simple signs; then, as he says, the defined sign would signify via
the signs, by which it is defined. But the other difficulty must be
faced, since we cannot be satisfied with a theory which deals only
with elementarypropositions.
The sense of propositions in general is explained by reference to
,elemehtarypropositions. With regardto n elementarypropositions
there are 2n possibilities of their truth and falsehood, which are
called the truth-possibilities of the elementary propositions; similarly there are 2n possibilities of existence and non-existence of the
'correspondingatomic facts. Mr. Wittgenstein says that any proposition is the expression of agreement and disagreement with the
truth-possibilities of certain elementary propositions, and its sense
is its agreementand disagreementwith the possibilities of existence
-and non-existence of the corresponding atomic facts. (44, 42.)
This is illustrated by the following symbolism for truth-functions.
'T stands for true, F for false and we write the 4 possibilities for 2
elementary propositions thus:p q
T T
F T
T F
F F
Now by setting a T against a possibility for agreement and leaving
;a blank for disagreement we can express, for example, p ) q, thus:
p q
T T T
F T T
T F
F F T
Or, adopting a conventionalorderfor the possibilities, (TT-T)(p, q).
Evidently this notation does not in any way require p, q to be
elementary propositions; and it can be extended to include propositions containing apparent variables. Thus p, q may be given
LUDWIG
Tractatus Logico-Philosophicus.
not by enumeration but as all values of a propositional function,
i.e., all propositions containing a certain expression (defined as
"any part of a proposition which characterisesits sense" (3-31));
and (--T)(s), where the solitary T expresses agreement only
with the possibility that all the arguments are false, and Z is the
set of values of fX, is what is written ordinarily as -: (Wx). fx.
So every propositionis a truth-functionof elementary propositions,
and many differently constructed propositional signs are the same
proposition, because, expressing agreement and disagreement with
the same truth-possibilities, they have the same sense and are the
same truth-function of elementary propositions. Thus:
q ) p:
q ) p and - ( - p v ) are the same as p.
This leads to an extremely simple theory of inference; if we call
those truth-possibilities with which a proposition agrees, its truthgrounds, then q follows from p, if the truth-grounds of p are contained among those of q. In this case Mr, Wittgenstein also says
that the sense of q is contained in that of p, that in asserting p we
are incidentally asserting q. I think this statement is really a definition of containing as regards senses, and an extension of the
meaning of assert partly in conformity with ordinary usage, which
probably agrees as regardsp. q and p, or (x) . fx and fa but not
otherwise.
There are two extreme cases of great importance; if we express
disagreement with all the truth-possibilitieswe get a contradiction,
if agreement with them all, a tautology, which says nothing. The
propositions of logic are tautologies and to have made clear this,
their essential characteristic,is a remarkableachievement.
We have now to consider whether the -above is an adequate
account of what it is for a proposition token to have a certain
sense; and it seems to me that it certainly is not. For it is really
only an account of what senses there are, not of what propositional
signs have what sense. It enables us to substitute for " 'p' says
p," ' " p ' expressesagreement with these truth-possibilitiesanddisagreement with these others," but the latter formulation cannot be
regarded as an ultimate analysis of the former, and it is not at all
clear how its furtheranalysis proceeds. We have therefore to look
elsewhere for the answer to our question. Towards this answer
Mr. Wittgenstein does make a clear contribution; in 5-542, he says
that in "'p ' says p " we have a co-ordination of facts by means of
a co-ordinationof taeir objects. But this account is incomplete
because the sense is not completely determinedby the objects which
'occurin it; nor is the propositional sign completely constituted by
the names which occur in it, for in it there may also be logical
constants which are not co-ordinatedwith objects and complete the
determinationof the sense in a way which is left obscure.
If we had only to deal with one logical symbolism I do not think
there would be any difficulty. For, apart from variation in the
names used, there would be a rule giving all propositional signs
472
which, in that symbolism, had a certain sense, and we could complete the definition of "sense" by adding to it these rules. Thus
" 'p ' says that
aRb" would, supposing us to be dealing with
the symbolism of FrincipiaMathematica, be analysed as follows:
call anything meaning a, " a " and so on, and call "a" 'R" "b "
q "; then 'p "iseither'' q ''or''
"
q "or' "q v q
or any of the other symbols constructed accordingto a definite rule.
(It may, of course, be doubted whether it is possible to formulate
this rule as it seems to presuppose the whole of symbolic logic;
but in any perfect notation it might be possible; for example in Mr.
Wittgenstein's notation with T's and F's there would be no difficulty.) But it is obvious that this is not enough; it will not give
an analysis of " A asserts p" but only of " A asserts p using such
and such a logical notation". But we may well know that a
Chinaman has a certain opinion without having an idea of the
logical notation he uses' Also the evidently.-significant statement
that German3use " nicht "for not becomes part of the definition
of such words as " believe," "think" when used of Germans.
It is very hard to see a way out of this difficulty; one may
perhaps be found in Mr. Russell's suggestion in the Analysis of
Mind (p. 250), that there may be special belief feelings occurring
in disjunction and implication. Logical constants might then be
significant as substitutes for these feelings, which would form the
basis of a universal logical symbolism of human thought. But
it looks as if Mr. Wittgenstein believes in another kind of solution,
going back to his earlier statement that the sense of a picture is
that the things are so combined with one another as are the elements of the picture. The natural interpretation of this in our
present context is that we can only represent that a does not have
a certain relation to b, by making " a " not have a certain relation
to " b," or in general that only a negative fact can assert a negative
fact, only an implicative fact an implicative fact and so on. This is
absurdand evidently not what he means; but he does seem to hold
that a proposition token resembles its sense somehow in this sort
of way. Thus he says (5&512),"That which denies in I', p ' is not
',' but that which all signs of this notation, which deny p, have
in common. Hence the common rule according to which '- p,'
'-_-- -p,"
-Zp,v
'p . -p,'
etc. etc. (to infinity) are
-p,'
constructed. And this which is common to them all mirrors
denial." I cannot understand how it mirrorsdenial. It certainly
does not do so in the simple way in which the conjunction of two
propositions mirrors the conjunction of their senses. This difference between conjunctionand the other truth-functionscan be seen
in the fact that to believe p and q is to believe p and to believe q;
but to believe p or q is not the same as to believe p or to believe q,
nor to believe not p as not to believe p.
We must now turn to one of the most interesting of Mr.
Wittgenstein's theories, that there are certain things which cannot
be said but only shown, and these constitute the Mystical. The
LUDWIG
Tractatus Logico-Philosophicus.
reason why they cannot be said is that they have to do with the
logical form, which propositions have in common with reality.
What sort of things they are is explained in 4'122. "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. (Instead of
property of the structure I also say 'internal property'; instead
of relation of structures 'internal relation'. I introduce these
expressions in order to show the reason for the confusion, very
widespread among philosophers, between internal relations and
proper (external)relations.) The holding of such internal properties
and relations cannot, however, be asserted by propositions, but
shows itself in the propositions, which presept the atomic facts and
treat of the objects in question." As I have already said, it does
not seem to me that the nature of the logical form is sufficiently
clear to provide any cogent arguments in favour of such conclusions; and I think that a better approach to the treatment of
internal properties may be given by the following criterion: "A
property is internal if it is unthinkable that its object does not
possess it" (4123).
It is a principle of Mr. Wittgenstein's, and, if true, is a very
important discovery, that every genuine proposition asserts something possible, but not necessary. This follows from his account
of a proposition as the expression of agreement and disagreement,
with truth-possibilitiesof independent elementary propositions, so
that the only necessity is that of tautology, the only impossibility
that of contradiction. There is great difficultyin holding this; for
Mr. Wittgenstein admits that a point in the visual field cannot be
both red and blue; and, indeed, otherwise, since he\thinks induction
has no logical basis, we should have no reason for thinking that we
may not come upon a visual point which is both red and blue.
Hence he says that " This is both red and blue " is a contradiction.
This implies that the apparently simple concepts red, blue (supposing us to mean by those words absolutely specific shades) are
really complex and formally incompatible. He tries to show how
this may be, by analysing them in terms of vibrations. But even
supposing that the physicist thus provides an analysis of what we
mean by " red " Mr. Wittgenstein is only reducing the difficulty to
that of the necessary properties of space, time, and matter, or the
ether. He explicitly makes it depend on the impossibility of a
particle being in two places at the same time. These necessary
properties of space and time are hardly capable of a further reduction of this kind. For example, considering between in point
of time as regards my experiences; if B is between A and D and
C between B and D, then C must be between A and D; but it is
hard to see how this can be a formal tautology.
But not all apparently necessary truths can be supposed, or are
by Mr. Wittgenstein supposed, to be tautologies. There are also
the internal properties of which it is unthinkablethat their objects
474
do not possess them. Sentences apparently asserting such, properties of objects are held by Mr. Wittgenstein to be nonsense, but
to stand in some obscure relation to something inexpressible.
This last seems to be involved by his reason for thinking that they
are nonsense, which is that what they are meant to assert cannot
be asserted. But it seems to maepossible to give reasons why these
sentences are nonsense and a general account of their origin and
apparentsignificance, which have no mystical implications.
Sentences of this kind, which we call "pseudo-propositions,"
arise i-n various ways depending on our language. One source is
the grammaticalnecessity for such nouns as " object " and " thing "
which do not like ordinary common nouns correspond to propositional functions. Thus from "this is a red object" appears to
follow the pseudo-proposition "this is an object," which in the
symbolism of PrincipiaMathemcticacould not be written at all.
But the commonest and most important source is the substitution
of names or relative names for descriptions. (I use "relative
names" to include " p," the expression for a given sense p; in contrast to a description of that sense, such as " what I said.")
Usually this is legitimate; for, if we have a propositional schema
containing blanks, the significance of the schema when the blanks
are filled by descriptions presupposes, in general, its significance
when they are filled by the names of things answering to the
descriptions. Thus the analysis of " The 4)is red " is " There is
one and only one thing which is 4); and it is red" and the occurrence in this of " it is red" shows that the significance of our
proposition presupposes the significance of " a is red" where a is
of the type of the 4. But sometimes this is not the case because
the proposition containing the description must be analysed a little
differently. Thus " The 4 exists " is not " There is one and only
one thing which is 4); and it exists," but simply " There is one
and only one thing which is 4)"; so that its significance does not
presupposethat of " a exists," which is nonsense, for its truth could
be seen by mere inspection without comparison with' reality, as is
never the case with a genuine proposition. But partly because we
sometimes fail to distinguish " a exists," from " The object meant
by ' ' exists," and partly because "- exists " is always significant
when the blank is filled by a description,and we are not sufficiently
sensitive to the difference between descriptions and names; " a
exists " sometimes feels as if it were significant. Mr. Wittgenstein
gives in to this deceptive feeling so far as to hold that the existence of
the name " a " shows that a exists, but that this cannot be asserted;
it seems, however, to be a principal component in the mystical:
"Not howthe world is, is the mystical, but that it is" (6 44).
Our next example is provided by identity, of which Mr. Wittgenstein gives an importantdestructive criticism; " 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 significant)" (5 5302). And
LUDWIG
Tractatus Logico-Philosophicus.
"a = b " must be a pseudo-proposition since it is true or false
a prioriaccording as " a," " b " are names for the same, or different
things. If now we acdoptthe new convention that two different
signs in one proposition must have different meanings, we get
a new analysis of descriptions not involving identity. For f(7x) (+x)
instead of
(Rc) :Ox$), x=x c . fc
we have
(ax) xfx i:* -(Ex, Y).qtx .4fy.
And since (7x)(ox) = c is analysed as oc: (x, y) . Ox . Oy we
is only significant when one blank at least is
see that "- -"
filled by a description. Incidentally this rejection of identity may
have serious consequences in the theory of aggregates and cardinal
number; it is, for example, hardly plausible to say that two classes
are only of equal number when there is a one-one relation whose
domain is the one and converse domain the other, unless such relations can be constructed by means of identity.
Next I shall show how this account applies-tointernal properties
of the senses of propositions, or, if they are true propositions, the
corresponding facts. "p is about a" is an example; its significance might be thought to follow from that of " He said something
about a"; but if we reflect on the analysis of the latter proposition
we shall see that this is not the case; for it evidently reduces not
to " There is p, which he asserted and which is about a" but to
"1There is a function b such that he asserted Oa,"which. does not
involve -the pseudo-proposition " p is about a ". Similarly " p is
contradictory to q " might be thought to be involved in "He contradicted me "; but it is seen to be a pseudo-propositionwhen-we
analyse the latter as " There is p such that I asserted p, he
p ".
Of course this is not a complete analysis, but it is the first step and
sufficient for our present purpose and shows how "-is contradictory to-" is only significant when one blank at least is filled by
a description.
Other pseudo-propositions are those of mathematics, which,
according to Mr. Wittgenstein are equations obtained by writing
I = "between two expressions which can be substituted for one
another. I do not see how this account can be supposed to cover
the whole of mathematics, and it is evidently incomplete since
there are also inequalities, which are more difficult to explain. It
is, however, easy to see that " I have more than two fingers " does
not presuppose the significance of " 10> 2 "; for, remembering
that different signs must have different meanings, it is simply
"(ax, y, z): x, y, z are fingers of mine ".
Just as the explanation of some apparently necessary truths as
tautologies met with difficulty in the field of colour, so does the
explanation of the remainder as pseudo-propositions. " This blue
colour and that," says Mr. Wittgenstein, " stand in the internal relation of brighter and darker eo ipso. It is unthinkable that -these
two objects should not stand in this relation" (4123). Accordingly
a sentence apparently asserting that one named colour is brighter
476
than another named colour must be a pseudo-proposition; but it
is hard to see how this can be reconciled with the indubitable significance of a sentence asserting that a described colour is brighter
than another, such as " My cushion at home is brighter than my
carpet ". But in this case the difficulty could be completely removed by the supposition that the physicist is really analysing the
meaning of " red; " for his analysis of a colour comes eventually to
a number, such as the length of a wave or what not, and the difficulty is reduced to that of reconciling the non-significance of an
inequality between two given numbers with the significance of an
inequality between two described numbers, which is evidently
somehow possible on the lines suggested for " I have more than
two fingers" above.
Let us now pass to Mr. Wittgenstein's account of philosophy.
"The object of philosophy," he says, " is the logical clarificationof
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" (4.112). It seems to me that we cannot be satisfied
with this account without some further explanation of " clarity,"
and I shall try to give an explanation in harmony with Mr.
Wittgenstein's system. I think that a written sentence is " clear "
in so far as it has visible properties correlatedwith or " showing"
the internal properties of its sense. Accordingto Mr. Wittgenstein
the latter always show themselves in internal properties of the
proposition; but owing to the type-token ambiguity of " proposition" it is not immediately clear what this means. Properties
of a proposition must, I think, mean properties of all its tokens;
but, the internal properties of a proposition are those properties of
the tokens which are, so to speak, internal not to the tokens but to
the type; that is, those which, one of the tokens must have if it is
to be a token of that type, not those which it is unthinkable that it
should not have anyhow. We must remember that there is no
necessity for a sentence to have the sense it does in fact have; so
that if a sentence says fa, it is not an internal property of the
sentence that there is something in it somehow connected with a;
but this is an internal property of the proposition, because the
sentence could not otherwise belong to that proposition type, i.e.,
have that sense. So we see that the internal properties of a
proposition which show those of its sense are not, in general,
visible ones, but complicated ones involving the notion of meaning.
But in a perfect language in which each thing had its own one
name, that in the sense of a sentence a certain object occurred,
would be also shown visibly by the occurrence in the sentence of
the name of that object; and this might be expected to happen
with regard to all internal properties of senses; that one sense, for
example, is contained in another (i.e., one proposition follows from
LUDWIG WITTGENSTEIN,
Tractatus Logico-Philosophicus.
another) might always appear visibly in the sentences expressing
them. (This is nearly achieved in Mr. Wittgenstein's T notation.)
Thus in a perfect language all sentences or thoughts would be perfectly clear. To give a general definition of "clear " we must replace " visible property of the sentence " by "internal property of
the propositionalsign," which we interpretanalogouslyto " internal
propertyof the proposition" as a property which a token must have
if it is to be that sign, which, if the token is written, is the same
as a visible property. We say then that a propositional sign is
clear in so far as the internal propertiesof its sense are shown not
only by internal properties of the proposition but also by internal
propertiesof the propositionalslgn.
(It may perhaps be confusion between the internal properties of
the proposition and those of the propositionalsign which gives rise
to the idea that Mr. Wittgenstein's doctrines are, in general, only
asserted of a perfect language.)
We can easily interpret this idea of philosophy in terms of the
non-mystical account of internal properties given above. First we
notice and explain the fact that we often apparently do or do not
recognise that something has an internal property, although this is
a pseudo-propositionand so cannot be recognised. What we really
recognise is that "the object or sense meant or asserted by the
words before us has this property,"which is significant because we
have substituted a description for a name. Thus as the result of
logical proof we recognise, not that p is a tautology which is a
pseudo-proposition,but that "p" says nothing. To make propositions clear is to facilitate the recognition of their logical
properties by expressing them in languagesuch that these properties
are associated with visible properties of the sentence.
But I think this activity will result in philosophical propositions
whenever we discover anything new about the logical form of the
senses of any interesting body of sentences, such as those expressing the facts of perception and thought. We must agree with Mr.
Wittgenstein that " p is of such and such a form " is nonsense, but
'9' p' has a sense of such and such a form " may nevertheless not
be nonsense. Whether it is or not depends on the analysis of
"' p' is significant,"which seems to me probablya disjunctive proposition, whose alternatives arise partly from the differentpossible
forms 'of the sense of " p ". If this is so, we can by excluding some
of these alternatives make a proposition as to the form of the sense
of "p ". And this in certaincases, such as when " p " is " He thinks
q" or "He sees a," could be appropriatelycalled a philosophical
proposition. Nor would this be incompatible with Mr. Wittgenstein's more moderate assertion that "IMost propositions and
questions, that have been written about philosophical matters, are
not false but senseless. We cannot therefore answer questions of
this sort at all but only state their senselessness. Most questions
and propositionsof the philosophers result from the fact that we
do not understand the logic of our language" (4 003).
478
Lastly I wish to touch on Mr. Wittgenstein's general view of the
world. " The world," he says, " is the totality of facts not of things "
(1-1) and " it is clear that however different from the real one an
imagined world may he, it must have something-a form-in
common with the real world. This fixed form consists of the
objects" (2-022,2 023). It is an unusual view that any imaginable
world must contain all the objects of the real one; but it seems to
follow from his principles, for if " a exists " is nonsense, we cannot
imaginethat it does not exist, but only that it does or does not have
some property.
Mr. Russell in his introduction finds an acute difficulty in the
fact that (x) . ox involves the totality of values of 4x and so, apparently, that of the values of x, which according to Mr. Wittgenstein cannot be spoken of; for it is one of his fundamental theses
" 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". It seems doubtful, however, whether this is a fair
expression of Mr. Wittgenstein's view; for one thing, it suggests
that it is impossible to say (x) . ox, but only perhaps " All S are
P," taken as asserting nothing about the non-S's, which he cer-
tainly does not maintain. It may, then, be interesting to consider
what he says which gives plausibility to Mr. Russell's interpretation.
He does undoubtedly deny that we can speak of the number of all
objects (4-1272). -But this is not because all objects form an illegitimate totality, but because "object" is a pseudo-concept expressed not by a function but by the variable x. (Incidentally I
do not see why the number of all objects should not be defined as
the sum of the number of things having any specified propertyand
the number of things not having that property.) Also he says that
"The feeling of the world as a limited whole is the mystical
feeling" (6A45). But I do not think we can follow Mr. Russell in
deducing from this that the totality of values of x is mystical, if
only because "the world is the totality of facts not of things"
(141). And I think that " limited " gives the key to the sentence
quoted above. The mystical feeling is the feeling that the world
is not everything, that there is something outside it, its " sense"
or Itmeaning '.
It must not be thought that the topics I have discussed nearly
exhaust the interest of the book; Mr. Wittgenstein makes remarks,
always interesting, sometimes extremely penetrating, on many
other subjects, such as the. Theory of Types, Ancestral-Relations,
Probability,the Philosophy of Physics and Ethics.
F. P. RAMSEY.