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Seite 17Ontologie
Was ist Wahrheit?—Wittgensteins Logisch-Philosophische Abhandlung
Marcus Hinz
ἔστιν ἔστιν
Inhalt
Inhalt
0 – Ein paar Worte zur Einführung1
0.1 – Das Ziel1
0.2 – Die Satznummern3
0.3 – Eine vorläufige Gliederung4
1 – Ontologie5
1.1 – Tatsachen6
1.2 – Sachverhalte7
1.3 – Gegenstände (Sachen, Dinge)9
1.3.1 - Kompasssatz 1: Gegenstände und Sachverhalte (Sätze 2.01*)9
1.3.2 - Kompasssatz 2: Das Wesen des Gegenstands (Sätze 2.02*)11
1.3.2.0 - Ein Experiment12
1.3.2.1 - Gegenstand und Welt14
Ein paar Worte zur Einführung
Ein paar vorläufige Bemerkungen.
Das Ziel
Da ich den Text im ersten Schritt inhaltlich betrachten möchte, fehlt bis hierher die Besprechung der Form.
Die Abhandlung ist kein klassischer Fließtext, der durch Kapitel gegliedert ist. Wittgensteins Text besteht vielmehr aus einer Reihe hierarchisch geordneter Sätze oder kurzer Textpassagen, die über Satznummern in Beziehung zueinander gesetzt werden.
Diese Form ist das wohl auffälligste Merkmal des Texts und gleichzeitig das größte Hindernis, ihn zu verstehen.
Wittgenstein wählt die Form natürlich nicht zufällig oder aus rein ästhetischen Gründen. Er versucht damit vielmehr die Darstellung seiner Ideen zu perfektionieren: Wittgenstein strebt mit der gewählten Form den Zusammenfall von Form und Gehalt an. Die „unantastbar[e] und definitiv[e]“1
LPA - Vorwort letzter Absatz Wahrheit der Abhandlung soll auch in der Form ihrer Darstellung unantastbar und definitiv sein.
Wittgensteins Vorhaben, mit der Abhandlung einen Text vorzulegen, der die endgültige Lösung der Probleme in eine ebenso endgültige Form bringt, scheitert aber auf ganzer Linie. Kein Text der Philosophie hat wohl zu mehr Missverständnissen geführt, als die Abhandlung.
Und so erreicht Wittgenstein mit der Abhandlung das genaue Gegenteil dessen, was er erreichen wollte: an die Stelle von Klarheit und Analyse tritt Unverständnis und das Ausweichen auf einen Mystizismus, der Wittgenstein sicher nicht fremd war, aber ebenso sicher nicht im Fokus seiner philosophischen Arbeit stand2
Die Abhandlung ist sicher das einzige wissenschaftliche Werk, das als Libretto einer Oper herhalten musste..
Selbst Russells Vorwort zur Abhandlung ist voll von Missverständnissen des Texts. Ich möchte zwei Gründe für diese Missverständnisse herausgreifen und an Russells Vorwort erläutern, um mein Vorhaben zu verdeutlichen.
Zunächst ist da das Fehlen von Beispielen und anschaulichen Erläuterungen an wichtigen Stellen des Texts. Ein Beispiel aus dem ersten Drittel von Russells Vorwort:3
Ich muss mich für eine zitierfähige Ausgabe entscheiden. Habe ich noch nicht. Wahrscheinlich die kritische Ausgabe von Suhrkamp
„What is complex in the world is a fact. Facts which are not compounded of other facts are what Mr. Wittgenstein calls Sachverhalte, whereas a fact which may consist of two or more facts is a Tatsache: thus, for example “Socrates is wise” is a Sachverhalt, as well as a Tatsache, whereas “Socrates is wise and Plato is his pupil” is a Tatsache but not a Sachverhalt.“
Russell bezieht sich im Wesentlichen auf Satz 2 der Abhandlung:
2Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten.
Russell versteht vieles richtig:
Er identifiziert „Tatsache“ und „Sachverhalt“ als Termini technici.
Er schreibt auch zu Recht, dass einer Tatsache immer mehr als ein Sachverhalt entspricht.
Die Deutung, dass einfachen Aussagesätzen Sachverhalte und Tatsachen, zusammengesetzten Sätzen aber nur Tatsachen entsprechen, ist dagegen falsch. Das kann man dem Text aber nirgends direkt entnehmen. Es ergibt sich nur indirekt aus Überlegungen zum Text4
Es ist zum Beispiel nicht möglich, dass etwas Tatsache und Sachverhalt zugleich ist, da Sachverhalte aus Gegenständen bestehen, Tatsachen dagegen nicht..
Ein einfaches Beispiel hätte hier Klarheit schaffen können. Wittgenstein liefert es nicht und so hat Russell schon vom ersten Satz der Abhandlung an keine die Chance, das Werk richtig zu verstehen.
Weiterhin ist bemerkenswert, dass die Abhandlung gerne als aphoristisch, oder gar als Sammlung von Aphorismen bezeichnet wird5
FIXME: Bleibe ich hier noch schuldig.
Von einem Buch, das in diesem Stil gehalten ist, würde man erwarten, dass die Sätze darin in losem oder gar keinem Zusammenhang zueinander stehen: ein Aphorismus ist seiner Definition nach ein Satz oder eine kurze Textpassage, die für sich – eben ohne Kontext – besteht6
vgl. dazu https://de.wikipedia.org/wiki/Aphorismus. .
Die Abhandlung ist aus Sätzen und kurzen Testpassagen aufgebaut, doch gibt Wittgenstein seinem Buch die genau gegenteilige Form: Die Satznummern legen die exakten Bezüge jedes einzelnen Satzes der Abhandlung im Netz aller anderen Sätze fest. Über-, Unter- oder Beiordnung eines Satzes zu jedem anderen Satz der Abhandlung ist damit vollständig bestimmt. Geschlossener kann man einen Text nicht aufbauen.
Die Satznummern gliedern den Text aber rein formal, an keiner Stelle erläutert Wittgenstein die Semantik dieser Bezüge. Und hier scheitert das Konzept erneut: die Semantik der formalen Bezüge erschließt sich eben nicht automatisch beim Lesen: der Textfluss geht verloren. Am Ende entsteht der Eindruck, man habe es mit einer Ansammlung von Einzelsätzen und nicht mit einem geschlossenen Gedankengebäude zu tun7
Das hat ganz praktische Gründe, die ich in Besprechung der Form aufzeigen möchte. Letztlich scheitert Wittgenstein daran, dass er ein zweidimensionales Gebilde - sein Netz von Sätzen - in eine eine eindimensionale Form - einen sequentiellen Text - presst..
Auch hier ein Beispiel in Russells Vorwort fast am Ende8
Dito:
„These considerations lead him to a somewhat curious discussion of Solipsism.
[…]
The metaphysical subject does not belong to the world but is a boundary of the world.
We must take up next the question of molecular propositions [...]”
Egal, wie man Wittgensteins Bemerkungen zum Solipsismus in de Abhandlung beurteilt, ist es interessant zu sehen, wie Russell das Thema im Vorwort behandelt: Schon der Start zeigt, dass Russell das Thema nicht in den Gedankengang der Abhandlung einordnen kann, und es statt dessen als „curious discussion“ abgrenzt. Und am Ende könnte der Abbruch nicht abrupter sein: Zunächst wiederholt Russell einen Kernsatz der Abhandlung, um sich dann – völlig aus dem Nichts – einem anderen Thema zu widmen9
Monty Phython: „And Now for Something Completely Different.“.
Russell gelingt es an dieser Stelle nicht, das Thema Solipsismus in Wittgensteins Gedankengebäude einzuordnen: Einstieg wie Ausstieg grenzen Wittgensteins Bemerkungen vom restlichen Text aus, statt sie in den Gedankengang zu integrieren.
Auch hier steht dem Textverständnis die Form im Weg: Wittgensteins Sicht des Solipsismus kenne ich so nur aus der Abhandlung. In der Regel wird der Solipsismus in philosophischen Texten bestenfalls als Teufel an die Wand gemalt, selten ernsthaft diskutiert.
Ein einfacher Hinweis, dass hier eine Sicht vertreten wird, die konträr zu üblichen Sichten des Solipsismus ist, wäre für Russell ein Hinweis gewesen, dieser Passage besondere Aufmerksamkeit zu widmen, statt sie als „curious discussion“ abzutun. Wittgenstein bietet statt dessen völlig abstrakte Satznummern.
Nun darf man von Russell ein paar Dinge sicher annehmen:
Er war ein geübter Leser und Verfasser philosophischer Texte.
Er kannte Wittgensteins Ideen auch aus Gesprächen mit ihm.
Er war Wittgenstein wohlgesonnen.
Nicht nur war er zu Beginn Wittgensteins Mentor, er hat auch dazu beigetragen, dass die Abhandlung überhaupt in Druck ging: Ohne sein Vorwort hätte der Verlag das Buch nicht angenommen.
Kurz gesagt: Das Verständnisproblem liegt nicht beim Leser.
Mit der vorliegenden Arbeit möchte ich zunächst nicht mehr erreichen, als die Inhalte der Abhandlung in eine verständliche Form zu bringen. Die Gedanken, die Wittgenstein dort formuliert, sind zu wertvoll, um sie in ihrem kryptischen Grab verschimmeln zu lassen.
Die Satznummern
Eine weitere formale Herausforderung stellen die Satznummern dar, die Wittgenstein nicht vollständig erläutert:
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 n.1, n.2, n.3, etc., sind Bemerkungen zum Sätze No. n; die Sätze n.m1, n.m2, etc. Bemerkungen zum Satze No. n.m; und so weiter10
LPA Fußnote zu Satz 1.
Nach dieser Fußnote würde man erwarten, dass auf Satz 1 Satz 1.1 folgt, auf Satz 1.1 dann Satz 1.11, usw. Das stimmt auch, aber nur für Satzreihe 1. Schon in Satzreihe 2 folgt auf Satz 2 ein Satz mit Nummer 2.01, statt, wie erwartet, 2.1. Wittgenstein gibt an keiner Stelle Auskunft, was er mit den eingefügten Nullen bezweckt.
Der beste Reim, den ich mir machen konnte ist folgender: Laut Wittgenstein gibt die Satznummer das logische Gewicht der Sätze an: je weniger Stellen die Nummer hat, desto größer ist ihr Gewicht.
Das Einfügen der Null in die Satznummer führt dazu, dass der so nummerierte Satz in der Sortierung vor den erwarteten Nachfolger rutscht, sein logisches Gewicht aber trotzdem geringer als das des Nachfolgers ist.
Am Beispiel: Nehmen wir Satz 2 und sagen er hat das logische Gewicht 511
Einfach zu errechnen: Die längste Satznummer ist 5.47321. Das sind 6 Stellen, ihr entspricht das niedrigste logische Gewicht, setzen wir dafür 0 an. Jetzt kann man einfach hochzählen: 5 Stellen = 1, 4 Stellen = 2, 3 Stellen = 3, 2 Stellen = 4 und eine Stelle schließlich 5.. Der erwartete Nachfolger wäre Satz 2.1 mit dem logischen Gewicht von 4. Die nächste reguläre Satznummer mit einem logischen Gewicht von 3 wäre Satznummer 2.11, die auf Satz 2.1 folgt. Durch einfügen der Null erhält man die Satznummer 2.01. Sie hat ein logisches Gewicht von 3, steht in der Sortierung aber vor Satz 2.1.
Wittgenstein nutzt die eingefügte Null, um Sätze an der regulären Ordnung vorbei vor andere Sätze zu schmuggeln, und ihnen trotzdem ein niedrigeres logisches Gewicht zu geben. Er kann so Vorbemerkungen zu Sätzen schreiben, ohne ihnen ein ungewollt hohes logisches Gewicht zu geben.
Inhaltlich stehen diese Passagen tatsächlich auch zwischen den jeweiligen Sätzen. Gegen die Annahme, dass Wittgenstein hier nur Vorbemerkungen machen möchte, spricht aber, dass über 50 % des Texts in Sätzen mit Nummern stehen, die Nullen enthalten.
Eine vorläufige Gliederung
Die folgende Gliederung der Abhandlung soll das fehlende Inhaltsverzeichnis ersetzen und so zumindest einen kleinen Ausblick auf das, was uns erwartet, erlauben.
Ich gliedere die Sätze wie folgt12
Die Gliederung ist weder abschließend noch eindeutig. Ziel meiner Gliederung ist eine möglichst einfache Darstellung des Inhalts der Abhandlung. Deswegen werfe ich die formale Korrektheit, nach der Wittgenstein die Sätze gliedert, einfach über Bord. Genauso sind mir Überlappungen der einzelnen Teile gleichgültig. Ich werde meine Gliederung zu Beginn jeden Abschnitts erläutern und Wittgensteins Sicht dagegen setzen. :
Satz 1 - 2.027: Ontologie
Die Welt als Gesamtheit der Tatsachen
Der Sachverhalt
Gegenstände als Bestandteile des Sachverhalts
Satz 2.03 - 3.01: Bild und logischer Raum
Bild als Abbildung eines Sachverhalts
Wirklichkeit als logischer Raum
Sachlagen als Konstituenten der Tatsache im logischen Raum
Satz 3 - 4.04 Gedanke und Ausdruck des Gedankens
Der Gedanke als logisches Bild
Das Satzzeichen als Ausdruck des Gedankens
Projektion des Satzzeichens zum Bild
Satz 4 - 5.01 Bild und Wahrheit
Das Bild als Inhalt des sinnvollen (nicht tautologischen) Satzes
Analysierbarkeit aller Sätze in Elementarsätze
Die allgemeine Satzform
Satz 5 - 6.0 Die Grenzen der Logik
Wahrheitsfunktion vs. Wahrheitsoperation
Grenzen der formalen Logik
Grenzen der Semantik
»Satzbedeutung«
Satz 6.0 - 7 Conclusio
Ontologie
Zu Beginn der Abhandlung stellt Wittgenstein in Satzreihe 1 recht kurz seine Ontologie vor.
Laut Wittgenstein ist die Welt die Gesamtheit aller Tatsachen, die existieren, ohne Einfluss aufeinander zu haben13
Ich vermeide hier das Wort unabhängig, weil Wittgenstein es an dieser Stelle auch nicht nutzt.
Von Sachverhalten sagt Wittgenstein dagegen schon, dass sie unabhängig voneinander sind. Ob Wittgenstein das mit Absicht tut, kann man bei der Kürze des Texts nicht sagen. Mir erspart der Kniff, darauf hinweisen zu müssen, dass die Unabhängigkeit der Tatsachen nichts mit der Unabhängigkeit der Sachverhalte zu tun hat..
Das war's auch schon. Etwas anderes gibt es nicht und außer ihrer Eigenständigkeit stellt Wittgenstein keine weiteren formalen oder inhaltlichen Anforderungen an eine Tatsache.
Lebendig wird Wittgensteins Idee erst in der Abgrenzung der Tatsache zum Sachverhalt. Doch Sachverhalte gehören nicht zur Ontologie, folglich werden sie erst mit Beginn von Satzreihe 2 eingeführt.
Genauso grenzt Wittgenstein seine Tatsachenontologie zwar in Satz 1.1 gegen eine Dingontologie ab, erläutert in Satzreihe 1 aber nicht, wo er Dinge denn statt dessen einordnet. Dinge sind nicht Teil der Ontologie und landen folglich auch in Satzreihe 2.
Ein rundes Bild ergibt sich frühestens in Satz 2.027: Dort ist einerseits das Verhältnis von Tatsache zu Sachverhalt geklärt und anderseits dargelegt, wie Wittgenstein Gegenstände (Sachen, Dinge) in seiner Ontologie einordnet. Ich werde im Thema Ontologie deshalb Sätze 1 - 2.027 behandeln.
Man hätte genauso gut Sätze 1 - 2.063 wählen können, weil erst dann beschrieben ist, wie Wittgenstein sich das, was wir Wirklichkeit nennen, vorstellt. Ich werde Sätze 2.03 - 2.063 als Teil des Themas Bild behandeln.
Tatsache und Sachverhalt sind im Deutschen Synonyme. Wittgenstein stellt die beiden Wörter zu Beginn der Abhandlung gegeneinander, ohne explizit zu erläutern, wie sich das eine denn dann gegen das andere abgrenzt. Ich möchte meine Idee dazu in den nächsten zwei Abschnitten anhand eines kleinen Problems erläutern. Da Wittgenstein die Wörter nicht gegeneinander abgrenzt, bleibe ich in Abschnitten 1.1 und 1.2 den harten Textbeleg schuldig.
Tatsachen
Tatsachen sind für Wittgenstein Stücke der Wirklichkeit, die für sich selbst, das heißt, ohne andere Stücke der Wirklichkeit zu kennen, betrachtet werden können. Also zum Beispiel so etwas14
Ich werde Tatsachen immer als Fotografien darstellen. Diese Darstellung ist natürlich unvollständig. Es fehlen z.B. Geräusche und Gerüche. In Buchform ist es aber das beste, was ich liefern kann.:
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Wolfgang Brendel als Papageno in Mozarts Zauberflöte, München 2005
Das Foto stellt ein Stück Wirklichkeit dar, über das wir, ohne den Kontext zu benötigen, Aussagen machen können. Das Foto stellt einen Mann auf einer Bühne dar. Man weiß aber z. B. nicht, ob das Foto aus einer Ausführung oder einer Probe stammt. Genausowenig erkennt man, ob, und wenn ja, welche anderen Schauspieler noch auf der Bühne sind. Trotzdem stellt das Bild eine geschlossene Sinneinheit dar: Man kann z. B. sagen, dass ein singender Mann zu sehen ist. Egal, wie sich der unbekannte Kontext der Tatsache gestaltet, diese Aussage ist wahr.
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Foto
In diesem Fall erkennt man die Sinneinheit nicht, weshalb man bestenfalls diffuse Aussagen zu diesem Stück Wirklichkeit machen kann. Es ist keine Tatsache, einfach, weil nicht klar ist, worin sie denn bestünde.
Das ist der gesamte Inhalt der Sätze 1*, konkreter wird Wittgenstein an dieser Stelle nicht. Interessanter wird es, wendet man sich den Sachverhalten zu.
Sachverhalte
Zu den Sachverhalten kommt man, stellt man die Frage, was denn auf dem ersten Bild zu sehen ist.
Es gibt sehr viele Antworten auf diese Frage, ein Beispiel hatte ich oben schon gegeben: Man sieht einen singenden Mann.
Ich möchte aus der Vielzahl möglicher Antworten zwei herausgreifen und ein wenig näher betrachten:
Man sieht Papagenos erstes Auftreten in der Zauberflöte.
Man sieht Wolfgang Brendels erstes Auftreten in der Zauberflöte.
Beide Aussagen sind wahr. Beide Aussagen widersprechen sich nicht. Beide Aussagen beziehen sich auf dasselbe Ding15
Man entschuldige die Ausdrucksweise. Es ist philosophisch nicht persönlich gemeint., nämlich
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das da.
Dieser simple Fakt stellt das Grundprinzip der Selbstidentität des Gegenstands in Frage: Ein Ding ist ein Ding, und nicht zwei Dinge zugleich: Entweder ist das da ein Schauspieler oder eine Opernfigur, beides zugleich ist nicht möglich.
Die Replik scheint einfach: Der Satz „Ich sehe Papagenos ersten Auftritt in der Zauberflöte.“ ist nicht vollständig und genausowenig ist es der Satz „Ich sehe Wolfgang Brendels ersten Auftritt in der Zauberflöte“. Richtig hätte man sagen müssen: „Ich sehe Wolfgang Brendel in der Rolle des Papageno bei seinem ersten Auftritt in der Zauberflöte.“
Der Widerspruch ist aufgehoben: Beide Aussagen wurden in ein gemeinsames, konsistentes logisches Konstrukt integriert.
So einfach sieht Wittgenstein die Sache nicht. Ein Gegenargument:
Die wenigsten werden gewusst haben, dass die singende Person Wolfgang Brendel ist, viele davon aber sehr wohl Papageno erkannt haben.
Der Sänger hat zunächst nichts mit der Opernfigur zu tun. Ich kann den Satz „Ich sehe Papagenos ersten Auftritt in der Zauberflöte.“ verstehen, ohne Wolfgang Brendel zu kennen. Die zugrunde liegende Tatsache stellt keine notwendige Beziehung zwischen dem Sänger und der Opernfigur her.
Deutlicher wird das Argument, kommt eine zweite Tatsache hinzu:
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Papageno in Mozarts Zauberflöte, Lindauer Marionettenoper, 2012 (?)
Wieder Papagenos erster Auftritt in der Zauberflöte. Dieser Umstand setzt beide Tatsachen in Beziehung zueinander: Man kann etwa Papagenos Kostüm oder sein Erscheinen auf der Bühne in der jeweiligen Inszenierung vergleichen.
Diesmal ist Papageno eine Marionette. Der Vergleich funktioniert also nur, wenn der Sänger für die Opernfigur unerheblich ist; wenn man vom Sänger absehen und trotzdem die Opernfigur betrachten kann.
Der Satz „Ich sehe Papagenos ersten Auftritt in der Zauberflöte.“ handelt nicht von Wolfgang Brendel und es ist eine wesentliche Eigenschaft des Satzes, nicht von Wolfgang Brendel zu handeln. Wäre dem nicht so, könnte man die Kostüme zum Beispiel nur vergleichen, wenn Wolfgang Brendel sie trägt.
Die Sätze „Ich sehe Papagenos ersten Auftritt in der Zauberflöte.“ und „Ich sehe Wolfgang Brendels ersten Auftritt in der Zauberflöte“ sind logisch unabhängig voneinander und müssen es sein.
Folglich sichert der Satz „Ich sehe Wolfgang Brendel in der Rolle des Papageno bei seinem ersten Auftritt in der Zauberflöte.“ die Selbstidentität der Gegenstände nur scheinbar: Mit ‚Papageno‘ meine ich eben Papageno und nicht Papageno, der von Wolfgang Brendel verkörpert wird. Und genauso meine ich mit ‚Wolfgang Brendel‘ Wolfgang Brendel und nicht Wolfgang Brendel in der Rolle des Papageno.
Es ist eine wesentliche Eigenschaft der Beispielsätze, logisch unabhängig voneinander zu sein. Trotzdem treffen beide Sätze gleichermaßen auf dasselbe Stück Wirklichkeit – dieselbe Tatsache – zu.
Die Sätze „Ich sehe Papagenos ersten Auftritt in der Zauberflöte.“ und „Ich sehe Wolfgang Brendels ersten Auftritt in der Zauberflöte.“ beschreiben zwei Sachverhalte, die unabhängig voneinander aber gleichberechtigt auf
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zutreffen.
Das ist Wittgensteins Grundgedanke:
2Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten.
Zu jeder Tatsache gibt es verschiedene, logisch voneinander unabhängige Zugangs-weisen, die nicht aufeinander reduziert werden können. Jeder dieser Zugangsweisen entspricht ein Sachverhalt, der gleichberechtigt neben allen anderen Sachverhalten, die auf die Tatsache zutreffen, besteht16
Ich hatte ja nur zwei Sachverhalte unter sehr vielen denkbaren Sachverhalten herausgegriffen..
Umgekehrt hebt Wittgenstein dieser Idee nach aber das Prinzip der Selbstidentität eines Gegenstands als Grundprinzip der Wirklichkeit auf:
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das da ist diesem Sinne nach tatsächlich zwei Dinge gleichzeitig: Papageno und Wolfgang Brendel.
Dieser Fakt stellt für uns im täglichen Umgang mit der Tatsache überhaupt kein Problem dar. Trotzdem verträgt sich diese Ansicht nicht mit der Verwendung des Wortes Ding: Ein Ding ist ein Ding und nicht zwei Dinge zugleich.
Wittgensteins Idee hebt die Selbstidentität des Dings auf.
Wittgenstein gibt die Idee aber nicht gänzlich auf, er reduziert das Prinzip nur auf eine Ebene unterhalb der Wirklichkeit. Der Gegenstand wird auf die Ebene des Sachverhalts, dessen Bestandteil er ist, reduziert.
Die Einführung des Sachverhalts nimmt dem Gegenstand (Sache, Ding) seine universelle und eigenständige ontologische Stellung als konstituierendes Element der Wirklichkeit. Der Gegenstand wird statt dessen zur abhängigen Größe, die durch den Sachverhalt bestimmt wird.
In Sätzen 2.01 – 2.063 erläutert Wittgenstein die daraus resultierenden Konsequenzen für das, was wir Wirklichkeit nennen:
Gegenstände (Sachen, Dinge)
Die Kompasssätze zum Thema Gegenstand, Sache, Ding:
2.01Der Sachverhalt ist eine Verbindung von Gegenständen (Sachen, Dingen).
[…]
2.02Der Gegenstand ist einfach.
Kompasssatz 1: Gegenstände und Sachverhalte (Sätze 2.01*)
2.01Der Sachverhalt ist eine Verbindung von Gegenständen (Sachen, Dingen).
Welcher der Beispielsätze welchen Sachverhalt beschreibt, wird durch die Gegenstände, von denen der Satz handelt, bestimmt. Der erste Satz handelt von einer Opernfigur, der zweite von einem Sänger.
Im Beispiel haben wir den Sachverhalt von der Tatsache her betrachtet: Einer Tatsache entsprechen mehrere Sachverhalte, die sich durch die Gegenstände, aus denen sie bestehen, unterscheiden. Ordnendes Element sind die Gegenstände: Sie bestimmen die Zugangsweise, zeigen den gemeinten Sachverhalt an.
2.011Es ist dem Ding wesentlich, der Bestandteil eines Sachverhaltes sein zu können.
Der erste Auftritt in der Zauberflöte ist aber nicht der einzige Sachverhalt, in dem Papageno eine Rolle spielt. Es gibt sehr viel mehr Sachverhalte, die auf Papageno zutreffen, z. B. dass er ein Vogelfänger ist, und leicht Angst bekommt.
In all diesen Sachverhalten ist von demselben Papageno die Rede. Der Gegenstand kann also nicht auf nur einen Sachverhalt reduziert werden und mehr: Der Gegenstand muss etwas sein, das den Sachverhalten, in denen er vorkommt, gemeinsam ist. Ein Mindestmaß an Selbständigkeit muss gegeben sein.
2.0122Das Ding ist selbständig, insofern es in allen möglichen Sachlagen[17
Sachlagen sind Sachverhalte im logischen Raum. Ich komme dazu. An dieser Stelle kann man das Wort als Synonym für Sachverhalt lesen.] 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.)
‚Papageno‘ in „Papageno“, „Ich sehe Papagenos ersten Auftritt in der Zauberflöte.“ und „Papageno ist ein Vogelfänger.“ muss denselben Gegenstand meinen. Jede andere Annahme hätte absurde Konsequenzen18
Das wird im nächsten Kapitel näher beleuchtet..
Soweit akzeptiert Wittgenstein die Selbständigkeit der Gegenstände. Diese Selbständigkeit birgt aber nichts, das dem Gegenstand eigen wäre, ihm ein eigenes ontologisches Gewicht geben würde: Die Selbständigkeit der Gegenstände ist eine Form der Unselbständigkeit.
Wittgenstein geht den kleinstmöglichen Schritt und reduziert den Gegenstand auf eine Konstante, die allen Sachverhalten eigen ist, in denen er vorkommt.
Soweit die Sachverhalte, die auf den Gegenstand zutreffen. Es gibt aber auch Sachverhalte, die nicht auf den Gegenstand zutreffen und trotzdem von ihm handeln.
‚Papageno‘ im Satz „Papageno heiratet Pamina.“ muss sich genauso, wie alle anderen Beispielsätze auch, auf denselben Papageno beziehen, der z. B. in „Papageno ist ein Vogelfänger.“ gemeint ist. Es wäre sonst unmöglich, festzustellen, dass der Sachverhalt nicht zutrifft.
Durch die bestehenden Sachverhalte allein ist die Konstante nicht vollständig bestimmt. Erst die Berücksichtigung aller möglichen Sachverhalte19
An dieser Stelle spricht Wittgenstein zum ersten Mal davon, dass etwas möglich oder denkbar ist.
Ich lese diese Wörter im umgangssprachlichen Sinn, nicht in dem Sinn, wie sie sehr häufig in philosophischen Seminaren verwendet werden.
Es geht nicht darum, ob etwas prinzipiell möglich ist, sondern darum, wie unsere Reaktion darauf wäre, wenn es ernsthaft vorgeschlagen würde.
Es ist z. B. unmöglich, dass Papageno mir mein Portemonnaie geklaut hat. Mag sein, dass ich mir eine Welt denken kann, in der es einen diebischen Papageno gibt. Der Praxistest zeigt aber etwas anderes: Gehe ich zur Polizei, zeige Papageno ernstens als Dieb an, wäre Gelächter das Beste, was ich zu erwarten hätte. Es ist unmöglich, dass Papageno mir mein Portemonnaie geklaut hat., in denen ein Gegenstand eine Rolle spielen kann, bestimmen ihn vollständig.
2.0123Wenn ich den Gegenstand kenne, so kenne ich auch sämtliche Möglichkeiten seines Vorkommens in Sachverhalten.
(Jede solche Möglichkeit muss in der Natur des Gegenstandes liegen.)
Es kann nicht nachträglich eine neue Möglichkeit gefunden werden.
Die Einschränkung, dass nachträglich keine neue Möglichkeit gefunden werden kann, folgt unmittelbar aus Wittgensteins Konstrukt des Gegenstands:
Der Gegenstand ist nicht mehr als die Konstante, die verschiedenen Sachverhalten20
Hier müsste eigentlich Sachlage stehen. eigen ist. Im Nachhinein etwas über die Konstante zu erfahren, hieße sie zu ändern, dann wäre es aber nicht mehr die Konstante: Ihre Semantik wäre unklar.
Diesem Denken nach ist es unmöglich einen Gegenstand nur teilweise zu kennen. Das heißt wiederum, dass die Gegenstände abschließend und vollständig vorgeben, welche Sachverhalte möglich – überhaupt denkbar – sind.
2.0124Sind alle Gegenstände gegeben, so sind damit auch alle möglichen Sachverhalte gegeben.
Wittgenstein begreift einen Gegenstand als Summe aller Möglichkeiten seines Auftretens in Sachverhalten21
Ich übergehe an dieser Stelle für den Moment Satz 2.01231. Die dort eingeführte Unterscheidung zwischen internen und externen Eigenschaften werde ich später aufnehmen.. Damit wird der Gegenstand den Tatsachen gegenüber überladen. Entscheidend ist nicht, was ist (die Sachverhalte, in denen ein Gegenstand wirklich vorkommt), sondern was sein kann (die Sachverhalte, in denen ein Gegenstand vorkommen kann – die Sachlagen). Der Gegenstand (Sache, Ding) ist das Zentrum eines Raums von Möglichkeiten, der ausgeschöpft werden kann, aber nicht muss:
2.012In der Logik ist nichts zufällig: Wenn das Ding im Sachverhalt vorkommen kann, so muss die Möglichkeit des Sachverhaltes im Ding bereits präjudiziert sein.
[ … ]
2.013Jedes Ding ist, gleichsam, in einem Raume möglicher Sachverhalte.
Diesen Raum kann ich mir leer denken, nicht aber das Ding ohne den Raum.
Dieser Raum ist der Kern des logischen Raums, von dem Wittgenstein spricht, wenn er die Wirklichkeit meint.
Zunächst steht aber das Wesen des Gegenstands – die formalen Eigenschaften, die gegeben sein müssen, damit etwas eine Konstante sein kann, die verschiedenen Sachverhalten eigen ist – im Zentrum seines Interesses.
Kompasssatz 2: Das Wesen des Gegenstands (Sätze 2.02*)
2.02Der Gegenstand ist einfach.
Die wesentliche Eigenschaft des Gegenstands ist seine Einfachheit. Das heißt, er ist nicht aus Teilen irgendwelcher Art zusammengesetzt.
2.021Die Gegenstände bilden die Substanz der Welt. Darum können sie nicht zusammengesetzt sein.
2.0211Hätte die Welt keine Substanz, so würde, ob ein Satz Sinn hat, davon abhängen, ob ein anderer Satz wahr ist.
2.0212Es wäre dann unmöglich, ein Bild der Welt (wahr oder falsch) zu entwerfen.
An der zitierten Stelle ist allein schon bemerkenswert, dass Wittgenstein seine Forderung nicht ontologisch oder empirisch begründet. Er sieht statt dessen das Funktionieren der Sprache gefährdet: Die Möglichkeit, sinnvolle Sätze zu formulieren, hängt seiner Auffassung nach davon ab, dass die Gegenstände einfach sind.
Sein Argument leuchtet aber nicht auf Anhieb ein: „so würde, ob ein Satz Sinn hat, davon abhängen, ob ein anderer Satz wahr ist“.
Am einfachsten kommt man dem Argument auf die Spur, probiert man es einfach aus.
- Ein Experiment
Für das Experiment brauchen wir zunächst einen Gegenstand. Zum Glück sind Wittgensteins Anforderungen an einen Gegenstand nicht sonderlich hoch:
2.02331Entweder 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.
[ … ]
Alles, was durch eine Beschreibung von anderen Gegenständen unterschieden werden kann, kann als Gegenstand betrachtet werden.
Ich war nun schon immer der Meinung, dass die Blütenfarbe bei Blumen sträflich vernachlässigt wird. Um das zu korrigieren, führe ich folgende Gegenstände ein:
Blaue Blume→ Blaume
Rote Blume →Blote
Gelbe Blume → Blelbe
Bunte Blume→Blunte
…
Wittgensteins Bedingung ist erfüllt: Ich kann die Gegenstände durch eine Beschreibung hervorheben (alles vor den Pfeilen) und dann auf den Gegenstand hinweisen (alles nach den Pfeilen).
Als Nächstes wird ein sinnvoller Satz, der vom Gegenstand handelt, benötigt. Nehmen wir den Satz „Die Blaume blüht.“
Man muss also zeigen können, dass der Sinn des Satzes „Die Blaume blüht.“ davon abhängt, dass eine Blaume einfach – nicht zusammengesetzt – ist. Es geht nicht darum, ob der Satz wahr oder falsch ist, sondern darum, ob er überhaupt einen Sinn hat, der wahr falsch sein kann.
Im Argument spricht Wittgenstein von einem zweiten Satz, von dessen Wahrheit der Sinn des betrachteten Satzes nicht abhängen darf. Die im Beispiel verwendeten Beschreibungen sind dafür gute Kandidaten: Entscheidend für Sätze – im Sinne Wittgensteins – ist die funktionale Abhängigkeit der Semantik des Gesamtkonstrukts von den Bestandteilen, aus denen es besteht – die Abhängigkeit des Satzsinns von den Satzbestandteilen:
4.032 […]
(Auch der Satz: „ambulo“, ist zusammengesetzt, denn sein Stamm ergibt mit einer anderen Endung, und seine Endung mit einem anderen Stamm, einen anderen Sinn.)[22
Eigentlich wäre Satz 5.47 hier die bessere Wahl. In diesem Satz werden aber zu viele bis jetzt noch nicht erläuterte Termini verwendet.]
Wird im Satz „Blaue Blume“ „Blau“ durch „Rot“ ersetzt, erhält man einen anderen Sinn. Genauso, ersetzt man „Blume“ durch „Auto“: Der Sinn des Gesamtkonstrukts ergibt sich aus den Bestandteilen des Konstrukts.
Beschreibungen sind Sätze, können also wahr oder falsch sein: „Blaue Blume“ trifft z. B. auf
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nicht zutrifft.
Geht man nun davon aus, dass auch die Definition ein Satz ist, könnte sie, wie die Beschreibung, wahr oder falsch sein.
Und wäre sie falsch, weil es sich in Wirklichkeit nicht um eine Blume, sondern ein Auto handelt, wäre der Satz „Die Blaume blüht.“ unsinnig. Der Sinn des Satzes „Die Blaume blüht.“ würde von der Wahrheit des Satzes „Blaue Blume“ abhängen.
Das ist unmöglich: Der Sinn des Satzes ist gegeben, ohne dass es eine Tatsache gibt, auf die er angewendet wird. Ein Vergleichsobjekt, das ich bräuchte, um festzustellen, ob „Blaue Blume“ wahr oder falsch ist, ist für das Verständnis des Sinns nicht notwendig.
Der Satz hat einen von den Tatsachen unabhängigen Sinn.
‚Blaume‘ leistet dasselbe, wie die Beschreibung „Blaue Blume“: Der Satz „Die blaue Blume blüht.“ hat denselben Sinn, wie der Satz „Die Blaume blüht.“
Ein Satz ist ‚Blaume‘ deshalb aber nicht: Es zerfällt nicht in Bestandteile. Es gibt keinen Sinn, der aus den Teilen hergeleitet werden könnte23
Und die Buchstaben, aus denen es zusammengesetzt ist, sind unwesentlich..
Die durch die Definition etablierte Bedeutung des einfachen Zeichens kann deshalb selbst auch nur einfach sein. Im anderen Falle müsste sich jede Differenzierung der Bedeutung im einfachen Zeichen ausdrücken lassen, weil sonst nicht klar wäre, was das Zeichen meint. Eine solche Differenzierung lässt ein einfaches Zeichen aber nicht zu.
Einfache Zeichen können nichts Zusammengesetztes bedeuten24
Mit seinem Argument greift Wittgenstein hier der Abhandlung weit vor. Warum einfache Zeichen nichts komplexes bedeuten können, wird später noch einmal im Zusammenhang mit dynamischen Modellen und der logischen Mannigfaltigkeit eines sprachlichen Ausdrucks thematisiert..
Beschreibung und das einfache Zeichen leisten dasselbe, aber auf verschiedene Art und Weise25
FIXME:
Vielleicht ein Zitat aus der Einleitung:
[...] It is impossible, for example, to make a statement about two men [Socrates and Plato] (assuming for the moment that the men may be treated as simples), without employing two names, […]
Russell wirft an dieser Stelle Definiens und Definiendum durcheinander → simple / name in einer Dingontologie zu erwarten.
Die Definition stellt dabei den Übergangspunkt von Sinn nach Bedeutung dar:
Ihre Form ist die eines Satzes: Ihr Sinn ergibt sich aus den Bestandteilen, aus denen sie besteht.
Anders als der Satz kann und darf sie aber nicht wahr oder falsch sein, stellt vielmehr klar, was ein einfaches Zeichen bedeutet.
Und das einfache Zeichen kann nur dann eine eindeutige Bedeutung haben, wenn die Definition etwas ebenso Einfaches etabliert.
Unsere Sätze bestehen aus einfachen Zeichen, die etwas Einfaches bedeuten müssen, obwohl sie durch Zusammengesetztes definiert sind.
Es wäre sonst unmöglich, ein Bild der Welt (wahr oder falsch) zu entwerfen26
Dem Sinn nach Satz 2.021.
q.e.di
Es gibt eine weitere Möglichkeit das Experiment aufzubauen, die weniger stark dem Text vorgreift, und deshalb näher an dem sein mag, was Wittgenstein meinte. Ich war aber nicht in der Lage, sie zu Ende zu führen.
Nehmen wir zunächst an, es gäbe ein Wort, das zwei Dinge gleichzeitig bezeichnet. Sagen wir ‚Blauto‘ steht gleichermaßen für Blume und Auto.
Im diesem Falle wäre nicht klar, ob der Satz „Das Blauto blüht.“ unsinnig ist oder nicht. Das Problem kann man lösen, indem im Zeichen ‚Blauto‘ Änderungen zulässt. ‚Blauto_a‘ könnte Blume, ‚Blauto_b‘ Auto bedeuten. Dann hätten wir es aber nicht mehr mit einem einfachen Zeichen zu tun. „Blauto“ wäre in Wittgensteins Sinne ein Satz.
Im anderen Falle würde die Sinnhaftigkeit von „Das Blauto blüht.“ davon abhängen, ob gerade die Blume oder das Auto gemeint ist, was nicht sein kann, soll der Satz einen klaren Sinn haben.
Mir ist an dieser Stelle aber nicht klar, welchen Satz Wittgenstein hier meint, wenn er von einem anderen Satz spricht, von dessen Wahrheit oder Falschheit der Sinn des betrachteten Satzes nicht abhängen darf. Der Satz „Mit Blauto meine ich jetzt Blume.“ würde das Beispiel ad absurdum führen, weil ein Zirkel eingeführt würde.
Im Ende ist das Ergebnis aber das Gleiche: Die durch ein einfaches Zeichen gegebene Bedeutung kann selbst wieder nur einfach sein.
Man kann bei dieser Version des Experiments, wenn ich mich nicht irre, auch ganz auf Phantasiewörter verzichten. Im Falle des Zeichens ‚Bank‘ ist es ja z.B. tatsächlich so, dass wir das Gemeinte erst aus dem Kontext ableiten – etwa im Falle von „Ich habe einen Kredit bei der Bank.“ oder wirklich nachfragen müssen – etwa im Falle von „Die Bank ist jetzt zehn Jahre alt.“ .
- Gegenstand und Welt
Eine Blaume ist nun nicht der interessanteste Gegenstand, den man sich vorstellen kann.
Die Kosten ihn einzuführen, waren aber auch nicht sonderlich hoch: Alles, was es braucht, ist eine Beschreibung, die auf eine Tatsache angewendet den Gegenstand zurückgibt.
Ich kann die Blütenfarbe der Beschreibung einer Blume hinzufügen, und so den Genstand Blume zu einem neuen Gegenstand – der Blaume – spezialisieren. Uninteressant ist das Ganze, weil die Blütenfarbe nichts Wesentliches der Blume beschreibt, keine Eigenschaft ist, die die Einführung eines eigenen Gegenstands rechtfertigen würde.
Wittgensteins Auffassung ermöglicht eine Inflation von Gegenständen fragwürdigen Werts, weil sie nur die formalen Eigenschaften der Gegenstände einbezieht: Die Einführung der Blaume mag abwegig sein, doch hindert mich nichts an Wittgensteins Idee daran, es trotzdem zu tun27
Hier zeigt sich eine Skepsis Wittgensteins Definitionen gegenüber, die in MS 104 (Prototractatus) deutlicher zum Ausdruck kommt. [Der Lesbarkeit halber habe ich das Zitat geglättet. Original im Anhang]
3·20107Die Zusammenfassung des Symbols eines Komplexes in ein einfaches Symbol kann durch eine Definition ausgedrückt werden. [...] Offenbar garantiert schon der Umstand der es möglich macht daß Gewisse Formen durch eine Definition zu einen Namen projiziert werden, dafür daß dieser Name dann auch wie ein wirklicher behandelt werden kann..
Gegenstände sind diesem Verständnis nach nur eine notwendige aber keine hinreichende Bedingung einer korrekten Beschreibung der Welt:
2.022Es ist offenbar, dass auch eine von der wirklichen noch so verschieden gedachte Welt Etwas – eine Form – mit der wirklichen gemein haben muss.
2.023Diese feste Form besteht eben aus den Gegenständen.
Aus systematischer Sicht bilden Gegenstände die Grundlage, die es erst ermöglicht, eine Beschreibung der Welt zu formulieren, aber eben nicht mehr:
Die Welt gibt keinen Kanon von Gegenständen vor, der zu ihrer korrekten Beschreibung notwendig wäre. Statt dessen gibt es verschiedene Bezugsweisen, anhand derer die Welt beschrieben werden kann, und diese Bezugsweisen unterscheiden sich in den Gegenständen, die in der Beschreibung genutzt werden.
Für Wittgenstein sind Gegenstände nicht Teil der Welt, sie bilden vielmehr den Werkzeugkasten, der es erst ermöglicht sinnvolle – überhaupt wahrheitsfähige – Beschreibungen der Welt zu geben.
2.0231Die Substanz der Welt kann nur eine Form und keine materiellen Eigenschaften bestimmen. Denn diese werden erst durch die Sätze dargestellt – erst durch die Konfiguration der Gegenstände gebildet.
2.0232Beiläufig gesprochen: Die Gegenstände sind farblos.
2.0233Zwei Gegenstände von der gleichen logischen Form sind – abgesehen von ihren externen Eigenschaften – von einander nur dadurch unterschieden, dass sie verschieden sind.
Man kann eine Definition in diesem Sinne als Messvorschrift begreifen: Immer, wenn die gegebene Beschreibung zutrifft, darf ich das definierte Wort nutzen.
Gegenstände sind dann so etwas wie Messapparate, die auf die Tatsachen angewendet werden, und immer dann anschlagen, wenn die Definition zutrifft.
Gegenstände sind Typen keine Instanzen. Ein Gegenstand repräsentiert Nichts, das in der Welt wäre, er ist Werkzeug, die Welt zu ordnen:
Wenn ich das Wort „Mutter“ falsch schreibe, nämlich so: „Muter“, welches ‚t‘ habe ich vergessen, das erste oder das zweite?
Die Frage ist unsinnig, weil in „Mutter“ dasselbe ‚t‘ zweimal notiert ist28
Das gleiche sieht man daran, dass es für einen Taschenspieler ein Leichtes ist, uns zwei Gegenstände als einen, oder umgekehrt einen Gegenstand als zwei vorzugaukeln. und nicht zwei Zeichen auf etwas Gemeinsames verweisen29
FIXME: Aspektabhängigkeit klar machen.
Ist eine Blaume blau? Sowenig wie ein Thermometer, dass 200 °C heißen Dampf misst, 200 °C heiß ist, sowenig ist eine Blaume blau: Der Gegenstand ist der Messapparat, nicht das Gemessene.
Die Welt allein ist unbestimmt, macht keine Vorgaben, wie sie zu beschreiben ist. Erst das hinzutreten der Gegenstände ermöglicht klare Bilder der Welt.
2.024Die Substanz ist das, was unabhängig von dem was der Fall ist, besteht.
Man liest häufig, Wittgenstein postuliere, dass die Tatsachen aus Gegenständen bestünden30
Z. B. Kellerkessel → Ressourcen. Ich habe bereits darauf hingewiesen, dass Gegenstände erst auf der Ebene des Sachverhalts in Wittgensteins Modell eintreten, und diese Beziehung nicht transitiv ist – Sachverhalte sind logisch unabhängig voneinander. Satz 2.024 macht Wittgensteins Position noch einmal deutlich: Die Substanz (sprich: die Gegenstände) besteht unabhängig von dem, was der Fall ist (den Tatsachen): Gegenstände sind nicht Teil der Welt, bilden vielmehr ein Gerüst, das als Bedingung einer sinnvollen Beschreibung zur Welt hinzutritt31
Diese Lesart kann auch als Einzige den diametralen Widerspruch zwischen einer Tatsachenontologie einerseits und einfachen Gegenständen, aus denen diese Tatsachen bestehen, andererseits vermeiden..
2.025Sie ist Form und Inhalt.
Gegenstände erfüllen dabei zwei Funktionen. Einerseits Stellen sie klar, von was die Rede ist, welche Bezugsweise gewählt wurde: Das ist der inhaltliche Aspekt. Andererseits geben sie der Welt Struktur. Schon in Satz 2.0123 (vgl. S.11) identifiziert Wittgenstein das Wissen, was ein Gegenstand ist, mit dem Wissen, in welchen Sachverhalten er eine Rolle spielen kann. Das ist der formale Aspekt des Gegenstands. Der Satz „Die Blume blüht.“ hat im Gegensatz zum Satz „Das Auto blüht.“ Sinn. Die Möglichkeit in bestimmten Sachverhalten vorkommen zu können, in anderen nicht, gibt dem Raum, der von den Gegenständen aufgespannt wird, Struktur.
Nun hat nicht jede Eigenschaft eines Gegenstands die gleiche Bedeutung, was seine Möglichkeiten des Vorkommens in Sachverhalten angeht.
2.01231Um einen Gegenstand zu kennen, muss ich zwar nicht seine externen – aber ich muss alle seine internen Eigenschaften kennen.
Die Farbe des Balls ist unerheblich dafür, ob er zum Fußballspielen verwendet werden kann, oder nicht. Folglich machen wir bezüglich der Farbe keine Einschränkungen, wenn wir beurteilen, ob etwas ein Ball ist. Sollte er dagegen nicht rund sein, wären wir nicht bereit, von einem Ball zu reden.
Alle Eigenschaften, die relevant dafür sind, ob ein Gegenstand in einem Sachverhalt vorkommen kann oder nicht, sind die internen Eigenschaften des Gegenstands, alle unwesentlichen die externen.
2.0272Die Konfiguration der Gegenstände bildet den Sachverhalt.
2.03Im Sachverhalt hängen die Gegenstände ineinander, wie die Glieder einer Kette.
In Sachverhalten sind Gegenstände nicht einfach wahllos zusammengewürfelt.
Entlang ihrer internen Eigenschaften lassen Gegenstände bestimmte Kombinationen zu, andere nicht.
2.031Im Sachverhalt verhalten sich die Gegenstände in bestimmter Art und Weise zueinander.
2.032Die Art und Weise, wie die Gegenstände im Sachverhalt zusammenhängen, ist die Struktur des Sachverhaltes.
2.033Die Form ist die Möglichkeit der Struktur.
Wittgenstein festigt an dieser Stelle einen Begriff, den er in der Abhandlung immer wieder als technischen Term nutzt:
2.026Nur wenn es Gegenstände gibt, kann es eine feste Form der Welt geben.
2.027Das Feste, das Bestehende und der Gegenstand sind Eins.
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.
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