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Seite 13
Gegenstände & Logischer Raum
Was ist Wahrheit?—WittgensteinsLogisch-Philosophische Abhandlung
Marcus Hinz
ἔστιν ἔστιν
Inhalt
Inhalt
1 Tatsachen und Sachverhalte1
1.1 Russells Sicht1
1.2 Die Idee2
1.2.1 Tatsachen3
1.2.2 Sachverhalte3
2 Gegenstände & Logischer Raum7
2.1 Gegenstände und Sachverhalte7
2.1.1 Die Substanz der Welt8
2.1.2 Die Form des Gegenstands11
2.2 Der logische Raum12
(Eine erste) Einleitung
—
Wittgenstein und der Linguistic Turn
Zu Beginn eine kurze Einordnung der Diskussion, die ich in diesem Buch führen möchte.
Der Ausgangspunkt meiner Überlegungen zur Abhandlung sind Wittgensteins einleitende Bemerkungen zur Ontologie (Satzreihe 1.* und Sätze 2 & 2.01 der Abhandlung), in denen er die Begriffe Tatsache und Sachverhalt einführt, aber eine klare Abgrenzung der Begriffe schuldig bleibt.
Zur Abgrenzung dieser Begriffe habe ich eine These formuliert, die es erlaubt, die Abhandlung insgesamt als geschlossenen Text zu verstehen, statt sie – wie häufig zu lesen – als Ansammlung zusammenhangloser Aphorismen zu begreifen.
Meine Idee unterstellt der Abhandlung ein klares ontologisches Konzept, das in Satzreihe 5 zum tragenden Element der allgemeinen Satzform wird, mit der Wittgenstein die philosophischen Probleme „im Wesentlichen endgültig gelöst zu haben“
LPA Einleitung, letzter Absatz glaubt.
Ontologische Überlegungen so sehr ins Zentrum Wittgensteins Denken zu rücken, passt nicht zu seinem philosophischen Hintergrund.
Der frühe Wittgenstein wird zu den Denkern des Linguistic Turn gerechnet, von manchen sogar als der eigentliche Protagonist der Sprachlichen Wende betrachtet.
Kennzeichnendes Merkmal des Linguistic Turn ist die Abwendung von ontologischen Fragestellungen hin zu einer Analyse der Sprache und ihres Funktionierens.
Zentral ist dabei die Annahme, dass die Komplexität und Intransparenz der Umgangssprache Ideen nahelegt, die in der alten Philosophie zu gravierenden Irrtümern geführt haben.
Ziel einer neuen Philosophie ist es deshalb, diese Irrtümer zu vermeiden.
An die Stelle einer Analyse der Wirklichkeit tritt die Analyse der Sprachmechanismen, die die Irrtümer der alten Philosophie verursachen.
Auf Basis dieser Analyse haben Bertrand Russell und Alfred North Whitehead auf der einen Gottlob Frege auf der anderen Seite versucht, Sprachen zu entwickeln, mit der sich die Welt ohne irreführenden Ballast beschreiben lässt.
Eine klare Sprache macht unklares Denken unmöglich.
Denken ist in diesem Sinne etwas genuin sprachliches, eine Art innerer Monolog, der nur richtig geführt werden muss, um den Irrtümern der alten Philosophie zu entgehen.
Auch Wittgenstein sieht in der Verwendung einer solchen Sprache den Schlüssel zur Vermeidung der Irrtümer, die am Anfang philosophischer Scheinprobleme stehen.
LPA Sätze 3.325 & 4.003
Er folgt deshalb den Denkansätzen Freges und Russells aber nicht kritiklos, sieht in ihnen vielmehr erste Schritte, die weitergeführt werden müssen, um das gesteckte Ziel zu erreichen.
In der Abhandlung vollendet Wittgenstein sozusagen den Kreis, der mit der Sprachlichen Wende begonnen wurde. Im Buch möchte ich Wittgensteins Ideen vorstellen, den Linguistic Turn zum Ziel zu führen.
Mit seinen Überlegungen hat Wittgenstein ein Modell der Welt sui generis geschaffen. Etwas Ähnliches habe nirgends gesehen.
Er kommt aus dem Linguistic Turn, die Ideen weißen aber auch eine erstaunliche Nähe zu z.B. Platon oder Leibnitz auf.
Der Versuch, Wittgenstein in einen Kontext zu stellen, und ihn aus diesem Kontext heraus zu verstehen, macht deshalb wenig Sinn. Insofern werde ich mich – von wenigen Stellen abgesehen – auf die Abhandlung selbst konzentrieren.
Nur Russell – genauer die Einleitung, die er zur Abhandlung verfasst hat – werde ich häufiger zitieren, um eine andere Meinung zum Text zu haben.
Ich tue Russell damit Unrecht.
Wittgenstein hat alles nur erdenkliche unternommen, um das Verständnis der Abhandlung zu erschweren oder unmöglich zu machen
Die Abhandlung ist sicher die einzige philosophische Schrift, die es zum Libretto einer Oper geschafft hat..
Und los …
Tatsachen und Sachverhalte
Eine der größten Schwierigkeiten, denen man beim Lesen der Abhandlung begegnet, ist Wittgensteins Eigenart, Termini technici einzuführen, ohne sie als solche zu kennzeichnen, geschweige denn ihre Bedeutung zu erläutern.
Den ersten Kandidaten begegnet man direkt zu Beginn der Abhandlung: Wittgenstein führt hier die Begriffe Tatsache und Sachverhalt ein.
Der Terminus Tatsache wird in Satzreihe 1 direkt zu Beginn der Abhandlung eingeführt. Dort handelt Wittgenstein in kurzen Worten seine Ontologie ab:
1Die Welt ist alles, was der Fall ist.
1.1Die Welt ist die Gesamtheit der Tatsachen, nicht der Dinge.
In Satz 1.1 grenzt Wittgenstein seine Tatsachenontologie gegen eine – sicherlich üblichere – Dingontologie ab.
Ihrem Grundgedanken nach betrachtet eine Dingontologie Dinge als die konstituierenden Elemente der Welt. Tatsachen sind Kombinationen von Dingen, sind also aus den Dingen hergeleitet.
In diesem Sinne ist die Welt die Gesamtheit der Dinge, alles andere nur eine Ableitung daraus.
Wittgenstein setzt dem Ding die Tatsache als konstituierendes Element der Welt entgegen.
Er kehrt das Verhältnis von Ding und Tatsache dabei aber nicht einfach nur um. Statt dessen führt er mit den Sachverhalten eine Ebene ein, die zwischen Tatsachen und Dingen steht:
2Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten.
2.01Der Sachverhalt ist eine Verbindung von Gegenständen. (Sachen, Dingen.)
Während Wittgenstein die Beziehung von Gegenstand und Sachverhalt erläutert, bleibt er in der Beschreibung der Beziehung von Tatsache und Sachverhalt vage:
Die Tatsache „ist das Bestehen von Sachverhalten“. „ist“ legt hier eine sehr enge Beziehung von Tatsache und Sachverhalt nahe, erklärt aber nicht, wie sich diese Beziehung gestaltet.
Russells Sicht
In seinem Vorwort zur Abhandlung erläutert Russell seine Sicht:
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 schwebt an dieser Stelle wohl ein hierarchisches Modell vor, in dem die Gegenstände die Bausteine von Komplexen sind, die selbst wieder Bausteine größerer Komplexe sein können.
Sachverhalt und Tatsache unterscheiden sich dieser Sicht nach nicht wesentlich:
Jeder Sachverhalt ist für sich selbst bereits eine Tatsache.
Die Beziehung von Tatsache und Sachverhalt ist analog der von Ding und Sachverhalt: Eine Tatsache ist eine einfache Verbindung von Sachverhalten.
Russell dehnt den Text an dieser Stelle:
In Satz 2 definiert Wittgenstein die Tatsache als das Bestehen von Sachverhalten
Einer Tatsachen entsprechen mehrere Sachverhalte.
In Satz 2.06 wird die Kardinalität noch etwas deutlicher:
2.06[ … ]
(Das Bestehen von Sachverhalten nennen wir auch eine positive, das Nichtbestehen eine negative Tatsache.). Strenger Lesart nach lässt diese Aussage keinen Raum, einen einzelnen Sachverhalt als Tatsache zu betrachten.
Wichtiger:
Russells Lesart nach wird die Abhandlung bereits an dieser Stelle inkonsistent:
Ist der Sachverhalt eine Verbindung von Gegenständen und die Tatsache wiederum eine Verbindung von Sachverhalten, ist auch die Tatsache – zumindest mittelbar – aus Gegenständen zusammengesetzt.
Dann wären aber die Gegenstände die konstituierenden Elemente der Welt, nicht, wie in Satz 1.1 postuliert, die Tatsachen.
Die Idee
Russells widersprüchliche Annahme kann im Text nicht direkt nachgewiesen werden:
Es gibt keine Stelle in der Abhandlung, in der Wittgenstein schreibt, dass eine Tatsache aus Gegenständen zusammengesetzt ist.
Genauso wenig gibt es eine Stelle, in der Wittgenstein schreibt, dass eine Tatsache eine Verbindung von Sachverhalten ist.
Der Widerspruch wäre vermieden, wenn die Beziehung von Sachverhalt und Tatsache so gestaltet ist, dass Sachverhalte zwar aus Gegenständen zusammengesetzt sind, Tatsachen dagegen nicht.
Hier eine These, die Russells Widerspruch vermeidet, und der Abhandlung darüber hinaus einen Überbau gibt, der eine Sicht auf den Text als schlüssiges Ganzes erlaubt, statt ihn – wie häufig zu lesen – als eine Ansammlung von Aphorismen erscheinen zu lassen.
Tatsachen
Eine Tatsache ist jedes Stück Welt, über das wir, ohne den Kontext zu kennen, sinnvolle Aussagen treffen können
Ich vermeide hier bewusst die Aussage, dass Tatsachen unabhängig voneinander sind.
Wittgenstein sagt von Sachverhalten zwar explizit, dass sie unabhängig voneinander sind (Satz 2.061), von Tatsachen sagt er das aber nicht (Satz 1.21).
Inzwischen glaube ich, dass der Unterschied, den Wittgenstein hier macht, eine Signifikanz mit Blick aus Satz 6.45 hat.
Selbst wenn es Abhängigkeiten zur Tatsache gibt, die wir nicht kennen, können wir doch Aussagen zur Tatsache machen.
Wir müssen nicht die Welt als Ganzes vor Augen haben, um Bilder der Welt haben zu können – das zeigt umgekehrt dann aber auch die Grenzen der Bilder.. Zum Beispiel so etwas
Ich werde Tatsachen immer als Fotografien darstellen. Das ist natürlich ein Kompromiss: Gerüche, Haptik und Geräusche werden so zum Beispiel nicht abgebildet, obwohl sie Teil der Tatsache sind. Es ist das Beste, das ich in einem Buch liefern kann.:
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Wolfgang Brendel als Papageno in Mozarts Zauberflöte, München 2005
Der Kontext der dargestellten Tatsache ist nicht bekannt. Man weiß z.B. nicht, ob sich noch weitere Sänger auf der Bühne befinden. Genauso wenig ist klar, ob es sich um eine Probe oder eine Aufführung handelt, etc..
Trotzdem ist es möglich sinnvolle Aussagen zur Tatsache zu machen, etwa, dass ein Mann auf einer Bühne steht.
Anders in diesem Fall:
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Foto
In diesem Fall kann man keine Sinneinheit erkennen, weshalb sich bestenfalls diffuse Aussagen treffen lassen. Es ist keine Tatsache, einfach weil nicht klar wäre, worin sie denn bestünde.
Sachverhalte
Zu den Sachverhalten kommt man, stellt man die Frage, aus welchen Dingen sich die Tatsache zusammensetzt.
Es gibt tausend Antworten auf diese Frage. Ich möchte zwei herausgreifen und ein wenig näher betrachten:
Es ist Papagenos erster Auftritt in Mozarts Zauberflöte.
Es ist Wolfgang Brendels erster Auftritt in Mozarts Zauberflöte.
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Beide Aussagen sind wahr, beide Aussagen beziehen sich auf denselben Gegenstand, nämlich
diesen da.
Aus dingontologischer Sicht ist das ein Problem:
Sollen die Dinge die konstituierenden Elemente der Welt sein, muss jederzeit klar sein, was ein Gegenstand ist, sonst wäre die Welt nicht eindeutig bestimmt.
Hier sieht es so aus, als wäre ein Ding zwei Dinge gleichzeitig: Ein Opernsänger und eine Opernfigur.
Die Antwort scheint zunächst einfach:
Die Aussagen, die ich ausgewählt habe, notieren nicht vollständig. Richtig hätte es heißen müssen:
„Es ist Wolfgang Brendel in der Rolle des Papageno bei seinem ersten Auftritt in Mozarts Zauberflöte.“
Das Subjekt dieser Aussage ist Wolfgang Brendel, der so als das konstituierende Ding in der Tatsache gekennzeichnet wird. Die Opernfigur Papageno wird als Attribut der Konstituente aufgelöst, und verschwindet damit als konstituierendes Element der Welt. Die geforderte Eindeutigkeit ist hergestellt.
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 „Es ist Papagenos erster Auftritt in Mozarts Zauberflöte.“ verstehen, ohne Wolfgang Brendel zu kennen.
Die zugrunde liegende Tatsache stellt also keine notwendige Beziehung zwischen Sänger und Opernfigur her.
Deutlicher wird das Argument, nimmt man 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 nur, wenn der Sänger für die Opernfigur unerheblich ist; wenn man vom Sänger absehen und trotzdem die Opernfigur betrachten kann.
Der Satz „Es ist Papagenos erster Auftritt in Mozarts 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 z.B. die Kostüme nur vergleichen, wenn Wolfgang Brendel sie trägt.
Die Sätze „Es ist Papagenos erster Auftritt in Mozarts Zauberflöte.“ und „Es ist Wolfgang Brendels erster Auftritt in Mozarts Zauberflöte“ sind logisch unabhängig voneinander und müssen es sein.
Trotzdem treffen beide Sätze gleichermaßen auf dasselbe Stück Welt – dieselbe Tatsache – zu.
Die Sätze 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 – jedem Stück Welt – gibt es verschiedene, logisch voneinander unabhängige Zugangsweisen, die nicht aufeinander reduziert werden können.
Jeder dieser Zugangsweisen entspricht ein Sachverhalt, der gleichberechtigt neben allen anderen Sachverhalten, die auf die Tatsache zutreffen, besteht.
Umgekehrt:
Ein Ding, das außerhalb jeder Bezugsweise – nur für sich – existiert, gibt es nicht.
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dieses da ist wirklich zwei Dinge gleichzeitig: Je nach Bezugsweise Papageno oder Wolfgang Brendel.
Gegenstände sind in diesem Sinne nichts in der Welt. Sie kennzeichnen vielmehr Aspekte der Welt – mögliche Bezugsweisen auf Tatsachen, die die Welt konstituieren.
1.1Die Welt ist die Gesamtheit der Tatsachen, nicht der Dinge.
Gegenstände & Logischer Raum
Mit Satzreihe 1 schließt Wittgenstein seine Gedanken zur Ontologie ab und wendet sich in Satzreihe 2 dem Bild zu.
Trotzdem sind Gegenstände (Sachen / Dinge) Thema der Vorbemerkungen
Ich habe den Teil zur Form der Abhandlung noch nicht in das neue Manuskript übernommen. Kurz zum Thema Vorbemerkung:
Wittgenstein erläutert die Systematik der Satznummern in Fußnote zu Satz 1.
Satznummern, die eine 0 enthalten, sollte es laut dieser Systematik nicht geben.
Über 50% des Textes findet sich in Sätzen mit Satznummern, die eine 0 enthalten.
Meine These zur Systematik dieser Nummern:
Die 0 in der Satznummer führt einerseits dazu, dass die Nummer länger wird. Das logische Gewicht so nummerierter Sätze wird dadurch geringer.
In der Sortierung rutscht der so nummerierte Satz aber vor die Sätze mit regulärer Nummerierung.
Die 0 in der Satznummer gibt Wittgenstein die Möglichkeit Sätze an der regulären Systematik vorbei, vor andere Sätze zu schmuggeln, ohne ihnen ein ungewollt hohes logisches Gewicht geben zu müssen.
Ich behandle diese Sätze als einleitende Bemerkungen zum eigentlichen Thema, das in den regulär nummerierten Sätzen besprochen wird.
0 steht für eine Vorbemerkung zu regulären Sätzen, 00 für Vorbemerkungen zu Sätzen, deren Nummer eine 0 enthält. zur Satzreihe (Sätze 2.0ff).
Was aus dingontologischer Sicht unsinnig ist, ist aus Wittgensteins tatsachenontologischer Sicht nur konsequent:
Gegenstände sind nicht die konstituierenden Elemente der Welt, kennzeichnen vielmehr Bezugsweisen auf die Welt. Gegenstände sind Teil des Wies, nicht des Was‘ der Welt
Dazu LPA Satz 5.552. und das Wie zeigt sich in Bildern.
Bilder stellen Sachverhalte da.
In den Vorbemerkungen betrachtet Wittgenstein zunächst die Bestandteile des Sachverhalts – Gegenstände (Sachen / Dinge). In einem zweiten Schritt betrachtet er ihre Möglichkeiten, sich zum Sachverhalt zu verbinden – den logischen Raum.
An dieser Stelle führt Wittgenstein in Satz 2.0121 mit der Sachlage auch einen neuen Terminus technicus ein. Die Abgrenzung der Sachlage ist besonders gegen der Sachverhalt nicht einfach
Liest man Satzreihe 2.0* mit Blick auf die Wörter „Sachverhalt“ und „Sachlage“ aufmerksam, kann man sie für Synonyme halten.
Mal benutzt Wittgenstein den einen mal den anderen Ausdruck, ohne dass sich eine Regel erkennen ließe (dazu besonders Sätze 2.0124 & 2.014).
Diese Beobachtung ist richtig. Trotzdem sind die Termini keine Synonyme. Wichtig zur Abgrenzung sind nicht die Termini selbst, sondern der logische Raum..
Zentral zur Abgrenzung ist der logische Raum, der zum Zeitpunkt der Einführung des Terminus aber noch nicht eingeführt ist.
Ich werde die Termini Sachverhalt und Sachlage deshalb zunächst synonym lesen, und die Abgrenzung nachholen, sobald der logische Raum eingeführt wurde.
Gegenstände und Sachverhalte
Sein erster Auftritt in der Zauberflöte ist nicht der einzige Sachverhalt, in dem Papageno vorkommt.
Papageno ist z.B. ein Vogelfänger und ein ziemlich ängstlicher Typ, der zum Trinken neigt.
In jedem dieser Sachverhalte spielt derselbe Papageno eine Rolle, der auch seinen ersten Auftritt in der Zauberflöte hat.
Der Gegenstand kann also nicht auf einen einzigen Sachverhalt reduziert werden.
Papageno muss ein gemeinsamer und deshalb unabhängiger Teil verschiedener Sachverhalte sein.
Ein Ding ist so gesehen im Minimum nichts weiter als das, was all diesen Sachverhalten gemeinsam ist und unabhängig von ihnen existieren muss. Dann sind Dinge aber doch konstituierende Elemente der Welt.
Dieses Argument ist zentrales Thema der Vorbemerkungen zu Satzreihe 2.
Der eigentlich argumentative Teil umfasst dabei Sätze 2.01ff und 2.02ff.
In Satzreihe 2.01 bedient Wittgensteins die tatsachenontologische Sicht – die Form des Gegenstands, während er in Satzreihe 2.02 die dingontologische Sicht – die Substanz der Welt – betrachtet.
Da ich bis hierher eine „Dingontologie“ als Blaupause für meine Diskussion der Abhandlung nutze, ist es an dieser Stelle günstiger, mit Satzreihe 2.02 zu beginnen:
Die Substanz der Welt
Die Annahme, dass es Dinge in der Welt gibt, hat Gründe:
Gegenstände sind Konstanten, die uns in verschiedenen Kontexten immer wieder begegnen.
Diese vom Einzelfall unabhängige Konstanz setzt eine gewisse Integrität – einen inneren Halt – des Gegenstands voraus, der nur durch ein Ding gegeben sein kann.
Oft ist von der Selbstidentität des Dings die Rede. Wittgenstein dazu in Satz 5.5303.
Manchen Lesarten nach ist das Kants Ding an sich.
Gibt man die Idee des Dings in der Welt auf, geht diese Integrität verloren.
Wittgenstein dazu:
2.02Der Gegenstand ist einfach.
[ … ]
2.021Die Gegenstände bilden die Substanz der Welt. Darum können sie nicht zusammengesetzt sein.
[ … ]
2.024Die Substanz ist das, was unabhängig von dem was der Fall ist, besteht.
[ … ]
2.027Das Feste, das Bestehende und der Gegenstand sind Eins.
2.0271Der Gegenstand ist das Feste, Bestehende; die Konfiguration ist das Wechselnde, Unbeständige.
2.0272Die Konfiguration der Gegenstände bildet den Sachverhalt.
Wittgenstein nimmt zwei Gedanken des Arguments oben auf:
Dinge sind vom Einzelfall unabhängig.
Dinge sind die Konstanten – das Feste, Bestehende – aus denen die Sachverhalte – die Konfigurationen – aufgebaut sind.
Diese Unabhängigkeit muss durch eine besondere Eigenschaft der Gegenstände gesichert sein:
Gegenstände sind einfach.
Wie weit Wittgenstein trotz dieser Äußerungen von einer Dingontologie entfernt ist, zeigt das Argument, das zeigen soll, warum Gegenstände nicht zusammengesetzt sein können:
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.
Schon beim ersten Hinsehen ist klar, dass Wittgenstein hier auf der bildlichen Ebene argumentiert.
Mit dem Argument greift er der Abhandlung aber weit vor. An dieser Stelle ist es am einfachsten, es auszuprobieren:
Nehmen wir an, ich sei der Auffassung, die Farbe sei bei der Namensgebung der Blume schon immer sträflich vernachlässigt worden.
Statt von Blumen möchte ich deshalb im Falle von:
roten Blumen→Bloten
gelben Blumen→Blelben
blauen Blumen→Blaumen
[ … ]
sprechen.
Mit der Blote, Blelbe und Blaume habe ich drei Gegenstände eingeführt, die Wittgensteins Anforderung an einen Gegenstand aus Satz 2.02331 genügen: Man kann Blote, Blelbe und Blaume „durch eine Beschreibung aus den anderen herausheben, und darauf hinweisen“.
Als sinnvollen Satz, der von einem der Gegenstände handelt, nehmen wir einfach „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 oder falsch sein kann.
Im Argument ist von einem zweiten Satz die Rede, von dessen Wahr- oder Falschheit der Sinn des Satzes „Die Blaume blüht.“ nicht abhängen darf.
Die zur Definition der Gegenstände genutzten Beschreibungen sind naheliegende Kandidaten.
Dass es sich bei den Beschreibungen um Sätze handelt, sieht man daran, dass sich ihr Sinn funktional aus den Satzbestandteilen herleiten lässt. Nehmen wir den Satz „blaue Blume“:
Ersetzt man „blaue“ durch „rote“ ergibt sich ein neuer Sinn, genauso ersetzt man „Blume“ durch „Auto“.
Dazu zunächst Satz 4.032.
Im Argument spielt Wittgenstein mit der Unterscheidung von Sinn und Bedeutung, die noch nicht eingeführt sind. Das Thema wird noch näher beleuchtet.
Die Änderung des Sinns ist in beiden Fällen eine Funktion der Änderung des Bestandteils.
Da sie Sätze sind, können Beschreibungen wahr oder falsch sein. „blaue Blume“ trifft z.B. auf
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nicht zutrifft.
Und wäre die Beschreibung 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.
Die Vergleichstatsache, die ich bräuchte, um festzustellen, ob „blaue Blume“ wahr oder falsch ist, ist für das Verständnis des Sinns nicht notwendig.
Noch etwas einfacher und plastischer kann man dasselbe Argument an einem logischen Zirkel in einer Bemerkung Russells in der Einleitung verdeutlichen:
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 […]
Mit den Personen meint Russell Sokrates und Platon.
In seiner Bemerkung in der Klammer bezweifelt er, dass diese Personen als einfache Dinge betrachtet werden können.
Im Umkehrschluss handelt es sich bei Sokrates und Platon um Komplexe – also zusammensetzte Dinge.
Als Nächstes stellt sich die Frage, aus welchen Dingen sich die Personen dann zusammensetzen.
Hier gibt es viele mögliche Antworten. Man kann sie etwa als die Summe ihrer Handlungen und Erlebnisse auffassen, oder als die Summe ihrer Organe, etc..
Die Diskussion, welche Bausteine denn die richtigen sind, und warum es ausgerechnet diese sein sollten, möchte ich an dieser Stelle außen vor lassen.
Für den Zirkel ist es unerheblich, welche Bausteine man für den Komplex wählt. Man kann auch die Summe aller möglichen Bausteine wählen.
Nehmen wir für den Moment an, dass die Körperteile einer Person die Bausteine sind, aus denen sie sich zusammensetzt.
Russells Beispielsatz
Plato liebt Sokrates.
ließt sich dann
Kopf, Arme, Beine und Rumpf lieben Kopf, Arme, Beine und Rumpf.
Passt fast, aber nicht ganz: Der Satz
Demokrits Kopf, Heraklits Arme, Kritias Beine und Thales Rumpf lieben Antiphons Kopf, Aristoteles Arme, Diogenes Beine und Epiktets Rumpf.
erfüllt den transformierten Satz, sagt aber nicht, was mit Plato liebt Sokrates gemeint ist.
Im Minimum muss sicher gestellt sein, dass die Körperteile zur jeweils gemeinten Person gehören. Also notieren wir:
Platos Kopf, Platos Arme, Platos Beine und Platos Rumpf lieben Sokrates Kopf, Sokrates Arme, Sokrates Beine und Sokrates Rumpf.
qed.
Der Satz hat einen von den Tatsachen unabhängigen Sinn.
„Blaume“ ist ein einfaches Zeichen.
Schreibe ich statt „Blaume“ „Blaame“ oder „Plaume“ sind das Fehler in der Rechtschreibung, ich erhalte keine andere Bedeutung.
Und wäre dem so, hätten wir es mit einem Satz und seinem Sinn zu tun.
Das ist der wesentliche Unterschied zwischen Sinn und Bedeutung. Dazu noch einmal Satz 4.032.
Bedeutung ist – im Gegensatz zum Sinn – keine Funktion der Bestandteile eines Ausdrucks.
Deshalb kann das, was das Zeichen vertritt – seine Bedeutung, auch nur einfach sein. Sollte es hier Differenzierungen geben, könnten sie im Zeichen keinen Ausdruck finden. Die Bedeutung des Zeichens wäre unklar.
Einfache Zeichen können nichts Zusammengesetztes bedeuten.
Die Bedeutung von „Blaume“ wurde durch einen Satz festgelegt.
Wesentlich für die Bedeutung ist aber, dass sie einfach ist und nicht wahr oder falsch sein kann. Nur so kann sie den Sinn eines Satzes eindeutig bestimmen.
Wittgenstein argumentiert an dieser Stelle rein formal – sprachmechanisch könnte man sagen.
Die Semantik von „Blaume“ spielt keine Rolle. Nehmen wir folgenden möglichen Einwand zur Illustration:
Der Satz „Die Blaume blüht.“ ist sinnvoll, weil Blaume von Blume hergeleitet ist:
Blaume ist nicht einfach, sondern aus der Farbe Blau und der Blume zusammengesetzt. Die Sinnhaftigkeit des Satzes „Die Blaume blüht“ ist dann – sozusagen – vom Blumenteil der Blaume geerbt. Wittgenstein:
2.0231Die Substanz der Welt kann nur eine Form [lies: Möglichkeiten] 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.
Der Einwand verfängt nicht, weil Wittgenstein früher ansetzt:
Die angeführte semantische Beziehung zwischen Blume und Blaume ist unstrittig gegeben.
Doch erfordert allein die Darstellung der Beziehung, dass „Blaume“ zunächst eine Bedeutung hat.
Diese Bedeutung meint Wittgenstein, wenn er vom Gegenstand spricht:
Sie muss gegeben sein.
Sie ist ihrem Wesen nach einfach.
Sie steht vor jeder möglichen Aussage über den Gegenstand, die wahr oder falsch sein könnte:
Der Gegenstand ist farblos.
Der Duktus der Argumentation in Satzreihe 2.02 ist klar dingontologisch: Wittgenstein schreibt von der Substanz der Welt, und Gegenständen, die einfach sein müssen.
Er reduziert die Argumente der Dingontologie aber deutlich auf die bildlich / sprachliche Ebene.
Gegenstände sind nichts in der Welt, sind vielmehr notwendige Bedingung der Bestimmtheit des Sinns eines Bildes.
Klarer wird diese Haltung noch, betrachtet man Satzreihe 2.01:
Die Form des Gegenstands
Ist der Gegenstand nicht Teil der Welt, kann es mit seiner Unabhängigkeit nicht so weit her sein, wie Satzreihe 2.02 bei flüchtigem Lesen vermuten lässt. Wittgenstein:
Zur Erinnerung: Derzeit lese ich Sachverhalt und Sachlage noch synonym.
2.01Der Sachverhalt ist eine Verbindung von Gegenständen. (Sachen, Dingen.)
2.011Es ist dem Ding wesentlich, der Bestandteil eines Sachverhaltes sein zu können.
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.
[ … ]
2.0122Das Ding ist selbständig, insofern es in allen möglichen 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.)
Wittgenstein deutet die Selbständigkeit der Gegenstände in ihr Gegenteil um: Ein Gegenstand ist nicht durch sich selbst, sondern durch die Sachverhalte, deren Teil er sein kann, bestimmt.
Sein Argument ist auch hier – wie Falle der Substanz der Welt – ein sprachliches.
Zum besseren Verständnis eine Metapher:
Die Dingontologie unterstellt ein Skelett, das dem Gegenstand von innen her seine Form gibt, und ihn deshalb unabhängig von den Kontexten, in denen er steht, klar abgrenzt.
Anders Wittgenstein: Er unterstellt ein Exoskelett, das die Integrität des Gegenstands von außen her sichert. Dieses Exoskelett sind die Sachverhalte, in denen der Gegenstand vorkommen kann.
Gemeinsam ist beiden Ideen aber, dass der Gegenstand jederzeit vollständig bestimmt sein muss.
Das eine Mal, um die Welt zu retten.
Das andere Mal, um zu wissen, wovon man spricht.
Im Rahmen einer Dingontologie leistet der Gegenstand das selbst.
Wittgensteins Idee nach kann der Gegenstand das nicht mehr leisten: Er ist eine abhängige Größe.
Wenn trotzdem jederzeit klar sein soll, ob man es mit Papageno zu tun hat, oder nicht, müssen die Größen, die Papageno bestimmen, jederzeit vollständig bekannt sein.
Das heißt, es muss jederzeit klar sein, in welchen Sachverhalten Papageno vorkommt oder auch nur vorkommen kann.
2.0123Wenn ich den Gegenstand kenne, so kenne ich auch sämtliche Möglichkeiten seines Vorkommens in Sachverhalten.
[ ... ]
Es kann nicht nachträglich eine neue Möglichkeit gefunden werden.
Wittgenstein reduziert den Gegenstand auf die abschließende Aufzählung aller Sachverhalte, in denen er vorkommen kann.
Damit wird der Gegenstand zur Hohlform: Zur Frage, was ein Ding ist, trägt das Ding selbst nichts bei.
Statt dessen wird seine Form durch die Sachverhalte bestimmt.
Ich weiß nicht, ob Wittgenstein hier ein Wortspiel sah.
2.0141Die Möglichkeit seines Vorkommens in Sachverhalten, ist die Form des Gegenstandes.
Der logische Raum
Die Beziehung von Gegenstand und Sachverhalt ist aber nicht beliebig. Der Gegenstand muss zum Sachverhalt passen, wie ein Schlüssel ins Schloss:
2.013Jedes Ding ist, gleichsam, in einem Raume möglicher Sachverhalte. Diesen Raum kann ich mir leer denken, nicht aber das Ding ohne den Raum.
2.0131Der räumliche Gegenstand muss im unendlichen Raume liegen. (Der Raumpunkt ist eine Argumentstelle.)
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 eine Höhe haben, der Gegenstand des Tastsinnes eine Härte, usw.
Gegenstände treten in die Argumentstellen
Für Leute die programmieren können:
Den Argumentstellen entsprechen in typisierten Sprachen die Methodensignaturen. der Sachverhalte ein, müssen also in Typ und Position zum Sachverhalt passen.
Ein konkreteres Beispiel als die Beispiele Wittgensteins macht die Sache anschaulicher:
Auch hier greift Wittgenstein der Abhandlung vor.
Ich habe das Beispiel deshalb ein wenig vereinfacht. Das Thema wird im Rahmen des logischen Urbilds (Satz 3.315) näher beleuchtet.
Nehmen wir den Sachverhalt „Cäsar war größer als Napoléon.“
Die Beziehung „größer sein als“ stellt zwei Argumentstellen zur Verfügung (im Beispiel durch Cäsar und Napoléon besetzt). Es gilt:
Die Argumentstellen können nicht mit beliebigen Typen besetzt werden:
„Wasser war größer als Napoléon.“ ist unsinnig.
Argumentstellen können auch nicht in beliebiger Reihenfolge besetzt werden:
„Napoléon war größer als Cäsar.“ sagt etwas anderes als „Cäsar war größer als Napoléon.“.
Die Argumentstelle bestimmt demnach den eintretenden Gegenstand. Sie bestimmt ihn aber nicht, indem sie auf etwas in der Welt zeigt:
Ob in die erste Position Cäsar, Napoléon, Wittgenstein oder ein Blauwal eintritt, ist unwesentlich. Wesentlich ist nur, dass man von dem Gegenstand sinnvoll sagen kann, dass er größer als ein anderer ist – Wasser erfüllt dieses Kriterium nicht. „ist größer als“ ist Teil der Form dieser Gegenstände.
Ein weiteres Beispiel führt zum logischen Raum:
Der Sachverhalt: „Cäsar wurde 55 Jahre alt“.
Auch die Beziehung „Jahre alt geworden sein“ bietet zwei Argumentstellen an. Je nach Besetzung der ersten Argumentstelle kann in die zweite ein sinnvolles Alter für die Besetzung der ersten Stelle eintreten.
Im Beispiel ist die erste Stelle von einem Menschen besetzt. Also kann in die zweite Stelle ein sinnvoller Wert für das Alter eines Menschen eintreten.
Setzen wir großzügig einen Wert zwischen 0 und 120 an. Ein einfacher Test:
„Cäsar wurde 67 Jahre alt“→ falsch aber sinnvoll.
„Cäsar wurde 5693 Jahre alt“ → Unsinn.
Der Test betrachtet die obere Grenze des Alters eines Menschen. Ein Test für die untere Grenze:
„Cäsar wurde -200 Jahre alt“ → Unsinn.
„Cäsar wurde 3 Jahre alt“ → Unsinn.
Der zweite Sachverhalt ist unsinnig, sollte aber nur falsch sein:
3 fällt in den sinnvollen Bereich des Alters eines Menschen.
Das Problem an dieser Stelle ist klarer Weise Cäsar:
Cäsar hat z.B. Gallien erobert und war römischer Diktator. Diese Sachverhalte passen nicht zu einem Lebensalter von nur 3 Jahren.