The overview sketched the frame of the picture theory; here it is close up, from the German. The spark was a magazine report. In a Paris courtroom a traffic accident had been re-enacted using a model made of dolls and toy cars. Wittgenstein wrote in his notebook on 29 September 1914: “a proposition is a model of reality as we think it is.” The model car stands in for a real car, the arrangement of the model for the arrangement in the street. And so the model can say how the accident went, without a word. Isn’t a proposition the same?
1. The world is made not of “things” but of “facts”
Die Welt ist die Gesamtheit der Tatsachen, nicht der Dinge.
The world is the totality of facts, not of things. (1.1. German quotations throughout; Japanese and English are L/LAB working translations.)
“Cat,” “mat,” “on,” however you line them up, make a dictionary, not a claim. To say anything, things must be joined in a definite way. When such a combination — a state of affairs (Sachverhalt) — obtains, that is a fact (2). What a proposition pictures is a fact.
2. A picture is a model of reality
The model car and the real car; the layout of the model and the layout of the street. Between them runs a relation of standing-for. Wittgenstein generalises it.
Das Bild ist ein Modell der Wirklichkeit.
A picture is a model of reality. (2.12)
In the picture, the elements are “correlated with” objects (2.13). “That the elements of the picture are combined with one another in a definite way represents (vorstellt) that the things are so combined” (2.15). This “way the elements are combined” Wittgenstein calls the picture’s structure (Struktur); the possibility of that structure is its pictorial form (Form der Abbildung).
3. What they share — logical form
For a picture to be a picture of its object, “something must be identical” in the two (2.161).
Was das Bild mit der Wirklichkeit gemein haben muß, um sie auf seine Art und Weise — richtig oder falsch — abbilden zu können, ist seine Form der Abbildung.
What a picture must have in common with reality in order to depict it — correctly or falsely — after its manner, is its pictorial form. (2.17)
A painting shares the form of colour and space; music another form; each kind of picture its own. But there is one thing every picture must share with what it depicts: logical form (2.18). A score, a performance and a record’s grooves can be translated into one another (4.014) because a common “logical structure” runs through them. Proposition and world stand in the same relation.
4. A proposition is a “logical picture”
Das logische Bild der Tatsachen ist der Gedanke.
The logical picture of facts is the thought. (3)
And “the thought is the proposition with a sense” (4). In the proposition a name (Name) stands in for an object — “the name means the object; the object is its meaning (Bedeutung)” (3.203). A name is a simple sign that cannot be analysed further, and what it means is fixed by convention. What is new in a proposition is the arrangement of names. “In a proposition a state of affairs is, as it were, assembled on trial” (4.031). Hence “to understand a proposition is to know what is the case if it is true” (4.024).
5. Truth and falsity are settled by “comparing” with reality
The arrangement of names assembles a state of affairs, but whether that state of affairs obtains cannot be read off the proposition.
Um zu erkennen, ob das Bild wahr oder falsch ist, müssen wir es mit der Wirklichkeit vergleichen.
To discover whether the picture is true or false we must compare it with reality. (2.223)
“From the picture alone it cannot be known whether it is true or false” (2.224). This is the hinge of the picture theory. A proposition is not true or false in advance; only against the world is it settled. “There is no picture that is true a priori” (2.225). Complex propositions are built as truth-functions of elementary propositions (Elementarsätze) (5) — “a proposition is a truth-function of elementary propositions.”
6. What cannot be pictured — logical form itself
Here is the bridge to the next theme. A proposition can picture every fact in reality. But one thing it cannot picture.
Der Satz kann die gesamte Wirklichkeit darstellen, aber er kann nicht das darstellen, was er mit der Wirklichkeit gemein haben muß, um sie darstellen zu können — die logische Form.
A proposition can represent the whole of reality, but it cannot represent what it must have in common with reality in order to represent it — logical form. (4.12)
Logical form mirrors itself in the proposition, but the proposition cannot say it (4.121) — you cannot paint “being paint.” This residue, “unsayable but shown,” is what pushes the Tractatus on toward the limits of language.
In sum
| stage | point | proposition |
|---|---|---|
| world | the unit is the fact (things in a relation), not the thing | 1.1, 2 |
| picture | a picture is a model of reality; elements correlate with objects | 2.12, 2.13 |
| form | every picture shares logical form with reality | 2.17, 2.18 |
| proposition | names stand in for objects; the arrangement tries out a state of affairs | 3.203, 4.031 |
| truth | not settled by the picture alone, but by comparison with reality | 2.223 |
| limit | logical form itself cannot be pictured (only shown) | 4.12, 4.121 |
Connections
- “Names stand in for objects, and their arrangement pictures structure” looks like the reverse of Saussure’s signifier and signified, yet meets it on one point: a sign does not work alone — meaning arises in the arrangement, the system.
- The late Wittgenstein makes this very “name = object” picture his target in Investigations §1. The point where the early work is refuted by the late begins here.
The Wittgenstein feature: overview / this essay / the limits of language / language-games / family resemblance / following a rule.
