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Tractatus Logico-philosophicus

Ludwig Wittgenstein

2.1–3.144

2.02–2.063

2.1–3.144, page 2

page 1 of 3

Summary

We represent facts to ourselves by means of pictures. The elements of a picture correspond to the elements of a fact, i.e. the objects that constitute it. If three objects combine in a particular way to form a fact, then the picture of that fact will consist of three elements combined in a similar way. Wittgenstein calls this combination of elements in the picture the "structure" of the picture and he calls the possibility of this structure "pictorial form" (2.15). That is, that a picture is the kind of thing that can arrange its elements in a certain determinate way is due to its pictorial form.

A picture must have something in common with what it represents in order to depict it properly (2.161). A painting must exist in space if it is to depict things that exist in space, and it must have color if it is to depict colors (2.171). Similarly, a picture of a fact must have a "logico-pictorial form" in common with that fact in order to depict it. Though a fact is made up of objects and a picture is made up of pictorial elements, they are both structured in the same way due to this common form.

Just as a spatial picture represents things in physical space, a logical picture represents things in logical space. A logical picture represents possible states of affairs: it is the most general kind of picture because logical form is the most general kind of form. However, a logical picture cannot represent logical space or logical form itself, in the same way that a spatial picture cannot represent physical space itself. Rather, it displays its form by depicting facts (2.172).

Logical pictures represent possible situations, which we can then compare with reality. The situation represented by a picture is the sense of the picture (2.221). If this sense agrees with reality (if what the picture depicts is the case), the picture is true. If not, the picture is false. We cannot tell just by looking at a picture whether it is true or false: we must compare it with reality (2.223).

"A logical picture of facts is a thought" (3). That is, a thought is a logical picture of a possible situation. Because thoughts must share the logical form of what they are about, it is impossible to have an illogical thought. Expressing an illogical thought is as impossible as representing a geometrical figure that contradicts the laws of space (3.032).

We express thoughts by means of propositions (3.1). Propositions are communicated by means of propositional signs through modes such as speech, writing, or body language. Like a picture, a proposition represents a possible state of affairs by sharing a form in common with it; i.e. its elements are arranged in a similar way. A random string of words cannot have a sense because there is no internal coherence in the way that these words are arranged. This is the upshot of 3.1432: "Instead of, 'the complex sign "aRb" says that a stands to b in the relation R,' we ought to put, 'That "a" stands to "b" in a certain relation says that aRb.'" A proposition does not say what relation holds between its elements; rather, that relation is what makes the proposition sayable.

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