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27 gennaio 2013

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The Proposition

Wittgenstein entitled the manuscript later published as the Tractatus logico-philosophicus (a title suggested by G.E. Moore), Der Satz (The proposition).

Why was the book written, and what was the problem Wittgenstein wanted to analyze?

One of the many aims of theTractatus was to clarify propositions in the languages we can construct. He was concerned with both verbal and non-verbal languages, but, in any event, the thought is the significant proposition (4), and is an image of reality (4.01).

No proposition can state anything about itself, because the propositional sign cannot be contained in itself. And this is the whole of the theory of types (3.332).

The rules of logical syntax must be comprehensible in themselves, always provided that one knows the way in.which every sign designates (3.334).

Definitions are rules of the translation from one language to another. Every correct sign language must be capable of translation into all others of the same type according to similar rules: that is what is common to all these languages (3.343).

All philosophy is a 'criticism of language. However, it should be made clear that for Wittgenstein the meaning of language is totally different from Mauthner's understanding.

It is to Russell's credit that he showed that the apparent logical form of the proposition is not necessarily its real form (4.0031). The proposition is an image of reality (4.01). In characterizing the elementary proposition, Wittgenstein states that thought is expressed there in a way perceptibie to the senses (3.1).

In the Tractatus, the proposition is a cluster of written, printed or recorded, or orally communicated words.

In each of these instances, the proposition is something perceived by the senses.

In 3.11, Wittgenstein argues that we use the sensibly perceptible sign, phonetic, graphic, etc., of the proposition as a projection of a possible state of affairs. This configuration, considered internally as proceeding from the image itself, externally as belonging to the propositon as a sensible expression , stands in a relation of projection to the facts.

Wittgenstein borrowed the concept of projection from geometry.

It seemed that the most suitable way of communicating the configuration symbolically is by analogy.

He also explained why he made this choice.

In this proposition, he defined the method of projection as the thinking of the senses of the proposition.

The problem was, how? And here we are at the heart of the problem of meaning, both in the sense of connotatum, and of denotatum.

The problem of the sense of a proposition is related to that of meaning as connotatum, and based on the logical concept of extension.

Let us examine why this is a central argument for understanding Wittgenstein’s proposition in 3.11, on the method of projection.

The method is the thinking of the sense of the proposition.

In the Tractatus, thinking means logically depicting, or giving a sense, a direction to, thought.

The method of projection is a particular configuration of thought conceived of as a logical configuration.

Wittgenstein placed a logical requirement as the basis of mathematical projection.

But, in what sense we can speak of a logic representation?

Here, Wittgenstein used the term projection not in the graphic sense, but in that of the conventional translation of a representation: that is, projection used in a symbolic sense. We use the proposition as a sensibly perceptible sign of symbolic projection in that the proposition as a whole is a symbolic projection of existing situations.

The sensibly perceptible sign of a proposition is graphic or phonetic. Here, Wittgenstein seems to refer to a part of the proposition, and not to its totality of signs.

In this instance, projection would refer individually to the signs making up a proposition, and be the projection of a possible state of affairs. We use a group of sensibly perceptible signs - the proposition - as the projection of a situation or state of affairs, in that we depict in language a state of affairs projectively.

In 3.141, Wittgenstein stated that the proposition has a determinate logical form and structure. In this way, it is not a mixture, but a specific symbolic configuration, exactly like a musical theme conceived of as the organic connection of sounds in harmony (those of the theme, that is, with an harmonic structure).

So, we can also say the proposition is articulated.

Black suggests comparing proposition 3.251, where the term means composed of units, and proposition 4.032, where it refers to a proposition as an image of the state of affairs’ only insofar as it is logically articulated.

With regard to the previous reference to music, Wittgenstein had previously said in the Notebooks 1914-16 that in a sense musical themes are propositions, and that, knowing the essence of logic would lead one to know the essence of music.

Indeed, melody is not a mixture of sounds, as those who have no ear to believe.

By analogy, the proposition is not a mixture of words.

The internal articulation of the proposition posed the problem for Wittgenstein of defining its component parts, and thus the problem of an original simplicity.

In the Notebooks, he had argued that the sense of a proposition is perfectly expressed in the proposition itself. It is always broken down into its simple components.

Further breakdown is impossible, while an apparent breakdown is just superfluous. These are objects in the original sense.

Only facts can express a meaning: a class of names cannot (3.142,).

He remarked in the Notes on Loqic, discussing the analysis of atomic propositions, indefinable generalities and predicates, that if we formulate all possible atomic propositions the world would be completely describe if, and only if, we established the truth or falsity of each one.

If a world was created where all the principles of logic were true, the whole of mathematics would hold good there.

No world or true proposition can be created without also creating all the constituents of that proposition (5.123).

After these statements about the function of propositions and logic, Wittgenstein said there are two kinds of indefinables, names and forms.

Proposition, cannot be made up of names alone, and cannot be classes of names. In 3.142 Wittgenstein also said that only facts can express a meaning.

In the Tractatus, Wittgenstein tried to explain why propositions cannot be made up of names alone. Here, we should analyze how this statement follows from the previous one which explained that a name can not only be used in two different propositions, but used in the same way in both.

Propositions, which are symbols referring to facts, are facts themselves .

We must be able to under-stand propositions we have never heard before, even if the proposition is a new symbol.

This is precisely why we must use general symbols, which are thus indispensable.

Only the doctrine of general indefinables can allow us to understand the nature of functions, and to ignore it leads to inextricable confusion.

Maura Braghieri Dell'Anno