Tractatus Logico-Philosophicus, Ludwig Wittgenstein [top inspirational books .txt] 📗

the laws of geometry. 3.04

An a priori true thought would be one whose possibility guaranteed its truth.

3.05

Only if we could know a priori that a thought is true if its truth was to be recognized from the thought itself (without an object of comparison).

3.1

In the proposition the thought is expressed perceptibly through the senses.

3.11

We use the sensibly perceptible sign (sound or written sign, etc.) of the proposition as a projection of the possible state of affairs.

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

3.12

The sign through which we express the thought I call the propositional sign. And the proposition is the propositional sign in its projective relation to the world.

3.13

To the proposition belongs everything which belongs to the projection; but not what is projected.

Therefore the possibility of what is projected but not this itself.

In the proposition, therefore, its sense is not yet contained, but the possibility of expressing it.

(“The content of the proposition” means the content of the significant proposition.)

In the proposition the form of its sense is contained, but not its content.

3.14

The propositional sign consists in the fact that its elements, the words, are combined in it in a definite way.

The propositional sign is a fact.

3.141

The proposition is not a mixture of words (just as the musical theme is not a mixture of tones).

The proposition is articulate.

3.142

Only facts can express a sense, a class of names cannot.

3.143

That the propositional sign is a fact is concealed by the ordinary form of expression, written or printed.

For in the printed proposition, for example, the sign of a proposition does not appear essentially different from a word.

(Thus it was possible for Frege to call the proposition a compounded name.)

3.1431

The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.

The mutual spatial position of these things then expresses the sense of the proposition.

3.1432

We must not say, “The complex sign ‘aRb’ says ‘a stands in relation R to b’ ”; but we must say, “That ‘a’ stands in a certain relation to ‘b’ says that aRb”.

3.144

States of affairs can be described but not named.

(Names resemble points; propositions resemble arrows, they have sense.)

3.2

In propositions thoughts can be so expressed that to the objects of the thoughts correspond the elements of the propositional sign.

3.201

These elements I call “simple signs” and the proposition “completely analysed.”

3.202

The simple signs employed in propositions are called names.

3.203

The name means the object. The object is its meaning. (“a” is the same sign as “a”.)

3.21

To the configuration of the simple signs in the propositional sign corresponds the configuration of the objects in the state of affairs.

3.22

In the proposition the name represents the object.

3.221

Objects I can only name. Signs represent them. I can only speak of them. I cannot assert them. A proposition can only say how a thing is, not what it is.

3.23

The postulate of the possibility of the simple signs is the postulate of the determinateness of the sense.

3.24

A proposition about a complex stands in internal relation to the proposition about its constituent part.

A complex can only be given by its description, and this will either be right or wrong. The proposition in which there is mention of a complex, if this does not exist, becomes not nonsense but simply false.

That a propositional element signifies a complex can be seen from an indeterminateness in the propositions in which it occurs. We know that everything is not yet determined by this proposition. (The notation for generality contains a prototype.)

The combination of the symbols of a complex in a simple symbol can be expressed by a definition.

3.25

There is one and only one complete analysis of the proposition.

3.251

The proposition expresses what it expresses in a definite and clearly specifiable way: the proposition is articulate.

3.26

The name cannot be analysed further by any definition. It is a primitive sign.

3.261

Every defined sign signifies via those signs by which it is defined, and the definitions show the way.

Two signs, one a primitive sign, and one defined by primitive signs, cannot signify in the same way. Names cannot be taken to pieces by definition (nor any sign which alone and independently has a meaning).

3.262

What does not get expressed in the sign is shown by its application. What the signs conceal, their application declares.

3.263

The meanings of primitive signs can be explained by elucidations. Elucidations are propositions which contain the primitive signs. They can, therefore, only be understood when the meanings of these signs are already known.

3.3

Only the proposition has sense; only in the context of a proposition has a name meaning.

3.31

Every part of a proposition which characterizes its sense I call an expression (a symbol).

(The proposition itself is an expression.)

Expressions are everything⁠—essential for the sense of the proposition⁠—that propositions can have in common with one another.

An expression characterizes a form and a content.

3.311

An expression presupposes the forms of all propositions in which it can occur. It is the common characteristic mark of a class of propositions.

3.312

It is therefore represented by the general form of the propositions which it characterizes.

And in this form the expression is constant and everything else variable.

3.313

An expression is thus presented by a variable, whose values are the propositions which contain the expression.

(In the limiting case the variable becomes constant, the expression a proposition.)

I call such a variable a “propositional variable.”

3.314

An expression has meaning only in a proposition. Every variable can be conceived as a propositional variable.

(Including the variable name.)

3.315

If we change a constituent part of a proposition into a variable, there is a class of propositions