3.31

Home
Su
1.
2.
3.
4.
5.
6.

 

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 which are all the values of the resulting variable proposition. This class in general still depends on what, by arbitrary agreement, we mean by parts of that proposition. But if we change all those signs, whose meaning was arbitrarily determined, into variables, there always remains such a class. But this is now no longer dependent on any agreement; it depends only on the nature of the proposition. It corresponds to a logical form, to a logical prototype.

3.316    What values the propositional variable can assume is determined.

The determination of the values is the variable.

3.317    The determination of the values of the propositional variable is done by indicating the propositions whose common mark the variable is.

The determination is a description of these propositions.

The determination will therefore deal only with symbols not with their meaning.

And only this is essential to the determination, that is only a description of symbols and asserts nothing about what is symbolized.

The way in which we describe the propositions is not essential.

3.318    I conceive the proposition - like Frege and Russell - as a function of the expressions contained in it.