An expression presupposes the forms of all propositions in which it can occur. It is the common characteristic mark of a class of propositions.
And in this form the expression is constant and everything else variable .
An expression has meaning only in a proposition. Every variable can be conceived as a propositional variable.
(Including the variable name.)
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.
What values the propositional variable can assume is determined.
The determination of the values is the variable.
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 it is only a description of symbols and asserts nothing about what is symbolized .
The way in which we describe the propositions is not essential.
I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it.
The sign is the part of the symbol perceptible by the senses.
Two different symbols can therefore have the sign (the written sign or the sound sign) in common—they then signify in different ways.
It can never indicate the common characteristic of two objects that we symbolize them with the same signs but by different methods of symbolizing . For the sign is arbitrary. We could therefore equally well choose two different signs and where then would be what was common in the symbolization?