Page:Wittengenstein - Tractatus Logico-Philosophicus, 1922.djvu/89
The expression of the formal concept is therefore a propositional variable in which only this characteristic feature is constant.
4.127 The propositional variable signifies the formal concept, and its values signify the objects which fall under this concept.
4.1271 Every variable is the sign of a formal concept.
For every variable presents a constant form, which all its values possess, and which can be conceived as a formal property of these values.
4.1272 So the variable name “x” is the proper sign of the pseudo-concept object.
Wherever the word “object” (“thing”, “entity”, etc.) is rightly used, it is expressed in logical symbolism by the variable name.
For example in the proposition “there are two objects which …”, by “(∃x,y)…”.
Wherever it is used otherwise, i.e. as a proper concept word, there arise senseless pseudo-propositions.
So one cannot, e.g. say “There are objects” as one says “There are books”. Nor “There are 100 objects” or “There are ℵ0 objects”.
And it is senseless to speak of the number of all objects.
The same holds of the words “Complex”, “Fact”, “Function”, “Number”, etc.
They all signify formal concepts and are presented in logical symbolism by variables, not by functions or classes (as Frege and Russell thought).
Expressions like “1 is a number”, “there is only one number nought”, and all like them are senseless.(It is as senseless to say, “there is only one 1”