4.127 The propositional variable signifies the formal concept, and its
values signify the objects that fall under the concept.


4.1271 Every variable is the sign for a formal concept. For every variable
represents a constant form that all its values possess, and this can be
regarded as a formal property of those values.


4.1272 Thus the variable name 'x' is the proper sign for the pseudo-concept
object. Wherever the word 'object' ('thing', etc.) is correctly used, it is
expressed in conceptual notation by a variable name. For example, in the
proposition, 'There are 2 objects which. . .', it is expressed by ' (dx,y)
... '. Wherever it is used in a different way, that is as a proper concept-
word, nonsensical pseudo-propositions are the result. So one cannot say,
for example, 'There are objects', as one might say, 'There are books'. And
it is just as impossible to say, 'There are 100 objects', or, 'There are !0
objects'. And it is nonsensical to speak of the total number of objects.
The same applies to the words 'complex', 'fact', 'function', 'number', etc.
They all signify formal concepts, and are represented in conceptual
notation by variables, not by functions or classes (as Frege and Russell
believed). '1 is a number', 'There is only one zero', and all similar
expressions are nonsensical. (It is just as nonsensical to say, 'There is
only one 1', as it would be to say, '2 + 2 at 3 o'clock equals 4'.)


4.12721 A formal concept is given immediately any object falling under it
is given. It is not possible, therefore, to introduce as primitive ideas
objects belonging to a formal concept and the formal concept itself. So it