4.126 In the sense of which we speak of formal properties, we can now also speak of formal concepts.
(I introduce this expression in order to make clear the basis of the confusion of formal concepts with proper concepts, which runs through the whole of the old logic.)
That something is an instance of a formal concept cannot be expressed through a proposition. Rather it shows itself in the sign of this object itself. (A name shows that it signifies an object, a numeral that it signifies a number, etc.)
Formal concepts cannot, in the way that proper concepts can, be presented by a function.
Because of their defining characteristics, formal properties are not expressed through functions.
The expression of a formal property is a feature of certain symbols.
The sign for the defining characteristics of a formal concept is therefore a characteristic feature of all symbols whose meaning falls under the concept.
The expression of a formal concept is therefore a propositional variable, in which only this characteristic feature is constant.
In the third sentence here I take Black’s suggestion (p. 199) of saying ‘is an instance of a formal concept’ rather than the more literal ‘falls under a formal concept as an object belonging to it,’ as
Cf. 4.122 and note that “the sense in which we speak of formal properties” might be no sense at all. Wittgenstein says that the term “Merkmal” (characteristic) here is taken from Frege’s terminology. See Letters to
Richard L. Mendelsohn The Philosophy of