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 Ogden has it. It is Black also (same page) who suggests ‘numeral’ instead of ‘numerical sign’ as Ogden has it. Black says that Merkmale should be translated as ‘marks,’ since it means criteria or defining properties. But “Because of their marks, formal properties…” sounds obscure to me.

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 Ogden, p. 28. See Joan Weiner pp. 47-49 of Future Pasts.

Richard L. Mendelsohn The Philosophy of Gottlob Frege Cambridge University Press, 2005, p. 82: “Wittgenstein clearly had Frege’s predicament about the concept horse in mind when he spoke about ‘formal concepts’… Frege’s concept and object are just such formal concepts.” (Anscombe (p. 122) and Black (p. 198) would seem to agree on that.) According to Mendelsohn (p. 81) “there is just no way of coherently expressing this principle [i.e. “No concept is an object”] in the symbolism.” Frege is thus committed to the view that the principle, which he wants to uphold, is meaningless. Michael Dummett (“Frege on Functions: A Reply,” Philosophical Review 64, pp. 96-107, 1955, reprinted in E. D. Klemke (ed.) Essays on Frege University of Illinois Press, Urbana, 1968, pp. 268-283, p. 269) argues that Frege could have avoided the appearance of paradox if he had talked only about kinds of expression and not the things for which expressions stand, but Mendelsohn objects. Predicates and concepts must have analogous properties, he says, as “an immediate consequence of Frege’s general view that the structure of language mirrors the structure of the world.” (p. 81)