5.02 It is natural to confuse the argument of functions with the affixes of names. This is because I recognize just as well from the argument as from the affix the meaning of the sign containing it.

In Russell’s “+_c”, e.g., “c” is an affix that indicates [hinweist] that the whole sign is the addition sign for cardinal numbers. But this signifying depends on arbitrary agreement and one could choose a simple sign instead of “+_c”; in “~p” however, “p” is not an affix, but an argument: the sense of “~p” cannot be understood without the sense of “p” having first been understood. (In the name Julius Caesar “Julius” is an affix. An affix is always a part of a description of an object, to whose name we attach it. E.g. the Caesar of the genus Julius.)

The confusion of argument and affix, if I am not mistaken, is at the bottom of Frege’s theory of the meaning [Bedeutung] of propositions and functions. For Frege the propositions of logic were names, and their arguments the affixes of these names.

Black (p. 239) says Wittgenstein gets Frege wrong here. “Wittgenstein’s allegation is incorrect. Had Frege really thought of the names composing a proposition as ‘indices’ [what I call affixes] in Wittgenstein’s sense, he must have conceded that the meaning of any proposition could just as well have been conveyed by a simple symbol—say T for a true proposition, and F for a false one. Now, Frege would have agreed that the reference (Bedeutung) of a proposition could be identified by a name; but he also held that the sense of a proposition was a function of the senses of its components (as Wittgenstein himself seems to recognize at 3.318 in his allusion to Frege).”

Russell uses “+_c” in Principia vol. II, p. 73.