4.442 This, e.g., is a propositional sign:
T T T
F T T
F F T"
(Frege’s “assertion sign” “–“ is logically quite meaningless [ganz bedeutungslos]; for Frege (and Russell) it shows only that these authors hold the propositions thus marked as true. Therefore “–“ belongs as little to the proposition as does the number of a proposition. A proposition cannot possibly assert of itself that it is true.)
If the order of the truth-possibilities in a schema is fixed once and for all by a rule of combination, then the last column by itself is already an expression of the truth-conditions. If we write this column as a row, then the propositional sign will be:
“(TT—T) _p, q)” Or more distinctly “(TTFT) (p, q)”.
(The number of places inside the brackets on the left is determined by the number of terms in the brackets on the right.)
cf. 4.022. Propositions, I suppose, implicitly say that they are true, in the sense that adding “It is true that” before a proposition (often) makes no difference, adds nothing to it. This is the sense in which they cannot possibly assert [any more than they already do] that they are true. Frege confusedly imports psychology into his logical work. Otherwise this all seems fairly straightforward.
Proops (see pp. 29-57) treats this, along with 4.064 and 4.063 as containing the core of Wittgenstein’s critique of Frege’s assertion sign. He argues that Wittgenstein misunderstands Frege’s position, noting that these remarks are virtually identical to ones Wittgenstein wrote in 1913 in his Notes on Logic (see Proops, p. 31, note 86). Proops (p. 38): “what Wittgenstein means by a “proposition” at 4.442 is, in effect, what Frege calls a “Proposition of Begriffsschrift”—i.e. a sentence of Begriffsschrift immediately preceded by the judgement stroke. Wittgenstein understands such signs … as translatable into English by expressions of the form ‘S is true’ and ‘S is false’, where ‘S’ is replaceable by a sentence of English. So ‘is true’ and ‘is false’ can also be said to be “verbs” in a derivative sense.”
Black (pp. 226-227) says that the assertion sign is unnecessary in Russell’s Principia because it is introduced explicitly (see vol. I, p. 8) to distinguish complete propositions from subordinate propositions contained within them. But, according to Black at least, this is unnecessary, as the difference is already clear, and so the effect is that the sign indicates simply that the authors are putting the proposition forward as true. Frege’s case is different. “Frege is not required to say, pace Wittgenstein, that the presence of his sign-post in his text means that Frege judges the proposition in question to be true. But on the other hand, it is hard to make sense of this supposedly ‘objective’ judgement, which cannot, on Frege’s principles, be a thought. Frege’s sign-post serves no purpose. … Frege’s introduction of the assertion-sign may be viewed as an unsuccessful attempt to restore to the propositional sign, which he had degraded to a mere designation, its truth-claiming aspect. Wittgenstein’s account of the proposition does justice to this aspect from the start.”
Philosophical Investigations § 22: “Frege’s idea that every assertion contains an assumption, which is the thing that is asserted, really rests on the possibility found in our language of writing every statement in the form: “It is asserted that such-and-such is the case.”—But “that such-and-such is the case” is not a sentence in our language—so far it is not a move in the language-game. And if I write, not “It is asserted that….”, but “It is asserted: such-and-such is the case”, the words “It is asserted” simply become superfluous.”