“For instance, the sign for negation:
T | F
F | W
is worth no more and no less than any other negation sign; it is a complex of lines just like the expression “not-p” and it is only made into a sign for negation by the way it works-I mean, the way it is used in the game. (The same goes for the T-F schemata for tautology and contradiction). What I want to say is that to be a sign a thing must be dynamic, not static.”
Several interesting things to note about this passage–which was taken from Philosophical Grammar, page p. 55, comment 17–but of striking importance is Wittgenstein’s claim that both “not-p” and the T-F (truth-false tables characteristic of first-order propositional logic) schemata are meaningful in virtue of the work they do–nothing about their meaning is inherent or intrinsic to their nature. The meaning of these signs is something “dynamic”–or so “[Wittgenstein] wants to say”–they do not have meaning absent what use we get from them in this or that game.
But what is the difference between “not-p” and the negation sign in logic? The question is misleading: according to Wittgenstein’s later philosophy, I don’t think he would grant that the question made much sense since it presupposes a strict “logical negation” in the sense of a logical contradiction of an assertion, p. We ought not be confused by questions such as “what is the semantic difference, if any, between “the negation of something” and the “logical sign of negation”. The question is asking us to compare the functions of two distinct operations occuring in very different language games. And we can’t think of “negation” absent “what is being negated”. Here, there is no strict sense of “not being”.