4.0621 But it is important that the signs “p” and “~p” can say the same thing. Because it shows that the sign “~” corresponds with nothing in reality.

That negation occurs in a proposition is still no characteristic [or sign: Merkmal] of its sense (~~p=p).

The propositions “p” and “~p” have opposite senses, but one and the same reality corresponds to them.

This seems pretty straightforward. If "p" could mean anything (as it surely could) then "~p" could mean anything too. In that sense "~" has no meaning at all. If I know that a movie review contains the word "not" then I really know nothing about the reviewer's verdict. If I know that it contains the words "masterful editing" or "woeful acting" then I do know something, in contrast, even though I realize that the full review might assert or deny that the movie contains good editing or bad acting. At least I know that the review talks about editing or acting. The sign "~" is unlike (at least some) other signs in this way. Presumably Wittgenstein is criticizing someone else's thoughts on the negation sign here, and that someone is probably Frege.