Can we not make ourselves understood by means of false propositions as hitherto with true ones, so long as we know that they are meant to be false? No! For a proposition is true, if what we assert by means of it is the case; and if by "p" we mean ~p, and what we mean is the case, then "p" in the new conception is true and not false.
4.0621 That, however, the signs "p" and "~p" can say the same thing is important, for it shows that the sign "~" corresponds to nothing in reality.
That negation occurs in a proposition, is no characteristic of its sense (~~p = p).
The propositions "p" and "~p" have opposite senses, but to them corresponds one and the same reality.