Truth-functions are not material functions.
If e.g. an affirmation can be produced by repeated denial, is the denial - in any sense - contained in the affirmation? Does "~~p" deny "~p", or does it affirm p; or both?
The proposition "~~p" does not treat of denial as an object, but the possibility of denial is already prejudged in affirmation.
And if there was an object called "~", then "~~p" would have to say something other than "p". For the one proposition would then treat of ~, the other would not.
5.441 This disappearance of the apparent logical constants also occurs if "~(x).~fx" says the same as "(x).fx", or "(x).fx . x=a" the same as "fa".
5.442 If a proposition is given to us then the results of all truth-operations which have it as their basis are given with it.