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5.44

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-opoerations which have it as their basis are given with it.