application of a finite number of truth-operations to elementary propositions.
5.4 Here it becomes clear that there are no such things as "logical objects" or "logical constants" (in the sense of Frege and Russell).
5.41 For all those results of truth-operations on truth-functions are identical, which are one and the same truth-function of elementary propositions.
5.42 That ∨, ⊃ etc., are not relations in the sense of right and left, etc., is obvious.
The possibility of crosswise definition of the logical "primitive signs" of Frege and Russell shows by itself that these are not primitive signs and that they signify no relations.
And it is obvious that the "⊃" which we define by means of "~" and "∨" is identical with that by which we define "∨" with the help of "~", and that this "∨" is the same as the first, and so on.
5.43 That from a fact p an infinite number of others should follow, namely ~ ~p, ~ ~ ~ ~p etc., is indeed hardly to be believed, and it is no less wonderful that the infinite number of propositions of logic (of mathematics) should follow from half a dozen "primitive propositions".
But all propositions of logic say the same thing. That is, nothing.
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