Wittg.–

     It is easy to suppose a contradiction in the fact that on the one hand every possible complex proposition is a simple ab-function of simple propositions, & that on the other hand the repeated application of one ab-function suffices to generate all these propositions. If e.g. an affirmation can be generated by double negation, is negation in any sense contained in affirmation? Does “p” deny “not-p” or assert “p”, or both? And how do matters stand with the definition of “ ⊃ ” by “ ⌵ ” & “~” “.”, or of “ ⌵ ” by “.” & “ ⊃ ”? And how e.g. shall we introduce p ∣ q (i.e. ~p ⌵ ~q), if not by saying that this expression says something indefinable about all arguments p & q? But the ab-functions must be introduced as follows: The function p ∣ q is merely a mechanical instrument for constructing all possible symbols of ab-functions. The symbols arising by repeated application of the symbol “❘” do not contain the symbol “p ∣ q”. We need a rule according to which we can form all symbols of ab-functions, in order to be able to speak of the class of them; & we now speak of them e.g. as those symbols of functions which can be generated by repeated application of the operation “❘”. And we say now: For all p's & q's, “p ∣ q” says something indefinable about the sense of those simple propositions which are contained in p & q.