Wittg.–

It is easy to suppose a contradiction in the fact that on the one hand all 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.

Ts-201a1,b15

(2015–) Wittgenstein Source Bergen Nachlass Edition (WS-BNE). Edited by the Wittgenstein Archives at the University of Bergen under the direction of Alois Pichler. In: Wittgenstein Source, curated by Alois Pichler (2009–) and Joseph Wang-Kathrein (2020–). (N) Bergen: WAB.