Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/163

Rh That "(x).fx:⊃:fa" is a tautology shows that fa follows from (x) ,fx, etc. etc.

It is clear that we could have used for this purpose contradictions instead of tautologies.

In order to recognize a tautology as such, we can, in cases in which no sign of generality occurs in the tautology, make use of the following intuitive method: I write instead of "p", "q", "r", etc., "TpF", "TqF", "TrF", etc. The truth-combinations I express by brackets, e.g.: and the co-ordination of the truth or falsity of the whole proposition with the truth-combinations of the truth-arguments by lines in the following way:



This sign, for example, would therefore present the proposition "p⊃q". Now I will proceed to inquire whether such a proposition as ~(p. ~p) (The Law of Contradiction) is a tautology. The form "~ ξ" is written in our notation