Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/109

Rh of the meaning of propositions and functions. For Frege the propositions of logic were names and their arguments the indices of these names.

The truth-functions can be ordered in series. That is the foundation of the theory of probability.

The truth-functions of every number of elementary propositions can be written in a schema of the following kind: {{smaller block| (T T T T) (p, q) Tautology (if p then p, and if q then q) [p$$\supset $$ p q$$\supset $$q] (F T T T) (p, q) in words: Not both p and q. [ $$\sim $$(p.q)] (T F T T) (p, q) „ „ If q then p. [q$$\supset $$p] (T T F T) (p, q) „ „ If p then q. [p$$\supset $$q] (T T T F) (p, q) „ „ p or q. [p$$\or $$q] (F F T T) (p, q) „ „ Not q. [p$$\or $$q] (F T F T) (p, q) „ „ Not p [p$$\or $$p] (F T T F) (p, q) „ „ p or q, but not both. [p. $$\or $$q : v : q. $$\or $$p] (T F F T) (p, q) „ „ If p then q ; and if q, then p [p$$\equiv $$q] {T F T F) (p, q) „ „ p (T T F F) (p, q) „ „ q (F F F T) (p, q) „ „ Neither p nor q. [$$\or $$p. $$\or $$q or p|q] (F F T F) (p, q) „ „ p and not q. [p. $$\or $$q] (F T F F) (p, q) „ „ q and not p [q. $$\or $$p] (T F F F) (p, q) „ „ p and q. [p.q] (F F F F) (p, q) Contradiction (p and notp and q and not q.)[p. $$\or $$p.q. $$\or $$q] }} Those truth-possibilities of its truth-arguments, which verify the proposition, I shall call its truth-grounds.

If the truth-grounds which are common to a number of propositions are all also truth-grounds of some one proposition, we say that the truth of this proposition follows from the truth of those propositions.

In particular the truth of a proposition p follows from that of a proposition q, if all the truth-grounds of the second are truth-grounds of the first. Rh