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

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

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

5.101 The truth-functions of every number of elementary propositions can be written in a schema of the following kind:

(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$\lor$q]
(F F T T) (p, q) „ „ Not q. [p$\lor$q]
(F T F T) (p, q) „ „ Not p [p$\lor$p]
(F T T F) (p, q) „ „ p or q, but not both. [p. $\lor$q : v : q. $\lor$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. [$\lor$p. $\lor$q or p|q]
(F F T F) (p, q) „ „ p and not q. [p. $\lor$q]
(F T F F) (p, q) „ „ q and not p [q. $\lor$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. $\lor$p.q. $\lor$q]

Those truth-possibilities of its truth-arguments, which verify the proposition, I shall call its truth-grounds.

5.11 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.

5.12 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.