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

This page has been proofread, but needs to be validated.


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 p qq]
(F T T T) (p, q) in words: Not both p and q. [ (p.q)]
(T F T T) (p, q) „ „ If q then p. [qp]
(T T F T) (p, q) „ „ If p then q. [pq]
(T T T F) (p, q) „ „ p or q. [pq]
(F F T T) (p, q) „ „ Not q. [pq]
(F T F T) (p, q) „ „ Not p [pp]
(F T T F) (p, q) „ „ p or q, but not both. [p. q : v : q. p]
(T F F T) (p, q) „ „ If p then q ; and if q, then p [pq]
{T F T F) (p, q) „ „ p
(T T F F) (p, q) „ „ q
(F F F T) (p, q) „ „ Neither p nor q. [p. q or p|q]
(F F T F) (p, q) „ „ p and not q. [p. q]
(F T F F) (p, q) „ „ q and not p [q. 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. p.q. 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.