Not p. (~p)
( F T T F ) ( p , q )
p or q, but not both. (p.~q:∨:q.~p)
( T F F T ) ( p , q )
If p, then q; and if q, then p. (p≡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. (~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)
( F F F F ) ( p , q )
Contradiction
(p and not p; 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.
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.
The truth-grounds of q are contained in those of p; p follows from q.
If p follows from q, the sense of “p” is contained in that of “q”.
If a god creates a world in which certain propositions are true, he creates thereby also a world in which all propositions consequent on them are true. And similarly he could not create a world in which the proposition “p” is true without creating all its objects.
A proposition asserts every proposition which follows from it.