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.q⊃q] |
| ( | 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. [q⊃p] |
| ( | T | T | F | T | ) | (p, q) | ” ” | If p then q. [p⊃q] |
| ( | T | T | T | F | ) | (p, q) | ” ” | p or q. [p∨q] |
| ( | F | F | T | T | ) | (p, q) | ” ” | Not q. [~q] |
| ( | F | T | F | T | ) | (p, q) | ” ” | 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] |
| ( | T | F | F | F | ) | (p, q) | ” ” | p and q. [p.q] |
| ( | 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.