Template:Individual-TLP-paragraph-en-5.101
5.101 The truth-functions of every number of elementary propositions can be written in a schema of the following kind:
| (TTTT)(p, q) | Tautology | (if p then p, and if q then q.) [p ⊃ p . q ⊃ q] |
| (FTTT)(p, q) | in words: | Not both p and q. [~(p . q)] |
| (TFTT)(p, q) | ” ” | If q then p. [q ⊃ p] |
| (TTFT)(p, q) | ” ” | If p then q. [p ⊃ q] |
| (TTTF)(p, q) | ” ” | p or q. [p ∨ q] |
| (FFTT)(p, q) | ” ” | Not q. ~q |
| (FTFT)(p, q) | ” ” | Not p. ~p |
| (FTTF)(p, q) | ” ” | p or q, but not both. [p . ~q : ∨ : q . ~p] |
| (TFFT)(p, q) | ” ” | If p, then q; and if q, then p. [p ≡ q] |
| (TFTF)(p, q) | ” ” | p |
| (TTFF)(p, q) | ” ” | q |
| (FFFT)(p, q) | ” ” | Neither p nor q. [~p . ~q or p | q] |
| (FFTF)(p, q) | ” ” | p and not q. [p . ~q] |
| (FTFF)(p, q) | ” ” | q and not p. [q . ~p] |
| (TFFF)(p, q) | ” ” | q and p. [q . p] |
| (FFFF)(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.