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.