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short method

Testing validity by assuming the conclusion false and every premise true, then working backward.

The short method tests validity by assigning F to the conclusion and T to every premise and then working out what the sentence letters must be. If a consistent assignment results, it is a countermodel; if every attempt forces a contradiction, the argument is valid.

Examples

  • To test P → Q, ¬Q ∴ ¬P: make ¬P false (P true) and ¬Q true (Q false); then P → Q is false, so no countermodel exists and the argument is valid.

See also

countermodel truth-table test
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