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Definitioner

Substantiv

  1. (logic) The classically valid but intuitionistically non-valid formula ((P → Q) → P) → P of propositional calculus, which can be used as an substitute for the law of excluded middle in implicational propositional calculus.

Exempel

  • Consider Peirce's law, ((P → Q) → P) → P) . If Q is true, then P → Q is also true so the law reads "If truth implies P then deduce P" which certainly makes sense. If Q is false, then (P → Q) → P ≡ (P → \bot) → P ≡ ¬ P → P ≡ ¬ P → P \and ¬ P ≡ ¬ P → \bot ≡ ¬ ¬ P so the law reads ¬ ¬ P → P , which is intuitionistically false but equivalent to the classical axiom ¬ P ∨ P.

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