Peirce's law

Proper noun

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.006

Proper noun

- (
*logic*) The classically valid but intuitionistically non-valid formula ((P \to Q) \to P) \to P of propositional calculus, which can be used as a substitute for the law of excluded middle in implicational propositional calculus.*Consider*Q**Peirce's law**, ((P \to Q) \to P) \to P) . If*is true, then P \to 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 \to Q) \to P \equiv (P \to \bot) \to P \equiv \neg P \to P \equiv \neg P \to P \and \neg P \equiv \neg P \to \bot \equiv \neg \neg P so the law reads \neg \neg P \to P , which is intuitionistically false but equivalent to the classical axiom \neg P \vee P .*

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.006