# Peirce's law

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## English[edit]

### Etymology[edit]

Named after the logician and philosopher Charles Sanders Peirce.

### Proper noun[edit]

- (logic) The classically valid but intuitionistically non-valid formula 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**, . If*is true, then is also true so the law reads "If truth implies*P*then deduce*P*" which certainly makes sense. If*Q*is false, then so the law reads , which is intuitionistically false but equivalent to the classical axiom .*