# Peirce's law

## 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 an substitute for the law of excluded middle in implicational propositional calculus.
- Consider
**Peirce's law**, . If*Q*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 .

- Consider