Peirce's law

Etymology
Named after the logician and philosopher.

Proper noun

 * 1)  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 Peirce's law, $$ ((P \to Q) \to P) \to P) $$. If Q 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 $$ \neg P \vee P $$.