Peirce's law

Definitions

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

Examples

“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→⊥)→P≡¬P→P≡¬P→P and ¬P≡¬P→⊥≡¬¬P so the law reads ¬¬P→P, which is intuitionistically false but equivalent to the classical axiom ¬P∨P.”

CEFR level