Meanings
- human sciencesThe 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.
1 more example
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.
Origin
Named after the logician and philosopher Charles Sanders Peirce.
Full word history & related roots →Cite this entry
Peirce's law. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Peirce's%20law
“Peirce's law.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Peirce's%20law. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “Peirce's law,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Peirce's%20law.
Source: Peirce's law on Wiktionary, CC BY-SA 4.0.