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Peirce’s Law [Awbrey] - mklabgr - 06-16-2026
Peirce's Law
by Jon Awbrey
Summary
In this essay, the author explains Peirce’s Law, a famous principle of classical logic usually written as $(((P \rightarrow Q) \rightarrow P) \rightarrow P)$. The article shows that although the formula appears unintuitive, it is always true in classical logic and can even serve as an alternative foundation for the entire propositional calculus.
It discusses the historical connection to Charles Sanders Peirce, examines the law’s logical meaning, and illustrates how it distinguishes classical logic from intuitionistic logic, where the law is not generally accepted. The post also highlights graphical and symbolic representations of the principle and emphasizes its importance in proof theory, logical reasoning, and the study of formal systems.
ARTICLE