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'''Peirce's law''' is a formula in [[propositional calculus]] that is commonly expressed in the following form:

'''Peirce's law''' is a formula in [[propositional calculus]] that is commonly expressed in the following form:

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{| align="center" cellpadding="10"

<p><math>((p \Rightarrow q) \Rightarrow p) \Rightarrow p</math></p>

| <math>((p \Rightarrow q) \Rightarrow p) \Rightarrow p</math>

Peirce's law holds in classical propositional calculus, but not in intuitionistic propositional calculus.  The precise axiom system that one chooses for classical propositional calculus determines whether Peirce's law is taken as an axiom or proven as a theorem.

Peirce's law holds in classical propositional calculus, but not in intuitionistic propositional calculus.  The precise axiom system that one chooses for classical propositional calculus determines whether Peirce's law is taken as an axiom or proven as a theorem.