Curry's paradox

Curry's paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules. The paradox is named after the logician Haskell Curry. The paradox may be expressed in natural language and in various mathematical settings, including certain forms of set theory, lambda calculus, and combinatory logic. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem.

Curry's paradox

Curry's paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules. The paradox is named after the logician Haskell Curry. The paradox may be expressed in natural language and in various mathematical settings, including certain forms of set theory, lambda calculus, and combinatory logic. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem.