Curry's paradox

Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F". The paradox requires only a few apparently-innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic.

The paradox is named after the logician Haskell Curry, who wrote about it in 1942.^[1] It has also been called Löb's paradox after Martin Hugo Löb,^[2] due to its relationship to Löb's theorem.