Curry's Paradox
Version 1.0.0 · Updated 2026-07-28
CORE DEFINITION
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 and lambda calculus.
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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 and lambda calculus.
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Curry's paradox arises from self-referential sentences such as 'This sentence is true if and only if it can derive any proposition'. In systems that allow deriving a proposition without premises, it can derive everything, posing a more acute threat to logical systems than the liar paradox.
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- en.wikipedia.orghttps://en.wikipedia.org/wiki/Curry%27s_paradoxverified
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