Curry's paradox

Curry's paradox, so named for its discoverer, namely Haskell B. Curry, is a paradox within the family of so-called paradoxes of self-reference (or paradoxes of circularity). Like the liar paradox (e.g., ‘this sentence is false’) and Russell's paradox , Curry's paradox challenges familiar naive theories, including naive truth theory (unrestricted T-schema) and naive set theory (unrestricted axiom of abstraction), respectively. If one accepts naive truth theory (or naive set theory), then Curry's paradox becomes a direct challenge to one's theory of logical implication or entailment. Unlike the liar and Russell paradoxes Curry's paradox is negation-free; it may be generated irrespective of one's theory of negation. An intuitive version of the paradox runs as follows.