Curry's Paradox

David Van Horn <[email protected]> Thu, 3 Mar 2005 00:06:15 -0500
Newsgroups gmane.org.ballistichelmet.lambda
Message-ID <[email protected]>
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.

http://plato.stanford.edu/entries/curry-paradox/