Curry's paradox is a logical paradox in which an arbitrary claim can be proved true from nothing more than the existence of a self-referential sentence that says of itself, "if this sentence is true, then that arbitrary claim is true." The derivation uses only a small number of deduction rules that appear individually innocuous, and because the claim being proved is arbitrary, any logical system that admits these rules can be made to prove anything whatsoever. The paradox can be expressed in natural language and reconstructed within various formal systems, including certain forms of set theory, lambda calculus and combinatory logic; it is named for the logician Haskell Curry, who described it in 1942, and is also known as Löb's paradox for its close relationship to Löb's theorem.
Facts
Sources
1. Curry Paradox (Stanford Encyclopedia of Philosophy)
Stanford Encyclopedia of PhilosophyCurry Paradox (SEP), on Currys 1942 presentation
Currys initial presentation in Curry 1942b
Curry Paradox (SEP), bibliography, Curry 1942b The Inconsistency of Certain Formal Logics
The Inconsistency of Certain Formal Logics, Journal of Symbolic Logic, 7(3): 115-117, 1942.
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