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Curry's paradox - Wikipedia

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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, 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. Claims of the form "if A, then B" are called conditional claims. Curry's paradox uses a particular kind of self-referential conditional sentence, as demonstrated in this example: Even though Germany does not border China, the example sentence certainly is a natural-language sentence, and so the truth of that sentence can be analyzed. The paradox fol

Curry's paradox - Wikipedia Jump to content From Wikipedia, the free encyclopedia Mathematical paradox For Paul Curry's optical illusion and dissection puzzle, see Missing square puzzle . 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

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