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", requiring 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. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem.
In natural language
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 follows from