Curry's paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules. It is named after the logician Haskell Curry. While naive set theory fails to identify it, a more rigorous examination reveals that the sentence is self-contradictory.
It has also been called Löb's paradox after Martin Hugo Löb.
Read more about Curry's Paradox: Natural Language, Formal Logic, Naive Set Theory, Combinatory Logic, Discussion
Famous quotes containing the word paradox:
“The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and the general principles of a scientific theory serve their purpose, i. e., if they establish the definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretive statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.”
—C.G. (Carl Gustav)