Paradox

A paradox is a statement that contradicts itself and yet might be true (or wrong at the same time). Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.

Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, are not yet resolved.