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A paradox is an argument that produces an inconsistency, typically within logic or common sense. Most logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking. However, some have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. Still others, such as Curry’s paradox, are not yet resolved. In common usage, the word “paradox” often refers to irony or contradiction.