In multivalued logic one can distinguish at contradictions (of the type $P\wedge\neg P$) and paradoxes (of type $P\leftrightarrow \neg P$). How about in mathematics? Does the appearance of contradictions and paradoxes (in proofs) have different quality or "color" despite the logical equivalence?
2026-04-06 16:11:54.1775491914
Difference between contradiction and paradox?
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AFAIK: Contradictions are used in proofs under the definition you have stated. The word paradox tends to be used to describe mathematical phenomena that while not necessarily entailing contradictions (the paradox may even be a theorem), are nonetheless in conflict with intuition. e.g. Russell's paradox (shows that some easily defined "sets" don't exist), Banach-Tarski paradox (contradicts our sense of the way that solids behave in euclidean space).