Paradox (from Greek para, against, and doxa, opinion; literally “contrary to opinion”) — A statement, argument, or situation that, from apparently acceptable premises and by apparently valid reasoning, leads to a contradictory, absurd, or self-undermining conclusion. Far from being mere games, paradoxes constitute a privileged field of inquiry because they reveal hidden tensions in our most basic intuitions about language, truth, reference, and infinity; dissolving one often requires revising a concept once thought clear. W.V.O. Quine, in The Ways of Paradox (1966), distinguishes three kinds: veridical paradoxes, whose conclusion sounds absurd but is in fact true; falsidical ones, in which a hidden error vitiates the reasoning; and antinomies, the gravest, in which the argument seems equally valid both for the conclusion and for its negation. The classic antinomy is the liar paradox (“this proposition is false”), a semantic trap generated by self-reference: Alfred Tarski showed that its rigorous solution requires separating the object language from the metalanguage that speaks about it. Equally famous is Russell’s paradox (1901) in set theory — does the set of all sets that are not members of themselves belong to itself? — which shook Frege’s logicist programme and led Russell to the theory of types. Zeno of Elea’s paradoxes, such as Achilles and the tortoise, fuel debates about infinity and the divisibility of space, while the sorites paradox (the heap of sand) exposes the vagueness of gradable predicates. Neighbouring concepts include the Kantian antinomy and aporia, the impasse opened by the clash of opposing theses.
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