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An apparently self-contradictory statement, which can only be true if it is false, and vice versa.
"This sentence is false" is a paradox.
1909, William James, A pluralistic universe. Hibbert lectures, page 347:
The active sense of living which we all enjoy, before reflection shatters our instinctive world for us, is self-luminous and suggests no paradoxes.
1962, Abraham Wolf, Textbook of Logic, page 255:
According to one version of an ancient paradox, an Athenian is supposed to say "I am a liar." It is then argued that if the statement is true, then he is telling the truth, and is therefore not a liar […]
How quaint the ways of Paradox! / At common sense she gaily mocks! / Though counting in the usual way years twenty-one I've been alive, / Yet reck'ning by my natal day, / Yet reck'ning by my natal day, / I am a little boy of five!
A thing involving contradictory yet interrelated elements that exist simultaneously and persist over time.[1][2]
He is a paradox; you would not expect him in that political party.
1999, Virginia Henley, A Year and a Day, →ISBN, page 315:
You are a paradox of bitch and angel.
An unanswerable question or difficult puzzle, particularly one which leads to a deeper truth.
1994, James Joseph Pirkl, Transgenerational Design, →ISBN, page 3:
And only by dismantling our preconceptions of age can we be free to understand the paradox: How young are the old?
(obsolete) A statement which is difficult to believe, or which goes against general belief.
1594, William Shakespeare, The Tragedy of Hamlet, Prince of Denmark, Act III:
Ay, truly; for the power of beauty will sooner / transform honesty from what it is to a bawd than the / force of honesty can translate beauty into his / likeness: this was sometime a paradox, but now the / time gives it proof.
1615, Ralph Hamor, A True Discourse of the Present State of Virginia, Richmond, published 1957, page 3:
they contended to make that Maxim, that there is no faith to be held with Infidels, a meere and absurd Paradox [...].
The need for paradox is no doubt rooted deep in the very nature of the use we make of language.
(uncountable,philosophy) A state in which one is logically compelled to contradict oneself.
1866, Edward Poste, Aristotle on Fallacies, Or, The Sophistici Elenchi, translation of original by Aristotle, page 43:
Thus, like modern disputants, they aimed either to confute the respondent or to land him in paradox.
(countable,uncountable,psychotherapy) The practice of giving instructions that are opposed to the therapist's actual intent, with the intention that the client will disobey or be unable to obey.
1988, Martin Lakin, Ethical Issues in the Psychotherapies, →ISBN, page 103:
Defiance-based paradox is employed so that the family will actively oppose and deliberately sabotage the prescription.
Usage notes
(self-contradictory statement): A statement which contradicts itself in this fashion is a paradox; two statements which contradict each other are an antinomy.
(counterintuitive outcome): This use may be considered incorrect or inexact.
1995 January 14, Ian Stewart, “Paradox of the Spheres”, in New Scientist:
Banach and Tarski's theorem (commonly known as the Banach-Tarski paradox, though it is not a true paradox, being counterintuitive rather than self-contradictory) […]
1998, Encyclopedia of Applied Physics, page 270:
It is not a true paradox, merely highly nonintuitive behavior, if one accepts the realistic and local assumptions of EPR.
(unanswerable question): This use may be considered incorrect or inexact.
Vietnamese: please add this translation if you can
References
^ Smith, W. K. and Lewis, M. W. (2011). Toward a theory of paradox: A dynamic equilibrium model of organizing. Academy of Management Review, 36, pp. 381-403
^ Zhang, Y., Waldman, D. A., Han, Y., and Li, X. (2015). Paradoxical leader behaviors in people management: Antecedents and consequences. Academy of Management Journal, 58, pp. 538-566
paradox in Bárczi, Géza and László Országh. A magyar nyelv értelmező szótára (“The Explanatory Dictionary of the Hungarian Language”, abbr.: ÉrtSz.). Budapest: Akadémiai Kiadó, 1959–1962. Fifth ed., 1992: →ISBN