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178:, along with self-reference, is a core feature of many paradoxes. The liar paradox, "This statement is false," exhibits contradiction because the statement cannot be false and true at the same time. The barber paradox is contradictory because it implies that the barber shaves himself if and only if the barber does not shave himself.
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But one must not think ill of the paradox, for the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion: a mediocre fellow. But the ultimate potentiation of every passion is always to will its own downfall, and so it is also the ultimate passion of
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Often a seemingly paradoxical conclusion arises from an inconsistent or inherently contradictory definition of the initial premise. In the case of that apparent paradox of a time-traveler killing his own grandfather, it is the inconsistency of defining the past to which he returns as being somehow
230:("'impossible' is not in my vocabulary") or rely on hasty assumptions (A father and his son are in a car crash; the father is killed and the boy is rushed to the hospital. The doctor says, "I can't operate on this boy. He's my son." There is no contradiction, the doctor is the boy's mother.).
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self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves
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refers to itself. Although statements can be self referential without being paradoxical ("This statement is written in
English" is a true and non-paradoxical self-referential statement), self-reference is a common element of paradoxes. One example occurs in the
279:, or that a time-traveller's interaction with the pastâhowever slightâwould entail making changes that would, in turn, change the future in which the time-travel was yet to occur, and would thus change the circumstances of the time-travel itself.
249:: it is a sentence that cannot be consistently interpreted as either true or false, because if it is known to be false, then it can be inferred that it must be true, and if it is known to be true, then it can be inferred that it must be false.
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from philosophy, a paradox that questions whether a ship repaired over time by replacing each and all of its wooden parts one at a time would remain the same ship. Paradoxes can also take the form of images or other media. For example,
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As with self-reference, a statement can contain a contradiction without being a paradox. "This statement is written in French" is an example of a contradictory self-referential statement that is not a paradox and is instead false.
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the understanding to will the collision, although in one way or another the collision must become its downfall. This, then, is the ultimate paradox of thought: to want to discover something that thought itself cannot think.
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The barber paradox also exemplifies vicious circularity: The barber shaves those who do not shave themselves, so if the barber does not shave himself, then he shaves himself, then he does not shave himself, and so on.
214:. Again, the liar paradox is an instructive example: "This statement is false"âif the statement is true, then the statement is false, thereby making the statement true, thereby making the statement false, and so on.
744:(prozone effect), of which there are several types. However, neither of these problems is common, and overall, antibodies are crucial to health, as most of the time they do their protective job quite well.
46:
contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites".
600:
and
Grelling's paradoxes to the latter. Ramsey introduced the by-now standard distinction between logical and semantical contradictions. Logical contradictions involve mathematical or logical terms like
359:) demonstrates that a decision that has an intuitive fiftyâfifty chance can instead have a provably different probable outcome. Another veridical paradox with a concise mathematical proof is the
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different from the one that leads up to the future from which he begins his trip, but also insisting that he must have come to that past from the same future as the one that it leads up to.
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is a paradox that is both true and false at the same time. It may be regarded as a fourth kind, or alternatively as a special case of antinomy. In logic, it is often assumed, following
237:, and require extending the context or language in order to lose their paradoxical quality. Paradoxes that arise from apparently intelligible uses of language are often of interest to
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were to kill his own grandfather before his mother or father had been conceived, thereby preventing his own birth. This is a specific example of the more general observation of the
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621:, which, according to Ramsey, are empirical (not formal) terms. Hence these contradictions are due to faulty ideas about thought or language, and they properly belong to
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are 'falsidical', concluding, for example, that a flying arrow never reaches its target or that a speedy runner cannot catch up to a tortoise with a small head-start.
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can be self-contradictory, i.e. it is possible for a majority of voters to support some outcome other than the one chosen (regardless of the outcome itself).
2023:
1644:"The Psychopharmacology of Agitation: Consensus Statement of the American Association for Emergency Psychiatry Project BETA Psychopharmacology Workgroup"
970:"By âparadoxâ one usually means a statement claiming something that goes beyond (or even against) âcommon opinionâ (what is usually believed or held)."
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paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.
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who shaves all and only those men who do not shave themselves will shave himself. In this paradox, the barber is a self-referential concept.
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Fraser MacBride; Mathieu Marion; MarĂa JosĂŠ FrĂĄpolli; Dorothy
Edgington; Edward Elliott; Sebastian Lutz; Jeffrey Paris (2020).
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721:(also known as ADHD), while others are rare and can be dangerous as they are not expected, such as severe agitation from a
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489:{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n}}=1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+\cdots .}
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is a paradox which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the
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Sorensen, 2005, A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind, Oxford University Press
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Chapter 2. The
Foundations of Logic and Mathematics, Frank Ramsey, < Stanford Encyclopedia of Philosophy>
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61:, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused
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Smith, W. K.; Lewis, M. W. (2011). "Toward a theory of paradox: A dynamic equilibrium model of organizing".
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William
Poundstone, 1989, Labyrinths of Reason: Paradox, Puzzles, and the Frailty of Knowledge, Anchor
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leads to a contradiction, was instrumental in the development of modern logic and set theory.
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Paradoxes that are not based on a hidden error generally occur at the fringes of context or
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Paradoxes and
Contemporary Logic (Fall 2017), <Stanford Encyclopedia of Philosophy>
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points out genuine problems in our understanding of the ideas of truth and description.
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Schad, Jonathan; Lewis, Marianne W.; Raisch, Sebastian; Smith, Wendy K. (2016-01-01).
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are famously vivid examples of a theory being taken to a logical but paradoxical end.
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Crossley, J.N.; Ash, C.J.; Brickhill, C.J.; Stillwell, J.C.; Williams, N.H. (1972).
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Waldman, David A.; Bowen, David E. (2016). "Learning to Be a
Paradox-Savvy Leader".
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85:, cannot be easily resolved by making foundational changes in a logical system.
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in the demonstration. Therefore, falsidical paradoxes can be classified as
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1421:(illustrated ed.). Springer Science & Business Media. p. 32.
807: â Problem requiring a choice between equally undesirable alternatives
524:(e.g., that 1 = 2) are classic examples of this, often relying on a hidden
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1719:, 2011, Paradoxymoron: Foolish Wisdom in Words and Pictures, Reverspective
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drew a distinction between logical paradoxes and semantic paradoxes, with
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is the opposite of what one would expect, such as becoming agitated by a
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Wilson MP, Pepper D, Currier GW, Holloman GH, Feifel D (February 2012).
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establishes a result that appears false and actually is false, due to a
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was created from a revision of this article dated 7 July 2005
1704:, Logic and Logical Philosophy, Vol. 21 No. 4 (2012), pp. 323â361.
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Mark
Sainsbury, 1988, Paradoxes, Cambridge: Cambridge University Press
1156:"Paradox Research in Management Science: Looking Back to Move Forward"
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1298:(Summer 2018 ed.), Metaphysics Research Lab, Stanford University
1236:(Winter 2016 ed.), Metaphysics Research Lab, Stanford University
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164:
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673:, among many others. Søren Kierkegaard, for example, writes in the
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are core elements of many paradoxes. Other common elements include
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Kierkegaard, Søren (1844). Hong, Howard V.; Hong, Edna H. (eds.).
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can rarely take paradoxical turns in certain ways. One example is
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1505:"Introduction to paradoxes | Brilliant Math & Science Wiki"
848: â List of statements that appear to contradict themselves
740:(immune enhancement) of a disease's virulence; another is the
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131:, and confusion or equivocation between different levels of
1621:. Princeton University Press (published 1985). p. 37.
245:. "This sentence is false" is an example of the well-known
65:
of mathematics and logic to be re-examined. One example is
535:, which falsely generalises from true specific statements
296:(1962) distinguished between three classes of paradoxes:
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825: â Faulty deductive reasoning due to a logical flaw
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1198:"Using Paradoxes to Teach Critical Thinking in Science"
1480:(reprinted ed.). Walter de Gruyter. p. 268.
910: â Theoretical paradox resulting from time travel
633:
A taste for paradox is central to the philosophies of
57:
arguments, yet are nevertheless valuable in promoting
1383:
Vicious
Circles and Infinity - A Panoply of Paradoxes
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is often used to describe a counterintuitive result.
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Pages displaying wikidata descriptions as a fallback
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Another core aspect of paradoxes is non-terminating
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1085:Zhang, Y.; Waldman, D. A.; Han, Y.; Li, X. (2015).
1031:. The Metaphysics Research Lab, Stanford University
1386:. Garden City, New York: Doubleday. pp. 1â8.
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784: â Theory that life in general is meaningless
488:
866: â Logical paradox in decision-making theory
1604:. Metaphysics Research Lab, Stanford University.
1585:. Metaphysics Research Lab, Stanford University.
1316:"Identity, Persistence, and the Ship of Theseus"
916: â Thought experiment in special relativity
854: â Term meaning 'not', 'without', or 'lack'
259:of all those sets that do not contain themselves
972:Cantini, Andrea; Bruni, Riccardo (2017-02-22).
872: â Contradiction between utility and price
318:, but is demonstrated to be true nonetheless:
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1908:
1862:The Oxford Handbook of Organizational Paradox
1228:Irvine, Andrew David; Deutsch, Harry (2016),
226:Other paradoxes involve false statements and
8:
53:, many paradoxes exist that are known to be
27:Statement that apparently contradicts itself
819: â Argument that uses faulty reasoning
328:rotating and in rapid motion around the Sun
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1418:Self-Reference: Reflections on Reflexivity
596:belonging to the former category, and the
563:Sometimes described since Quine's work, a
314:produces a result that appears counter to
267:can also yield interesting paradoxes. The
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1004:. Oxford University Press. Archived from
887: â Example of a paradoxical argument
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1596:Cantini, Andrea; Riccardo Bruni (2021).
1474:Myrdene Anderson; Floyd Merrell (2014).
831: â Any logic with four truth values
719:attention deficit hyperactivity disorder
344:demonstrates the surprising result that
186:Vicious circularity, or infinite regress
163:, which poses the question of whether a
1296:The Stanford Encyclopedia of Philosophy
1234:The Stanford Encyclopedia of Philosophy
938:
1702:Librationist Closures of the Paradoxes
1196:Eliason, James L. (MarchâApril 1996).
1855:Smith, Wendy K.; Lewis, Marianne W.;
1648:Western Journal of Emergency Medicine
1537:The Ways of Paradox, and other essays
1447:C.I. Lewis: The Last Great Pragmatist
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1341:"The Mathematical Art of M.C. Escher"
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922: â Set of philosophical problems
813: â Type of dilemma in philosophy
7:
1563:The Ways of Paradox and Other Essays
577:exist, but they are allowed in some
368:Hilbert's paradox of the Grand Hotel
2799:Analytic and synthetic propositions
2670:Formal semantics (natural language)
1847:Internet Encyclopedia of Philosophy
1812:Stanford Encyclopedia of Philosophy
1797:Stanford Encyclopedia of Philosophy
1290:Shapiro, Lionel; Beall, Jc (2018),
1202:Journal of College Science Teaching
983:Stanford Encyclopedia of Philosophy
88:Examples outside logic include the
73:on the identification of sets with
2233:What the Tortoise Said to Achilles
1792:"Paradoxes and Contemporary Logic"
1598:"Paradoxes and Contemporary Logic"
1121:Academy of Management Perspectives
974:"Paradoxes and Contemporary Logic"
404:
336:rises and falls throughout the day
25:
1805:Spade, Paul Vincent (Fall 2013).
1450:. SUNY Press. 2005. p. 376.
876:Paradoxes of material implication
751:, cigarette smoking, despite its
253:, which shows that the notion of
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1830:"Zeno and the Paradox of Motion"
1755:
1415:S.J. Bartlett; P. Suber (2012).
898: â Idea that refutes itself
837: â Type of optical illusion
765:
271:, for example, would arise if a
1790:Cantini, Andrea (Winter 2012).
841:Category:Mathematical paradoxes
194:Vicious circularity illustrated
738:antibody-dependent enhancement
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324:approximately spherical object
286:
1:
1809:. In Zalta, Edward N. (ed.).
1794:. In Zalta, Edward N. (ed.).
1294:, in Zalta, Edward N. (ed.),
1232:, in Zalta, Edward N. (ed.),
1175:10.5465/19416520.2016.1162422
1094:Academy of Management Journal
81:were flawed. Others, such as
1163:Academy of Management Annals
1052:Academy of Management Review
1865:. Oxford University Press.
1661:10.5811/westjem.2011.9.6866
1255:What is mathematical logic?
1208:(5): 341â44. Archived from
522:invalid mathematical proofs
3111:
1539:. New York: Random House.
1339:Skomorowska, Amira (ed.).
1257:. London-Oxford-New York:
334:illuminated by a Sun that
303:
29:
3006:
2883:Necessity and sufficiency
2639:
2571:
1890:
1885:Links to related articles
1027:Bolander, Thomas (2013).
366:In 20th-century science,
3070:Concepts in epistemology
860: â Figure of speech
332:approximately flat plane
32:Paradox (disambiguation)
3080:Concepts in metaphysics
2152:Paradoxes of set theory
1859:; Langley, Ann (2017).
1618:Philosophical Fragments
1259:Oxford University Press
676:Philosophical Fragments
585:Ramsey's classification
558:GrellingâNelson paradox
357:three prisoners problem
1751:
1731:Listen to this article
1320:faculty.washington.edu
686:
490:
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377:The divergence of the
287:Quine's classification
195:
3018:Philosophy portal
1842:""Logical Paradoxes""
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1533:"The ways of paradox"
1133:10.5465/amp.2015.0070
1106:10.5465/amj.2012.0995
1064:10.5465/amr.2009.0223
986:(Fall 2017 ed.).
952:mathworld.wolfram.com
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579:paraconsistent logics
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372:Ugly duckling theorem
322:That the Earth is an
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104:Informally, the term
2518:Kavka's toxin puzzle
2290:Income and fertility
1782:More spoken articles
1698:Frode Alfson Bjørdal
1477:On Semiotic Modeling
864:Paradox of tolerance
717:in the treatment of
695:paradoxical reaction
514:fallacious arguments
385:
129:circular definitions
30:For other uses, see
3090:Philosophical logic
2680:Philosophy of logic
2177:Temperature paradox
2100:Free choice paradox
1964:Fitch's knowability
1857:Jarzabkowski, Paula
1560:W.V. Quine (1976).
1493:Extract of page 268
1463:Extract of page 376
1230:"Russell's Paradox"
1008:on February 5, 2013
946:Weisstein, Eric W.
902:Syntactic ambiguity
342:Condorcet's paradox
269:grandfather paradox
265:Thought-experiments
2979:Rules of inference
2948:Mathematical logic
2690:Semantics of logic
2553:Prisoner's dilemma
2239:Heat death paradox
2227:Unexpected hanging
2192:Chicken or the egg
1752:
1434:Extract of page 32
1261:. pp. 59â60.
896:Self-refuting idea
506:falsidical paradox
500:Falsidical paradox
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353:Monty Hall paradox
204:circular reasoning
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1487:978-3-11-084987-5
1457:978-0-7914-8282-7
1428:978-94-009-3551-8
1292:"Curry's Paradox"
1002:Oxford Dictionary
846:List of paradoxes
835:Impossible object
829:Four-valued logic
788:Animalia Paradoxa
773:Philosophy portal
594:Russell's paradox
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355:(or equivalently
312:veridical paradox
300:Veridical paradox
251:Russell's paradox
202:, in the form of
99:perspective-based
67:Russell's paradox
59:critical thinking
16:(Redirected from
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1038:
1036:
1029:"Self-Reference"
1024:
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994:
988:
987:
978:Zalta, Edward N.
968:
962:
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959:
958:
943:
920:Zeno's paradoxes
908:Temporal paradox
881:
870:Paradox of value
775:
770:
769:
768:
749:smoker's paradox
705:or sedated by a
539:Zeno's paradoxes
526:division by zero
495:
493:
492:
487:
476:
468:
463:
455:
450:
442:
437:
429:
418:
410:
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402:
361:birthday paradox
277:butterfly effect
208:infinite regress
125:infinite regress
21:
3110:
3109:
3105:
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3055:
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3012:
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2998:
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2953:Boolean algebra
2927:
2778:
2769:Metamathematics
2747:
2699:
2653:
2635:
2630:
2600:
2595:
2567:
2478:Decision-making
2424:Decision theory
2419:
2248:
2172:Hilbert's Hotel
2105:GrellingâNelson
2048:
1927:
1921:
1886:
1873:
1854:
1840:
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1789:
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1763:This audio file
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1374:Hughes, Patrick
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891:Revision theory
879:
811:Ethical dilemma
771:
766:
764:
761:
728:The actions of
691:
671:G.K. Chesterton
655:Meister Eckhart
631:
587:
548:
502:
383:
382:
379:harmonic series
308:
302:
289:
224:
188:
173:
141:
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112:Common elements
90:ship of Theseus
83:Curry's paradox
35:
28:
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5:
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2062:
2056:
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2024:Rule-following
2021:
2016:
2011:
2006:
2001:
1996:
1991:
1986:
1981:
1976:
1971:
1966:
1961:
1956:
1951:
1949:Dream argument
1946:
1941:
1935:
1933:
1929:
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1725:External links
1723:
1721:
1720:
1717:Patrick Hughes
1714:
1711:
1708:
1705:
1694:
1692:
1689:
1686:
1685:
1634:
1627:
1607:
1588:
1579:"Frank Ramsey"
1569:
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1496:
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1466:
1456:
1437:
1427:
1407:
1392:
1378:Brecht, George
1356:
1331:
1307:
1282:
1267:
1245:
1217:
1214:on 2013-10-23.
1188:
1146:
1127:(3): 316â327.
1111:
1100:(2): 538â566.
1077:
1058:(2): 381â403.
1042:
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855:
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826:
823:Formal fallacy
820:
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797:
791:
785:
778:
777:
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760:
757:
723:benzodiazepine
690:
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294:W. V. O. Quine
288:
285:
223:
222:Other elements
220:
187:
184:
172:
169:
161:barber paradox
146:occurs when a
144:Self-reference
140:
139:Self-reference
137:
117:Self-reference
113:
110:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
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2994:Logic symbols
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2873:Logical truth
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2814:Contradiction
2812:
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2800:
2797:
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2792:
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2789:
2785:
2775:
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2762:
2760:
2759:Argumentation
2757:
2756:
2754:
2750:
2744:
2743:Philosophical
2741:
2739:
2738:Non-classical
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2523:Morton's fork
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2463:Buridan's ass
2461:
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2436:Apportionment
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2295:DownsâThomson
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2240:
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2212:Plato's beard
2210:
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2110:KleeneâRosser
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2034:Theseus' ship
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2027:
2025:
2022:
2020:
2017:
2015:
2012:
2010:
2007:
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2002:
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1994:Mere addition
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1977:
1975:
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1932:Philosophical
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1872:9780198754428
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1834:MathPages.com
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1509:brilliant.org
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927:
921:
918:
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912:
909:
906:
903:
900:
897:
894:
892:
889:
886:
885:Plato's beard
883:
877:
874:
871:
868:
865:
862:
859:
856:
853:
852:Mu (negative)
850:
847:
844:
842:
839:
836:
833:
830:
827:
824:
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815:
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685:
680:
678:
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672:
668:
664:
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652:
648:
644:
640:
636:
629:In philosophy
628:
626:
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620:
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612:
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595:
591:
582:
580:
576:
572:
568:
567:
561:
559:
555:
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545:
540:
537:
534:
533:horse paradox
530:
527:
523:
519:
518:
517:
515:
511:
507:
499:
483:
480:
477:
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469:
464:
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399:
396:
393:
389:
380:
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373:
369:
365:
362:
358:
354:
350:
347:
346:majority rule
343:
340:
337:
333:
329:
325:
321:
320:
319:
317:
313:
307:
299:
297:
295:
291:
284:
280:
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274:
273:time-traveler
270:
266:
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252:
248:
244:
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236:
231:
229:
221:
219:
215:
213:
209:
205:
201:
192:
185:
183:
179:
177:
176:Contradiction
171:Contradiction
170:
168:
166:
162:
158:
153:
149:
145:
138:
136:
134:
130:
126:
122:
121:contradiction
118:
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100:
96:
91:
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84:
80:
76:
72:
68:
64:
60:
56:
52:
47:
44:
40:
33:
19:
2913:Substitution
2818:
2733:Mathematical
2658:Major fields
2543:Preparedness
2375:Productivity
2355:Mandeville's
2147:Opposite Day
2075:Burali-Forti
2070:Bhartrhari's
1924:
1861:
1845:
1833:
1810:
1807:"Insolubles"
1795:
1701:
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3028:WikiProject
2898:Proposition
2893:Probability
2846:Description
2787:Foundations
2473:Condorcet's
2325:Giffen good
2285:Competition
2039:White horse
2014:Omnipotence
1529:Quine, W.V.
1169:(1): 5â64.
742:hook effect
689:In medicine
663:Kierkegaard
228:half-truths
133:abstraction
95:M.C. Escher
3059:Categories
2958:Set theory
2856:Linguistic
2851:Entailment
2841:Definition
2809:Consequent
2804:Antecedent
2548:Prevention
2538:Parrondo's
2528:Navigation
2513:Inventor's
2508:Hedgehog's
2468:Chainstore
2451:Population
2446:New states
2380:Prosperity
2360:Mayfield's
2202:Entailment
2182:Barbershop
2095:Epimenides
1778:Audio help
1769:2005-07-07
1514:2019-12-05
1350:2013-01-22
1325:2019-12-05
1302:2019-12-05
1277:0251.02001
1240:2019-12-05
957:2019-12-05
928:References
730:antibodies
651:Bhartrhari
647:Heraclitus
575:dialetheia
573:, that no
566:dialetheia
304:See also:
150:, idea or
79:predicates
75:properties
71:set theory
3065:Paradoxes
2989:Fallacies
2984:Paradoxes
2974:Logicians
2908:Statement
2903:Reference
2868:Induction
2831:Deduction
2794:Abduction
2764:Metalogic
2711:Classical
2675:Inference
2563:Willpower
2558:Tolerance
2533:Newcomb's
2498:Fredkin's
2385:Scitovsky
2305:Edgeworth
2300:Easterlin
2265:Antitrust
2162:Russell's
2157:Richard's
2130:Pinocchio
2085:Crocodile
2004:Newcomb's
1974:Goodman's
1969:Free will
1954:Epicurean
1925:paradoxes
1820:Paradoxes
1183:1941-6520
998:"paradox"
948:"Paradox"
800:Contronym
782:Absurdism
707:stimulant
667:Nietzsche
619:symbolism
571:Aristotle
481:⋯
405:∞
390:∑
316:intuition
239:logicians
200:recursion
97:featured
43:logically
3023:Category
2923:Validity
2824:Antinomy
2752:Theories
2716:Informal
2591:Category
2488:Ellsberg
2340:Leontief
2320:Gibson's
2315:European
2310:Ellsberg
2280:Braess's
2275:Bertrand
2253:Economic
2187:Catch-22
2167:Socratic
2009:Nihilism
1979:Hedonism
1939:Analysis
1923:Notable
1780: ¡
1680:22461918
1531:(1966).
1402:74-17611
1380:(1975).
1072:41318006
858:Oxymoron
759:See also
734:antigens
711:Adderall
703:sedative
643:Zhuangzi
615:language
553:antinomy
546:Antinomy
326:that is
235:language
148:sentence
3095:Thought
3038:changes
3030: (
2888:Premise
2819:Paradox
2649:History
2644:Outline
2493:Fenno's
2458:Arrow's
2441:Alabama
2431:Abilene
2410:Tullock
2365:Metzler
2207:Lottery
2197:Drinker
2140:Yablo's
2135:Quine's
2090:Curry's
2053:Logical
2029:Sorites
2019:Preface
1999:Moore's
1984:Liberal
1959:Fiction
1767: (
1738:minutes
1671:3298219
1141:2034932
1035:21 June
1012:21 June
980:(ed.).
817:Fallacy
805:Dilemma
747:In the
715:Ritalin
611:thought
510:fallacy
370:or the
212:vicious
152:formula
106:paradox
55:invalid
39:paradox
18:PARADOX
2940:topics
2726:Reason
2704:Logics
2695:Syntax
2400:Thrift
2370:Plenty
2345:Lerner
2335:Jevons
2330:Icarus
2260:Allais
2222:Ross's
2060:Barber
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1989:Meno's
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607:number
165:barber
63:axioms
2967:other
2932:Lists
2918:Truth
2685:Proof
2633:Logic
2503:Green
2483:Downs
2415:Value
2350:Lucas
2217:Raven
2125:No-no
2080:Court
2065:Berry
1159:(PDF)
1137:S2CID
1090:(PDF)
1068:JSTOR
976:. In
933:Notes
697:to a
659:Hegel
635:Laozi
603:class
51:logic
41:is a
3032:talk
2878:Name
2863:Form
2581:List
2405:Toil
2120:Card
2115:Liar
1867:ISBN
1676:PMID
1623:ISBN
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1482:ISBN
1452:ISBN
1423:ISBN
1398:LCCN
1388:ISBN
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1179:ISSN
1037:2016
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713:and
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1666:PMC
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