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167:, 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
271:
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
219:("'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.).
34:
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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143:
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
268:, 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.
238:: 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.
81:
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,
170:
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.
206:
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.
203:. 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.
733:(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.
35:
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".
1731:
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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
348:) 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
226:, 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
264:
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
1815:
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610:, 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.
337:
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).
1628:"The Psychopharmacology of Agitation: Consensus Statement of the American Association for Emergency Psychiatry Project BETA Psychopharmacology Workgroup"
954:"By âparadoxâ one usually means a statement claiming something that goes beyond (or even against) âcommon opinionâ (what is usually believed or held)."
90:
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.
598:, and hence show that our logic or mathematics is problematic. Semantical contradictions involve, besides purely logical terms, notions like
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58:, which questions whether a "list of all lists that do not contain themselves" would include itself and showed that attempts to found
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Fraser MacBride; Mathieu Marion; MarĂa JosĂŠ FrĂĄpolli; Dorothy
Edgington; Edward Elliott; Sebastian Lutz; Jeffrey Paris (2020).
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710:(also known as ADHD), while others are rare and can be dangerous as they are not expected, such as severe agitation from a
148:, which is commonly formulated as the self-referential statement "This statement is false". Another example occurs in the
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478:{\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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Roy
Sorensen, 2005, A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind, Oxford University Press
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199:. When this recursion creates a metaphysical impossibility through contradiction, the regress or circularity is
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Chapter 2. The
Foundations of Logic and Mathematics, Frank Ramsey, < Stanford Encyclopedia of Philosophy>
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50:, 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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1550:(REVISED AND ENLARGED ed.). Cambridge, Massachusetts and London, England: Harvard University Press.
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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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779: â Mythical, magical or otherwise suspect animals mentioned in Systema Naturae
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1071:"Paradoxical leader behaviors in people management: Antecedents and consequences"
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in the demonstration. Therefore, falsidical paradoxes can be classified as
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1405:(illustrated ed.). Springer Science & Business Media. p. 32.
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791: â Problem requiring a choice between equally undesirable alternatives
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513:(e.g., that 1 = 2) are classic examples of this, often relying on a hidden
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235:
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1703:, 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
1688:, Logic and Logical Philosophy, Vol. 21 No. 4 (2012), pp. 323â361.
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635:
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59:
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Mark
Sainsbury, 1988, Paradoxes, Cambridge: Cambridge University Press
1140:"Paradox Research in Management Science: Looking Back to Move Forward"
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1282:(Summer 2018 ed.), Metaphysics Research Lab, Stanford University
1220:(Winter 2016 ed.), Metaphysics Research Lab, Stanford University
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695:
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841:
718:
699:
691:
662:, among many others. Søren Kierkegaard, for example, writes in the
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116:
are core elements of many paradoxes. Other common elements include
1599:
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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703:
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1824:
1489:"Introduction to paradoxes | Brilliant Math & Science Wiki"
832: â List of statements that appear to contradict themselves
782:
153:
51:
729:(immune enhancement) of a disease's virulence; another is the
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1855:
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1457:
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31:
120:, and confusion or equivocation between different levels of
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1989:
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1605:. Princeton University Press (published 1985). p. 37.
687:
234:. "This sentence is false" is an example of the well-known
174:
54:
of mathematics and logic to be re-examined. One example is
524:, which falsely generalises from true specific statements
285:(1962) distinguished between three classes of paradoxes:
2602:
809: â Faulty deductive reasoning due to a logical flaw
1182:"Using Paradoxes to Teach Critical Thinking in Science"
1464:(reprinted ed.). Walter de Gruyter. p. 268.
894: â Theoretical paradox resulting from time travel
622:
A taste for paradox is central to the philosophies of
46:
arguments, yet are nevertheless valuable in promoting
1398:
1367:
Vicious
Circles and Infinity - A Panoply of Paradoxes
1137:
376:
97:
is often used to describe a counterintuitive result.
864:
Pages displaying wikidata descriptions as a fallback
751:
187:
Another core aspect of paradoxes is non-terminating
1069:Zhang, Y.; Waldman, D. A.; Han, Y.; Li, X. (2015).
1015:. The Metaphysics Research Lab, Stanford University
1370:. Garden City, New York: Doubleday. pp. 1â8.
1193:
773: â Theory that life in general is meaningless
477:
1068:
850: â Logical paradox in decision-making theory
3057:
1588:. Metaphysics Research Lab, Stanford University.
1569:. Metaphysics Research Lab, Stanford University.
1300:"Identity, Persistence, and the Ship of Theseus"
900: â Thought experiment in special relativity
838: â Term meaning 'not', 'without', or 'lack'
248:of all those sets that do not contain themselves
956:Cantini, Andrea; Bruni, Riccardo (2017-02-22).
856: â Contradiction between utility and price
307:, but is demonstrated to be true nonetheless:
2618:
1909:
1885:
1863:The Oxford Handbook of Organizational Paradox
1573:
1212:Irvine, Andrew David; Deutsch, Harry (2016),
1211:
215:Other paradoxes involve false statements and
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1273:
1102:
955:
42:, many paradoxes exist that are known to be
16:Statement that apparently contradicts itself
1598:
803: â Argument that uses faulty reasoning
317:rotating and in rapid motion around the Sun
2625:
2611:
2577:
1916:
1902:
1554:
1543:
1402:Self-Reference: Reflections on Reflexivity
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585:belonging to the former category, and the
573:
552:Sometimes described since Quine's work, a
303:produces a result that appears counter to
256:can also yield interesting paradoxes. The
1653:
1643:
988:. Oxford University Press. Archived from
871: â Example of a paradoxical argument
275:
1814:) is being considered for deletion. See
1757:, and does not reflect subsequent edits.
1740:
1580:Cantini, Andrea; Riccardo Bruni (2021).
1458:Myrdene Anderson; Floyd Merrell (2014).
1010:
815: â Any logic with four truth values
708:attention deficit hyperactivity disorder
333:demonstrates the surprising result that
178:
175:Vicious circularity, or infinite regress
152:, which poses the question of whether a
1773:
1322:
1280:The Stanford Encyclopedia of Philosophy
1218:The Stanford Encyclopedia of Philosophy
1179:
3058:
1686:Librationist Closures of the Paradoxes
1180:Eliason, James L. (MarchâApril 1996).
2606:
1923:
1897:
1884:
1856:Smith, Wendy K.; Lewis, Marianne W.;
1788:
1632:Western Journal of Emergency Medicine
1537:
1521:The Ways of Paradox, and other essays
1511:
1431:C.I. Lewis: The Last Great Pragmatist
1352:
1350:
1348:
1346:
1344:
1325:"The Mathematical Art of M.C. Escher"
1207:
1205:
929:
906: â Set of philosophical problems
797: â Type of dilemma in philosophy
488:
1547:The Ways of Paradox and Other Essays
566:exist, but they are allowed in some
357:Hilbert's paradox of the Grand Hotel
288:
2800:Analytic and synthetic propositions
2671:Formal semantics (natural language)
1848:Internet Encyclopedia of Philosophy
1796:Stanford Encyclopedia of Philosophy
1781:Stanford Encyclopedia of Philosophy
1274:Shapiro, Lionel; Beall, Jc (2018),
1186:Journal of College Science Teaching
967:Stanford Encyclopedia of Philosophy
77:Examples outside logic include the
62:on the identification of sets with
13:
2234:What the Tortoise Said to Achilles
1776:"Paradoxes and Contemporary Logic"
1727:
1582:"Paradoxes and Contemporary Logic"
1341:
1202:
1105:Academy of Management Perspectives
958:"Paradoxes and Contemporary Logic"
393:
325:rises and falls throughout the day
100:
14:
3107:
1818:to help reach a consensus. âş
1789:Spade, Paul Vincent (Fall 2013).
1708:
1434:. SUNY Press. 2005. p. 376.
860:Paradoxes of material implication
740:, cigarette smoking, despite its
242:, which shows that the notion of
210:
127:
3012:
2587:
2586:
2576:
1831:"Zeno and the Paradox of Motion"
1739:
1399:S.J. Bartlett; P. Suber (2012).
882: â Idea that refutes itself
821: â Type of optical illusion
754:
617:
260:, for example, would arise if a
183:Vicious circularity illustrated.
159:
1774:Cantini, Andrea (Winter 2012).
1674:
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825:Category:Mathematical paradoxes
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1004:
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923:
727:antibody-dependent enhancement
677:
313:approximately spherical object
1:
1803:
1793:. In Zalta, Edward N. (ed.).
1778:. In Zalta, Edward N. (ed.).
1278:, in Zalta, Edward N. (ed.),
1216:, in Zalta, Edward N. (ed.),
1159:10.5465/19416520.2016.1162422
1078:Academy of Management Journal
911:
70:were flawed. Others, such as
1147:Academy of Management Annals
1036:Academy of Management Review
7:
1866:. Oxford University Press.
1645:10.5811/westjem.2011.9.6866
1239:What is mathematical logic?
1192:(5): 341â44. Archived from
747:
534:
511:invalid mathematical proofs
10:
3112:
1523:. New York: Random House.
1323:Skomorowska, Amira (ed.).
1241:. London-Oxford-New York:
323:illuminated by a Sun that
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18:
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2884:Necessity and sufficiency
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1886:Links to related articles
1011:Bolander, Thomas (2013).
355:In 20th-century science,
3071:Concepts in epistemology
1816:templates for discussion
916:
844: â Figure of speech
321:approximately flat plane
21:Paradox (disambiguation)
3081:Concepts in metaphysics
2153:Paradoxes of set theory
1860:; Langley, Ann (2017).
1602:Philosophical Fragments
1243:Oxford University Press
665:Philosophical Fragments
574:Ramsey's classification
547:GrellingâNelson paradox
346:three prisoners problem
1735:
1715:Listen to this article
1304:faculty.washington.edu
675:
479:
397:
366:The divergence of the
276:Quine's classification
184:
3019:Philosophy portal
1843:""Logical Paradoxes""
1734:
1517:"The ways of paradox"
1117:10.5465/amp.2015.0070
1090:10.5465/amj.2012.0995
1048:10.5465/amr.2009.0223
970:(Fall 2017 ed.).
936:mathworld.wolfram.com
670:
568:paraconsistent logics
480:
377:
361:Ugly duckling theorem
311:That the Earth is an
182:
93:Informally, the term
2519:Kavka's toxin puzzle
2291:Income and fertility
1766:More spoken articles
1682:Frode Alfson Bjørdal
1461:On Semiotic Modeling
848:Paradox of tolerance
706:in the treatment of
684:paradoxical reaction
503:fallacious arguments
374:
118:circular definitions
19:For other uses, see
3091:Philosophical logic
2681:Philosophy of logic
2178:Temperature paradox
2101:Free choice paradox
1965:Fitch's knowability
1858:Jarzabkowski, Paula
1544:W.V. Quine (1976).
1477:Extract of page 268
1447:Extract of page 376
1214:"Russell's Paradox"
992:on February 5, 2013
930:Weisstein, Eric W.
886:Syntactic ambiguity
331:Condorcet's paradox
258:grandfather paradox
254:Thought-experiments
2980:Rules of inference
2949:Mathematical logic
2691:Semantics of logic
2554:Prisoner's dilemma
2240:Heat death paradox
2228:Unexpected hanging
2193:Chicken or the egg
1736:
1418:Extract of page 32
1245:. pp. 59â60.
880:Self-refuting idea
495:falsidical paradox
489:Falsidical paradox
475:
342:Monty Hall paradox
193:circular reasoning
185:
3086:Critical thinking
3076:Concepts in logic
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2837:Deductive closure
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2722:Critical thinking
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2271:Arrow information
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1471:978-3-11-084987-5
1441:978-0-7914-8282-7
1412:978-94-009-3551-8
1276:"Curry's Paradox"
986:Oxford Dictionary
830:List of paradoxes
819:Impossible object
813:Four-valued logic
777:Animalia Paradoxa
762:Philosophy portal
583:Russell's paradox
464:
451:
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344:(or equivalently
301:veridical paradox
289:Veridical paradox
240:Russell's paradox
191:, in the form of
88:perspective-based
56:Russell's paradox
48:critical thinking
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1743:
1742:
1733:
1723:
1721:
1716:
1668:
1667:
1657:
1647:
1623:
1617:
1616:
1596:
1590:
1589:
1577:
1571:
1570:
1558:
1552:
1551:
1541:
1535:
1534:
1509:
1503:
1502:
1500:
1499:
1485:
1479:
1475:
1455:
1449:
1445:
1426:
1420:
1416:
1396:
1390:
1389:
1354:
1339:
1338:
1336:
1335:
1329:Lapidarium notes
1320:
1314:
1313:
1311:
1310:
1296:
1290:
1289:
1288:
1287:
1271:
1265:
1264:
1234:
1228:
1227:
1226:
1225:
1209:
1200:
1199:
1197:
1177:
1171:
1170:
1144:
1135:
1129:
1128:
1100:
1094:
1093:
1075:
1066:
1060:
1059:
1031:
1025:
1024:
1022:
1020:
1013:"Self-Reference"
1008:
1002:
1001:
999:
997:
978:
972:
971:
962:Zalta, Edward N.
952:
946:
945:
943:
942:
927:
904:Zeno's paradoxes
892:Temporal paradox
865:
854:Paradox of value
764:
759:
758:
757:
738:smoker's paradox
694:or sedated by a
528:Zeno's paradoxes
515:division by zero
484:
482:
481:
476:
465:
457:
452:
444:
439:
431:
426:
418:
407:
399:
396:
391:
350:birthday paradox
266:butterfly effect
197:infinite regress
114:infinite regress
3111:
3110:
3106:
3105:
3104:
3102:
3101:
3100:
3056:
3055:
3054:
3049:
3048:
3043:
3013:
3011:
2999:
2963:
2954:Boolean algebra
2928:
2779:
2770:Metamathematics
2748:
2700:
2654:
2636:
2631:
2601:
2596:
2568:
2479:Decision-making
2425:Decision theory
2420:
2249:
2173:Hilbert's Hotel
2106:GrellingâNelson
2049:
1928:
1922:
1887:
1874:
1841:
1829:
1819:
1770:
1769:
1758:
1752:
1750:
1747:This audio file
1744:
1737:
1728:
1725:
1719:
1718:
1714:
1711:
1706:
1677:
1672:
1671:
1624:
1620:
1613:
1597:
1593:
1578:
1574:
1559:
1555:
1542:
1538:
1531:
1510:
1506:
1497:
1495:
1487:
1486:
1482:
1472:
1456:
1452:
1442:
1428:
1427:
1423:
1413:
1397:
1393:
1378:
1358:Hughes, Patrick
1355:
1342:
1333:
1331:
1321:
1317:
1308:
1306:
1298:
1297:
1293:
1285:
1283:
1272:
1268:
1253:
1235:
1231:
1223:
1221:
1210:
1203:
1178:
1174:
1142:
1136:
1132:
1101:
1097:
1073:
1067:
1063:
1032:
1028:
1018:
1016:
1009:
1005:
995:
993:
980:
979:
975:
953:
949:
940:
938:
928:
924:
919:
914:
909:
875:Revision theory
863:
795:Ethical dilemma
760:
755:
753:
750:
717:The actions of
680:
660:G.K. Chesterton
644:Meister Eckhart
620:
576:
537:
491:
456:
443:
430:
417:
398:
392:
381:
375:
372:
371:
368:harmonic series
297:
291:
278:
213:
177:
162:
130:
103:
101:Common elements
79:ship of Theseus
72:Curry's paradox
24:
17:
12:
11:
5:
3109:
3099:
3098:
3093:
3088:
3083:
3078:
3073:
3068:
3051:
3050:
3045:
3044:
3042:
3041:
3036:
3026:
3021:
3008:
3005:
3004:
3001:
3000:
2998:
2997:
2992:
2987:
2982:
2977:
2971:
2969:
2965:
2964:
2962:
2961:
2956:
2951:
2945:
2943:
2934:
2930:
2929:
2927:
2926:
2921:
2916:
2911:
2906:
2901:
2896:
2891:
2886:
2881:
2876:
2871:
2866:
2861:
2860:
2859:
2849:
2844:
2839:
2834:
2829:
2828:
2827:
2822:
2812:
2807:
2802:
2797:
2791:
2789:
2785:
2784:
2781:
2780:
2778:
2777:
2772:
2767:
2762:
2756:
2754:
2750:
2749:
2747:
2746:
2741:
2736:
2731:
2730:
2729:
2724:
2714:
2708:
2706:
2699:
2698:
2693:
2688:
2683:
2678:
2673:
2668:
2662:
2660:
2656:
2655:
2653:
2652:
2647:
2641:
2638:
2637:
2630:
2629:
2622:
2615:
2607:
2598:
2597:
2595:
2594:
2584:
2573:
2570:
2569:
2567:
2566:
2561:
2556:
2551:
2546:
2541:
2536:
2531:
2526:
2521:
2516:
2511:
2506:
2501:
2496:
2491:
2486:
2481:
2476:
2471:
2466:
2461:
2456:
2455:
2454:
2449:
2444:
2434:
2428:
2426:
2422:
2421:
2419:
2418:
2413:
2408:
2403:
2398:
2396:St. Petersburg
2393:
2388:
2383:
2378:
2373:
2368:
2363:
2358:
2353:
2348:
2343:
2338:
2333:
2328:
2323:
2318:
2313:
2308:
2303:
2298:
2293:
2288:
2283:
2278:
2273:
2268:
2263:
2257:
2255:
2251:
2250:
2248:
2247:
2242:
2237:
2230:
2225:
2220:
2215:
2210:
2205:
2200:
2195:
2190:
2185:
2180:
2175:
2170:
2165:
2160:
2155:
2150:
2145:
2144:
2143:
2138:
2133:
2128:
2123:
2113:
2108:
2103:
2098:
2093:
2088:
2083:
2078:
2073:
2068:
2063:
2057:
2055:
2051:
2050:
2048:
2047:
2042:
2037:
2032:
2027:
2025:Rule-following
2022:
2017:
2012:
2007:
2002:
1997:
1992:
1987:
1982:
1977:
1972:
1967:
1962:
1957:
1952:
1950:Dream argument
1947:
1942:
1936:
1934:
1930:
1929:
1921:
1920:
1913:
1906:
1898:
1892:
1889:
1888:
1879:
1878:
1872:
1853:
1839:
1827:
1801:
1786:
1759:
1745:
1738:
1726:
1713:
1712:
1710:
1709:External links
1707:
1705:
1704:
1701:Patrick Hughes
1698:
1695:
1692:
1689:
1678:
1676:
1673:
1670:
1669:
1618:
1611:
1591:
1572:
1563:"Frank Ramsey"
1553:
1536:
1529:
1504:
1480:
1470:
1450:
1440:
1421:
1411:
1391:
1376:
1362:Brecht, George
1340:
1315:
1291:
1266:
1251:
1229:
1201:
1198:on 2013-10-23.
1172:
1130:
1111:(3): 316â327.
1095:
1084:(2): 538â566.
1061:
1042:(2): 381â403.
1026:
1003:
973:
947:
921:
920:
918:
915:
913:
910:
908:
907:
901:
895:
889:
883:
877:
872:
866:
857:
851:
845:
839:
833:
827:
822:
816:
810:
807:Formal fallacy
804:
798:
792:
786:
780:
774:
767:
766:
765:
749:
746:
712:benzodiazepine
679:
676:
619:
616:
575:
572:
536:
533:
532:
531:
525:
518:
490:
487:
486:
485:
474:
471:
468:
463:
460:
455:
450:
447:
442:
437:
434:
429:
424:
421:
416:
413:
410:
405:
402:
395:
390:
387:
384:
380:
364:
353:
338:
328:
290:
287:
283:W. V. O. Quine
277:
274:
212:
211:Other elements
209:
176:
173:
161:
158:
150:barber paradox
135:occurs when a
133:Self-reference
129:
128:Self-reference
126:
106:Self-reference
102:
99:
15:
9:
6:
4:
3:
2:
3108:
3097:
3094:
3092:
3089:
3087:
3084:
3082:
3079:
3077:
3074:
3072:
3069:
3067:
3064:
3063:
3061:
3040:
3037:
3034:
3030:
3027:
3025:
3022:
3020:
3010:
3009:
3006:
2996:
2995:Logic symbols
2993:
2991:
2988:
2986:
2983:
2981:
2978:
2976:
2973:
2972:
2970:
2966:
2960:
2957:
2955:
2952:
2950:
2947:
2946:
2944:
2942:
2938:
2935:
2931:
2925:
2922:
2920:
2917:
2915:
2912:
2910:
2907:
2905:
2902:
2900:
2897:
2895:
2892:
2890:
2887:
2885:
2882:
2880:
2877:
2875:
2874:Logical truth
2872:
2870:
2867:
2865:
2862:
2858:
2855:
2854:
2853:
2850:
2848:
2845:
2843:
2840:
2838:
2835:
2833:
2830:
2826:
2823:
2821:
2818:
2817:
2816:
2815:Contradiction
2813:
2811:
2808:
2806:
2803:
2801:
2798:
2796:
2793:
2792:
2790:
2786:
2776:
2773:
2771:
2768:
2766:
2763:
2761:
2760:Argumentation
2758:
2757:
2755:
2751:
2745:
2744:Philosophical
2742:
2740:
2739:Non-classical
2737:
2735:
2732:
2728:
2725:
2723:
2720:
2719:
2718:
2715:
2713:
2710:
2709:
2707:
2703:
2697:
2694:
2692:
2689:
2687:
2684:
2682:
2679:
2677:
2674:
2672:
2669:
2667:
2664:
2663:
2661:
2657:
2651:
2648:
2646:
2643:
2642:
2639:
2635:
2628:
2623:
2621:
2616:
2614:
2609:
2608:
2605:
2593:
2585:
2583:
2575:
2574:
2571:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2545:
2542:
2540:
2537:
2535:
2532:
2530:
2527:
2525:
2524:Morton's fork
2522:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2492:
2490:
2487:
2485:
2482:
2480:
2477:
2475:
2472:
2470:
2467:
2465:
2464:Buridan's ass
2462:
2460:
2457:
2453:
2450:
2448:
2445:
2443:
2440:
2439:
2438:
2437:Apportionment
2435:
2433:
2430:
2429:
2427:
2423:
2417:
2414:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2394:
2392:
2389:
2387:
2384:
2382:
2379:
2377:
2374:
2372:
2369:
2367:
2364:
2362:
2359:
2357:
2354:
2352:
2349:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2327:
2324:
2322:
2319:
2317:
2314:
2312:
2309:
2307:
2304:
2302:
2299:
2297:
2296:DownsâThomson
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2272:
2269:
2267:
2264:
2262:
2259:
2258:
2256:
2252:
2246:
2243:
2241:
2238:
2235:
2231:
2229:
2226:
2224:
2221:
2219:
2216:
2214:
2213:Plato's beard
2211:
2209:
2206:
2204:
2201:
2199:
2196:
2194:
2191:
2189:
2186:
2184:
2181:
2179:
2176:
2174:
2171:
2169:
2166:
2164:
2161:
2159:
2156:
2154:
2151:
2149:
2146:
2142:
2139:
2137:
2134:
2132:
2129:
2127:
2124:
2122:
2119:
2118:
2117:
2114:
2112:
2111:KleeneâRosser
2109:
2107:
2104:
2102:
2099:
2097:
2094:
2092:
2089:
2087:
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2058:
2056:
2052:
2046:
2043:
2041:
2038:
2036:
2035:Theseus' ship
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2016:
2013:
2011:
2008:
2006:
2003:
2001:
1998:
1996:
1995:Mere addition
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1973:
1971:
1968:
1966:
1963:
1961:
1958:
1956:
1953:
1951:
1948:
1946:
1943:
1941:
1938:
1937:
1935:
1933:Philosophical
1931:
1927:
1919:
1914:
1912:
1907:
1905:
1900:
1899:
1896:
1890:
1883:
1875:
1873:9780198754428
1869:
1865:
1864:
1859:
1854:
1850:
1849:
1844:
1840:
1836:
1835:MathPages.com
1832:
1828:
1826:
1822:
1817:
1813:
1812:
1807:
1802:
1798:
1797:
1792:
1787:
1783:
1782:
1777:
1772:
1771:
1767:
1763:
1748:
1702:
1699:
1696:
1693:
1690:
1687:
1683:
1680:
1679:
1665:
1661:
1656:
1651:
1646:
1641:
1637:
1633:
1629:
1622:
1614:
1612:9780691020365
1608:
1604:
1603:
1595:
1587:
1583:
1576:
1568:
1564:
1557:
1549:
1548:
1540:
1532:
1530:9780674948358
1526:
1522:
1518:
1514:
1508:
1494:
1493:brilliant.org
1490:
1484:
1478:
1473:
1467:
1463:
1462:
1454:
1448:
1443:
1437:
1433:
1432:
1425:
1419:
1414:
1408:
1404:
1403:
1395:
1387:
1383:
1379:
1377:0-385-09917-7
1373:
1369:
1368:
1363:
1359:
1353:
1351:
1349:
1347:
1345:
1330:
1326:
1319:
1305:
1301:
1295:
1281:
1277:
1270:
1262:
1258:
1254:
1252:0-19-888087-1
1248:
1244:
1240:
1233:
1219:
1215:
1208:
1206:
1196:
1191:
1187:
1183:
1176:
1168:
1164:
1160:
1156:
1152:
1148:
1141:
1134:
1126:
1122:
1118:
1114:
1110:
1106:
1099:
1091:
1087:
1083:
1079:
1072:
1065:
1057:
1053:
1049:
1045:
1041:
1037:
1030:
1014:
1007:
991:
987:
983:
977:
969:
968:
963:
959:
951:
937:
933:
926:
922:
905:
902:
899:
896:
893:
890:
887:
884:
881:
878:
876:
873:
870:
869:Plato's beard
867:
861:
858:
855:
852:
849:
846:
843:
840:
837:
836:Mu (negative)
834:
831:
828:
826:
823:
820:
817:
814:
811:
808:
805:
802:
799:
796:
793:
790:
787:
784:
781:
778:
775:
772:
769:
768:
763:
752:
745:
743:
739:
734:
732:
728:
724:
720:
715:
713:
709:
705:
701:
697:
693:
689:
685:
674:
669:
667:
666:
661:
657:
653:
649:
645:
641:
637:
633:
629:
625:
618:In philosophy
615:
613:
609:
605:
601:
597:
593:
588:
584:
580:
571:
569:
565:
561:
557:
556:
550:
548:
544:
543:
529:
526:
523:
522:horse paradox
519:
516:
512:
508:
507:
506:
504:
500:
496:
472:
469:
466:
461:
458:
453:
448:
445:
440:
435:
432:
427:
422:
419:
414:
411:
408:
403:
400:
388:
385:
382:
378:
369:
365:
362:
358:
354:
351:
347:
343:
339:
336:
335:majority rule
332:
329:
326:
322:
318:
314:
310:
309:
308:
306:
302:
296:
286:
284:
280:
273:
269:
267:
263:
262:time-traveler
259:
255:
251:
249:
247:
241:
237:
233:
229:
225:
220:
218:
208:
204:
202:
198:
194:
190:
181:
172:
168:
166:
165:Contradiction
160:Contradiction
157:
155:
151:
147:
142:
138:
134:
125:
123:
119:
115:
111:
110:contradiction
107:
98:
96:
91:
89:
85:
80:
75:
73:
69:
65:
61:
57:
53:
49:
45:
41:
36:
33:
29:
22:
2914:Substitution
2819:
2734:Mathematical
2659:Major fields
2544:Preparedness
2376:Productivity
2356:Mandeville's
2148:Opposite Day
2076:Burali-Forti
2071:Bhartrhari's
1925:
1862:
1846:
1834:
1809:
1794:
1791:"Insolubles"
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2899:Proposition
2894:Probability
2847:Description
2788:Foundations
2474:Condorcet's
2326:Giffen good
2286:Competition
2040:White horse
2015:Omnipotence
1804:âš The
1513:Quine, W.V.
1153:(1): 5â64.
731:hook effect
678:In medicine
652:Kierkegaard
217:half-truths
122:abstraction
84:M.C. Escher
3060:Categories
2959:Set theory
2857:Linguistic
2852:Entailment
2842:Definition
2810:Consequent
2805:Antecedent
2549:Prevention
2539:Parrondo's
2529:Navigation
2514:Inventor's
2509:Hedgehog's
2469:Chainstore
2452:Population
2447:New states
2381:Prosperity
2361:Mayfield's
2203:Entailment
2183:Barbershop
2096:Epimenides
1762:Audio help
1753:2005-07-07
1498:2019-12-05
1334:2013-01-22
1309:2019-12-05
1286:2019-12-05
1261:0251.02001
1224:2019-12-05
941:2019-12-05
912:References
719:antibodies
640:Bhartrhari
636:Heraclitus
564:dialetheia
562:, that no
555:dialetheia
293:See also:
139:, idea or
68:predicates
64:properties
60:set theory
3066:Paradoxes
2990:Fallacies
2985:Paradoxes
2975:Logicians
2909:Statement
2904:Reference
2869:Induction
2832:Deduction
2795:Abduction
2765:Metalogic
2712:Classical
2676:Inference
2564:Willpower
2559:Tolerance
2534:Newcomb's
2499:Fredkin's
2386:Scitovsky
2306:Edgeworth
2301:Easterlin
2266:Antitrust
2163:Russell's
2158:Richard's
2131:Pinocchio
2086:Crocodile
2005:Newcomb's
1975:Goodman's
1970:Free will
1955:Epicurean
1926:paradoxes
1821:Paradoxes
1167:1941-6520
982:"paradox"
932:"Paradox"
771:Absurdism
696:stimulant
656:Nietzsche
608:symbolism
560:Aristotle
470:⋯
394:∞
379:∑
305:intuition
228:logicians
189:recursion
86:featured
32:logically
3024:Category
2924:Validity
2825:Antinomy
2753:Theories
2717:Informal
2592:Category
2489:Ellsberg
2341:Leontief
2321:Gibson's
2316:European
2311:Ellsberg
2281:Braess's
2276:Bertrand
2254:Economic
2188:Catch-22
2168:Socratic
2010:Nihilism
1980:Hedonism
1940:Analysis
1924:Notable
1806:template
1764: ¡
1664:22461918
1515:(1966).
1386:74-17611
1364:(1975).
1056:41318006
842:Oxymoron
748:See also
723:antigens
700:Adderall
692:sedative
632:Zhuangzi
604:language
542:antinomy
535:Antinomy
315:that is
224:language
137:sentence
3096:Thought
3039:changes
3031: (
2889:Premise
2820:Paradox
2650:History
2645:Outline
2494:Fenno's
2459:Arrow's
2442:Alabama
2432:Abilene
2411:Tullock
2366:Metzler
2208:Lottery
2198:Drinker
2141:Yablo's
2136:Quine's
2091:Curry's
2054:Logical
2030:Sorites
2020:Preface
2000:Moore's
1985:Liberal
1960:Fiction
1808:below (
1751: (
1722:minutes
1655:3298219
1125:2034932
1019:21 June
996:21 June
964:(ed.).
801:Fallacy
789:Dilemma
736:In the
704:Ritalin
600:thought
499:fallacy
359:or the
201:vicious
141:formula
95:paradox
44:invalid
28:paradox
2941:topics
2727:Reason
2705:Logics
2696:Syntax
2401:Thrift
2371:Plenty
2346:Lerner
2336:Jevons
2331:Icarus
2261:Allais
2223:Ross's
2061:Barber
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1990:Meno's
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154:barber
52:axioms
2968:other
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2919:Truth
2686:Proof
2634:Logic
2504:Green
2484:Downs
2416:Value
2351:Lucas
2218:Raven
2126:No-no
2081:Court
2066:Berry
1143:(PDF)
1121:S2CID
1074:(PDF)
1052:JSTOR
960:. In
917:Notes
686:to a
648:Hegel
624:Laozi
592:class
40:logic
30:is a
3033:talk
2879:Name
2864:Form
2582:List
2406:Toil
2121:Card
2116:Liar
1868:ISBN
1660:PMID
1607:ISBN
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1382:LCCN
1372:ISBN
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1163:ISSN
1021:2016
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702:and
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