2599:
2589:
1752:
191:
3025:
767:
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.
683:
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
282:
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.).
45:
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
494:
154:
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.
92:
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,
181:
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.
684:
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.
217:
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".
1742:
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
384:
283:
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.
1740:
569:
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
275:
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
1826:
1192:
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
1741:
541:
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.
348:
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).
1639:"The Psychopharmacology of Agitation: Consensus Statement of the American Association for Emergency Psychiatry Project BETA Psychopharmacology Workgroup"
965:"By âparadoxâ one usually means a statement claiming something that goes beyond (or even against) âcommon opinionâ (what is usually believed or held)."
101:
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.
992:
167:
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.
609:, and hence show that our logic or mathematics is problematic. Semantical contradictions involve, besides purely logical terms, notions like
1205:
2035:
69:, which questions whether a "list of all lists that do not contain themselves" would include itself and showed that attempts to found
1872:
718:
2183:
367:
1572:
Fraser MacBride; Mathieu Marion; MarĂa JosĂŠ FrĂĄpolli; Dorothy
Edgington; Edward Elliott; Sebastian Lutz; Jeffrey Paris (2020).
3049:
1480:
1450:
1421:
1527:
721:(also known as ADHD), while others are rare and can be dangerous as they are not expected, such as severe agitation from a
159:, which is commonly formulated as the self-referential statement "This statement is false". Another example occurs in the
1556:
1335:
489:{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n}}=1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+\cdots .}
2681:
1926:
1858:
1806:
1791:
977:
556:
is a paradox which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the
2810:
2244:
1708:
Roy
Sorensen, 2005, A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind, Oxford University Press
3081:
2959:
2213:
2050:
1975:
1882:
1621:
1539:
1386:
1261:
870:
17:
3091:
3043:
2469:
2635:
835:
210:. When this recursion creates a metaphysical impossibility through contradiction, the regress or circularity is
2964:
1578:
Chapter 2. The
Foundations of Logic and Mathematics, Frank Ramsey, < Stanford Encyclopedia of Philosophy>
737:
78:
61:, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused
2462:
658:
532:
378:
1045:
Smith, W. K.; Lewis, M. W. (2011). "Toward a theory of paradox: A dynamic equilibrium model of organizing".
3101:
2286:
1000:
589:
3039:
2116:
1757:
557:
1561:(REVISED AND ENLARGED ed.). Cambridge, Massachusetts and London, England: Harvard University Press.
3096:
3086:
2990:
2238:
2178:
1831:
1224:
2233:
1705:
William
Poundstone, 1989, Labyrinths of Reason: Paradox, Puzzles, and the Frailty of Knowledge, Anchor
2969:
2894:
2676:
2306:
2281:
2121:
1776:
1286:
752:
2867:
2401:
1150:
968:
31:
1786:
1592:
873: â logical contradictions centred on the difference between natural language and logic theory
2951:
2529:
2489:
2366:
2163:
2081:
1985:
1980:
1919:
1711:
1571:
1368:
1253:
675:
356:
330:, rather than the apparently obvious and common-sensical appearance of the Earth as a stationary
1692:
2406:
2296:
755:, has a surprising inverse correlation with the epidemiological incidence of certain diseases.
211:
147:
1487:
1457:
261:
leads to a contradiction, was instrumental in the development of modern logic and set theory.
3005:
2564:
2549:
2524:
2519:
2447:
2391:
2371:
2276:
2111:
2005:
1611:
1428:
371:
74:
1376:
709:. Some are common and are used regularly in medicine, such as the use of stimulants such as
233:
Paradoxes that are not based on a hidden error generally occur at the fringes of context or
2924:
2770:
2569:
2554:
2544:
2509:
2457:
2386:
2301:
2173:
2168:
2091:
2086:
2015:
1772:
858:
694:
593:
578:
250:
98:
66:
1310:
1271:
662:
8:
2879:
2862:
2842:
2805:
2754:
2749:
2691:
2628:
2331:
2291:
2255:
2188:
2055:
2025:
2020:
1990:
1955:
1950:
1597:
Paradoxes and
Contemporary Logic (Fall 2017), <Stanford Encyclopedia of Philosophy>
914:
896:
748:
666:
538:
268:
151:
128:
560:
points out genuine problems in our understanding of the ideas of truth and description.
3076:
2815:
2744:
2701:
2602:
2559:
2539:
2504:
2479:
2452:
2250:
2203:
2193:
2151:
2146:
2106:
2101:
2010:
1970:
1912:
1868:
1665:
1638:
1131:
1062:
890:
352:
264:
203:
82:
1149:
Schad, Jonathan; Lewis, Marianne W.; Raisch, Sebastian; Smith, Wendy K. (2016-01-01).
3029:
3000:
2995:
2985:
2919:
2847:
2732:
2592:
2574:
2514:
2494:
2484:
2411:
2396:
2316:
2311:
2141:
2136:
2096:
1965:
1878:
1670:
1617:
1535:
1476:
1446:
1417:
1392:
1382:
1257:
1173:
1081:
840:
829:
823:
787:
772:
374:
are famously vivid examples of a theory being taken to a logical but paradoxical end.
341:
256:
58:
1248:
Crossley, J.N.; Ash, C.J.; Brickhill, C.J.; Stillwell, J.C.; Williams, N.H. (1972).
1114:
Waldman, David A.; Bowen, David E. (2016). "Learning to Be a
Paradox-Savvy Leader".
1023:
3106:
2934:
2660:
2655:
2534:
2499:
2474:
2426:
2351:
2326:
2321:
2223:
2198:
1660:
1650:
1499:
1267:
1165:
1135:
1123:
1096:
1054:
902:
879:
864:
790: â Mythical, magical or otherwise suspect animals mentioned in Systema Naturae
525:
360:
276:
207:
124:
54:
1169:
2780:
2722:
2442:
2421:
2416:
2376:
2218:
2208:
2045:
2040:
2030:
1995:
1821:
1470:
1440:
1411:
1082:"Paradoxical leader behaviors in people management: Antecedents and consequences"
972:
885:
805:
670:
654:
323:
89:
1655:
85:, cannot be easily resolved by making foundational changes in a logical system.
3034:
2727:
2706:
2621:
2381:
2356:
2346:
2341:
2271:
2071:
1960:
1801:
817:
722:
293:
160:
143:
116:
899: â Sentences with structures permitting multiple possible interpretations
796: â State of puzzlement or expression of doubt, in philosophy and rhetoric
3070:
2884:
2825:
2361:
2228:
2076:
1841:
1816:
1573:
1372:
1177:
846:
521:
345:
327:
175:
120:
1891:
942:
512:
in the demonstration. Therefore, falsidical paradoxes can be classified as
2874:
2696:
2158:
2131:
2126:
1674:
1416:(illustrated ed.). Springer Science & Business Media. p. 32.
908:
802: â Problem requiring a choice between equally undesirable alternatives
638:
622:
597:
524:(e.g., that 1 = 2) are classic examples of this, often relying on a hidden
305:
246:
156:
1714:, 2011, Paradoxymoron: Foolish Wisdom in Words and Pictures, Reverspective
1127:
1100:
1058:
592:
drew a distinction between logical paradoxes and semantic paradoxes, with
2909:
2904:
2857:
2336:
741:
701:
is the opposite of what one would expect, such as becoming agitated by a
642:
335:
272:
242:
132:
94:
1637:
Wilson MP, Pepper D, Currier GW, Holloman GH, Feifel D (February 2012).
1066:
508:
establishes a result that appears false and actually is false, due to a
2852:
2820:
2785:
1760:
was created from a revision of this article dated 7 July 2005
1699:, Logic and Logical Philosophy, Vol. 21 No. 4 (2012), pp. 323â361.
1523:
650:
646:
565:
331:
227:
70:
1702:
Mark
Sainsbury, 1988, Paradoxes, Cambridge: Cambridge University Press
1151:"Paradox Research in Management Science: Looking Back to Move Forward"
2914:
2775:
2686:
1293:(Summer 2018 ed.), Metaphysics Research Lab, Stanford University
1231:(Winter 2016 ed.), Metaphysics Research Lab, Stanford University
781:
706:
570:
315:
199:
1904:
2835:
852:
729:
710:
702:
673:, among many others. Søren Kierkegaard, for example, writes in the
552:
234:
127:
are core elements of many paradoxes. Other common elements include
1610:
Kierkegaard, Søren (1844). Hong, Howard V.; Hong, Edna H. (eds.).
736:
can rarely take paradoxical turns in certain ways. One example is
2899:
1853:
811:
799:
733:
714:
513:
509:
1396:
190:
2737:
1835:
1500:"Introduction to paradoxes | Brilliant Math & Science Wiki"
843: â List of statements that appear to contradict themselves
793:
164:
62:
740:(immune enhancement) of a disease's virulence; another is the
2929:
2644:
1866:
1590:
1468:
1247:
634:
238:
50:
42:
131:, and confusion or equivocation between different levels of
2889:
2000:
1636:
1616:. Princeton University Press (published 1985). p. 37.
698:
245:. "This sentence is false" is an example of the well-known
185:
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:
2613:
820: â Faulty deductive reasoning due to a logical flaw
1193:"Using Paradoxes to Teach Critical Thinking in Science"
1475:(reprinted ed.). Walter de Gruyter. p. 268.
905: 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
1409:
1378:
Vicious
Circles and Infinity - A Panoply of Paradoxes
1148:
387:
108:
is often used to describe a counterintuitive result.
875:
Pages displaying wikidata descriptions as a fallback
762:
198:
Another core aspect of paradoxes is non-terminating
1080:Zhang, Y.; Waldman, D. A.; Han, Y.; Li, X. (2015).
1026:. The Metaphysics Research Lab, Stanford University
1381:. Garden City, New York: Doubleday. pp. 1â8.
1204:
784: â Theory that life in general is meaningless
488:
1079:
861: â Logical paradox in decision-making theory
3068:
1599:. Metaphysics Research Lab, Stanford University.
1580:. Metaphysics Research Lab, Stanford University.
1311:"Identity, Persistence, and the Ship of Theseus"
911: â Thought experiment in special relativity
849: â Term meaning 'not', 'without', or 'lack'
259:of all those sets that do not contain themselves
967:Cantini, Andrea; Bruni, Riccardo (2017-02-22).
867: â Contradiction between utility and price
318:, but is demonstrated to be true nonetheless:
2629:
1920:
1896:
1874:The Oxford Handbook of Organizational Paradox
1584:
1223:Irvine, Andrew David; Deutsch, Harry (2016),
1222:
226:Other paradoxes involve false statements and
1367:
1284:
1113:
966:
53:, many paradoxes exist that are known to be
27:Statement that apparently contradicts itself
1609:
814: â Argument that uses faulty reasoning
328:rotating and in rapid motion around the Sun
2636:
2622:
2588:
1927:
1913:
1565:
1554:
1413:Self-Reference: Reflections on Reflexivity
1044:
596:belonging to the former category, and the
584:
563:Sometimes described since Quine's work, a
314:produces a result that appears counter to
267:can also yield interesting paradoxes. The
1664:
1654:
999:. Oxford University Press. Archived from
882: â Example of a paradoxical argument
286:
1825:) is being considered for deletion. See
1768:, and does not reflect subsequent edits.
1751:
1591:Cantini, Andrea; Riccardo Bruni (2021).
1469:Myrdene Anderson; Floyd Merrell (2014).
1021:
826: â Any logic with four truth values
719:attention deficit hyperactivity disorder
344:demonstrates the surprising result that
189:
186:Vicious circularity, or infinite regress
163:, which poses the question of whether a
1784:
1333:
1291:The Stanford Encyclopedia of Philosophy
1229:The Stanford Encyclopedia of Philosophy
1190:
14:
3069:
1697:Librationist Closures of the Paradoxes
1191:Eliason, James L. (MarchâApril 1996).
2617:
1934:
1908:
1895:
1867:Smith, Wendy K.; Lewis, Marianne W.;
1799:
1643:Western Journal of Emergency Medicine
1548:
1532:The Ways of Paradox, and other essays
1522:
1442:C.I. Lewis: The Last Great Pragmatist
1363:
1361:
1359:
1357:
1355:
1336:"The Mathematical Art of M.C. Escher"
1218:
1216:
940:
917: â Set of philosophical problems
808: â Type of dilemma in philosophy
499:
1558:The Ways of Paradox and Other Essays
577:exist, but they are allowed in some
368:Hilbert's paradox of the Grand Hotel
299:
2811:Analytic and synthetic propositions
2682:Formal semantics (natural language)
1859:Internet Encyclopedia of Philosophy
1807:Stanford Encyclopedia of Philosophy
1792:Stanford Encyclopedia of Philosophy
1285:Shapiro, Lionel; Beall, Jc (2018),
1197:Journal of College Science Teaching
978:Stanford Encyclopedia of Philosophy
88:Examples outside logic include the
73:on the identification of sets with
24:
2245:What the Tortoise Said to Achilles
1787:"Paradoxes and Contemporary Logic"
1738:
1593:"Paradoxes and Contemporary Logic"
1352:
1213:
1116:Academy of Management Perspectives
969:"Paradoxes and Contemporary Logic"
404:
336:rises and falls throughout the day
111:
25:
3118:
1829:to help reach a consensus. âş
1800:Spade, Paul Vincent (Fall 2013).
1719:
1445:. SUNY Press. 2005. p. 376.
871:Paradoxes of material implication
751:, cigarette smoking, despite its
253:, which shows that the notion of
221:
138:
3023:
2598:
2597:
2587:
1842:"Zeno and the Paradox of Motion"
1750:
1410:S.J. Bartlett; P. Suber (2012).
893: â Idea that refutes itself
832: â Type of optical illusion
765:
628:
271:, for example, would arise if a
194:Vicious circularity illustrated.
170:
1785:Cantini, Andrea (Winter 2012).
1685:
1630:
1603:
1516:
1492:
1462:
1433:
1403:
1327:
1303:
1278:
1241:
836:Category:Mathematical paradoxes
1184:
1142:
1107:
1073:
1038:
1015:
985:
959:
934:
738:antibody-dependent enhancement
688:
324:approximately spherical object
13:
1:
1814:
1804:. In Zalta, Edward N. (ed.).
1789:. In Zalta, Edward N. (ed.).
1289:, in Zalta, Edward N. (ed.),
1227:, in Zalta, Edward N. (ed.),
1170:10.5465/19416520.2016.1162422
1089:Academy of Management Journal
922:
81:were flawed. Others, such as
1158:Academy of Management Annals
1047:Academy of Management Review
7:
1877:. Oxford University Press.
1656:10.5811/westjem.2011.9.6866
1250:What is mathematical logic?
1203:(5): 341â44. Archived from
758:
545:
522:invalid mathematical proofs
10:
3123:
1534:. New York: Random House.
1334:Skomorowska, Amira (ed.).
1252:. London-Oxford-New York:
334:illuminated by a Sun that
303:
29:
3018:
2978:
2950:
2943:
2895:Necessity and sufficiency
2798:
2763:
2715:
2669:
2651:
2643:
2583:
2435:
2264:
2064:
1943:
1902:
1897:Links to related articles
1022:Bolander, Thomas (2013).
366:In 20th-century science,
3082:Concepts in epistemology
1827:templates for discussion
927:
855: â Figure of speech
332:approximately flat plane
32:Paradox (disambiguation)
3092:Concepts in metaphysics
2164:Paradoxes of set theory
1871:; Langley, Ann (2017).
1613:Philosophical Fragments
1254:Oxford University Press
676:Philosophical Fragments
585:Ramsey's classification
558:GrellingâNelson paradox
357:three prisoners problem
1746:
1726:Listen to this article
1315:faculty.washington.edu
686:
490:
408:
377:The divergence of the
287:Quine's classification
195:
3030:Philosophy portal
1854:""Logical Paradoxes""
1745:
1528:"The ways of paradox"
1128:10.5465/amp.2015.0070
1101:10.5465/amj.2012.0995
1059:10.5465/amr.2009.0223
981:(Fall 2017 ed.).
947:mathworld.wolfram.com
681:
579:paraconsistent logics
491:
388:
372:Ugly duckling theorem
322:That the Earth is an
193:
104:Informally, the term
2530:Kavka's toxin puzzle
2302:Income and fertility
1777:More spoken articles
1693:Frode Alfson Bjørdal
1472:On Semiotic Modeling
859:Paradox of tolerance
717:in the treatment of
695:paradoxical reaction
514:fallacious arguments
385:
129:circular definitions
30:For other uses, see
3102:Philosophical logic
2692:Philosophy of logic
2189:Temperature paradox
2112:Free choice paradox
1976:Fitch's knowability
1869:Jarzabkowski, Paula
1555:W.V. Quine (1976).
1488:Extract of page 268
1458:Extract of page 376
1225:"Russell's Paradox"
1003:on February 5, 2013
941:Weisstein, Eric W.
897:Syntactic ambiguity
342:Condorcet's paradox
269:grandfather paradox
265:Thought-experiments
2991:Rules of inference
2960:Mathematical logic
2702:Semantics of logic
2565:Prisoner's dilemma
2251:Heat death paradox
2239:Unexpected hanging
2204:Chicken or the egg
1747:
1429:Extract of page 32
1256:. pp. 59â60.
891:Self-refuting idea
506:falsidical paradox
500:Falsidical paradox
486:
353:Monty Hall paradox
204:circular reasoning
196:
3097:Critical thinking
3087:Concepts in logic
3064:
3063:
3058:
3057:
3014:
3013:
2848:Deductive closure
2794:
2793:
2733:Critical thinking
2611:
2610:
2282:Arrow information
1743:
1482:978-3-11-084987-5
1452:978-0-7914-8282-7
1423:978-94-009-3551-8
1287:"Curry's Paradox"
997:Oxford Dictionary
841:List of paradoxes
830:Impossible object
824:Four-valued logic
788:Animalia Paradoxa
773:Philosophy portal
594:Russell's paradox
475:
462:
449:
436:
417:
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
18:Counter-intuitive
16:(Redirected from
3114:
3028:
3027:
3026:
2948:
2947:
2713:
2712:
2677:Computer science
2638:
2631:
2624:
2615:
2614:
2601:
2600:
2591:
2590:
2402:Service recovery
2256:Olbers's paradox
1956:Buridan's bridge
1929:
1922:
1915:
1906:
1905:
1893:
1892:
1888:
1863:
1849:
1811:
1796:
1767:
1765:
1754:
1753:
1744:
1734:
1732:
1727:
1679:
1678:
1668:
1658:
1634:
1628:
1627:
1607:
1601:
1600:
1588:
1582:
1581:
1569:
1563:
1562:
1552:
1546:
1545:
1520:
1514:
1513:
1511:
1510:
1496:
1490:
1486:
1466:
1460:
1456:
1437:
1431:
1427:
1407:
1401:
1400:
1365:
1350:
1349:
1347:
1346:
1340:Lapidarium notes
1331:
1325:
1324:
1322:
1321:
1307:
1301:
1300:
1299:
1298:
1282:
1276:
1275:
1245:
1239:
1238:
1237:
1236:
1220:
1211:
1210:
1208:
1188:
1182:
1181:
1155:
1146:
1140:
1139:
1111:
1105:
1104:
1086:
1077:
1071:
1070:
1042:
1036:
1035:
1033:
1031:
1024:"Self-Reference"
1019:
1013:
1012:
1010:
1008:
989:
983:
982:
973:Zalta, Edward N.
963:
957:
956:
954:
953:
938:
915:Zeno's paradoxes
903:Temporal paradox
876:
865: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:
407:
402:
361:birthday paradox
277:butterfly effect
208:infinite regress
125:infinite regress
21:
3122:
3121:
3117:
3116:
3115:
3113:
3112:
3111:
3067:
3066:
3065:
3060:
3059:
3054:
3024:
3022:
3010:
2974:
2965:Boolean algebra
2939:
2790:
2781:Metamathematics
2759:
2711:
2665:
2647:
2642:
2612:
2607:
2579:
2490:Decision-making
2436:Decision theory
2431:
2260:
2184:Hilbert's Hotel
2117:GrellingâNelson
2060:
1939:
1933:
1898:
1885:
1852:
1840:
1830:
1781:
1780:
1769:
1763:
1761:
1758:This audio file
1755:
1748:
1739:
1736:
1730:
1729:
1725:
1722:
1717:
1688:
1683:
1682:
1635:
1631:
1624:
1608:
1604:
1589:
1585:
1570:
1566:
1553:
1549:
1542:
1521:
1517:
1508:
1506:
1498:
1497:
1493:
1483:
1467:
1463:
1453:
1439:
1438:
1434:
1424:
1408:
1404:
1389:
1369:Hughes, Patrick
1366:
1353:
1344:
1342:
1332:
1328:
1319:
1317:
1309:
1308:
1304:
1296:
1294:
1283:
1279:
1264:
1246:
1242:
1234:
1232:
1221:
1214:
1189:
1185:
1153:
1147:
1143:
1112:
1108:
1084:
1078:
1074:
1043:
1039:
1029:
1027:
1020:
1016:
1006:
1004:
991:
990:
986:
964:
960:
951:
949:
939:
935:
930:
925:
920:
886:Revision theory
874:
806:Ethical dilemma
771:
766:
764:
761:
728:The actions of
691:
671:G.K. Chesterton
655:Meister Eckhart
631:
587:
548:
502:
467:
454:
441:
428:
409:
403:
392:
386:
383:
382:
379:harmonic series
308:
302:
289:
224:
188:
173:
141:
114:
112:Common elements
90:ship of Theseus
83:Curry's paradox
35:
28:
23:
22:
15:
12:
11:
5:
3120:
3110:
3109:
3104:
3099:
3094:
3089:
3084:
3079:
3062:
3061:
3056:
3055:
3053:
3052:
3047:
3037:
3032:
3019:
3016:
3015:
3012:
3011:
3009:
3008:
3003:
2998:
2993:
2988:
2982:
2980:
2976:
2975:
2973:
2972:
2967:
2962:
2956:
2954:
2945:
2941:
2940:
2938:
2937:
2932:
2927:
2922:
2917:
2912:
2907:
2902:
2897:
2892:
2887:
2882:
2877:
2872:
2871:
2870:
2860:
2855:
2850:
2845:
2840:
2839:
2838:
2833:
2823:
2818:
2813:
2808:
2802:
2800:
2796:
2795:
2792:
2791:
2789:
2788:
2783:
2778:
2773:
2767:
2765:
2761:
2760:
2758:
2757:
2752:
2747:
2742:
2741:
2740:
2735:
2725:
2719:
2717:
2710:
2709:
2704:
2699:
2694:
2689:
2684:
2679:
2673:
2671:
2667:
2666:
2664:
2663:
2658:
2652:
2649:
2648:
2641:
2640:
2633:
2626:
2618:
2609:
2608:
2606:
2605:
2595:
2584:
2581:
2580:
2578:
2577:
2572:
2567:
2562:
2557:
2552:
2547:
2542:
2537:
2532:
2527:
2522:
2517:
2512:
2507:
2502:
2497:
2492:
2487:
2482:
2477:
2472:
2467:
2466:
2465:
2460:
2455:
2445:
2439:
2437:
2433:
2432:
2430:
2429:
2424:
2419:
2414:
2409:
2407:St. Petersburg
2404:
2399:
2394:
2389:
2384:
2379:
2374:
2369:
2364:
2359:
2354:
2349:
2344:
2339:
2334:
2329:
2324:
2319:
2314:
2309:
2304:
2299:
2294:
2289:
2284:
2279:
2274:
2268:
2266:
2262:
2261:
2259:
2258:
2253:
2248:
2241:
2236:
2231:
2226:
2221:
2216:
2211:
2206:
2201:
2196:
2191:
2186:
2181:
2176:
2171:
2166:
2161:
2156:
2155:
2154:
2149:
2144:
2139:
2134:
2124:
2119:
2114:
2109:
2104:
2099:
2094:
2089:
2084:
2079:
2074:
2068:
2066:
2062:
2061:
2059:
2058:
2053:
2048:
2043:
2038:
2036:Rule-following
2033:
2028:
2023:
2018:
2013:
2008:
2003:
1998:
1993:
1988:
1983:
1978:
1973:
1968:
1963:
1961:Dream argument
1958:
1953:
1947:
1945:
1941:
1940:
1932:
1931:
1924:
1917:
1909:
1903:
1900:
1899:
1890:
1889:
1883:
1864:
1850:
1838:
1812:
1797:
1770:
1756:
1749:
1737:
1724:
1723:
1721:
1720:External links
1718:
1716:
1715:
1712:Patrick Hughes
1709:
1706:
1703:
1700:
1689:
1687:
1684:
1681:
1680:
1629:
1622:
1602:
1583:
1574:"Frank Ramsey"
1564:
1547:
1540:
1515:
1491:
1481:
1461:
1451:
1432:
1422:
1402:
1387:
1373:Brecht, George
1351:
1326:
1302:
1277:
1262:
1240:
1212:
1209:on 2013-10-23.
1183:
1141:
1122:(3): 316â327.
1106:
1095:(2): 538â566.
1072:
1053:(2): 381â403.
1037:
1014:
984:
958:
932:
931:
929:
926:
924:
921:
919:
918:
912:
906:
900:
894:
888:
883:
877:
868:
862:
856:
850:
844:
838:
833:
827:
821:
818:Formal fallacy
815:
809:
803:
797:
791:
785:
778:
777:
776:
760:
757:
723:benzodiazepine
690:
687:
630:
627:
586:
583:
547:
544:
543:
542:
536:
529:
501:
498:
497:
496:
485:
482:
479:
474:
471:
466:
461:
458:
453:
448:
445:
440:
435:
432:
427:
424:
421:
416:
413:
406:
401:
398:
395:
391:
375:
364:
349:
339:
301:
298:
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:
9:
6:
4:
3:
2:
3119:
3108:
3105:
3103:
3100:
3098:
3095:
3093:
3090:
3088:
3085:
3083:
3080:
3078:
3075:
3074:
3072:
3051:
3048:
3045:
3041:
3038:
3036:
3033:
3031:
3021:
3020:
3017:
3007:
3006:Logic symbols
3004:
3002:
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2983:
2981:
2977:
2971:
2968:
2966:
2963:
2961:
2958:
2957:
2955:
2953:
2949:
2946:
2942:
2936:
2933:
2931:
2928:
2926:
2923:
2921:
2918:
2916:
2913:
2911:
2908:
2906:
2903:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2885:Logical truth
2883:
2881:
2878:
2876:
2873:
2869:
2866:
2865:
2864:
2861:
2859:
2856:
2854:
2851:
2849:
2846:
2844:
2841:
2837:
2834:
2832:
2829:
2828:
2827:
2826:Contradiction
2824:
2822:
2819:
2817:
2814:
2812:
2809:
2807:
2804:
2803:
2801:
2797:
2787:
2784:
2782:
2779:
2777:
2774:
2772:
2771:Argumentation
2769:
2768:
2766:
2762:
2756:
2755:Philosophical
2753:
2751:
2750:Non-classical
2748:
2746:
2743:
2739:
2736:
2734:
2731:
2730:
2729:
2726:
2724:
2721:
2720:
2718:
2714:
2708:
2705:
2703:
2700:
2698:
2695:
2693:
2690:
2688:
2685:
2683:
2680:
2678:
2675:
2674:
2672:
2668:
2662:
2659:
2657:
2654:
2653:
2650:
2646:
2639:
2634:
2632:
2627:
2625:
2620:
2619:
2616:
2604:
2596:
2594:
2586:
2585:
2582:
2576:
2573:
2571:
2568:
2566:
2563:
2561:
2558:
2556:
2553:
2551:
2548:
2546:
2543:
2541:
2538:
2536:
2535:Morton's fork
2533:
2531:
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2481:
2478:
2476:
2475:Buridan's ass
2473:
2471:
2468:
2464:
2461:
2459:
2456:
2454:
2451:
2450:
2449:
2448:Apportionment
2446:
2444:
2441:
2440:
2438:
2434:
2428:
2425:
2423:
2420:
2418:
2415:
2413:
2410:
2408:
2405:
2403:
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2325:
2323:
2320:
2318:
2315:
2313:
2310:
2308:
2307:DownsâThomson
2305:
2303:
2300:
2298:
2295:
2293:
2290:
2288:
2285:
2283:
2280:
2278:
2275:
2273:
2270:
2269:
2267:
2263:
2257:
2254:
2252:
2249:
2246:
2242:
2240:
2237:
2235:
2232:
2230:
2227:
2225:
2224:Plato's beard
2222:
2220:
2217:
2215:
2212:
2210:
2207:
2205:
2202:
2200:
2197:
2195:
2192:
2190:
2187:
2185:
2182:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2160:
2157:
2153:
2150:
2148:
2145:
2143:
2140:
2138:
2135:
2133:
2130:
2129:
2128:
2125:
2123:
2122:KleeneâRosser
2120:
2118:
2115:
2113:
2110:
2108:
2105:
2103:
2100:
2098:
2095:
2093:
2090:
2088:
2085:
2083:
2080:
2078:
2075:
2073:
2070:
2069:
2067:
2063:
2057:
2054:
2052:
2049:
2047:
2046:Theseus' ship
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2027:
2024:
2022:
2019:
2017:
2014:
2012:
2009:
2007:
2006:Mere addition
2004:
2002:
1999:
1997:
1994:
1992:
1989:
1987:
1984:
1982:
1979:
1977:
1974:
1972:
1969:
1967:
1964:
1962:
1959:
1957:
1954:
1952:
1949:
1948:
1946:
1944:Philosophical
1942:
1938:
1930:
1925:
1923:
1918:
1916:
1911:
1910:
1907:
1901:
1894:
1886:
1884:9780198754428
1880:
1876:
1875:
1870:
1865:
1861:
1860:
1855:
1851:
1847:
1846:MathPages.com
1843:
1839:
1837:
1833:
1828:
1824:
1823:
1818:
1813:
1809:
1808:
1803:
1798:
1794:
1793:
1788:
1783:
1782:
1778:
1774:
1759:
1713:
1710:
1707:
1704:
1701:
1698:
1694:
1691:
1690:
1676:
1672:
1667:
1662:
1657:
1652:
1648:
1644:
1640:
1633:
1625:
1623:9780691020365
1619:
1615:
1614:
1606:
1598:
1594:
1587:
1579:
1575:
1568:
1560:
1559:
1551:
1543:
1541:9780674948358
1537:
1533:
1529:
1525:
1519:
1505:
1504:brilliant.org
1501:
1495:
1489:
1484:
1478:
1474:
1473:
1465:
1459:
1454:
1448:
1444:
1443:
1436:
1430:
1425:
1419:
1415:
1414:
1406:
1398:
1394:
1390:
1388:0-385-09917-7
1384:
1380:
1379:
1374:
1370:
1364:
1362:
1360:
1358:
1356:
1341:
1337:
1330:
1316:
1312:
1306:
1292:
1288:
1281:
1273:
1269:
1265:
1263:0-19-888087-1
1259:
1255:
1251:
1244:
1230:
1226:
1219:
1217:
1207:
1202:
1198:
1194:
1187:
1179:
1175:
1171:
1167:
1163:
1159:
1152:
1145:
1137:
1133:
1129:
1125:
1121:
1117:
1110:
1102:
1098:
1094:
1090:
1083:
1076:
1068:
1064:
1060:
1056:
1052:
1048:
1041:
1025:
1018:
1002:
998:
994:
988:
980:
979:
974:
970:
962:
948:
944:
937:
933:
916:
913:
910:
907:
904:
901:
898:
895:
892:
889:
887:
884:
881:
880:Plato's beard
878:
872:
869:
866:
863:
860:
857:
854:
851:
848:
847:Mu (negative)
845:
842:
839:
837:
834:
831:
828:
825:
822:
819:
816:
813:
810:
807:
804:
801:
798:
795:
792:
789:
786:
783:
780:
779:
774:
763:
756:
754:
750:
745:
743:
739:
735:
731:
726:
724:
720:
716:
712:
708:
704:
700:
696:
685:
680:
678:
677:
672:
668:
664:
660:
656:
652:
648:
644:
640:
636:
629:In philosophy
626:
624:
620:
616:
612:
608:
604:
599:
595:
591:
582:
580:
576:
572:
568:
567:
561:
559:
555:
554:
540:
537:
534:
533:horse paradox
530:
527:
523:
519:
518:
517:
515:
511:
507:
483:
480:
477:
472:
469:
464:
459:
456:
451:
446:
443:
438:
433:
430:
425:
422:
419:
414:
411:
399:
396:
393:
389:
380:
376:
373:
369:
365:
362:
358:
354:
350:
347:
346:majority rule
343:
340:
337:
333:
329:
325:
321:
320:
319:
317:
313:
307:
297:
295:
291:
284:
280:
278:
274:
273:time-traveler
270:
266:
262:
260:
258:
252:
248:
244:
240:
236:
231:
229:
219:
215:
213:
209:
205:
201:
192:
183:
179:
177:
176:Contradiction
171:Contradiction
168:
166:
162:
158:
153:
149:
145:
136:
134:
130:
126:
122:
121:contradiction
118:
109:
107:
102:
100:
96:
91:
86:
84:
80:
76:
72:
68:
64:
60:
56:
52:
47:
44:
40:
33:
19:
2925:Substitution
2830:
2745:Mathematical
2670:Major fields
2555:Preparedness
2387:Productivity
2367:Mandeville's
2159:Opposite Day
2087:Burali-Forti
2082:Bhartrhari's
1936:
1873:
1857:
1845:
1820:
1805:
1802:"Insolubles"
1790:
1696:
1686:Bibliography
1649:(1): 26â34.
1646:
1642:
1632:
1612:
1605:
1596:
1586:
1577:
1567:
1557:
1550:
1531:
1518:
1507:. Retrieved
1503:
1494:
1471:
1464:
1441:
1435:
1412:
1405:
1377:
1343:. Retrieved
1339:
1329:
1318:. Retrieved
1314:
1305:
1295:, retrieved
1290:
1280:
1249:
1243:
1233:, retrieved
1228:
1206:the original
1200:
1196:
1186:
1161:
1157:
1144:
1119:
1115:
1109:
1092:
1088:
1075:
1050:
1046:
1040:
1028:. Retrieved
1017:
1005:. Retrieved
1001:the original
996:
987:
976:
961:
950:. Retrieved
946:
936:
909:Twin paradox
753:proven harms
746:
727:
692:
682:
674:
639:Zeno of Elea
632:
623:epistemology
618:
614:
610:
606:
602:
598:liar paradox
590:Frank Ramsey
588:
574:
564:
562:
551:
549:
520:The various
505:
503:
311:
309:
306:Veridicality
292:
290:
281:
263:
254:
247:liar paradox
243:philosophers
232:
225:
216:
197:
180:
174:
157:liar paradox
142:
115:
105:
103:
87:
48:
38:
36:
3040:WikiProject
2910:Proposition
2905:Probability
2858:Description
2799:Foundations
2485:Condorcet's
2337:Giffen good
2297:Competition
2051:White horse
2026:Omnipotence
1815:âš The
1524:Quine, W.V.
1164:(1): 5â64.
742:hook effect
689:In medicine
663:Kierkegaard
228:half-truths
133:abstraction
95:M.C. Escher
3071:Categories
2970:Set theory
2868:Linguistic
2863:Entailment
2853:Definition
2821:Consequent
2816:Antecedent
2560:Prevention
2550:Parrondo's
2540:Navigation
2525:Inventor's
2520:Hedgehog's
2480:Chainstore
2463:Population
2458:New states
2392:Prosperity
2372:Mayfield's
2214:Entailment
2194:Barbershop
2107:Epimenides
1773:Audio help
1764:2005-07-07
1509:2019-12-05
1345:2013-01-22
1320:2019-12-05
1297:2019-12-05
1272:0251.02001
1235:2019-12-05
952:2019-12-05
923: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
3077:Paradoxes
3001:Fallacies
2996:Paradoxes
2986:Logicians
2920:Statement
2915:Reference
2880:Induction
2843:Deduction
2806:Abduction
2776:Metalogic
2723:Classical
2687:Inference
2575:Willpower
2570:Tolerance
2545:Newcomb's
2510:Fredkin's
2397:Scitovsky
2317:Edgeworth
2312:Easterlin
2277:Antitrust
2174:Russell's
2169:Richard's
2142:Pinocchio
2097:Crocodile
2016:Newcomb's
1986:Goodman's
1981:Free will
1966:Epicurean
1937:paradoxes
1832:Paradoxes
1178:1941-6520
993:"paradox"
943:"Paradox"
782:Absurdism
707:stimulant
667:Nietzsche
619:symbolism
571:Aristotle
481:⋯
405:∞
390:∑
316:intuition
239:logicians
200:recursion
97:featured
43:logically
3035:Category
2935:Validity
2836:Antinomy
2764:Theories
2728:Informal
2603:Category
2500:Ellsberg
2352:Leontief
2332:Gibson's
2327:European
2322:Ellsberg
2292:Braess's
2287:Bertrand
2265:Economic
2199:Catch-22
2179:Socratic
2021:Nihilism
1991:Hedonism
1951:Analysis
1935:Notable
1817:template
1775: ¡
1675:22461918
1526:(1966).
1397:74-17611
1375:(1975).
1067:41318006
853: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
3107:Thought
3050:changes
3042: (
2900:Premise
2831:Paradox
2661:History
2656:Outline
2505:Fenno's
2470:Arrow's
2453:Alabama
2443:Abilene
2422:Tullock
2377:Metzler
2219:Lottery
2209:Drinker
2152:Yablo's
2147:Quine's
2102:Curry's
2065:Logical
2041:Sorites
2031:Preface
2011:Moore's
1996:Liberal
1971:Fiction
1819:below (
1762: (
1733:minutes
1666:3298219
1136:2034932
1030:21 June
1007:21 June
975:(ed.).
812:Fallacy
800:Dilemma
747:In the
715:Ritalin
611:thought
510:fallacy
370:or the
212:vicious
152:formula
106:paradox
55:invalid
39:paradox
2952:topics
2738:Reason
2716:Logics
2707:Syntax
2412:Thrift
2382:Plenty
2357:Lerner
2347:Jevons
2342:Icarus
2272:Allais
2234:Ross's
2072:Barber
2056:Zeno's
2001:Meno's
1881:
1836:Curlie
1822:Curlie
1673:
1663:
1620:
1538:
1479:
1449:
1420:
1395:
1385:
1270:
1260:
1176:
1134:
1065:
794:Aporia
679:that:
669:, and
617:, and
607:number
165:barber
63:axioms
2979:other
2944:Lists
2930:Truth
2697:Proof
2645:Logic
2515:Green
2495:Downs
2427:Value
2362:Lucas
2229:Raven
2137:No-no
2092:Court
2077:Berry
1154:(PDF)
1132:S2CID
1085:(PDF)
1063:JSTOR
971:. In
928:Notes
697:to a
659:Hegel
635:Laozi
603:class
51:logic
41:is a
3044:talk
2890:Name
2875:Form
2593:List
2417:Toil
2132:Card
2127:Liar
1879:ISBN
1671:PMID
1618:ISBN
1536:ISBN
1477:ISBN
1447:ISBN
1418:ISBN
1393:LCCN
1383:ISBN
1258:ISBN
1174:ISSN
1032:2016
1009:2016
713:and
699:drug
605:and
531:The
351:The
255:the
241:and
123:and
2786:Set
1834:at
1661:PMC
1651:doi
1268:Zbl
1166:doi
1124:doi
1097:doi
1055:doi
732:on
550:An
257:set
206:or
77:or
49:In
3073::
1856:.
1844:.
1731:23
1695:,
1669:.
1659:.
1647:13
1645:.
1641:.
1595:.
1576:.
1530:.
1502:.
1391:.
1371:;
1354:^
1338:.
1313:.
1266:.
1215:^
1201:15
1199:.
1195:.
1172:.
1162:10
1160:.
1156:.
1130:.
1120:30
1118:.
1093:58
1091:.
1087:.
1061:.
1051:36
1049:.
995:.
945:.
725:.
693:A
665:,
661:,
657:,
653:,
649:,
645:,
641:,
637:,
625:.
613:,
581:.
516::
504:A
310:A
135:.
119:,
37:A
3046:)
2637:e
2630:t
2623:v
2247:"
2243:"
1928:e
1921:t
1914:v
1887:.
1862:.
1848:.
1810:.
1795:.
1779:)
1771:(
1766:)
1735:)
1728:(
1677:.
1653::
1626:.
1544:.
1512:.
1485:.
1455:.
1426:.
1399:.
1348:.
1323:.
1274:.
1180:.
1168::
1138:.
1126::
1103:.
1099::
1069:.
1057::
1034:.
1011:.
955:.
528:.
484:.
478:+
473:5
470:1
465:+
460:4
457:1
452:+
447:3
444:1
439:+
434:2
431:1
426:+
423:1
420:=
415:n
412:1
400:1
397:=
394:n
381::
363:.
338:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
