1709:
1699:
83:
Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by
Thursday, there is only one day left – and so it won't be
87:
He then reasons that the surprise hanging cannot be on
Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday noon, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning, he concludes that the hanging
122:
Given this announcement the prisoner can deduce that the hanging will not occur on the last day of the week. However, in order to reproduce the next stage of the argument, which eliminates the penultimate day of the week, the prisoner must argue that his ability to deduce, from statement (A), that
167:
Chow (1998) provides a detailed analysis of a version of the paradox in which a surprise hanging is to take place on one of two days. Applying Chow's analysis to the case of the unexpected hanging (again with the week shortened to two days for simplicity), we start with the observation that the
246:
that it is true. Further, even if the prisoner knows something to be true in the present moment, unknown psychological factors may erase this knowledge in the future. Finally, Chow suggests that because the statement which the prisoner is supposed to "know" to be true is a statement about his
154:
has shown that this statement can still be expressed in formal logic. Using an equivalent form of the paradox which reduces the length of the week to just two days, he proved that although self-reference is not illegitimate in all circumstances, it is in this case because the statement is
831:
79:
A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.
31:
about a person's expectations about the timing of a future event which they are told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging or a surprise school test. It was first introduced to the public in
163:
Various epistemological formulations have been proposed that show that the prisoner's tacit assumptions about what he will know in the future, together with several plausible assumptions about knowledge, are inconsistent.
632:
The author argues that a surprise exam (or unexpected hanging) can indeed take place on the last day of the period and therefore that the very first premise that launches the paradox is, despite first appearances, simply
242:
to be true. This assumption seems unwarranted on several different grounds. It may be argued that the judge's pronouncement that something is true can never be sufficient grounds for the prisoner
230:
The prisoner's reasoning, which gives rise to the paradox, is able to get off the ground because the prisoner tacitly assumes that on Monday evening, he will (if he is still alive) know
91:
The next week, the executioner knocks on the prisoner's door at noon on
Wednesday – which, despite all the above, was an utter surprise to him. Everything the judge said came true.
580:
116:
The prisoner will be hanged next week and the date (of the hanging) will not be deducible the night before from the assumption that the hanging will occur during the week
212:
Chow's analysis points to a subtle flaw in the prisoner's reasoning. What is impossible is not a
Tuesday hanging. Rather, what is impossible is a situation in which
197:
As a first step, the prisoner reasons that a scenario in which the hanging occurs on
Tuesday is impossible because it leads to a contradiction: on the one hand, by
84:
a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.
804:
The author defends and extends Wright and
Sudbury's solution. He also updates the history and bibliography of Margalit and Bar-Hillel up to 1991.
1145:
618:
88:
can also not occur on
Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.
1293:
574:
The first appearance of the paradox in print. The author claims that certain contingent future tense statements cannot come true.
251:
to "know" certain things, there is reason to believe that the unexpected hanging paradox is simply a more intricate version of
772:
The author claims that the prisoner assumes, falsely, that if he knows some proposition, then he also knows that he knows it.
255:. A suitable analogy can be reached by reducing the length of the week to just one day. Then the judge's sentence becomes:
484:
145:
The prisoner will be hanged next week and its date will not be deducible the night before using this statement as an axiom
1036:
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426:
1323:
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If the hanging occurs on
Tuesday, then the prisoner will not know on Monday evening that it will occur on Tuesday.
184:
If the hanging occurs on Monday, then the prisoner will not know on Sunday evening that it will occur on Monday.
999:
1572:
994:
201:, the prisoner would not be able to predict the Tuesday hanging on Monday evening; but on the other hand, by
95:
Other versions of the paradox replace the death sentence with a surprise fire drill, examination, pop quiz,
49:
There is no consensus on its precise nature and consequently a canonical resolution has not been agreed on.
1738:
1733:
1396:
1748:
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900:
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the hanging occurs on
Tuesday despite the prisoner knowing on Monday evening that the judge's assertions
37:
1288:
288:
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is made difficult by the vague meaning of the word "surprise". An attempt at formulation might be:
1000:"The Surprise Examination Paradox: A review of two so-called solutions in dynamic epistemic logic"
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1273:
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1095:
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analyses focus on "truth values", for example by identifying it as paradox of self-reference.
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Stanford
Encyclopedia discussion of hanging paradox together with other epistemic paradoxes
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the hanging will not occur on the last day, implies that a second-to-last-day hanging
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Completely analyzes the paradox and introduces other situations with similar logic.
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Wright, C. & Sudbury, A. (1977). "the Paradox of the Unexpected Examination".
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The first complete formalization of the paradox, and a proposed solution to it.
273:
151:
33:
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699:
651:
326:
Chow, T. Y. (1998). "The surprise examination or unexpected hanging paradox".
1727:
1471:
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129:
not deducible from the assumption that the hanging will occur during the week
657:
The author critiques O'Connor and discovers the paradox as we know it today.
1268:
1241:
1236:
874:
Sorensen, R. A. (1982). "Recalcitrant versions of the prediction paradox".
108:
1446:
96:
987:"The Surprise Examination Paradox and the Second Incompleteness Theorem"
469:
456:
Fitch, F. (1964). "A Goedelized formulation of the prediction paradox".
972:
939:"A Procedural Solution to the Unexpected Hanging and Sorites Paradoxes"
790:
758:
726:
521:
403:
357:
826:
504:
340:
59:
1014:
1011:: a song based on this paradox, composed and performed by Simon Beck
921:
745:
Chihara, C. S. (1985). "Olin, Quine, and the Surprise Examination".
513:
395:
349:
382:
Binkley, Robert (1968). "The Surprise Examination in Modal Logic".
681:
The author claims that the prisoner's premises are self-referring.
1046:
990:
740:
A history and bibliography of writings on the paradox up to 1983.
28:
127:. But since the meaning of "surprising" has been restricted to
50:
898:
Kacser, Claude (1986). "On the unexpected hanging paradox".
67:. Some regard it as a "significant problem" for philosophy.
1110:
811:"Une analyse dichotomique du paradoxe de l'examen surprise"
57:
studies of the paradox instead focus on issues relating to
843:
The Unexpected Hanging and Other * Mathematical Diversions
209:
be able to predict the Tuesday hanging on Monday evening.
140:
This suggests that a better formulation would in fact be:
713:& Bar-Hillel, M. (1983). "Expecting the Unexpected".
777:
Kirkham, R. (1991). "On Paradoxes and a Surprise Exam".
485:"The surprise examination or unexpected hanging paradox"
99:
launch, a lion behind a door, or a marriage proposal.
257:
You will be hanged tomorrow, but you do not know that
168:judge's announcement seems to affirm three things:
853:Quine, W. V. O. (1953). "On a So-called Paradox".
709:
841:(1969). "The Paradox of the Unexpected Hanging".
638:Scriven, M. (1951). "Paradoxical Announcements".
1725:
63:; for example, one interpretation reduces it to
662:Shaw, R. (1958). "The Unexpected Examination".
555:O'Connor, D. J. (1948). "Pragmatic Paradoxes".
280:of which uses a similar mechanism as its proof.
1030:
685:
107:Formulation of the judge's announcement into
554:
176:The hanging will occur on Monday or Tuesday.
1004:Faculty of Science: University of Amsterdam
581:"The Solution to the Surprise Exam Paradox"
75:The paradox has been described as follows:
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1023:
808:
954:
596:
503:
339:
205:and process of elimination, the prisoner
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416:
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317:
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852:
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661:
578:
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325:
38:March 1963 Mathematical Games column
306:
13:
1355:What the Tortoise Said to Achilles
876:Australasian Journal of Philosophy
688:Australasian Journal of Philosophy
607:10.1111/j.2041-6962.2009.tb00088.x
547:
14:
1760:
980:
492:The American Mathematical Monthly
328:The American Mathematical Monthly
102:
1708:
1707:
1697:
135:not deducible from statement (A)
585:Southern Journal of Philosophy
476:
449:
435:
410:
364:
70:
1:
299:
443:"Unexpected Hanging Paradox"
7:
937:Shapiro, Stuart C. (1998).
901:American Journal of Physics
421:. Oxford: Clarendon Press.
262:
137:, the argument is blocked.
16:Thought experiment in logic
10:
1765:
676:10.1093/mind/lxvii.267.382
289:Interesting number paradox
21:unexpected hanging paradox
1693:
1545:
1374:
1174:
1053:
1002:by Alexandru Marcoci, at
888:10.1080/00048408212340761
700:10.1080/00048407712341031
569:10.1093/mind/lvii.227.358
384:The Journal of Philosophy
965:10.1093/mind/107.428.751
867:10.1093/mind/lxii.245.65
417:Sorensen, R. A. (1988).
1274:Paradoxes of set theory
989:by Shira Kritchman and
809:Franceschi, P. (2005).
652:10.1093/mind/lx.239.403
125:would not be surprising
159:Epistemological school
93:
1009:"Jethro On Death Row"
747:Philosophical Studies
77:
25:surprise test paradox
1640:Kavka's toxin puzzle
1412:Income and fertility
483:Chow, T. Y. (1998).
155:self-contradictory.
1739:Works about prisons
1734:Epistemic paradoxes
1299:Temperature paradox
1222:Free choice paradox
1086:Fitch's knowability
914:1986AmJPh..54..296K
832:English translation
43:Scientific American
1749:1963 introductions
1675:Prisoner's dilemma
1361:Heat death paradox
1349:Unexpected hanging
1314:Chicken or the egg
791:10.1007/bf02381968
759:10.1007/bf00354146
727:10.1007/BF02379182
579:Levy, Ken (2009).
531:on 7 December 2015
269:Bottle Imp paradox
1721:
1720:
1392:Arrow information
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805:
773:
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706:
682:
658:
634:
575:
294:List of paradoxes
284:Crocodile dilemma
1756:
1711:
1710:
1701:
1700:
1512:Service recovery
1366:Olbers's paradox
1066:Buridan's bridge
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1032:
1025:
1016:
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958:
949:(428): 751–761.
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827:10.7202/011875ar
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770:
739:
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721:(3–4): 337–344.
704:
703:
680:
679:
670:(267): 382–384.
656:
655:
646:(239): 403–407.
631:
630:
628:
626:
621:on 20 March 2017
617:. Archived from
600:
598:10.1.1.1027.1486
573:
572:
563:(227): 358–359.
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540:
538:
536:
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524:. Archived from
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278:Nash equilibrium
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1600:Decision-making
1546:Decision theory
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1294:Hilbert's Hotel
1227:Grelling–Nelson
1170:
1049:
1043:
983:
922:10.1119/1.14658
894:
624:
622:
550:
548:Further reading
545:
544:
534:
532:
528:
514:10.2307/2589525
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396:10.2307/2024556
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350:10.2307/2589525
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253:Moore's paradox
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65:Moore's paradox
55:Epistemological
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981:External links
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956:10.1.1.33.3808
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908:(4): 296–297.
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882:(4): 355–362.
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861:(245): 65–66.
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821:(2): 399–421.
815:Philosophiques
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785:(1–2): 31–51.
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1192:Bhartrhari's
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1136:Omnipotence
839:Gardner, M.
779:Philosophia
715:Philosophia
535:30 December
458:Am. Phil. Q
71:Description
1728:Categories
1670:Prevention
1660:Parrondo's
1650:Navigation
1635:Inventor's
1630:Hedgehog's
1590:Chainstore
1573:Population
1568:New states
1502:Prosperity
1482:Mayfield's
1324:Entailment
1304:Barbershop
1217:Epimenides
445:. Wolfram.
419:Blindspots
300:References
132:instead of
46:magazine.
1685:Willpower
1680:Tolerance
1655:Newcomb's
1620:Fredkin's
1507:Scitovsky
1427:Edgeworth
1422:Easterlin
1387:Antitrust
1284:Russell's
1279:Richard's
1252:Pinocchio
1207:Crocodile
1126:Newcomb's
1096:Goodman's
1091:Free will
1076:Epicurean
1047:paradoxes
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799:144611262
767:170830855
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625:2 January
593:CiteSeerX
249:inability
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1442:Gibson's
1437:European
1432:Ellsberg
1402:Braess's
1397:Bertrand
1375:Economic
1309:Catch-22
1289:Socratic
1131:Nihilism
1101:Hedonism
1061:Analysis
1045:Notable
470:20009132
263:See also
97:A/B test
1744:Hanging
1615:Fenno's
1580:Arrow's
1563:Alabama
1553:Abilene
1532:Tullock
1487:Metzler
1329:Lottery
1319:Drinker
1262:Yablo's
1257:Quine's
1212:Curry's
1175:Logical
1151:Sorites
1141:Preface
1121:Moore's
1106:Liberal
1081:Fiction
995:ams.org
991:Ran Raz
973:2659782
910:Bibcode
615:1435806
522:2589525
404:2024556
358:2589525
244:knowing
51:Logical
29:paradox
1522:Thrift
1492:Plenty
1467:Lerner
1457:Jevons
1452:Icarus
1382:Allais
1344:Ross's
1182:Barber
1166:Zeno's
1111:Meno's
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633:false.
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1247:No-no
1202:Court
1187:Berry
993:, at
969:JSTOR
926:S2CID
795:S2CID
763:S2CID
731:S2CID
529:(PDF)
518:JSTOR
500:arXiv
488:(PDF)
466:JSTOR
400:JSTOR
354:JSTOR
336:arXiv
207:would
152:Fitch
27:is a
1703:List
1527:Toil
1242:Card
1237:Liar
943:Mind
855:Mind
664:Mind
640:Mind
627:2018
611:SSRN
557:Mind
537:2007
423:ISBN
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