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Unexpected hanging paradox

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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
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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
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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
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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
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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
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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
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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.
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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
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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.
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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
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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
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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
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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.
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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
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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
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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
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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.
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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.
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can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.
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The first appearance of the paradox in print. The author claims that certain contingent future tense statements cannot come true.
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to "know" certain things, there is reason to believe that the unexpected hanging paradox is simply a more intricate version of
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The author claims that the prisoner assumes, falsely, that if he knows some proposition, then he also knows that he knows it.
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The prisoner will be hanged next week and its date will not be deducible the night before using this statement as an axiom
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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.
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If the hanging occurs on Monday, then the prisoner will not know on Sunday evening that it will occur on Monday.
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Other versions of the paradox replace the death sentence with a surprise fire drill, examination, pop quiz,
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There is no consensus on its precise nature and consequently a canonical resolution has not been agreed on.
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the hanging occurs on Tuesday despite the prisoner knowing on Monday evening that the judge's assertions
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is made difficult by the vague meaning of the word "surprise". An attempt at formulation might be:
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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.
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Chow, T. Y. (1998). "The surprise examination or unexpected hanging paradox".
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not deducible from the assumption that the hanging will occur during the week
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The author critiques O'Connor and discovers the paradox as we know it today.
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Sorensen, R. A. (1982). "Recalcitrant versions of the prediction paradox".
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Fitch, F. (1964). "A Goedelized formulation of the prediction paradox".
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Chihara, C. S. (1985). "Olin, Quine, and the Surprise Examination".
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Binkley, Robert (1968). "The Surprise Examination in Modal Logic".
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The author claims that the prisoner's premises are self-referring.
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A history and bibliography of writings on the paradox up to 1983.
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Kacser, Claude (1986). "On the unexpected hanging paradox".
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studies of the paradox instead focus on issues relating to
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The Unexpected Hanging and Other * Mathematical Diversions
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be able to predict the Tuesday hanging on Monday evening.
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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".
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launch, a lion behind a door, or a marriage proposal.
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You will be hanged tomorrow, but you do not know that
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"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: 1698: 1037: 1023: 808: 954: 596: 503: 339: 205:and process of elimination, the prisoner 158: 873: 416: 936: 837: 776: 744: 637: 381: 1726: 897: 375: 321: 319: 317: 315: 313: 311: 309: 1044: 1018: 852: 455: 661: 578: 482: 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 849: 805: 773: 741: 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 1039: 1032: 1025: 1016: 1015: 976: 958: 949:(428): 751–761. 933: 891: 870: 847: 846: 830: 827:10.7202/011875ar 803: 802: 771: 770: 739: 738: 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:. 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Index

paradox
Martin Gardner
March 1963 Mathematical Games column
Scientific American
Logical
Epistemological
knowledge
Moore's paradox
A/B test
formal logic
Fitch
Moore's paradox
Bottle Imp paradox
Centipede game
Nash equilibrium
Crocodile dilemma
Interesting number paradox
List of paradoxes







arXiv
math/9903160
doi
10.2307/2589525
JSTOR

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