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unexpected hanging paradox

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A paradox of prediction. Sentencing a man on Friday, a judge says: ‘You will be hanged at noon on a day next week, but you will not know which day it is until the morning of the fateful day.’ The prisoner reasons that he cannot be hanged next Saturday, because by Friday afternoon he would know that he was to be hanged the next day, and that he cannot be hanged on Friday because, with Saturday ruled out, by Thursday afternoon he would know that he was to be hanged on Friday, and that all the other days of the week can be excluded by the same argument, so he concludes with relief that he cannot be hanged on any day next week and that therefore the judge's sentence cannot be correctly carried out. However, if he is hanged on Wednesday, the judge's sentence is correctly carried out, because the hanging would indeed be a surprise, given the prisoner's reasoning, because he appears to have ruled out every day including Wednesday. The paradox was discovered by the Swedish mathematician Lennart Ekbom (born 1919) and discussed with students in 1943 or 1944 after the Swedish broadcasting system announced that a civil defence drill would be held the following week but that no one would know in advance on which day it would take place. It was first discussed in print in 1948 by the British philosopher D(aniel) John O'Connor (born 1914) in an article in the journal Mind, where it was commented on by several eminent philosophers in subsequent issues, and it has generated by far the greatest attention of all epistemic paradoxes without producing anything resembling a consensus as to the right solution. At first the judge's sentence was interpreted as a classic self-defeating prophecy (and O'Connor described the problem as ‘rather frivolous’), but later commentators pointed out that if the hanging took place on Wednesday, then it would indeed be unexpected, which implies that the sentence is not self-defeating. Also called the surprise examination paradox or the prediction paradox. See also Oedipus effect.

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