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Here's my take. The prisoner considers the statement "I will be hanged, and it will be a surprise", and after "proving" it false, takes its negation "Either I
by pieguy 8y ago
Here's my take. The prisoner considers the statement "I will be hanged, and it will be a surprise", and after "proving" it false, takes its negation "Either I won't be hanged, or it won't be a surprise". But this is not correct. The prisoner actually disproves the statement "I will be hanged, and it will be a surprise no matter which day it happens". When you negate this statement, you obtain "Either I won't be hanged, or there is a day that it would not be a surprise", which is consistent with the outcome.
- p1esk 8y agoThe paradox is because the prisoner does indeed disprove the statement "I will be hanged, and it will be a surprise no matter which day it happens", but the statement turns out to be true (he is both hanged, and surprised no matter what day he's hanged).
- pieguy 8y agoNo, it would not have been a surprise if he were hanged on Friday. The prisoner disproves the existence of a strategy for the judge that guarantees surprise, but does not disprove the existence of a strategy that gives the possibility of surprise.
- p1esk 8y agoIt would have been a surprise if he were hanged on Friday, because he believes he wouldn't be hanged at all.
- pieguy 8y agoHe cannot logically conclude that. He can only conclude that either he won't be hanged or his hanging might not be a surprise.
- p1esk 8y agoHe concludes that because he assumes what the judge said is true. If we assume that, we must reject the scenario where he gets executed without surprise.
- pieguy 8y ago> he believes he wouldn't be hanged at all > he assumes what the judge said is true The judge says he will be hanged. Your comments are inconsistent.
- p1esk 8y agoActually, you're right. However, the paradox arises no matter what the prisoner concludes. If he concludes that the hanging won't be a surprise, he will be surprised by the outcome (the knock on Wednesday).
- pieguy 8y agoLet me say it again in a different way. My resolution of the paradox is that the prisoner incorrectly negates "x will happen" as "x won't happen" instead of negating "x definitely will happen" as "x might not happen". Thus,the prisoner cannot conclude that the hanging won't be a surprise. The prisoner can only conclude that the hanging might not be a surprise.
- p1esk 8y agoIt seems like you're right again, but I don't have time to think more about this at the moment, unfortunately.