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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.
This paradox isn’t a play on the definition of “surprise”, that’s just a weakness accidentally introduced by lax wording.
One way to think about this paradox is as a game with two players—a prisoner and an executioner. The game progresses over five turns, representing the days of the week. On each turn, the prisoner secretly chooses whether or not they expect to be killed on that day. Then the executioner chooses whether or not to kill the prisoner. The game ends on the turn the executioner decides to kill the prisoner. If the prisoner…
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 hange…
The 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).
One way to think about this paradox is as a game with two players—a prisoner and an executioner. The game progresses over five turns, representing the days of the week. On each turn, the prisoner secretly chooses whether or not they expect to be killed on that day. Then the executioner chooses whether or not to kill the prisoner. The game ends on the turn the executioner decides to kill the prisoner. If the prisoner…
I quite like the puzzle and this paradox, but something always feels off about it.
Earlier quoted context omitted.
I don't follow. Can you please explain? I am very aware of that line.
The judge says the prisoner would be surprised exactly when the knock on the door happens (not before). As a consequence, the prisoner is right to believe he won't be hanged at all (following his reasoning), but as a consequence of that , he is surprised when the knock happens. In turn, as a consequence of that , the judge turns out to be right. Therefore, both the prisoner, and the judge are correct. Thus the parado…
. . .
The prisoners reasoning is wrong.
> if he hasn't been hanged by Thursday, there is only one day left - and so it won't be 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.
What the prisoner doesn't realize is that, by noon on Thursday, he would have ALREADY been surprised by the news of his Friday hanging. That moment occurred when he did not hear the knock!
The moment of surprise for a Thursday hanging or Friday hanging happen at the SAME point in the future. In other words, at 11:59am on Thursday he will not know if his hanging takes place on Thursday or Friday. At 12pm he will be surprised to know for certain which one it is: it will be Thursday if he hears a knock and it will be Friday if he does not.
"If he hasn't been hanged by Thursday" (ie. has not heard the knock) IS, ITSELF, the surprise of a Friday hanging. He wrongly assumes that his moment of surprise can ONLY happen following a knock. He doesn't realize that this assumption is true for every scenario EXCEPT a Friday hanging, where his surprise will happen in the ABSENCE of a knock on Thursday.
Because he cannot envision himself being surprised by a Friday knock (correct) and assumes he can ONLY be surprised by a knock (incorrect), he wrongly concludes that a Friday hanging is an impossibility, and subsequently concludes the same for a Thursday hanging, etc.
Earlier quoted context omitted.
The 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).
No, 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.
Earlier quoted context omitted.
No, 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.
It would have been a surprise if he were hanged on Friday, because he believes he wouldn't be hanged at all.
One way to think about this paradox is as a game with two players—a prisoner and an executioner. The game progresses over five turns, representing the days of the week. On each turn, the prisoner secretly chooses whether or not they expect to be killed on that day. Then the executioner chooses whether or not to kill the prisoner. The game ends on the turn the executioner decides to kill the prisoner. If the prisoner…
In other words the judge's sentence can't be guaranteed to be carried out.
Earlier quoted context omitted.
The judge says the prisoner would be surprised exactly when the knock on the door happens (not before). As a consequence, the prisoner is right to believe he won't be hanged at all (following his reasoning), but as a consequence of that , he is surprised when the knock happens. In turn, as a consequence of that , the judge turns out to be right. Therefore, both the prisoner, and the judge are correct. Thus the parado…
My post is all about how the prisoner's reasoning is WRONG. My mistake: I obfuscated it by having the reader take the perspective of the prisoner. I reworded the OP, but I can't edit it anymore. I have a simpler revised version that I'll include below: . . . The prisoners reasoning is wrong. > if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Si…
The judge not only said that the prisoner will be surprised, he also said precisely when the prisoner will be surprised, which is noon on Friday, for Friday execution.
It does not matter if he gets surprised by the absence of the knock on Thursday. All that matters is that he would not be surprised when the knock happens on Friday.