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You did not understand the paradox. The word "surprise" here means that the prisoner won't know his date of execution until he is told. [Edited]

mcphage 2y ago
I did understand the paradox. Those are the instructions he was given: he won’t know the date of his execution until he is told. He performs some reasoning, and concludes that he can’t get executed any day that week: therefore he will go free. But if “he will go free” is a possibility, then his chain of reasoning falls apart. Previously he had argued “if I survive to the last day, I will be executed today. That won’t be a surprise. Therefore I can’t be executed on the last day.” But once he has “…or I won’t get executed at all” as an option, then his reasoning would begin “if I survive to the last day, then either I’ll get executed today, or I won’t get executed at all” … and that’s as far as he can go. He can’t use that to conclude he won’t get executed on the last day, and he can’t then use that to conclude he won’t be executed on the second last day, and so on. The entire argument breaks apart immediately.
mcphage 2y ago
Ah, sorry—I saw your "You did not understand the paradox", and thought you were replying to me, instead of replying to a reply. In my defense, the way HN uses indentations to indicate depth is hard to follow on a phone screen where the comment and its replies might be screens apart.
- jerf 2y ago
  Eh, it works for me. I endorse your answer, though I also endorse more things than that. I referenced that there were many ways to "resolve the paradox" which isn't really "resolving" anything, based on how you carefully define the terms. It is certainly valid to define the terms in such a way that the prisoner is logically correct. In that case, there is no paradox, just perhaps lies. You can define it such that the prisoner is simply in error. You can also define it such that the answer is "indeterminate"... but that's not a paradox either. "Indeterminate" comes up in logic all the time and if you run around yelling "paradox! paradox!" every time that happens you're going to get hoarse pretty quickly. The only "paradox" is that people insist on not being careful with their definitions, and any time anyone tries, someone else flips to a different definition (without being clear about it) and then starts arguing from that new point of view. That's not a paradox either. That's just lifting unclear thinking to the level of moral imperative. I have no patience or sympathy for that.

mcphage 2y ago

I did understand the paradox. Those are the instructions he was given: he won’t know the date of his execution until he is told. He performs some reasoning, and concludes that he can’t get executed any day that week: therefore he will go free. But if “he will go free” is a possibility, then his chain of reasoning falls apart. Previously he had argued “if I survive to the last day, I will be executed today. That won’t be a surprise. Therefore I can’t be executed on the last day.” But once he has “…or I won’t get executed at all” as an option, then his reasoning would begin “if I survive to the last day, then either I’ll get executed today, or I won’t get executed at all” … and that’s as far as he can go. He can’t use that to conclude he won’t get executed on the last day, and he can’t then use that to conclude he won’t be executed on the second last day, and so on. The entire argument breaks apart immediately.

mcphage 2y ago

Ah, sorry—I saw your "You did not understand the paradox", and thought you were replying to me, instead of replying to a reply. In my defense, the way HN uses indentations to indicate depth is hard to follow on a phone screen where the comment and its replies might be screens apart.

jerf 2y ago
Eh, it works for me. I endorse your answer, though I also endorse more things than that. I referenced that there were many ways to "resolve the paradox" which isn't really "resolving" anything, based on how you carefully define the terms. It is certainly valid to define the terms in such a way that the prisoner is logically correct. In that case, there is no paradox, just perhaps lies. You can define it such that the prisoner is simply in error. You can also define it such that the answer is "indeterminate"... but that's not a paradox either. "Indeterminate" comes up in logic all the time and if you run around yelling "paradox! paradox!" every time that happens you're going to get hoarse pretty quickly. The only "paradox" is that people insist on not being careful with their definitions, and any time anyone tries, someone else flips to a different definition (without being clear about it) and then starts arguing from that new point of view. That's not a paradox either. That's just lifting unclear thinking to the level of moral imperative. I have no patience or sympathy for that.