71–80 of 87 posts
If the prisoner is allowed to pick a day every day, they'd pick the next day each time and win.
- Will not be hung this week
- Will be hung on Monday
- Will be hung on Tuesday
- Will be hung on Wednesday
- Will be hung on Thursday
- Will be hung on Friday
You can use logic in order to determine that each of the above outcome is logically impossible. But once you've ruled out all possible outcomes as being "impossible", why would the prisoner stubbornly believe the very first outcome to be true. It too contradicts what the Judge had explicitly said. In such a situation, the prisoner should consider that all 6 possibilities have some significant likelihood of being true, since they all deviate from the Judge's promise in some way. And when dealing with such a rational prisoner, the Judge's promise is impossible to uphold.
Perhaps that is the true resolution to the paradox. The judge was able to make and deliver on his promise, only because he correctly anticipated the prisoner's irrational response. When dealing with a rational prisoner, it would be impossible to uphold such a promise.
I understand the paradox but to me it really just highlights the ambiguity of the English language. The surprise in this case doesn’t literally mean he will be surprised, it really just means that he will not be given the information. The logic of hanging can’t be Friday because it’s not a surprise doesn’t really work for me. Maybe it’s just the Wikipedia example that’s flawed.
So the prisoner reasons: if it is thursday night, then being hung on a friday would not a be surprise. So I will not be hung on friday.
Then there is a kind of induction which further rules out each successive day. I think the thursday night argument is correct, but the induction argument is wrong.
Earlier quoted context omitted.
He cannot logically conclude that. He can only conclude that either he won't be hanged or his hanging might not be a surprise.
He 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.
> he assumes what the judge said is true
The judge says he will be hanged. Your comments are inconsistent.
I understand the paradox but to me it really just highlights the ambiguity of the English language. The surprise in this case doesn’t literally mean he will be surprised, it really just means that he will not be given the information. The logic of hanging can’t be Friday because it’s not a surprise doesn’t really work for me. Maybe it’s just the Wikipedia example that’s flawed.
If I said, "you will be hung tomorrow, and it will be a surprise." That statement can not be true. So the prisoner reasons: if it is thursday night, then being hung on a friday would not a be surprise. So I will not be hung on friday. Then there is a kind of induction which further rules out each successive day. I think the thursday night argument is correct, but the induction argument is wrong.
Earlier quoted context omitted.
He 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.
> 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.
Earlier quoted context omitted.
> 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.
Actually, 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).
The prisoner's anticipated response seems entirely irrational here. There are a range of possible outcomes the prisoner faces: - Will not be hung this week - Will be hung on Monday - Will be hung on Tuesday - Will be hung on Wednesday - Will be hung on Thursday - Will be hung on Friday You can use logic in order to determine that each of the above outcome is logically impossible. But once you've ruled out all possibl…