[pieguy]

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.

[p1esk]

It would have been a surprise if he were hanged on Friday, because he believes he wouldn't be hanged at all.

[pieguy]

He cannot logically conclude that. He can only conclude that either he won't be hanged or his hanging might not be a surprise.

[p1esk]

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.

[pieguy]

> 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]

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).

[pieguy]

Let 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.