The main issue is how intelligent the prisoner is. As it is, the prisoner used some clever logic to prove that he will not be executed that week, failing to consider the possibility that the judge will predict that. If he thought about it a bit more, he might realize that in fact the judge might well be anticipating that, and therefore, expect the hangman to come on any given day.
Then, if he kept thinking, it might occur to him that it is possible that the judge predicted that too, and so might not send the hangman. However, the judge is capable of making mistakes. He is human. So, the prisoner can come to the conclusion that he may well be hanged this week, even though it won’t be a surprise, or that the hangman will not come, and in fact the judge has predicted him perfectly.
This paradox is only confusing (from the prisoner’s standpoint) if you consider the judge to be infallible. He’s not. If the judge were Omega, on the other hand, we might run into some problems.
The main issue is how intelligent the prisoner is. As it is, the prisoner used some clever logic to prove that he will not be executed that week, failing to consider the possibility that the judge will predict that. If he thought about it a bit more, he might realize that in fact the judge might well be anticipating that, and therefore, expect the hangman to come on any given day.
Then, if he kept thinking, it might occur to him that it is possible that the judge predicted that too, and so might not send the hangman. However, the judge is capable of making mistakes. He is human. So, the prisoner can come to the conclusion that he may well be hanged this week, even though it won’t be a surprise, or that the hangman will not come, and in fact the judge has predicted him perfectly.
This paradox is only confusing (from the prisoner’s standpoint) if you consider the judge to be infallible. He’s not. If the judge were Omega, on the other hand, we might run into some problems.