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Earlier quoted context omitted.
It would have been a surprise if he were hanged on Friday, because he believes he wouldn't be hanged at all.
He cannot logically conclude that. He can only conclude that either he won't be hanged or his hanging might not be a surprise.
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 this view of the world (where the prisoner can play "I expect to die today" exactly once, there is actually not a Nash equilibrium where the executioner is guaranteed to win. In other words the judge's sentence can't be guaranteed to be carried out.
For everyone saying the prisoner can just expect to be hanged every day and thus never be surprised.... Why do you say that? What reason, on Monday, does he have to believe that he would be executed on Monday and not the other days? He can say the words, but I'm not convinced he would be convinced.
(In fact, he has a valid argument for anything he might want to believe since the original statement made by the judge is self-contradictory.)
The judge has underspecified the process. Judge says "on a weekday," and that it will be a surprise to the person being executed. But the judge has not specified which weekdays are actually in play. Now, let's attempt to specify it: "Judge will schedule the execution for one of the following days in the upcoming week: Monday, Tuesday, Wednesday, Thursday, or Friday. Judge will pick one of these days at random. This r…
If we don't care about randomness, can't the judge just use the strategy of Always pick Wednesday?
If we do care about randomness, the job is to explore whether we're guaranteed to surprise the convict, and of course we're not: if the random process selects Friday, the convict won't be surprised.
Consider Friday: The prisoner know that he will be hanged today, so he realizes he can't be hanged because it wouldn't be a surprise, which makes the hanging surprising... Or in other words, "I will be hanged" means "I won't be hanged" (because it won't be a surprise) and "I won't be hanged" means "I will be hanged" (because it will be a surprise)
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…
Quoting Wikipedia:
"Anxiety is an emotion characterized by an unpleasant state of inner turmoil, often accompanied by nervous behaviour such as pacing back and forth, somatic complaints, and rumination. It is the subjectively unpleasant feelings of dread over anticipated events, such as the feeling of imminent death." [1]
As well as -perhaps even more so- depression.
The expected outcome has a related effect on the psyche, but the fact is that in reality the prisoner has no effect on their death. Which means that the most useful way to deal with your last days (how many they are) is akin to the principles of carpe diem. [2] Which is something both anxiety and depression hamper.
There is a simple resolution to this "paradox": it's only a paradox if you consider the judge's initial statement to be True. If the judge's initial statement is False (i.e. he's lying) then the whole situation is logically consistent. The truth table for modus ponens helps clarify, both F->T and F->F evaluate as T https://en.wikipedia.org/wiki/Modus_ponens#Justification_via... The judge is saying he can predict how…
"Surprise" isn't meant primarily as "the prisoner will feel surprised" (though the ending is more pithy if it is put that way), but rather "the event will not be logically predictable for the prisoner".
> He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. I have placed a ball under one of five cups. You can check only sequentially if the ball is under each cup. Do you know which cup the ball is under? If you start turning over the cups one by one, will you be surprised when you find it? You won’t be surprised after you’ve turned over all but one cup, if you still…
> The simple reality is that the judge can only promise you a surprise Monday thru Thursday.
Which means that the execution is on either monday/tuesday/wednesday/thursday but you don't know which one.
That'd result in a 1 in 4 (25%) chance of being right, if he's allowed to vote once. Which day he'd vote on, could be related to how much patience or how nervous he is, how eager he wants to live perhaps?