Attempt to Solve Hangman Paradox
I just encountered this paradox lately and think about it. And it quite paradoxial on sense of "surprise vs expectation". Given on the fact that the prisoner expects the execution will happen within the week makes the execution is no longer a surprise.
But there is also a matter i felt that is quite disregarded.
Limit.
Considering the parameters of the example given to me (i dont know if there is any examples are there) it should fulfil these things.
Hanged within a week
Its a noon
What day is random
Its a surprise
Prisoner trust judge
Prisoner expect it will happen everyday.
So where does my point of "limit" comes in?
Its on first one. Within a week, so let say judgement is given on sunday, so he is 100% dead on next week monday. So its now technically a chance game some way or like this in my opinion and no longer a paradox. (Its now like a logic of how long does a two meter step will take if first step is 1 meter in 1 second, next step is 1/2 meter is taken in 1/2 second and so on so forth)... we know the answer here is 2 second in total of infinity step of halves of previous steps.
So where this analogy comes is?
It goes on "when does the prisoner will be hanged" ...
Every day on noon (12:00 -12:59) he will is aranged everyday on a noose.
The surprise will now burn hard on this time. It will be in the next second? Or next milisecond? Or in next nanosecond? So even he expect he will be hanged today given the judgement is a surprise... the surprise of death is not longer on death but now on survival. Because even if he expect that he will be died on monday, he can argue that "im expecting to be hanged on monday, so its no longer a surprise so the judge lied" it will now compressed on verification of "i've been hanged on 12:59:9999999..." this will give the judge a escape on the arguement that the hanging still a surprise. Since in between on those decimal.is the process of logic of verification before saying the surprise of hanging is invalid and death happened.