Talk:Unexpected hanging paradox

Simple refutation

 * Shouldn't this one read ".., but you will not know that"? --User:unmanaged — Preceding undated comment added 10:36, 19 November 2014‎
 * Shouldn't this one read ".., but you will not know that"? --User:unmanaged — Preceding undated comment added 10:36, 19 November 2014‎

On the nature of this "paradox"
An event is a surprise if it cannot be guessed. In this case any day chosen would be a surprise, including Friday because although he will have known for certain by Tuesday, he will also have spent the entirety of Thursday thinking his time has come, so in a sense he will indeed be surprised that his execution is on Friday. But that is besides the point, a surprise refers to the incapability of guessing the outcome of an event at a given time, what matters here is that, at the time when the judge is talking to him, the prisoner is unable to know when he will die no matter how hard he thinks about it, because he simply does not have any "truths" to leverage into making a deduction.

This is not to mention the fact that the feeling of being surprised is something that depends entirely on the prisonner's psychology, which is not necessarily logical. — Preceding unsigned comment added by 135.0.217.3 (talk) 20:22, 28 April 2019 (UTC)

Nature of information required to not be surprised
The prisoner can only be unsurprised if he knows which day he'll be hanged, but his process of elimination doesn't give him that information. Because all days are eliminated, he's still mystified, and therefore surprised.

The "paradox" arises from not understanding what information the prisoner requires to not be surprised. — Preceding unsigned comment added by 96.55.236.116 (talk) 01:59, 3 July 2020 (UTC)

Game Theoric Model
We can model the scenario as a zero sum game where the hangman decides the date of he hanging and the convict tries to guess it. The hangman can make the guess once, and if he guesses the day before he is hung he wins. The equilibrium solution shows that neither the hangman nor the convict has a guaranteed victory. That translates in logic to the fact the hangman cannot guarantee that he will surprise the convict, but the convict also cannot guarantee that he won’t be surprised. If we got back to the original problem, the convict’s reasoning is valid as a proof by contradiction to prove that he cannot be guaranteed to be surprised. His error is in assuming it means he can’t be hanged. The way it ends up unfolding the convict was surprised, but there is no guarantee this would happen as a real scenario, it was just forced by framing the paradox as something that happened after the fact. Ganondox (talk) 23:21, 6 January 2022 (UTC)

?
If you reduce the parodox to one day, you get the following:

A judge tells a prisoner that he will be hanged today, but only if he does not know he will be executed.

The prisoner deduces that since he is aware of his sentence he can not be executed. So when he is executed it is a complete surprise to him.

The iteration to other days in this paradox is just smoke and mirrors.

More formal;

if A is his 'surprise', true when he is not certain he will be hanged, false when he is certain.

and B wether he is hanged.

then if A is false then B must be true (if being hanged is a certainty, then you will be hanged)

however according to the judge if A is false then B must be false, wich is saying if B is true then B is false.

And B can not be both true and false.

109.135.19.79 (talk) 14:52, 2 October 2022 (UTC)

belief is not knowledge
Here is another explanation as to why this is not actually a paradox. I find it the easiest to understand, but obviously I can’t speak for everyone, so I am just passing it along.

You cannot believe something and at the same time know the opposite. If you believe something, then either that thing is true and you know something, or that thing is false and you do not know something.

On the final day, the prisoner believes he will not be hanged, based on the given reasoning. But does he know that he will not be hanged? No, because he is hanged.

Thus he is hanged on a day when he does not know he would be hanged, which is just what the judge said would happen. There is no contradiction, and no paradox. 2600:4040:5D30:4800:697B:8A71:5EC4:66EF (talk) 22:07, 10 November 2023 (UTC)


 * This is not a valid explanation because your definitions are not in agreement with the general philosophical consensus. The relation between "knowing" and "believing" has been a widely discussed topic for millennia.  You should educate yourself on it before contributing to the discourse: https://en.wikipedia.org/wiki/Definitions_of_knowledge#Justified_true_belief 2601:2C6:4A7F:8D40:E123:2C41:3D9:4149 (talk) 02:05, 15 April 2024 (UTC)