The Unexpected Hanging Paradox

The Unexpected Hanging Paradox
(My take on it)

This is a logical paradox invented in the 1940s and first written about by Michael Scriven in 1951, and then later by Martin Gardner in his 1963 "Mathematical Games" column in "Scientific American" magazine.

It goes by several names, including: the Unexpected Hanging, the Surprise Examination, the Unexpected Tiger, etc.

Wikipedia:

David R. Tribble
Sep 2020

[juliusdrohm]

As soon as he excludes the possibility of being executed on Friday, he makes the execution on Friday (then being unexpected) fulfill the rule set by the judge.

[disaus]

good point, basically you cannot cancel out Friday until the Friday comes

[williamhughes]

Not convincing at all. You seem to think that on Sunday the prisoner has an expectation of 1/5 for each or five days. There is no reason to think that the probabilities are equal. Indeed the prisoner can conclude that the expectation of being executed on Monday is 100% (he cannot be executed on any other day so it must be Monday ) and as well the prisoner can conclude that the expectation of being executed on Monday is 0% (he cannot be executed on a day where his expectation is 100%). The paradox persists.

[danmeyer]

You also have to consider the effect of the prisoner's logic in eliminating every day. By following his logic as far as he did, he created the scenario in which he was surprised when the executioner showed up on Wednesday. The prisoner was correct in eliminating Friday, but that's as far as he should have taken it.

[krishjain]

When you are philosopher but bad at maths so you invent a paradox😂

[bradensorensen]

Nice try, but it can’t be Friday. He’d be 100% expecting it on that day. Therefore he wouldn’t be surprised.

That being said you can’t make Thursday or any other day 100%. Because that would make every day after that day 0%. Thus those days are now a surprise.

In other words, it could literally be any of the days and the prisoner would be surprised based on his logic.

It would be even more sound though if the Judge said the prisoner MIGHT be hanged that week. Then he could re-sentence the criminal over and over and which date was real would be a total mystery.

[jamestagge]

I may wind up with egg on my face, but I would say that this supposed paradox fails as such and seems more ridiculous than Russell’s paradox, which is not a paradox either. I will refer to it as one for the sake of expediency. So…I think that the resolution to this is the following; if they came for him on any day, before noon he would not know if they would and would be thus surprised, making the time of day as significant as the day itself in his calculations. Also, most significantly, in the paradox it is stated clearly that “IF” the man were not hanged on Thursday, he could not be on Friday for then it would not be a surprise. It is only for that reason that Friday is excluded from the possible days for the hanging. The meaning of this is clear in the definition of the paradox and carries a significant measure of weight in terms of the logic and structure. The “IF” conveys that the execution “COULD” take place on Thursday and the entire paradox collapses (this extends to each preceding day of the week). Additionally, that the paradox states that the hangman came on Wednesday, demonstrates an aspect to the logical structure which seems to be ignored by all who have contemplated the resolution.

So, “IF” the man were still alive on Wednesday, the possibility of Thursday still existed for the execution as stated above. I think that the hangman coming for him on Wednesday is because he was putting a buffer zone (day) between the date of the hanging and Friday, that day of the week under which circumstance it could not take place by definition. This in effect, broke the chain used in the defining of the paradox.

What do you all think? I am still working on this but I don’t see it as the big deal it is purported to be on the videos. Please comment. It’s a fun study.

[kevinciviclord]

God once said to human, you will die within a hundred year, but I will not let you know which date to come, otherwise you will become eternity. So all human live happily