

Unexpected Hanging Paradox - ddinh
https://en.wikipedia.org/wiki/Unexpected_hanging_paradox#

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mcphage
I feel like the prisoner's explanation is circular logic—akin to reducing
something down to 0 = 0:

1\. He claims he can't be executed on Friday, because it wouldn't be a
surprise.

2\. He then argues similarly that he can't be executed any other day.

3\. He concludes therefore that he can't be executed.

But if "I won't be executed at all" was a possibility, then he could never
even rule out Friday: on Friday, he'll either get executed, or not at all.
Both are possible, so he can't claim an execution on Friday would be
predictable beforehand.

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danbruc
Without having it thought out carefully I suggest the following. The judge's
statement is impossible, i.e. it is not possible that the prisoner will be
hanged on any day and is surprised by this. From this impossible statement -
similar to a wrong premise - the prisoner draws the false conclusion that he
will not be hanged at all and is then obviously surprised by someone knocking
on his door.

~~~
mcphage
Well, I don't think you can conclude the judge's statement is impossible,
since (at least in the story) it happened. So it had to be at least possible.
(The judge doesn't claim that the hanging could happen any day and be a
surprise, just that the day it happens it will be a surprise).

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arfar
Is the last part actually part of the paradox, or just a funny quip at the
end. I found that bit quite hilarious, I could imagine that fitting into a
Monty Python sketch or something quite well.

>The next week, the executioner knocks on the prisoner's door at noon on
Wednesday — which, despite all the above, was an utter surprise to him.
Everything the judge said came true.

~~~
mcphage
It's part of the paradox. The prisoner believes he has proven that his
execution is impossible—however, he was wrong. The paradox is how a seemingly
correct argument leads to a false conclusion.

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SilasX
What's interesting to me about this paradox is that it's (IMO) a clever
repackaging of self-referential paradoxes: this statement is false, this
statement can't be proven, etc.

In this case, it's "You will die on a day not deducible from this statement",
but the self-reference is concealed by asserting it will be a "surprise".

