this post was submitted on 26 Mar 2024
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The Unexpected Hanging Paradox: A man is sentenced to death, but the judge decides to have a little fun with it. The man will be killed at noon on a day of the judge's choosing in the next week, from Monday to Friday. The only stipulation is that the man will not expect it when he's called to be killed.
The man does some quick logic in his head. If Friday is the last day he could be killed, then if he makes it to Friday without dying, he knows he must die on that day. And since that wouldn't be a surprise, he cannot be killed on Friday.
He then extends the logic. Since he can't be killed on Friday, the last day he can be killed is on Thursday. Thus, all the prior logic regarding Friday applies, and he cannot be killed on Thursday either. This then extends to Wednesday, then Tuesday, and then Monday. At the end, he grins with the knowledge that, through logic, he knows he cannot be killed on any of the days, and will therefore not be killed.
Therefore, the man is astonished when he's called to be killed on Wednesday.
How does the judge determine whether the condemned man is "expecting it"?
Regardless of when he's called, he could simply state that he was expecting to be called, and therefore the hanging would be called off.
Its a bad paradox because it pivots on something that cannot be properly defined.
I think it's an anti-riddle, or a joke, more than anything else.
I always thought it was a way to show the foibles of using pure logic in a regular setting.
Cannot be properly defined? "Expecting it" means "regarding it likely to happen", according to the dictionary. He regarded it as impossible to happen, so he was not expecting it. His own logic disproving the event (him being surprised) allowed the event to happen (he was surprised).
Why does the paradox suffer if he lies about the solution? The paradox has already played out, and anything after that is just set dressing.
Just off the top of my head, maybe the judge has a camera set to gauge his reaction to the knock on the door? Or maybe he goes into denial and tries to explain his logic, thus proving the paradox? Or maybe the judge doesn't actually care as much as he said, but trusts the logic to hold out and make for a funny story?
You provide three flawed ways of measuring expectation; that's the issue in a nutshell.
Its not a true paradox as the whole gambit rests on a changeable emotion, not logic.
The prisoner could wake up each morning and simply say "I expect to die today". How would the judge determine the truth? It would be impossible.
If someone punches you in the face after saying "knock knock", it doesn't make it a knock knock joke, and nor is this a paradox.
My dude. The paradox doesn't change based on whether or not the judge knows the truth, or even if the man dies.
The truth is the man was made not to expect a thing by his own logic proving he would always expect a thing. The paradox is based on his own prediction being wrong because of his prediction. In this instance, his prediction was what his emotions would be.
A horse walks into a bar, and the barman says "why the long face?" I haven't said how they remove the horse from the bar, so does that mean I didn't tell a joke? Or does horse removal not actually matter to the joke?
No. A paradox is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
In this case, there is no true premesis.
That's the core of the problem. Your incorrect interpretation of the joke metaphor demonstrates that you don't understand this.
I find it funny that you directly quoted wikipedia to write that (exact wording from the paradox article, I checked), but ignored the sentence immediately before it (...or a statement that runs contrary to one's expectation). Also, the linked articles at the bottom include the unexpected hanging page. Maybe read the entire wiki page before citing it?
Also, in case wikipedia suddenly isn't enough, here's an article on wolfram to back me up: https://mathworld.wolfram.com/UnexpectedHangingParadox.html
It doesn't "back you up" at all, it simply restates the paradox. Maybe learn how to argue?
When you get to the point where you're nitpicking sources, you're admitting that you have no substantive argument available.
This is how I proposed to my wife. I said I'd propose at some point in the next year, and that according the the unexpected hanging paradox, we're doomed to break up at the end of the year. Then I proposed on a random day in the year and she was totally surprised.