Makes me wonder if a good way to deal with rationality or akrasia or self-improvement would be the kind of support group where everyone tries to find fault with everyone else. It's so easy to see flaws in others compared to flaws in ourselves, why not use that to our advantage?
Finding the right people to do this who could both handle it and keep it from turning into an insult trading group might be difficult.
Isn't that exactly what we do here (and on other forums)?
The hangman comes for him on Wednesday, and he is surprised.
This is how it is described in the original post.
(I have a weak feeling that you may be making fun of me. If so, my sense of humour is probably incompatible with yours. If not, please include some explanation to your questions, I find it hard to guess what exactly you disagree with and why. Thanks.)
Wasn't that line (the one saying that the hangman comes for him on wednesday) just supposed to be an example? I didn't think that the problem required the hangman to come on wednesday; I thought that it left open when he would actually come.
(And, no, I'm definitely not making fun of you.)
He is executed on wednesday. The warden knew it all along. And even if he didn't, his statements are true.
Wait, why on wednesday?
The warden had made two statements:
Both statements are true. In your "paradox" at least one man is wrong.
What about if the prisoner is still alive on thursday in the afternoon?
That's not exactly like that, is it? In the hanging paradox the warden was correct in the end. There was no contradiction, at least not one easy to pinpoint.
the warden was correct in the end
Where?
Okay, it seems we have hit another problem with words.
For the purposes of this definition to predict something means to have sufficient evidence to assign it a probability very close to 1.
Can you accurately predict whether a coin will come up heads or tails? I can't.
No, but I can accurately predict that a coin will come heads or tails.
Benelliott worded it well. Your objections are similar to the ones I was raising.
Oh, I see.
At first, I missed the significance of this passage:
The warden's statement is then false and unparadoxical. This is similar to the one-day analogue, where the warden says "You will be executed tomorrow at noon, and will be surprised" and the prisoner says "wtf?".
If the warden is wrong, the paradox is no more. The paradox depends on the assumption that the warden tells the truth, and the prisoner knows for certain that the warden tells the truth.
Then here's an analogous "paradox":
So, yeah, that's why I said that it sounds like a garden variety contradiction.
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A lot of failings people have are things that are hard to notice online.
Good point.