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 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.
I suppose Wednesday was not required, but if you accept the story as it is told, then it is counterfactual to ask “what if the prisoner was still alive on Thursday evening”. But even if he were, since he deduced that he couldn’t be hanged, he would be surprised even then, after the hangman appeared on Friday. (Some interpretations may require the hanging to happen sooner than Friday to preserve paradoxness.)
This comment links to a good article by Chow, where he analyses the paradox in detail from different points of view, and shows that there is indeed a contradiction in one specific (reasonable) interpretation of the paradox, but it isn’t apparent because the interpretation relies on self-referential formulation of the problem. It is far less clear than “X says A, Y says not A, both are right”.
Then here’s an analogous “paradox”:
There were two men standing in front of me. One said that the ground was red, and the other said that it was blue. Neither of them are ever wrong.
So, yeah, that’s why I said that it sounds like a garden variety contradiction.
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.
Where?
The warden had made two statements:
The prisoner will be hanged on one of the five specified occasions.
The prisoner will never know for sure when he is going to be hanged before the hangman comes.
Both statements are true. In your “paradox” at least one man is wrong.
What if the prisoner were thinking about it in the afternoon on thursday?
What about if the prisoner is still alive on thursday in the afternoon?
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?
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.)
Sorry for misinterpretation, then.
I suppose Wednesday was not required, but if you accept the story as it is told, then it is counterfactual to ask “what if the prisoner was still alive on Thursday evening”. But even if he were, since he deduced that he couldn’t be hanged, he would be surprised even then, after the hangman appeared on Friday. (Some interpretations may require the hanging to happen sooner than Friday to preserve paradoxness.)
This comment links to a good article by Chow, where he analyses the paradox in detail from different points of view, and shows that there is indeed a contradiction in one specific (reasonable) interpretation of the paradox, but it isn’t apparent because the interpretation relies on self-referential formulation of the problem. It is far less clear than “X says A, Y says not A, both are right”.