Why would anybody in that situation ever be surprised?
I mean, they would know that somebody will execute them at noon on one of the days (monday, tuesday, wednesday, thursday, or friday). No matter what day it come on, why would they be surprised? If it comes at noon on monday, they would think, “Oh, it’s noon on monday, and I’m about to die; nothing surprising here.” If it doesn’t come at noon on monday, they would think, “Oh, it’s noon on monday, and I’m not about to die; nothing surprising here (I guess that it will come on one of the other days).” Or whatever.
(Assuming that the the warden told the truth, and the prisoner assumed that.)
This is an old problem, and apparently it’s a lot harder than it looks. Wikipedia says ‘no consensus on its correct resolution has yet been established.’
My preferred solution, if the question is posed in vague enough language, is for the warden to show up just before noon on Friday to hang the prisoner, while wearing a sequined evening gown and scuba gear in place of his usual uniform. The prisoner didn’t see that coming!
For the purposes of the problem, to be surprised just means that something happened to you which you didn’t predict beforehand.
Its not the usual definition (among other things it implies I should be ‘surprised’ if a coin I flip comes up heads) but presumably whoever first came up with the paradox couldn’t think of a better word to express whatever they meant.
For the purposes of the problem, to be surprised just means that something happened to you which you didn’t predict beforehand.
Okay, I understand that.
Its not the usual definition (among other things it implies I should be ‘surprised’ if a coin I flip comes up heads) but presumably whoever first came up with the paradox couldn’t think of a better word to express whatever they meant.
But I don’t understand that.
I mean, why couldn’t I simply predict that it would be heads or tails?
Then wouldn’t the prisoner be surprised no matter what?
But, wait, when exactly are we judging whether he’s surprised?
Let’s say that it’s thursday in the afternoon, and he’s sitting around saying to himself, “I’m totally surprised that it’s going to come on friday. I was online reading about this exact situation, and I thought that it couldn’t come on friday, because it would be the last available day, and I would know that it would be coming.” Or are we waiting for that surprise to dissipate, and turn into “well, I guess that I’m going to die tomorrow”?
From what I can see at this point, I think that the “paradox” comes of an equivocation between those two situations (being surprised right after it doesn’t happen, and then having that surprise dissipate into expectation). But I could be wrong.
The improper use of surprise is distracting you from the main point here, so I suggest you ignore it.
Allow me to rephrase:
The warden tells a prisoner on death row that he will be executed on some day in the following week (last possible day is Friday) at noon, and that on the day he is hanged he will not know he is going to be hanged until he sees the man with the noose at his cell door.
Not as pithy, but that’s the price you sometimes pay to avoid ambiguity.
the paradox is because the prisoner would know the hangman will come at noon on friday if he is alive thursday afternoon he wouldn’t be surprised if he did come. then he concludes that it can’t come friday because he would predict it and be not surprised. but since the judge knows he will say it can’t happen on friday he will actually be surprised if the hangman does come on friday
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.
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”.
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?”.
Does the same reasoning not tell you that nobody is ever surprised by their death? I mean, I know I will die on some day, but if I have a fatal heart attack right now I’d certainly be surprised.
Sure, you would be surprised that you were about to die now.
But would you also be surprised that your life didn’t end up being eternal? No, because you know that you will die someday.
But what’s the significance of this distinction for this problem? Well, I don’t understand how the prisoner could think anything other than, “I guess that I’m going to end up dead one of these days around noon (monday, tuesday, wednesday, thursday, or friday).” It’s not like he has any reason to think that it would be more likely to happen one of the days rather than another. But, in your example, you do have a reason for that (dying now would be less likely than dying later).
But, wait, isn’t that the whole issue in contention (whether he has any reason to think that it would be more likely to happen one of the days rather than another)? Yeah, so let me get back to that.
Let’s say that the hangman shows up on the first day at noon (monday). Would the prisoner be “surprised” that it was monday rather than one of the other days? Why would he? He wouldn’t have any information besides that it would be on one of those days. Or let’s say that the hangman shows up on the second day at noon (tuesday). Would the prisoner be “surprised” that it was tuesday instead of one of the other days? I mean, why would he? He wouldn’t have any knowledge except that it would be on one of the next 3 days.
I’m totally confused.
Why would anybody in that situation ever be surprised?
I mean, they would know that somebody will execute them at noon on one of the days (monday, tuesday, wednesday, thursday, or friday). No matter what day it come on, why would they be surprised? If it comes at noon on monday, they would think, “Oh, it’s noon on monday, and I’m about to die; nothing surprising here.” If it doesn’t come at noon on monday, they would think, “Oh, it’s noon on monday, and I’m not about to die; nothing surprising here (I guess that it will come on one of the other days).” Or whatever.
(Assuming that the the warden told the truth, and the prisoner assumed that.)
This is an old problem, and apparently it’s a lot harder than it looks. Wikipedia says ‘no consensus on its correct resolution has yet been established.’
My preferred solution, if the question is posed in vague enough language, is for the warden to show up just before noon on Friday to hang the prisoner, while wearing a sequined evening gown and scuba gear in place of his usual uniform. The prisoner didn’t see that coming!
Perfect!
For the purposes of the problem, to be surprised just means that something happened to you which you didn’t predict beforehand.
Its not the usual definition (among other things it implies I should be ‘surprised’ if a coin I flip comes up heads) but presumably whoever first came up with the paradox couldn’t think of a better word to express whatever they meant.
Okay, I understand that.
But I don’t understand that.
I mean, why couldn’t I simply predict that it would be heads or tails?
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.
what if it lands on its edge like in batman
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.
Oh okay.
Then wouldn’t the prisoner be surprised no matter what?
But, wait, when exactly are we judging whether he’s surprised?
Let’s say that it’s thursday in the afternoon, and he’s sitting around saying to himself, “I’m totally surprised that it’s going to come on friday. I was online reading about this exact situation, and I thought that it couldn’t come on friday, because it would be the last available day, and I would know that it would be coming.” Or are we waiting for that surprise to dissipate, and turn into “well, I guess that I’m going to die tomorrow”?
From what I can see at this point, I think that the “paradox” comes of an equivocation between those two situations (being surprised right after it doesn’t happen, and then having that surprise dissipate into expectation). But I could be wrong.
The improper use of surprise is distracting you from the main point here, so I suggest you ignore it.
Allow me to rephrase:
Not as pithy, but that’s the price you sometimes pay to avoid ambiguity.
Sounds like a garden variety contradiction.
(If it’s past noon on thursday, obviously he would know that it’s going to come the next day at noon; the warden simply would have been wrong.)
Or am I still misunderstanding it?
the paradox is because the prisoner would know the hangman will come at noon on friday if he is alive thursday afternoon he wouldn’t be surprised if he did come. then he concludes that it can’t come friday because he would predict it and be not surprised. but since the judge knows he will say it can’t happen on friday he will actually be surprised if the hangman does come on friday
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”:
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”.
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:
(blink?)
Does the same reasoning not tell you that nobody is ever surprised by their death? I mean, I know I will die on some day, but if I have a fatal heart attack right now I’d certainly be surprised.
Sure, you would be surprised that you were about to die now.
But would you also be surprised that your life didn’t end up being eternal? No, because you know that you will die someday.
But what’s the significance of this distinction for this problem? Well, I don’t understand how the prisoner could think anything other than, “I guess that I’m going to end up dead one of these days around noon (monday, tuesday, wednesday, thursday, or friday).” It’s not like he has any reason to think that it would be more likely to happen one of the days rather than another. But, in your example, you do have a reason for that (dying now would be less likely than dying later).
But, wait, isn’t that the whole issue in contention (whether he has any reason to think that it would be more likely to happen one of the days rather than another)? Yeah, so let me get back to that.
Let’s say that the hangman shows up on the first day at noon (monday). Would the prisoner be “surprised” that it was monday rather than one of the other days? Why would he? He wouldn’t have any information besides that it would be on one of those days. Or let’s say that the hangman shows up on the second day at noon (tuesday). Would the prisoner be “surprised” that it was tuesday instead of one of the other days? I mean, why would he? He wouldn’t have any knowledge except that it would be on one of the next 3 days.
I’m completely confused by this “paradox”.
Maybe you could help me out?