# Hangman´s paradox real paradox or psuedo **URL:** \ **Category:** Factual Questions\ **Created:** [April 7, 2003, 9:41pm UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171 "2003-04-07T21:41:35Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [April 9, 2003, 1:35am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/61 "2003-04-09T01:35:07Z")
> [@](#): > > \*originally posted by \ ***Joe Random** > > Actually, to say that he can’t be executed on Friday is false. To say that he can be executed on Friday is also false. > Thus the prisoner can be executed on any day other than Friday. You’re condradicting yourself here **Joe** > [@](#): > > \*originally posted by \ ***Bill H.** > > What is missing: > a) what is the process for the prisoner to declare his prediction for which day he will be executed? will he say before the week begins, “I think it’ll be wednesday”, or does he each morning declare, “I think it will be today”? What the answer to these questions are is irrelevant. What we’re trying to figure out is what possible day could be picked for this man to be killed. Could it be Friday? No, or Thursday night he would Know it. Could it be Thursday? No, because on Wednesday night he would know since it’s already been determined he can’t be killed on Friday, he must be getting killed on Thursday, and so on this goes throughout the week. ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [April 9, 2003, 1:41am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/62 "2003-04-09T01:41:43Z")
> [@](#): > > \*originally posted by \ ***Roadfood** > > Bill H. kinda beat me to this, but the OP really mistated the problem somewhat, which is causing most of the confusion on this thread. The problem should go something like this: The OP didn’t mistate the problem at all. Your problem is a different one altogether. Let’s deal with the original post. ---
**Author:** ![Joe\_Random](https://avatars.discourse-cdn.com/v4/letter/j/e8c25b/32.png) [@Joe\_Random](https://boards.straightdope.com/u/Joe_Random)\ **Post date:** [April 9, 2003, 1:53am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/63 "2003-04-09T01:53:36Z")
> [@](#): > > \*Originally posted by x-ray vision \* > **What we’re trying to figure out is what possible day could be picked for this man to be killed. Could it be Friday? No, or Thursday night he would Know it.** No, he wouldn’t know it. He _couldn’t_ know it. Because as soon as he knows it, he can no longer be executed on Friday, per the rules given to him. But then, he will know that he can’t be executed on Friday, and that makes it so that he _can_ be executed on Friday. He both can and cannot be executed on Friday. As soon as one of those is assumed, the other becomes true. And once the other becomes true, the nature of the problem forces it to become false again. That is what a paradox is. A paradox is a statement that is both true and false at the same time. Thus, you cannot say that he can’t be executed on Friday, because he both can and can’t _at the same time_. That means that you can’t even begin to examine Thursday, because doing so requires that you first determine whether or not he can be executed on Friday, and it is not possible to make that determination due to the paradox. ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [April 9, 2003, 2:01am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/64 "2003-04-09T02:01:57Z")
**Joe** , I can see your logic on why he can’t be killed on Friday, but not on how he can. He definitely can’t be killed on Friday, because that means on Thursday night he will know he will be killed on Friday and that violates one of the conditions. ---
**Author:** ![Severian](https://avatars.discourse-cdn.com/v4/letter/s/49beb7/32.png) [@Severian](https://boards.straightdope.com/u/Severian)\ **Post date:** [April 9, 2003, 2:14am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/65 "2003-04-09T02:14:35Z")
> [@](#): > > \*Originally posted by x-ray vision \* > \*\ ***Joe** , I can see your logic on why he can’t be killed on Friday, but not on how he can. He definitely can’t be killed on Friday, because that means on Thursday night he will know he will be killed on Friday and that violates one of the conditions. \*\* Asked when he will be executed, the prisoner states “I know it won’t be Friday.” So Friday it is. The condition says the prisoner won’t know his execution date until the day comes. Well, he’s already reasoned and stated he knows it’s **not** going to be Friday, so he can’t know it will be Friday. He can’t know that it will and will not be Friday at the same time. That’s the paradox. At least, I think that’s what **Joe** is saying. ---
**Author:** ![Joe\_Random](https://avatars.discourse-cdn.com/v4/letter/j/e8c25b/32.png) [@Joe\_Random](https://boards.straightdope.com/u/Joe_Random)\ **Post date:** [April 9, 2003, 2:40am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/66 "2003-04-09T02:40:18Z")
> [@](#): > > \*Originally posted by x-ray vision \* > \*\ ***Joe** , I can see your logic on why he can’t be killed on Friday, but not on how he can. He definitely can’t be killed on Friday, because that means on Thursday night he will know he will be killed on Friday and that violates one of the conditions. \*\* Well, I had a nice, long response written up, and the server ate it. Let’s try again. Let’s assume that it is late on Thursday night, with no chance to be executed on Thursday. The prisoner knows that Friday is the last chance they have to execute him. According to the rules, they can’t execute him if he knows about it the day before, and since he knows, he can’t be executed. That’s where you stopped, but that’s not the end. He now believes that he can’t be executed on Friday. Now, what was the only reason that he couldn’t be executed on Friday? It was because he knew that he _would_ be executed. But now he knows that he _won’t_ be executed, so the original assessment is no longer valid. Since he doesn’t know that he can be executed on Friday (in fact, he assumes that he _won’t_ be), that means that the rule that was invoked – namely, knowing beforehand that he was to be executed – is no longer in effect. Thus, he can be executed. Of course, being an intelligent person, he knows this, and so the whole thing goes back to square one. This is simply an expanded version of “This sentence is false”. If you assume that it’s false, it must be true; but if it’s true, it must be false. You keep going back and forth over and over again without ever being able to say if it’s true or false. That’s what a paradox is. A paradox is true and false at the same time. Or maybe it’s neither true _nor_ false. It doesn’t really matter. The point is, you can never determine whether or not he can be executed on Friday, because everytime you assume one, it causes the other one to be true. Thus, you cannot assert that he can not be executed on Friday, because whether or not he can be executed on Friday is a paradox. And since your line of reasoning requires you to assert that he _cannot_ be executed on Friday, your line of reasoning is flawed. ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [April 9, 2003, 2:50am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/67 "2003-04-09T02:50:33Z")
> [@](#): > > \*originally posted by \ ***Joe Random** > > Now, what was the only reason that he couldn’t be executed on Friday? It was because he knew that he would be executed. But now he knows that he _won’t_ be executed No, now he knows that he \*will[/] be executed on Friday. It’s the only day left. Don’t you see this is why Friday could never have been picked for him? ---
**Author:** ![Joe\_Random](https://avatars.discourse-cdn.com/v4/letter/j/e8c25b/32.png) [@Joe\_Random](https://boards.straightdope.com/u/Joe_Random)\ **Post date:** [April 9, 2003, 3:28am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/68 "2003-04-09T03:28:49Z")
> [@](#): > > \*Originally posted by x-ray vision \* > \*\*No, now he knows that he _will_ be executed on Friday. It’s the only day left. Don’t you see this is why Friday could never have been picked for him? \*\* You’re contradicting yourself. If he _will_ be executed on Friday, then Friday must have been picked. So you cannot say that it could never have been picked. You’re trying to reason your way out of a paradox, and that’s simply not possible. I think that the only way to convince you of this is to pretend that you’re the prisoner and I’m your captor. Today is Sunday, and I have already decided what day you will be executed on. Now, what would you say to me to convonce me not to execute you? ---
**Author:** ![ChalkPit](https://avatars.discourse-cdn.com/v4/letter/c/a88e4f/32.png) [@ChalkPit](https://boards.straightdope.com/u/ChalkPit)\ **Post date:** [April 9, 2003, 7:36am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/69 "2003-04-09T07:36:48Z")
It has been said earlier in this thread, that the ‘hangmans paradox’ and the ‘surprise test’ paradox are versions of the same thing. So would anyone here, if told they were getting a surprise exam the following week, **NOT** revise for it ? [Solution to the Surprise test paradox](http://www.nyu.edu/gsas/dept/philo/faculty/sorensen/papers/solution.html) ---
**Author:** ![Bill\_H](https://avatars.discourse-cdn.com/v4/letter/b/a5b964/32.png) [@Bill\_H](https://boards.straightdope.com/u/Bill_H)\ **Post date:** [April 9, 2003, 7:37am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/70 "2003-04-09T07:37:39Z")
**x-ray vision** , you either didn’t read my post or didn’t read it. Which is no more paradoxical then this silly thing. Answer the 3 questions I posed, to give complete info to the question, and I’ll show you why that version that you define is not a paradox. Or, more likely – as you strike me as a sharp fellow – you’ll immediately see that once you do have a complete question, you’ll have a clear answer. ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [April 9, 2003, 8:04am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/71 "2003-04-09T08:04:28Z")
Forgive me if I skipped past a few posts on the second page. I read this paradox years ago and it has always been a favorite. That having been said… As soon as the prisoner reasons that Friday is no longer an eligible date of execution it becomes, from his reasoning, an eligible date of execution, inasmuch as he has eliminated from the realm of possibility and would be surpirsed if they did it. I am reminded of a condensed version (I think) #1) Statement #2 is false. #2) Statement #1 is true. The conditions of the hangman experiment are irreconilible though they seem to be reasonable on first inspection. Still one of my favorites, though. ---
**Author:** ![Joe\_Random](https://avatars.discourse-cdn.com/v4/letter/j/e8c25b/32.png) [@Joe\_Random](https://boards.straightdope.com/u/Joe_Random)\ **Post date:** [April 9, 2003, 8:15am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/72 "2003-04-09T08:15:28Z")
> [@](#): > > \*Originally posted by MonkeyMensch \* > **The conditions of the hangman experiment are irreconilible though they seem to be reasonable on first inspection.** That’s the entire reason that some people can’t see the parodox correctly (I’m looking at you, **x-ray vision** 😉 ). The extra information confuses the issue. Condition 1) The prisoner will be executed on one of five days, M-F Condition 2) The prisoner can not know the day of executon beforehand. The logic put forth by those arguing that execution is impossible states that, since, on Thursday, the prisoner knows that he will be executed the following day, he cannot be executed the following day because it would violate condition 2. What they fail to notice is that _not_ executing him the following day would violate condition 1. Hence the paradox. However, the paradox does not prevent the prisoner from being executed. It just makes him waste time thinking about paradoxes instead of planning an escape 😃 ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [April 9, 2003, 8:27am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/73 "2003-04-09T08:27:16Z")
Well put, **Joe Random**. ---
**Author:** ![Kamino\_Neko](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kamino_neko/32/34_2.png) [@Kamino\_Neko](https://boards.straightdope.com/u/Kamino_Neko)\ **Post date:** [April 9, 2003, 9:34am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/74 "2003-04-09T09:34:51Z")
> [@](#): > > \*Originally posted by MonkeyMensch \* > \*\*#1) Statement #2 is false. > #2) Statement #1 is true. > > The conditions of the hangman experiment are irreconilible though they seem to be reasonable on first inspection. Still one of my favorites, though. \*\* I’ve always been fond of the Ubercompressed version. ‘Everything I say is a lie.’ ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [April 9, 2003, 9:39am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/75 "2003-04-09T09:39:26Z")
> [@](#): > > \*Originally posted by Tengu \* > \*\*I’ve always been fond of the Ubercompressed version. > > ‘Everything I say is a lie.’ \*\* That’s not quite the same though. Either, you are telling the truth in but you can’t be because you must be lying etc etc. **Or** , you are lying. In actual fact only _some_ things you say are lies, this being one of them. No paradox. ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [April 9, 2003, 10:55am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/76 "2003-04-09T10:55:31Z")
Hmm… the paradox is normally stated as with some reason for supposing the Judge is infallible, not merely intended to have the man excecuted as described. (Also, the knocking him out thing I’ve never seen before, but would solve it nicely… shall we consider the case where this is not allowed?) I tend to consider a simpler version of the paradox: the judge says (1) You will be executed at noon on friday. (2) This will be a surprise. **If the Judge is stated to be infallible** we might easily get a paradox; most knowledge of future events or perfect decision machines do produce paradoxes. **If not** The only way the judge can be right is if I’m execued! So I’m expecting it. But then I can’t be. So I won’t be. But now I’m not expecting it. So I can be. Can’t be. Can be. I DON’T KNOW!.. what? now? ---
**Author:** ![ChalkPit](https://avatars.discourse-cdn.com/v4/letter/c/a88e4f/32.png) [@ChalkPit](https://boards.straightdope.com/u/ChalkPit)\ **Post date:** [April 9, 2003, 11:08am UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/77 "2003-04-09T11:08:18Z")
You dont have to knock the prisoner out, just dont let him know what time of day it is and keep him in a cell with no windows. He could only assume that he gets meals at the same time, but you could spread them out a bit and he wouldnt notice. If he has no way of knowing what the time is or what day it is, then the paradox falls down. ---
**Author:** ![refusal](https://avatars.discourse-cdn.com/v4/letter/r/ac91a4/32.png) [@refusal](https://boards.straightdope.com/u/refusal)\ **Post date:** [April 9, 2003, 1:05pm UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/78 "2003-04-09T13:05:18Z")
**Roadfood** ’s version of the problem is an excellent simplification of the paradox to a version which can be evaluated without knowledge of the prisoner’s internal mental state: it states the problem in such a way that we do not have to say what the prisoner knows, only study what he says and does. The problem is that the original statement of the paradox depends on an understanding of what it means to know something. The nature of knowledge has been debated by philosophers for 2500 years, so it is a little arrogant to think you can solve the paradox and at the same time one of the greatest problems in philosophical thought. If the paradox was reworded so that the second proposition was “The prisoner cannot logically deduce when he will die”, then there would be a clear logical contradiction. In the dilemma, the prisoner has a clear reason for believing he will die (the rules imposed on him by the judge), and also a clear reason for not believing he will die (his chain of logical reasoning). However, the problem is that being able to logically deduce something is not the same as knowing it. I believe it is possible to know something without having logically deduced something (e.g. to know that you are seeing a yellow object, or to know your telephone number or the capital of France). But I also believe it is possible to logically deduce something and yet still not know it. For instance, if we already have a reason to believe that what has been deduced is impossible or unlikely, we may not accept the result of the deduction. (Another example would be an abtruse mathematical proof which you might be told is valid and see no flaws in, but not be able to understand the result.) A specific example of a false belief justified by logic is Newtonian physics. Anyone who has studied philosophy knows it is possible to have an argument which seems logically compelling yet reaches a conclusion which you disagree with or is false: this may be due to an error in the argument, but the slipperiness of language makes it impossible to definitively prove the veracity of arguments expressed in words. The consequence is that whether or not this is a paradox, it is an interesting puzzle to reflect upon to consider the nature of knowledge. ---
**Author:** ![moc.liamtoh\_rorrim](https://avatars.discourse-cdn.com/v4/letter/m/f17d59/32.png) [@moc.liamtoh\_rorrim](https://boards.straightdope.com/u/moc.liamtoh_rorrim)\ **Post date:** [April 9, 2003, 1:22pm UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/79 "2003-04-09T13:22:36Z")
He can only come to the conclusion that he cant be executed if he lives till thursday. He is saying “its thursday now, cant be executed tomorrow” then he works back in time. This logic only comes into play on thursday. Kill him on Wednesday. ---
**Author:** ![dil](https://avatars.discourse-cdn.com/v4/letter/d/f04885/32.png) [@dil](https://boards.straightdope.com/u/dil)\ **Post date:** [April 9, 2003, 4:17pm UTC](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171/80 "2003-04-09T16:17:42Z")
1. Surprise breakfast tomorrow 2. It will be Belgian Waffles Same problem. Hehe, great puzzle! Joe: Hey, Waffles for breakfast. All right! Tim: No you moron, it says it’s a surprise, so if you KNOW that it’s going to be waffles then it must be something else. Joe: OK, so I know that it CAN’T be waffles, because that wouldn’t be a surprise. Tim: You know what’d really be surprising now? Waffles. Joe: Damn. [Previous page](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171.md?page=3) [Next page](https://boards.straightdope.com/t/hangman-s-paradox-real-paradox-or-psuedo/167171.md?page=5)