# The Unexpected Hanging Paradox **URL:** \ **Category:** Factual Questions\ **Created:** [September 29, 2009, 4:02pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993 "2009-09-29T16:02:32Z")\ **Posts on this page:** 20\ **Page:** 8
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 11, 2009, 2:11am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/141 "2009-10-11T02:11:29Z")
> [@RaftPeople](#): > > I think the problem you are having is looking at the person’s statement “it is raining” (which **is** a statement by a person, there is no mistaking that, right?) and you are extracting the information about rain and thinking that is what was just communicated. > > That is not what was just communicated. > > What was just communicated was a statement about the person’s set of beliefs. I see what you’re saying. You really do think that when I say “It’s raining” I really do mean–what I really am trying to say is–_not_ that it’s raining but rather that I believe it’s raining. Do I have you right? What if I point out that this means that, in your view, it’s impossible to talk about _anything_ other than one’s own beliefs? Does that mean I misunderstood you? Or is that a bullet you bite? -Kris ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 11, 2009, 2:15am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/142 "2009-10-11T02:15:22Z")
> [@RaftPeople](#): > > I have spent a lot of time (in the past) converting written and spoken word into predicate logic and evaluating the results. In that case we had predicates not propositions. Terminological correction: A statement in predicate logic is not a predicate, but a proposition. A predicate could be thought of as a part of a proposition, but no statement translated into the language of predicate logic would yield a predicate alone. Here’s a proposition: Ex(Gx & Hx) \<—turn that E backwards of course In that proposition, here are the predicates: G, H ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [October 11, 2009, 2:19am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/143 "2009-10-11T02:19:44Z")
> [@Frylock](#): > > I see what you’re saying. You really do think that when I say “It’s raining” I really do mean–what I really am trying to say is–_not_ that it’s raining but rather that I believe it’s raining. > > Do I have you right? > What if I point out that this means that, in your view, it’s impossible to talk about _anything_ other than one’s own beliefs? Does that mean I misunderstood you? Or is that a bullet you bite? > > -Kris Yes to raining question, unless it is provided at the start of the exercise as a statement of fact and not a statement from a human. I think that within a logical exercise, we can have statements of fact that we are provided, and we can have statements from humans which can’t be given the same true/false status as the other facts provided. Unless we agree by convention that we want to elevate those to fact. I don’t think this really causes a problem with either the judge or the rain, do you? ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [October 11, 2009, 2:25am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/144 "2009-10-11T02:25:53Z")
> [@Frylock](#): > > Terminological correction: A statement in predicate logic is not a predicate, but a proposition. A predicate could be thought of as a part of a proposition, but no statement translated into the language of predicate logic would yield a predicate alone. > > Here’s a proposition: > > Ex(Gx & Hx) \<—turn that E backwards of course > > In that proposition, here are the predicates: > > G, H Yes, that is correct, it’s been a while. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 11, 2009, 2:27am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/145 "2009-10-11T02:27:33Z")
> [@RaftPeople](#): > > I don’t think this really causes a problem with either the judge or the rain, do you? Having come to understand this about your view, I now see why you would think the things trivial and obvious that you’ve been calling trivial and obvious. For you, if I understand you right, most statements “X” really only mean “I believe X,” while (I assume you think) a statement “I believe Y” means “I believe Y.”\* If that’s your view, then there is, trivially, a contradiction in saying “X and I don’t believe X.” For in your view, that _means_ (doesn’t just pragmatically signal, but _means_) “I believe X and I don’t believe X.” Contradiction. I’m not sure what you think or should think about **ianzin** ’s judge. The judge says “You will be hanged” and “You will be surprised.” In your view, these mean “I believe you will be hanged” and “I believe you will be surprised.” No contradiction there, since the judge is just telling us what he believes. He would not even be contradicting himself if he said “You will be hanged” and “You will not be hanged.” For these actually mean, on your view, “I believe you will be hanged” and “I believe you will not be hanged.” No contradiction there. A weird thing to say, but not, on your view, as far as I understand it, contradictory. \*I assumed you thought that “I believe Y” means “I believe Y” and not “I believe that I believe Y” because if you think the latter, the Moore stuff becomes non-trivial for you after all. For the Moore pair become: “I believe it’s raining” “I don’t believe I believe it’s raining.” No contradiction, but unsayable, and strange in all the same ways Moore’s sentence pair is strange. This can’t be your understanding of “I believe Y” on my hypothesis, since on my hypothesis, your understanding makes Moore-ish sentence pairs trivially and obviously self-contradictory. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 11, 2009, 2:28am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/146 "2009-10-11T02:28:34Z")
> [@RaftPeople](#): > > Yes, that is correct, it’s been a while. 😉 ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [October 11, 2009, 2:44am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/147 "2009-10-11T02:44:46Z")
> [@Frylock](#): > > Having come to understand this about your view, I now see why you would think the things trivial and obvious that you’ve been calling trivial and obvious. > > For you, if I understand you right, most statements “X” really only mean “I believe X,” while (I assume you think) a statement “I believe Y” means “I believe Y.”\* > > If that’s your view, then there is, trivially, a contradiction in saying “X and I don’t believe X.” For in your view, that _means_ (doesn’t just pragmatically signal, but _means_) “I believe X and I don’t believe X.” Contradiction. Yes to all with the caveat that when it is a spoken statement or a thought. If, however, it is laid out as a fact by an external party to the logic problem (the teacher, the op, whatever), then it is indeed a fact (or at least a proposition). > [@](#): > > I’m not sure what you think or should think about **ianzin** ’s judge. The judge says “You will be hanged” and “You will be surprised.” In your view, these mean “I believe you will be hanged” and “I believe you will be surprised.” No contradiction there, since the judge is just telling us what he believes. And my assumption is that his belief is based on logically sound reasoning, as opposed to random beliefs. > [@](#): > > He would not even be contradicting himself if he said “You will be hanged” and “You will not be hanged.” For these actually mean, on your view, “I believe you will be hanged” and “I believe you will not be hanged.” No contradiction there. A weird thing to say, but not, on your view, as far as I understand it, contradictory. What? How can those not be a contradiction? ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 11, 2009, 2:52am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/148 "2009-10-11T02:52:28Z")
> [@RaftPeople](#): > > What? How can those not be a contradiction? A contradiction always has the form A & not-A. “I believe X and I believe not-X” does not have the form A & not-A. “Believe(I, X) & Believe(I, not-X)” is not a contradiction. Note that “I believe not-X” is _not the same_ as “I don’t believe X.” The latter denotes a lack of a belief. The former denotes the presence of a belief. “I believe X and I don’t believe X” _would_ be a contradiction. But that’s a different statement than “I believe X and I believe not-X.” ---
**Author:** ![PBear42](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@PBear42](https://boards.straightdope.com/u/PBear42)\ **Post date:** [October 11, 2009, 6:59am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/149 "2009-10-11T06:59:41Z")
> [@ianzin](#): > > Hi **Pbear42**. Sorry, no offence, but what you have written has nothing whatsoever to do with the point I was making. If you go back and read what I wrote, you will see that this is so. How ironic that this rather confirms what I wrote. > > I was not commenting on the fact that some people prefer this or that type of explanation. This is completely irrelevant. > > I was commenting on the fact that _some_ people (and let’s pause for a second to emphasise the word _ **‘some’** _) who have participated in this thread have asserted that a given point or explanation does not make sense or fails to resolve the paradox, while their comments indicate that they have not taken the time to read and understand the very points or explanations they are so swift to dismiss. > > And if it pleases you, I will amend my final clause to say ‘…while _in my opinion_ their comments indicate…’. > > Just for the record, you are correct about my own views concerning the resolution of the paradox. I believe the easiest way to resolve it is to consider an ‘only Friday’ version, and to consider how we would evaluate any statement analogous to ‘I am stating what is going to happen and I am telling you it will be unexpected’. However, to classify this as an ‘epistemological’ approach or solution is incorrect. It has nothing to do with the word ‘epistemological’. It is a case of logical inconsistency. As requested, I’ve reviewed your post, also the earlier ones and those which followed this one. With all due respect (and I’ve noticed you’re a smart guy and a well-regarded poster), I believe my point was well taken. **Nivlac** posted to say, in effect, how can you guys still be talking about this? We gave you the correct answer back on Page 1. You said he was justifiably exasperated and that the continuation of the discussion shows he was right that some people just won’t get it. What I’m saying is that is that there are several ways to look at the problem and no one of them is manifestly correct, as evidenced by the fact that professional philosphers are still wrestling with the problem sixty years after if was first propounded. As for whether the resolution you prefer is epistemelogical, I think so for the reason **Frylock** stated. What follows from the logical inconsistency as you see it (obvious in the one-day scenario, not obvious and I would argue not true in the five-day one) is that the prisoner simply can’t know what to believe. That’s an epistemelogical proposition. I don’t like this resolution (not saying it’s wrong) because it doesn’t go to why most people find the problem interesting. What’s interesting is that the prisoner’s reasoning seems valid and yet, somehow, the judge’s sentence is carried out as stated. Like the Missing Dollar paradox mentioned upthread, we know the prisoner’s reasoning must be invalid, the question is why. The epistemelogical approach is one answer. To me, that backwards induction doesn’t work (for reasons articulated by many posters in this thread and several of the articles I linked in [Post #99](http://boards.straightdope.com/sdmb/showpost.php?p=11644443&postcount=99)) is a better one. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [October 11, 2009, 5:35pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/150 "2009-10-11T17:35:53Z")
> [@Frylock](#): > > A contradiction always has the form A & not-A. “I believe X and I believe not-X” does not have the form A & not-A. > > “Believe(I, X) & Believe(I, not-X)” is not a contradiction. > > Note that “I believe not-X” is _not the same_ as “I don’t believe X.” The latter denotes a lack of a belief. The former denotes the presence of a belief. > > “I believe X and I don’t believe X” _would_ be a contradiction. But that’s a different statement than “I believe X and I believe not-X.” But you could derive a contradiction from that information right? If your answer is no, then clearly the judge’s statement can not be contradictory, by this same reasoning, right? Here’s the more important question back on topic (it seems like you do, but just wanted to make sure): Do you believe the judge’s statement is contradictory? ---
**Author:** ![PlainJain](https://avatars.discourse-cdn.com/v4/letter/p/5daacb/32.png) [@PlainJain](https://boards.straightdope.com/u/PlainJain)\ **Post date:** [October 11, 2009, 5:59pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/151 "2009-10-11T17:59:38Z")
Here’s the problem in my opinion: “\* His reasoning is in several parts. He begins by concluding that the “surprise hanging” can’t be on a Friday, as **if** he hasn’t been hanged by Thursday”\* On Tuesday (for example) the “if” hasn’t happened yet. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 11, 2009, 6:09pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/152 "2009-10-11T18:09:22Z")
> [@RaftPeople](#): > > But you could derive a contradiction from that information right? If your answer is no, then clearly the judge’s statement can not be contradictory, by this same reasoning, right? > Here’s the more important question back on topic (it seems like you do, but just wanted to make sure): > Do you believe the judge’s statement is contradictory? If you mean the statement “You’ll be hanged on one of the five days from Monday to Friday, at noon, and when you find out you are to be hanged on that day, you will be surprised,” then no, I don’t think the statement is contradictory. I think it’s self-defeating in ways I’ve been talking about, but I don’t think that the statement, in and of itself, contains a contradiction. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [October 11, 2009, 6:13pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/153 "2009-10-11T18:13:26Z")
To everyone who complains that the 5 day scenario isn’t the same as the 1 day scenario, what about the 2 day scenario? Is the 2 day scenario equivalent to the 5 day scenario? It certainly is. "You will be hanged on Monday or Tuesday. You will be surprised about the day of the hanging. " Therefore, if the prisoner is not hanged on Monday, he’ll know he’ll be hanged on Tuesday. But then a hanging on Tuesday would not be a suprise, and therefore can’t be hanged on Tuesday. Therefore, the prisoner knows he will be hanged on Monday. Therefore, he can’t be hanged on Monday, because he can predict he will be hanged on Monday. Therefore, a hanging on Monday would not be a suprise, and therefore he can’t be hanged on Monday. Therefore, the 2 day scenario is the same as the 5 day scenario. The only resolution that makes both statements from the Judge true is that, since the prisoner won’t be suprised on either day, he’ll be surprised on either day. Note that this means that in the 5 day scenario, you can’t rule out Friday either, because the prisoner rules it out, and then when it happens he’s suprised! And so, since the prisoner can be surprised by a hanging on Friday (since he ruled it out since it wouldn’t be suprise), he can be surprised on ANY DAY. And this is why the 1 day scenario is the same as the 5 day scenario. The Judge says, “You will be hanged in 10 minutes. You will be suprised by the hanging.” The prisoner therefore reasons that since he knows he’ll be hanged in 10 minutes, he won’t be surpised by the hanging, therefore there can’t be a hanging since it wouldn’t be a surprise, therefore when the Judge hangs him 10 minutes later the prisoner is surprised. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [October 11, 2009, 7:55pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/154 "2009-10-11T19:55:47Z")
**Lemur866** , the evidence I would offer that the 5 day is not the same as the 1 day, is that in the real world, I can surprise you by choosing a day early in the week (if you haven’t already, take my spoiler test on page 3), but I can’t surprise you with only 1 day. So, there is clearly a difference in the real world. Also, as a side note, I don’t think the 2 day is the same as the 1 day or the 5 day, but it sure seems closer to the 1 day. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [October 11, 2009, 7:58pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/155 "2009-10-11T19:58:08Z")
> [@Frylock](#): > > If you mean the statement “You’ll be hanged on one of the five days from Monday to Friday, at noon, and when you find out you are to be hanged on that day, you will be surprised,” then no, I don’t think the statement is contradictory. I think it’s self-defeating in ways I’ve been talking about, but I don’t think that the statement, in and of itself, contains a contradiction. Did you read **Pbear’s** first link from his/her post with links to various papers on this, and what do you think of it? ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 11, 2009, 9:14pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/156 "2009-10-11T21:14:14Z")
> [@RaftPeople](#): > > Did you read **Pbear’s** first link from his/her post with links to various papers on this, and what do you think of it? I scanned the Ned Block article, and couldn’t digest it on a first reading so would have to go over it again later–something I don’t presently really have time for. Anticipating similar experiences in the other articles, I didn’t read them. None of **Pbear** ’s summaries, though, mention any of the articles claiming that the judge’s statements are in contradiction. Moreover, I confess I’d be extremely surprised if any of them did. The idea that the statements (the ones I put in quote marks in my previous post) are contradictory goes against my deepest Logic 101 instincts. The statements defeat themselves, but they are not contradictory. ---
**Author:** ![Delayed\_Reflex](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/delayed_reflex/32/3172_2.png) [@Delayed\_Reflex](https://boards.straightdope.com/u/Delayed_Reflex)\ **Post date:** [October 11, 2009, 11:08pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/157 "2009-10-11T23:08:39Z")
I generally agree with **Frylock** that there is no inherent contradiction in the judge’s statement. If we take a look at **ianzin** ’s breakdown on the first page: > [@ianzin](#): > > I studied this paradox as part of my philosophy degree. I have also read Martin Gardner’s excellent commentary on the problem, which is probably the most lucid and succinct. > > The judge’s assertions constitute a contradiction, but the wording disguises this fact so it is not immediately obvious. > > Thr simplest way to see this is to consider a case where there is only one possible day for the hanging, and that day is tomorrow. The judge’s assertions would sound like this, ‘You will be hanged tomorrow, but you will not know in advance that you will be hanged tomorrow’. The first assertion informs the prisoner that something is going to happen, but the second assertion informs the prisoner that he will not know it is going to happen. **If the judge expects the first assertion to be believed (considered true), then he cannot consistently expect the second part to be believed** - and vice-versa. It has to be one or the other: _either_ he will be hanged tomorrow _or_ he will not know it is going to happen. One cannot consistently assert both. > > The situtation is analogous to me pointing to a box I’ve placed in front of you and saying, ‘When you open the box and find a penny inside, you will be surprised’. At most, one of these assertions can be true. But not both. > > The customary wording of the problem involves a _range_ of possible days for the hanging (= all of the supposedly possible days involved in ‘next week’). This tends to mask or disguise the self-contradictory nature of the judge’s set of assertions; nonetheless the self-contradiction remains, which is why the prisoner’s reasoning leads to an apparent contradiction. (bolding added) I do not think that the bolded section necessarily follows - the judge could be making the statement assuming that the prisoner will NOT believe it to be true. I think there are actually two separate properties that the judge is making a statement on: 1. Whether the prisoner will be hanged tomorrow 2. Whether the prisoner THINKS that he will be hanged tomorrow It seems to be assumed that the judge saying “You will be hung tomorrow” leads to the prisoner believing “I will be hung tomorrow”, but this doesn’t necessarily follow, does it? In fact, we can see by the prisoner’s logic that for 2), one of the expected results of the judge’s statements are that the prisoner does NOT believe that he will be hung tomorrow (the other expected result is that he expects to be hung, but will not be surprised). I think **Frylock** is pointing out that since the fact of whether the prisoner will be hanged tomorrow is a separate property from what the prisoner believes, the two statements are not contradictory. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [October 11, 2009, 11:34pm UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/158 "2009-10-11T23:34:43Z")
> [@Frylock](#): > > I scanned the Ned Block article, and couldn’t digest it on a first reading so would have to go over it again later–something I don’t presently really have time for. Anticipating similar experiences in the other articles, I didn’t read them. If you skip to page 57 you will at least see his reasoning for why he thinks the student’s logic is invalid. > [@](#): > > None of **Pbear** ’s summaries, though, mention any of the articles claiming that the judge’s statements are in contradiction. Moreover, I confess I’d be extremely surprised if any of them did. The idea that the statements (the ones I put in quote marks in my previous post) are contradictory goes against my deepest Logic 101 instincts. The statements defeat themselves, but they are not contradictory. Not sure why you state this, hopefully I didn’t give you the impression that they did, although other posters did make that claim about the judge’s statements. I scanned back through the thread and I don’t see how you think the judge’s statements are problematic, can you summarize? Also, do you believe the 1 day case is the same as the 5 day case? If so, can you provide any kind of logic that takes us from 5 days down to 1 without losing any critical elements of the problem (the most critical being that there are multiple days in the future that can not be eliminated as a possible choice with evidence to support being my spoiler test)? As a side note, in that article, Ned Block also concludes that the 5 day is significantly different than the 1 day. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 12, 2009, 12:23am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/159 "2009-10-12T00:23:22Z")
> [@RaftPeople](#): > > If you skip to page 57 you will at least see his reasoning for why he thinks the student’s logic is invalid. Thanks, I’ll take a look. > [@](#): > > Not sure why you state this, hopefully I didn’t give you the impression that they did, although other posters did make that claim about the judge’s statements. Oh, I said it because in the post where you asked if I’d read the articles, you seemed to be asking that in response to a post of mine which you were quoting–and in that quote, what I’m saying is that the statements aren’t contradictory. So I thought you were asking if I’d checked the articles for arguments against the claim that they’re not contradictory. But I bet you didn’t mean for the relationship between the quote and your question to be that direct. Sorry about that. > [@](#): > > I scanned back through the thread and I don’t see how you think the judge’s statements are problematic, can you summarize? In both the five day and the one day case, by saying one thing (“…you will be surprised…”) the judge makes it impossible for the hearer to accept the other thing he says (“…you will be hanged…”). (Not that he makes it impossible for the hearer to believe he will be hanged, but rather, he makes it impossible for the hearer to accept _the judge’s word_ that he will be hanged.) > [@](#): > > Also, do you believe the 1 day case is the same as the 5 day case? I’m actually very interested in this question now that it’s been brought up. I’d instinctively say they are substantively identical, but I suspect I need to think about it more. Sorry I can’t say more than that. > [@](#): > > If so, can you provide any kind of logic that takes us from 5 days down to 1 without losing any critical elements of the problem (the most critical being that there are multiple days in the future that can not be eliminated as a possible choice with evidence to support being my spoiler test)? But what about **Indistinguishable** ’s point that apparently valid reasoning should lead us to be surprised in the one day case as well? “He said it would be a surprise. But if I were to be hanged tomorrow, it _wouldn’t_ be a surprise, since I know about it already. So it must be that I’m not going to be hanged tomorrow after all.” And—surprise! He’s hanged. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [October 12, 2009, 2:02am UTC](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993/160 "2009-10-12T02:02:49Z")
> [@Frylock](#): > > But what about **Indistinguishable** ’s point that apparently valid reasoning should lead us to be surprised in the one day case as well? “He said it would be a surprise. But if I were to be hanged tomorrow, it _wouldn’t_ be a surprise, since I know about it already. So it must be that I’m not going to be hanged tomorrow after all.” And—surprise! He’s hanged. That hinges on specific reasoning by the prisoner whereas the 5 day does not. **1 day scenarios:** 1. Prisoner concludes no hanging In this case he is hanged and surprised, judge is successful 2. Prisoner concludes no surprise In this case he is hanged but not surprised, judge failed 3. Prisoner realizes this is a difficult logic problem and decides not to reason at all In this case he is hanged and surprised because he didn’t know what to expect, judge is successful **5 day scenarios:** Regardless of what the prisoner reasons, he can not entirely eliminate the “hanged and surprised” result. This has been proven in real world tests. 🙂 That’s the difference. [Previous page](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993.md?page=7) [Next page](https://boards.straightdope.com/t/the-unexpected-hanging-paradox/511993.md?page=9)