Wikipedia:Reference desk/Archives/Language/2016 April 7

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April 7

Unexpected hanging paradox

Why is this called a paradox when it is just wordplay? The judge, by saying that the date of the hanging would be "a surprise", meant simply that it would not have been announced beforehand, not that it could not be deduced. He could very well be hanged on Friday, too, because the reason behind its being unannounced was to make him (or, at least, the average prisoner) wait anxiously and nothing more than that. This prisoner, however, takes the judge's words literally, arguing that, using pure logic, it cannot be unexpected and concludes that it will not happen at all. And, of course, he is hanged on Wednesday and it was a surprise. And it was not a surprise because the judge knew beforehand that he would go through all this train of thought: it was a surprise because the judge meant that the day would be unannounced. (Of course, in this prisoner's case, it was a double surprise because he was certain that he would escape the hanging)--The Traditionalist (talk) 03:11, 7 April 2016 (UTC)

P.S.

Also, I am not sure if I understand how he eliminated Monday. Certainly, using his reasoning, it cannot be on Friday because it is the last day of the week. And it cannot be on Thursday because, if he is alive on Wednesday night then Thursday will not be a surprise. And it cannot be on Wednesday because if he is alive on Tuesday night it cannot be a surprise. And it cannot be Tuesday because if he is alive on Monday night it cannot be a surprise. But how does he know that it cannot be Monday, since he must first reach Monday night for the other days not to be surprises?--The Traditionalist (talk) 03:11, 7 April 2016 (UTC)

if you carefully look at the logic for why he eliminates each day, you'll see it is sound...but then..!!!!..so you get a paradoxical situation where the prisoner is right and the judge is right...so it's a true paradox and, therefore, interesting....68.48.241.158 (talk) 03:29, 7 April 2016 (UTC)

It is certainly interesting but not a paradox: they were both right because they used the word "surprise" differently.--The Traditionalist (talk) 03:39, 7 April 2016 (UTC)

are you sure the answer is so simple? I'd bet you wouldn't find it so interesting if you did!!! :) 68.48.241.158 (talk) 03:43, 7 April 2016 (UTC)

in the same way Tuesday is eliminated because of Wednesday, Monday is eliminated because of Tuesday...68.48.241.158 (talk) 03:36, 7 April 2016 (UTC)

I think it is largely a definitional game, but so are most paradoxes. It's (potentially) interesting because it highlights the trickiness of defining certain words.

Generally the judge explicitly asserts something about the prisoner's belief, saying he won't know/expect the hanging on the day it happens. Maybe a real judge wouldn't say that, but the problem isn't interesting otherwise.

The paradox is just as strong with just two days, and I think it's easier to think about that way. Here are a couple of scenarios to consider:

1. The judge says "you'll be hanged on Monday or Tuesday but won't know (=believe) in advance which day." The prisoner thinks "obviously it can't be Tuesday. It's gotta be Monday. I know it's Monday. But then the judge was lying. But if he was lying then I don't know anything. I might even be hanged on Tuesday. But if I might then how did I know in the first place I wouldn't? But then the judge might have been telling the truth. But..." etc. There's an interesting interplay between the truth value of the judge's statement and the prisoner's thought processes, kind of like a more subtle version of the flip-flopping truth value of the liar's paradox. Can you formalize that?
2. The judge says "you'll be hanged on Monday or Tuesday but won't know in advance which day." The judge is omniscient and speaks the truth. The prisoner thinks "obviously it can't be Tuesday," but the rest of the argument doesn't occur to him, so he believes he'll be hanged on Monday. He isn't hanged on Monday. Now what? Does he now believe he'll be hanged on Tuesday? That hardly seems fair. Obviously if he believes he'll be hanged on every day then the judge never had a chance. To make the problem nontrivial, he oughtn't to be allowed to believe he'll be hanged on more than one day. But then he can be hanged on Tuesday without violating the judge's statement. So even the beginning of the prisoner's reasoning, the part that seems most obviously right, is wrong when you consider it carefully.

-- BenRG (talk) 04:19, 7 April 2016 (UTC)

1b. The one-day version: the judge tells you "you'll be hanged on Monday, but you won't expect it." Come Monday, what do you expect to happen? Clearly the judge is a crazy person. But if you allow yourself to believe that, it's just what he needs to actually be crazy like a fox. But he may really just be crazy; there's no way to know. That uncertainty is enough for him to be right. This version doesn't admit the "unannounced" interpretation. -- BenRG (talk) 04:38, 7 April 2016 (UTC)

• What the paradox really gets at is the imprecision of time-based concepts in language. For example, If I say "You can expect to die soon", then I have only defined the time as "any time after now, out to an undefined point in the near future, however you choose to define that". Even if I say "You can expect to die Monday..." I mean "the interval of time we call Monday" and so on down to smaller and smaller times. The paradox comes in applying the concept of an instantaneous event to an interval of time. Really, it's a calculus problem at it's most abstract: all of our expressions of time exist as intervals where we define the start and end points of the interval. All intervals of time contain an infinite number of instants, so if I tell you "This instantaneous event will happen at some time during this other interval of time" You literally can't predict at which instant within that interval it would happen, because there are an infinite number of instants. Even if I say "You'll die within the next second, but you can never know when", that's strictly true. You know you'll be dead by t = 1 second from now, but you don't know if that will happen at 0.1 second, 0.2 seconds, 0.21 seconds, etc. This paradox plays around with that sort of uncertainty. --Jayron32 13:35, 7 April 2016 (UTC)

see what you're getting at in general...don't think it's relevant to this particular paradox, however...as the days (times) of potential execution are strictly and simply defined...idk..perhaps someone else can chime in...68.48.241.158 (talk) 17:22, 7 April 2016 (UTC)

Yes, but the moment of execution is an instant. That's the source of the paradox; there are always an infinite number of instants (the possible moment they are executed) contained within any arbitrary interval of time. After all, this is just a variation of the good old Zeno's paradox, which is based on the same principle. --Jayron32 17:28, 7 April 2016 (UTC)

there's a lot of paradoxes related to Zeno's/variations on Zeno's...don't think this one is though (ie different category of paradox)...as the particular instant of execution is of no relevance...pretty sure....????68.48.241.158 (talk) 17:36, 7 April 2016 (UTC)

I think people normally treat this paradox as discrete. Sometimes it's explicitly made discrete, for example by having the judge say that the executioners will arrive precisely at noon. Most discussions I've seen could just as well be about, e.g., five cards face down, exactly one of which has a red face, which you turn over in a prescribed order, and the person who set them up claims that you won't know in advance which card is red. -- BenRG (talk) 19:36, 7 April 2016 (UTC)

It's all Greek Dutch to me

I'm trying to figure out where redirects Nederlands and Nederlandse should go. They pointed to Dutch, a dab page, but that doesn't seem right. For the moment, I've set Nederlands to Dutch language, but I'm not sure that that's right, and I have no clue what (if anything) should be done with Nederlandse. Clarityfiend (talk) 22:26, 7 April 2016 (UTC)

Hi. Have you read this RFD discussion? <<< SOME GADGET GEEK >>> (talk) 22:29, 7 April 2016 (UTC)

I have now. Don't know that I agree with it, but the people have spoken. Clarityfiend (talk) 02:59, 8 April 2016 (UTC)

The two are really one word - an adjective meaning simply "Dutch" - with different endings depending on the case of the noun. Used without a noun, as is often the case with such words, they take the case of the assumed noun. Linking to the disambiguation makes sense as the context in which the word is used may be the only thing making the exact sense clear. 217.44.50.87 (talk) 08:49, 8 April 2016 (UTC)

217.44.50.87 is right, they are both forms of a single adjective which can refer to both language and ethnicity/nationality. When used as a noun however, Nederlands refers to the Dutch language, and Nederlandse means "Dutchwoman". I agree that linking to the dab page is best. - Lindert (talk) 09:57, 8 April 2016 (UTC)

I notice that if you search for français or française you get sent to the French DAB. 217.44.50.87 (talk) 10:06, 8 April 2016 (UTC)