The unexpected (?) hanging

[KrazyHorse]

Examine proposition (c) carefully: "you will not know in advice that you are to be hanged."

I.e. you have no idea if you will ever get hanged. However if you do get hanged, then
(a) it will happen next week and
(b) it will happen at noon.

Zevico, I had a typo. "that you are to be hanged" was supposed to be logically equivalent to the original c

EDIT: change the "that" to a "when" and you'll see what the point was.

[KrazyHorse]

As far as why the lack of NECESSITY to be hanged removes the contradiction, it is very straightforward.

Try using the logic that the prisoner originally used to demonstrate he couldn't be hanged any day of the week. It fails at step 1. He now CAN be hanged on Sunday, because the lack of a REQUIREMENT that he be hanged that day means that he will not be certain when he wakes up on Sunday whether or not he will be hanged that day, thus the contradiction will be removed.

Again, this is very straightforward if you reduce the entire problem down to its barest essentials. A prisoner is told at 6am that

a) he will be hanged that day
b) he will be hanged at noon
c) he will not know in advance when he is to be hanged



The fact that so many of you are obviously struggling with this is hilarious to me.

[Zevico]

Maybe some day I'll be just as smart as you.

[KrazyHorse]

I doubt it.

[chequita guevara]

I voted for self-defeating logic. Since the prisoner thinks he cannot be hanged, he cannot know in advance that he is to be hanged.

[YurYu]

Try using the logic that the prisoner originally used to demonstrate he couldn't be hanged any day of the week. It fails at step 1. He now CAN be hanged on Sunday, because the lack of a REQUIREMENT that he be hanged that day means that he will not be certain when he wakes up on Sunday whether or not he will be hanged that day, thus the contradiction will be removed.

Yes, of course. I knew that all along. Obviously...
If you put it that way it IS pretty obvious. What surprises me how most people here (including me) fail to grasp this basic form of logic instantly.

Human minds wtf

[KrazyHorse]

It's not at all surprising. I'm just being a bit of a dick.

Most people aren't asked to think rigourously, so they don't learn how to. Throw in the usual fuzziness of natural language and you can usually get people going round in circles without too much effort.

Our brains seem to be hardwired for at least an approximation of deductive reasoning. The problem is that it's only an approximation unless you apply conscious effort. With enough practice it becomes effortless.

[loinburger]

I read a study a long time ago (wish I could find it again) that found that people really suck at abstract logic questions but do much better if the question involves money in some way. "Can you apply modus tollens to answer these simple questions?" "Nope." "How about if the simple questions involve money?" "Hell yes."

[Solomwi]

I'm interested to know what the hell people mean by claiming (b)

At least one of them claimed (b) simply to irritate others, since the resolution had already been given in the thread.

The man's reasoning is similar to the reasoning behind the rational strategy in a finite series of prisoner's dilemma, as are the results (defect every time v. can't be hanged on any day).

[Lul Thyme]

I read a study a long time ago (wish I could find it again) that found that people really suck at abstract logic questions but do much better if the question involves money in some way. "Can you apply modus tollens to answer these simple questions?" "Nope." "How about if the simple questions involve money?" "Hell yes."

Read something similar a few months ago.

They tested people in two different set ups.

Set up A : you are a police in a bar. There are some people in this bar. Some are adults, some are minors. Some are drinking juice, some alcohol. You know only one "information" about each person out of :
-this one is a minor
-this one is an adult
-this one is drinking juice
-this one is drinking alcohol
The question is, which people must you "check" (that is discover the missing information) to make sure that only adults are drinking alcohol.

Set up B : cards have two sides, on one side is an integer either even or odd, on the other a color, either red or green.
There are a bunch of cards on the table, you can only see one side of each card (so you see either odd, even, red or green).
The question is which of these 4 "type" of cards must you flip over to check whether the statement "on the other side of every green cards is an even integer" is true.



I'm paraphrasing here, but in the original study, the set ups were phrased much closer, with the only difference being the context (the questions are logically equivalent). Results were that people were much fast and more correct in the first setup than in the second one. I've tested this with a few friends and the difference is striking. Even people that are "trained" like KH says, will at least get the second one right (as opposed to most people), but will still take a little longer than in the first set-up. It's a bit like it's a different part of your brain solving it. In one case, logical thinking, while in the other it's somehow just "instinctive".

[MikeH]

If you give them those scenarios back to back anyone 'trained' should immediately spot that it's the same question again and get it instantly.

[Lul Thyme]

If you give them those scenarios back to back anyone 'trained' should immediately spot that it's the same question again and get it instantly.

I've actually done this to a few math grads and even when asked back to back, it takes a few more seconds to do the card one. Even after spotting the fact that it's the same problem, it takes a moment to "map" it back to the previous problem.

[Dry]

Read something similar a few months ago.
the set ups were phrased much closer, with the only difference being the context (the questions are logically equivalent).

Then, either the question to the first problem has to be:
which people must you "check" (that is discover the missing information) to make sure that all minors are drinking juice.

Or, the question to the second problem has to be:
only the cards with red backs have an odd integer

Otherwise, while logically equivalent, the questions are not strictly equivalents.

[Nikolai]

This thread is silly. Also, sunday is the last day of the week, so this thread is double-silly.