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Unanswerable multiple choice question

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Re: Unanswerable multiple choice question

#41

Post by sqrt17 »

Since A and D give you the same result, the question is a "check all that apply question". Excluding contradictory combinations, there are four answers:

* nothing checked (i.e., none of A,B,C,D)

* A+D

* B

* C

Assume the correct choice is among these four answers (it is, since we also include a "none of these" option); then you have a one-in-four chance to get it right. Hence, A+D is right.

If this is not a "check all that apply" question, then having both A and D is contradictory and the person posing this question deserves a whack on the head.

Re: Unanswerable multiple choice question

#42

Post by ZachPruckowski »

kqr2 wrote: post #8
pook wrote: post #2

It is answerable... with a swift kick to the balls of the person asking it.

But there's only a 50% chance that the person asking that will have balls.

I would speculate that of the people to ask annoying trick questions, the vast majority of them are smug males.

Re: Unanswerable multiple choice question

#45

Post by JoeAltmaier »

tdmackey wrote: post #26
jaekwon wrote: post #18

Earlier quoted context omitted.

Is "The above question has no solution", which is choice C, not a Godel sentence?

No. Godel's incompleteness theorems say nothing about non-arithmetical or non-mathematical statements nor do they apply in contexts where no formal system exists. Some sort of paradox, sure, but Godel doesn't apply. Truth is not a mathematical concept, and determining the "truth" or "falsehood" of a sentence has nothing to do with Godel's incompleteness theorems.

Boolean logic is an "arithmetic system"

Re: Unanswerable multiple choice question

#46

Post by cb18 »

Where is correctness defined?

What is the antecedent for 'it,' the 'answer' or the 'question'?

Does this phrase even make sense? I suspect it is supposed to be some 'recursive cleverness,' or just not make sense?

C) 0% because for something to be correct it follows that it fits a given definition of correctness of which none is given.

now the recursion has started to work based on the above reasoning

So if C)0% is the "correct answer"(that is, there is no correct answer) then choosing an answer at random will be correct 25% of the time, if you shift to viewing 25% as the "correct answer" then you have a 50% chance of randomly selecting a "correct answer"

what is the chance [the question] will be correct? C)0%

q1=what is the chance [the question] will be correct?

what is the chance [an answer to q1] will be correct? 25%

q2=what is the chance [an answer to q1] will be correct?

what is the chance [an answer to q2] will be correct? 50%

Re: Unanswerable multiple choice question

#47

Post by jaekwon »

Chirono wrote: post #33
jaekwon wrote: post #24

Earlier quoted context omitted.

Can you prove or disprove this statement? "Godel's first incompleteness theorem is a Godel sentence" Anyways, it is my belief that Godel's Incompleteness Theorem is false by definition of Truth. That is, what is true is provable and vice versa. Once you depart from this definition, you get statements that are paradoxical, and by my definition of Truth, the Godel Incompleteness Theorem is certainly paradoxical (thus F…

The thing is, that Godel's theorem is provable. So by your definition, it is true. The usual definition of false is not "I can't prove it's true" as that is pretty hard to decide. Suppose I have a statement S that I can't prove. Is it false, or am I just not clever enough to prove that it is true? The normal definition of S being false is that the negation of S is true. Part of what the incompleteness theorem says is…

Well, my definition does not imply that what is False is easy to decide, and that's OK. If N != NP, then the statement "X is factorable" would be hard to decide, even if it's False (or True for that matter).

Godel, in the proof of GIT, chose inconsistency (by concluding that G is True, even though it is also False).

So, by your own conclusions, I choose GIT to be false, and there are no contradictions.

Re: Unanswerable multiple choice question

#50

Post by danteembermage »

Completely different question:

This question is posed to a large number of people who all attempt to answer is correctly. "What fraction of respondents answered the same as you? a) 25% b) 50% c) 0% d) 25%"

If you choose the answer to this question at random, what is the chance it will be correct?

What if you change it to "What fraction of respondents not including you answered the same as you"?

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