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Unanswerable multiple choice question

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Re: Unanswerable multiple choice question

#21

Post by [deleted] »

jaekwon wrote: post #18
tdmackey wrote: post #13

Earlier quoted context omitted.

Gödel's first incompleteness theorem states that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory (Kleene 1967, p. 250) per http://en.wikipedia.org/wiki/Göd…

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

[deleted]

Re: Unanswerable multiple choice question

#24

Post by jaekwon »

[deleted] wrote: post #21
jaekwon wrote: post #18

Earlier quoted context omitted.

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

[deleted]

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 False).

Re: Unanswerable multiple choice question

#25

Post by david »

Well, any multple choice question is going to be unanswerable if none of the choices given are a correct answer.

Since I think most would define a multiple choice question as one with a list of answers from which you pick the correct one, I say this question fails to validate.

Thus not only is this multiple choice question unanswerable, it's not even a multiple choice question. Try wrapping that around your head.

Re: Unanswerable multiple choice question

#26

Post by tdmackey »

jaekwon wrote: post #18
tdmackey wrote: post #13

Earlier quoted context omitted.

Gödel's first incompleteness theorem states that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory (Kleene 1967, p. 250) per http://en.wikipedia.org/wiki/Göd…

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.

Re: Unanswerable multiple choice question

#29

Post by joubee »

spicyj wrote: post #6
[deleted] wrote: post #5

[deleted]

But then you're implying that you'll get a correct answer 1/2 of the time, which means that the answer is B, but then the answer is correct only 1/4 of the time, and you've got yourself in an infinite loop.

x^y/y = z x= chance of a correct answer (1/4) y= number of random attempts

1/4^2 divided by 2 = 1/32 (The odds of picking the correct answer twice in two attempts) and so on..... the more you try the less chance you have of succeeding so just give up and cheat off the guy next to you. I made this crap up so what's the chance of it being right? a)0% b)0^ c)what he wrote d)no chance

Re: Unanswerable multiple choice question

#30

Post by [deleted] »

jaekwon wrote: post #24
[deleted] wrote: post #21

Earlier quoted context omitted.

[deleted]

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…

[deleted]
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