Unanswerable multiple choice question

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/Gödels_incompleteness_theorems

Just because you title something an "Unanswerable question" doesn't mean it actually is, and certainly doesn't mean the first incompleteness theorem is relevant.

jaekwon• 16 years ago

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

sordidarray• 16 years ago

Godel's Incompleteness Theorems are probably some of--if not the most---misunderstood concepts in all of mathematics (rivaling Cantor's Uncountability Theorem).

While the usual analogy for the first theorem is drawn to the liar's paradox ("This is a false statement."), it's important to remember that it is only an analogy. The first theorem states, in layman's terms, that we can construct a valid mathematical statement which is complete and utter nonsense. (Much like "This is a false statement." is neither true nor false, but nonsensical.)

The second incompleteness theorem simply states (again, in layman's terms) that the consistency (where we say something is consistent if it contains no contradictions) of certain systems cannot be shown from the rules of the system itself. (Or alternatively and more correctly, if you're able to show the consistency of these systems using their own rules, then they're inconsistent.)

That said, please remember that these are mathematical theorems and as such their "applications" to other areas such as metaphysics, even by their creator, are not rigorous or necessarily meaningful. They live where they belong: in the depths of mathematical logic, in the heart of mathematics.

RevRal• 16 years ago

The answer is. . . A plus D.

(Seriously, if I saw this on a test I'd just circle A and D then write "= 50%".)

gurtwo• 16 years ago

I say B. Now prove me wrong.

jey• 16 years ago

"You're wrong because the answer key says so. Were you not paying attention when I gave the answers to use during the 'review' session?"

pathik• 16 years ago

wendroid• 16 years ago

Your rubric doesn't denote whether I can answer more than one item for the question therefore based on "you can only choose one" then 25% is the chance of being right, as the correct answer is still one of A,B,C,D.

david• 16 years ago

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.

LaPingvino• 16 years ago

I choose E) 20%

jonsen• 16 years ago

The answer is C because it's B.

ErrantX• 16 years ago

A B C D

(as it is not specified that only one must be chosen)

EDIT: the problem is ill defined...

clvv• 16 years ago

Saw this one before and if that was the source of this, then the answer will be E) 0% What a nice one!

rontol2• 16 years ago

B) for me

jjs• 16 years ago

0% chance.

Answering randomly may give you a result that coincidentally matches the truth, but you have provided no logical or epistemological support for your choice, nor any chain of reasoning that leads you from the available evidence to a conclusion that there even is a correct answer.

You have a 25% chance of randomly choosing the "right" answer, (C) 0%, but no paradox is created because you answered without establishing knowledge of the answer, and therefore your answer cannot rightly be called correct.

rontol2• 16 years ago

Normally it would be 1 out 4 = 25% but if all answer given in the list is wrong then 0%

The answer is not in the list thus unanswerable?

sqrt17• 16 years ago

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.

goodside• 16 years ago

A more distilled version:

Which of the following is the answer to this question?

A) B

B) A

yaroslavvb• 16 years ago

Except here you could say "both are correct" or "neither are correct", whereas in the original question those also cause a paradox

JoeAltmaier2• 16 years ago

If "I" choose the answer, I use a weighted 4-sided die that comes up "B" half the time. So B is correct.

cb18• 16 years ago

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%

paraschopra2• 16 years ago

I refuse to play silly mind games which make me feel incompetent.

stcredzero2• 16 years ago

A good way to discourage learning in fields like mathematics, science, and programming.

paraschopra2• 16 years ago

Most problems in mathematics, science, and programming aren't as silly as this one.

techiferous• 16 years ago

My random answer is "splorichoo".

danteembermage• 16 years ago

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"?

Ashtone• 16 years ago

If I choose to answer this question at random (with the constraints of having to choose one of the choices) then the chance of it being correct is going to be 25%, because I am answering at RANDOM, therefore not using any intellect and not applying any sense to the question.

However, the question merely states IF you choose, not that you have to.

Therefore, I am entirely correct by answering either A or D.

Thus it is not unanswerable and is incorrect in stating so.

jheriko2• 16 years ago

i don't get it... maybe i'm being incredibly dense but it looks like it should be B. this makes the correct answer 25%, so the probability of getting it right at random is 50% because 2 out of 4 answers are 25% - so the answer is B = 50%, and indeed the chance of choosing B is 25%

answering the question at random is not the same as answering the question posed - so the fact that the two answers are not equal shouldn't be a problem. right?

edit: i hate paradoxes, i'm pretty certain i'm wrong, but i can't put my finger on precisely why. :)

Unanswerable multiple choice question

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