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Tim Cooke
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If you choose an answer to this question at random, what is the chance you will be correct?
a) 25%
b) 50%
c) 60%
d) 25%
 
Stephan van Hulst
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I think Kurt Gödel would have something to say about that.

One of those answers might be correct, but it can not be proven within the framework of the question.
 
Henry Wong
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I can argue that this is somewhat similar to Schrödinger's cat. The act of trying to answer the question, would affect the answer...

Henry
 
Paul Anilprem
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The question seems fallacious. Something like, "Can God create a stone that he himself cannot lift?"
 
Stephan van Hulst
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Not necessarily. I'm going to assume that your question has a couple of premises:

p) God can lift all stones.
q) God can create a stone he cannot lift.

The question "p AND q ?" leads to a direct logical contradiction.

However, the question that Tim posed is self-referential, meaning you can not construct a logical statement that can be proven in a mathematical framework that is both complete and consistent, as per Gödel's incompleteness theorems.

[edit]

tl;dr: Paul's question has a definite answer: "no". Any answer to Tim's question can not be proven.
 
Paul Anilprem
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Stephan van Hulst wrote:Not necessarily. I'm going to assume that your question has a couple of premises:

p) God can lift all stones.
q) God can create a stone he cannot lift.

The question "p AND q ?" leads to a direct logical contradiction.

However, the question that Tim posed is self-referential, meaning you can not construct a logical statement that can be proven in a mathematical framework that is both complete and consistent, as per Gödel's incompleteness theorems.

[edit]

tl;dr: Paul's question has a definite answer: "no". Any answer to Tim's question can not be proven.

The premise that you need to consider is that God is God, He can do everything (not just lift all stones). The question cannot be answered because the question is based on an assumption that is contradictory to both the answers of the question. "No" answer implies God cannot create a stone of certain property thus contradicting God can do everything and "Yes" answer implies God cannot lift a particular stone, thus contradicting that God can do everything.
 
Jeanne Boyarsky
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You made my brain hurt first thing in the morning!
 
Paul Anilprem
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Tim Cooke wrote:If you choose an answer to this question at random, what is the chance you will be correct?
a) 25%
b) 50%
c) 60%
d) 25%

Now, that I am thinking about it. The question starts with an "If". It doesn't ask you to actually answer it randomly. That means the possibility of picking one correct answer out of 4 is 25%. Hence answer to this should be a).
 
Stephan van Hulst
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Exactly. You just added another trivial premise:

r) God is omnipotent

The truthfulness of this premise is equivalent to "p AND q" if we are in a universe with no other premises (or: all anybody can do at a given moment is lift stones or not lift stones).

There is a simple logical conclusion from this. We just proved that God is not omnipotent.

There is a difference between logic statements that have flawed premises and logic statements that are improvable. Yours has a flawed premise. Tim's is improvable.
 
Stephan van Hulst
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Paul Anilprem wrote:Now, that I am thinking about it. The question starts with an "If". It doesn't ask you to actually answer it randomly. That means the possibility of picking one correct answer out of 4 is 25%. Hence answer to this should be a).

No. If there are two correct answers among four possible answers, statistically you'll have 50% chance to randomly pick the right one. The question here is, how many correct answers are there? Any answer to that question is improvable.

Refer to Russell's Paradox.
 
Paul Anilprem
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Stephan van Hulst wrote:
Paul Anilprem wrote:Now, that I am thinking about it. The question starts with an "If". It doesn't ask you to actually answer it randomly. That means the possibility of picking one correct answer out of 4 is 25%. Hence answer to this should be a).

No. If there are two correct answers among four possible answers, statistically you'll have 50% chance to randomly pick the right one. The question here is, how many correct answers are there? Any answer to that question is improvable.

Refer to Russell's Paradox.

The problem statement says, "choose an answer". I imagine it implies there is one correct answer out of four and "what if" you picked one randomly? There will be 25% chance that you will answer it correctly. Not sure why should it be interpreted has having a variable number of correct answers.
 
Stephan van Hulst
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Paul Anilprem wrote:I imagine it implies there is one correct answer out of four and "what if" you picked one randomly?

That's not how statistics works. It doesn't imply there is one correct answer. There could be multiple correct answers. There could be no correct answer. What if the four possible answers were:

a) 100%
b) 100%
c) 100%
d) 100%

If you picked one at random and followed your logic, your answer would still be 25%, even though statistically you have 100% change of randomly picking the correct answer. Statistics deals with information you know A Priori. If the possible answers in the original question were whited out, you would be correct to say 25%. However, you know the possible answers A Priori, so you have to factor that into your statistical analysis.
 
Stephan van Hulst
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https://en.wikipedia.org/wiki/Prior_probability
 
Tim Cooke
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Jeanne Boyarsky wrote:You made my brain hurt first thing in the morning!
Doesn't it just.

This thread turned out much better than I could ever have hoped. Great stuff.
 
Paul Anilprem
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Stephan van Hulst wrote:
Paul Anilprem wrote:I imagine it implies there is one correct answer out of four and "what if" you picked one randomly?

That's not how statistics works. It doesn't imply there is one correct answer. There could be multiple correct answers. There could be no correct answer. What if the four possible answers were:

a) 100%
b) 100%
c) 100%
d) 100%

If you picked one at random and followed your logic, your answer would still be 25%, even though statistically you have 100% change of randomly picking the correct answer. Statistics deals with information you know A Priori. If the possible answers in the original question were whited out, you would be correct to say 25%. However, you know the possible answers A Priori, so you have to factor that into your statistical analysis.

To be honest, I am not sure what are you talking about. I am not an expert in this area so I will assume that you know what you are talking about
To me, the problem statement clearly shows 4 different options and one out of those 4 options is indeed a correct option. The only thing that is left to be considered is "what if".

 
Stephan van Hulst
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Paul Anilprem wrote:To me, the problem statement clearly shows 4 different options and one out of those 4 options is indeed a correct option.

Here's where the issue lies. From what do you deduce that there's exactly one correct option among the four given options?
 
Paul Anilprem
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Stephan van Hulst wrote:
Paul Anilprem wrote:To me, the problem statement clearly shows 4 different options and one out of those 4 options is indeed a correct option.

Here's where the issue lies. From what do you deduce that there's exactly one correct option among the four given options?

I guess it is the format of the question. There is a problem statement asking you to select "an" answer and it is coupled with 4 options. Supporting question banks containing 1000s of such questions has preconditioned my mind
 
Stephan van Hulst
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Here's what I like about the original question:

I can answer c) 60%, and nobody will be able to prove that I'm wrong.
 
Bear Bibeault
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Henry Wong
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Hmmm. What if I choose to ... not make a choice?

 
Stephan van Hulst
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Campbell Ritchie
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The only winning move is not to play? Has anybody asked Yossarian?
The Klein bottle is of course designed specifically to have only one “side” which is neither inside nor outside. Or maybe both simultaneously.
 
Piet Souris
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What a nice confusing puzzle this is! Thanks for sharing.

It doesn't remind me so much of Gödel, but more of that famous question: is the sentence "this sentence is untrue" true? (or similar: is the sentence "the sentence 'this sentence in untrue' is untrue" true or untrue?).

And maybe, given Stephans remarks, it is even more fun to add a fifth option: e) 0% (and adjust the other percentages accordingly).
 
Tim Cooke
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I shared this with my team at work during the week. There was some furious head scratching going on for a while but they seemed to enjoy it as much as you lot did.
 
L Foster
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Fun question.  This comes down to certain assumptions:
1. The four 'answers to the question' are the letters A, B, C, and D.
2. The question is not fair, because one of the percentages is listed twice (an argument will ensue if the correct answer _value_ is "25%", but that's irrelevant).

Therefore the odds of getting it right are 25%, because there are four answers (A,B,C,D), and despite the unfairness, if the correct answer is 'A', then 'D' will be considered wrong.

I know that is a different take.  Usually, folks would take the "question" to be "If you choose...".  But I am backing off from the actual text, and considering the four percentages as answers to a nonsense question, that a "random answerer" is going to ignore anyway.
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