What is the incorrect answer to this question?

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Girl-With-A-Math-Fetish
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What is the incorrect answer to this question?

Postby Girl-With-A-Math-Fetish » Sun Aug 31, 2014 10:55 pm UTC

Is this an existing paradox? If so, would it be possible to actually provide a "correct" incorrect answer since it's not Boolean in nature?
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Re: What is the incorrect answer to this question?

Postby eSOANEM » Sun Aug 31, 2014 11:20 pm UTC

There is no valid response for the same reason there is no set of all sets that do not contain themselves.
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Re: What is the incorrect answer to this question?

Postby Girl-With-A-Math-Fetish » Mon Sep 01, 2014 10:55 pm UTC

eSOANEM wrote:There is no valid response for the same reason there is no set of all sets that do not contain themselves.

How is it like that paradox? I mean, I can see that in terms of self-referentiality, but it seems more like the "this statement is false" paradox, not the recursive set of all sets paradox.
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Re: What is the incorrect answer to this question?

Postby firechicago » Mon Sep 01, 2014 11:37 pm UTC

Girl-With-A-Math-Fetish wrote:How is it like that paradox? I mean, I can see that in terms of self-referentiality, but it seems more like the "this statement is false" paradox, not the recursive set of all sets paradox.

I think it's more like the barber who shaves everyone who doesn't shave themselves.

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Re: What is the incorrect answer to this question?

Postby gmalivuk » Tue Sep 02, 2014 12:28 am UTC

Girl-With-A-Math-Fetish wrote:
eSOANEM wrote:There is no valid response for the same reason there is no set of all sets that do not contain themselves.

How is it like that paradox? I mean, I can see that in terms of self-referentiality, but it seems more like the "this statement is false" paradox, not the recursive set of all sets paradox.

The correct answer to the question is in the set of all statements that are not correct answers to the question. That adds a bit of structure to it that the Liar Paradox doesn't have, but that Russell's Paradox (and the barber version) do.
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Re: What is the incorrect answer to this question?

Postby Farabor » Wed Sep 03, 2014 2:13 am UTC

My advice for a reference on this and many other beautiful concepts is a book everyone should read: Gödel, Escher, Bach: An Eternal Golden Braid." Go get it, now. It addresses, amongst other things, paradoxes and self reference quite well.

(On a side note, I love the Gödel filter here!)

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Re: What is the incorrect answer to this question?

Postby Qaanol » Thu Sep 04, 2014 12:12 am UTC

Smoking crack.

Smoking crack is always the incorrect answer.
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Re: What is the incorrect answer to this question?

Postby mathmannix » Fri Sep 12, 2014 3:52 pm UTC

Girl-With-A-Math-Fetish wrote:What is the incorrect answer to this question?


This answer is incorrect.
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Re: What is the incorrect answer to this question?

Postby Quizatzhaderac » Tue Sep 16, 2014 3:57 pm UTC

An incorrect answer is to silently put one's shoes on their head and walk out of the room.

The action described in blue is an incorrect way to answer the question. The context in green and it's reference to the blue action is a correct answer. This resolves the paradox because Green referencing Blue is a qualitatively different answer than Blue.

This is only an answer that doesn't create a paradox, and isn't technically correct, since you asked for "the answer" not "an answer"; an infinite variety of silliness could fulfill the blue spot.

In actuality, I'm using this entire post to answer your question. I could (and will below) answer with a single statement, but I felt an extended explanation was a better way to absorb all of the subtleties at play here.

The best possible answer needs to
  1. be consistent
  2. exhaustive ("the answer" not "an answer")
  3. convey the information you seek.
(1) was covered right away. (3) is covered by the entirety of this post, or just by the answer below if one already understands all the subtleties. (2) can be satisfied by describing the entire set of answers that are incorrect, in lieu of an example of an incorrect answer.

The incorrect answer is any answer that doesn't describe this set of answers (defined exclusively in blue here) as incorrect.

Semantically (in natural languages, computer languages and formal math) recursive things are defined in two steps: The reference first and then the referent. The reference is the name "Blue Set" and it's identification as a set. The referent is the criterion to test a statement for membership in this Blue Set, which includes a reference to the Blue Set, but doesn't require it to be constructed.
The thing about recursion problems is that they tend to contain other recursion problems.


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