**Next message:**Eugene Leitl: "Re: "analog computer" = useless hypothesis?"**Previous message:**Eliezer S. Yudkowsky: "Re: MATH/COMP/PHIL: "Omega Man""**In reply to:**Lee Corbin: "Re: MATH/COMP/PHIL: "Omega Man""**Next in thread:**CurtAdams@aol.com: "Re: MATH/COMP/PHIL: "Omega Man""**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

<snip>

*> The formalists were pretty upset; and, although I don't
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*> really like the metaphor, the image that does come to
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*> mind that fits the metaphor is The List of All True Math
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*> Relationships (listed in the appendix of God's Book,
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*> according to Paul Eotvos--- 'scuse the spelling, it's
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*> pronounced Ehrdish).... anyway, The List has lots of
*

His name is Pál Erdös -- not Paul Eotvos; I presume?

*> Relationships that can't properly be called Theorems
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*> because they don't have proofs. Each such unprovable
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*> theorem WOULD indeed look like a gaping hole to a
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*> formalist.
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<snip>

*> Here is a puzzle that I formulated on this subject that's fun.
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*> A great mathematician is at a party, and two students come
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*> up to him. One says, "I have found a proof that Goldbach's
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*> Conjecture is unprovable!". The mathematician snorts, "Go
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*> away, you crackpot". Then the other student says, "I have
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*> found a proof that whether or not there exist infinitely
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*> many prime pairs is unprovable!", and the mathematician's
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*> eyes light up and he says "Oh, really!? Please tell me
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*> more!". Why was the mathematician eager to hear out the
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*> second student, but not the first?
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To begin with, the Goldbach conjecture is one of the very most

crackpot-prone existing.

Furthermore, if it is unprovable whether there exists infinitely many prime

pairs, then the existence of an upper bond on the prime pairs is unprovable,

and thus -- perchance -- one might argue that the unprovability proves the

theorem.

This seems (to me) to be the case with any negative proposal; but not with

positive such -- if FLT would have been proven unprovable, we would know

that the theorem would hold, because any counterexample is a proof against

it -- a proof that we would have proven not to exist :-)

*> Lee Corbin
*

// Mikael Johansson

**Next message:**Eugene Leitl: "Re: "analog computer" = useless hypothesis?"**Previous message:**Eliezer S. Yudkowsky: "Re: MATH/COMP/PHIL: "Omega Man""**In reply to:**Lee Corbin: "Re: MATH/COMP/PHIL: "Omega Man""**Next in thread:**CurtAdams@aol.com: "Re: MATH/COMP/PHIL: "Omega Man""**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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