Re: MATH/COMP/PHIL: "Omega Man"

From: John Clark (
Date: Fri Apr 06 2001 - 10:00:20 MDT

 Lee Corbin <> Wrote:

>suppose that there was a proof that GC could not be proved or
>disproved. Then since it could not be disproved, it means that you
>could not find any such even number. But since one might
>pick any even number, that in turn would imply that there
>is no even number that is not the sum of two primes. But
>that would prove the theorem.

Yes, but it would be nice if you could prove it was either false or
true but unprovable, then we could just stop worrying about it and
move on to something more productive. However Turing demonstrated
that there are statements where it is impossible to do this; GC may or
may not be one of these. If it is and it's true then we will never know about it.
Instead a trillion years from now our hyper intelligent descendants will still
be looking, unsuccessfully, for a proof, and still be grinding through numbers
looking, unsuccessfully, for a counterexample.

    John K Clark

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