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Eliezer S. Yudkowsky <sentience@pobox.com> Wrote:

* >You could, of course, "cheat" by adding GC as an axiom without having
*

* > any idea whether or not it was true, just as a Turing machine might get
*

* > the halting problem for a GC machine correct by coincidence - but it's an
*

* > odd use of the word "proof" to describe a result that contributes nothing
*

* > whatsoever to your beliefs about the problem one way or the other.
*

It could also be quite dangerous. Mathematicians would undoubtedly build on top

of this "Goldbach Axiom" and come up with all sorts of interesting things, but suppose

one fine day a computer happened to run across an even number greater than 4 that

was not the sum of two odd primes. Then that soaring mathematical edifice everybody

was so proud of would turn out to be pure distilled gibberish. I can live with an incomplete

mathematical system but not a inconsistent one. And you're correct, it is chilling.

John K Clark jonkc@att.net

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