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
This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:59:44 MDT