John Clark wrote:
>
> 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.
Hey, here's another fascinating question: Is it possible to nontrivially
map one Chaitlin-unproveable problem onto another? Are some problems
Chaitlin-complete, in the sense that a proof of one would enable you to
prove any other Chaitlin-unproveable question? (Obviously you can't prove
Chaitlin-completeness, but you can prove "If this problem is true, it must
be Chaitlin-complete.")
-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence
This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:59:44 MDT