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John Clark wrote:

*>
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*> It could also be quite dangerous. Mathematicians would undoubtedly build on top
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*> of this "Goldbach Axiom" and come up with all sorts of interesting things, but suppose
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*> one fine day a computer happened to run across an even number greater than 4 that
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*> was not the sum of two odd primes. Then that soaring mathematical edifice everybody
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*> was so proud of would turn out to be pure distilled gibberish. I can live with an incomplete
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*> mathematical system but not a inconsistent one. And you're correct, it is chilling.
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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

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