oxymoron@waste.org (Oliver Xymoron) wrote on 03.01.00 in <Pine.LNX.4.10.10001032118300.6915-100000@waste.org>:
> Yes, but most of the well defined sets aren't interesting. Godel's theorem
> tells us this.
No, actually, it does no such thing. Gödel would be horrified at how many
people completely misunderstand his results. They are far more specific
than most people assume.
Specifically, Gödel is _not_ about the halting problem. That's a
completely unrelated question.
And note that while Gödel says that classical number theory cannot be
complete, most problems involving positive integers in everyday life are
actually easily enough to solve - that is, while the _theories_ that don't
have this problem are not very interesting, that doesn't mean the theories
that do have it don't have an enormously large class of interesting
_theorems_.
MfG Kai
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