From: Ben Goertzel (email@example.com)
Date: Sun Apr 27 2003 - 20:12:34 MDT
>The sort of mathematics we have got at
> the moment is presumably very basic and simple in
> comparison, but its hard to imagine that ALL the
> mathematical discoveries that SIs will ever make will
> fall into the "formalizable" category. At some point
> we are bound to hit some really weird stuff which
> cannot even be axiomatized!
Hmmm... it's a fascinating but vague mental image you're painting here...
There are two questions really
a) whether such structures as you describe will ever exist [I suspect so!]
b) whether they will be justly called "mathematics" [I dunno... I tend to
think if something is nonformalizable it's adequately different from what we
know of as "math" that it maybe shouldn't use the same label]
Anyway, now that I know you're referring to structures and concepts that no
humans yet know, I'm not so uncomfortable with your statement. Maybe indeed
superintelligent AI's will come up with something fairly describable as
"nonformalizable math." who knows...
-- ben G
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