RE: Infinity and the mind was: Infinite universe

From: Ben Goertzel (
Date: Thu May 01 2003 - 21:35:03 MDT

Well, Godel's Theorem seems most AGI-relevant to me in its Chaitin
reformulation... i.e. "You can't use a 10-pound formal system to prove a
20-pound theorem." Equivalently, "You can't use a 10-pound AI system to
solve a 20-pound problem of survival in a difficult environment."


In this sense, Marcus Hutter's AGI theory -- and his systems AIXI and AIXItl
as extensively discussed on this list -- are closely tied in with Godel's

In this sense, though, all Godel's Theorem says is that no finite system is
ever gonna be infinitely intelligent -- every finite system has its limits
in terms of the problems it can solve. And if you get rid of the finitude
restriction, you get AIXI which can solve any finitely given problem -- it
supersedes the Godel problem by being uncomputable!

Penrose seems to argue that minds can't be computers because any computer
has finite problem-solving and modeling capability whereas in his view human
minds aren't so limited. I think human minds *are* limited in the same
basic was as finite computer systems...

ben g

> -----Original Message-----
> From: []On Behalf Of Shane
> Antyr
> Sent: Thursday, May 01, 2003 11:20 PM
> To:
> Subject: Re: Infinity and the mind was: Infinite universe
> Hash: SHA1
> OK Simon. You've made your assertion. On what do you base your
> opinion?
> - -S
> On Thursday, May 1, 2003, at 07:14 PM, Simon Gordon wrote:
> > Sorry to bring up the same thread but i do believe
> > that metamathematics, particularly Godels theorems (if
> > you are to take Penrose's suggestions with any
> > seriousness), do have at least some level of relevance
> > to AGI. I also see SIs themselves being particularly
> > occupied with the intricacies of metamathematics (what
> > else is there for them to do with all that excessive
> > intelligence!!
> Version: GnuPG v1.2.1 (Darwin)
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> rnUAn39hUTjbg0ppIP7q1pI+fyLxTWJJ
> =qNhJ

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