From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Wed Aug 17 2005 - 09:35:23 MDT
Ben Goertzel wrote:
>
>>A paper-clip maximizer would be blocked by Godel,
>>since it couldn't have full self-awareness and hence
>>couldn't recursively self-improve.
>
> Godelian arguments can show, at most, that for any finite computational
> system there is some limit (of theorem-proving power) beyond which
> self-improvement can't lead the system.
Let's be precise: For every *consistent* mathematical system, whether of
finite or infinite computational power, whether self-improving or
not-self-improving, there are theorems which the system will provably never
output given that the system is consistent. This fact is itself easily
provable in the system, but the system's consistency is not.
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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