From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Fri May 26 2006 - 13:28:19 MDT
Psy Kosh wrote:
> On 5/26/06, Ben Goertzel <ben@goertzel.org> wrote:
>
>> IMO, you're way off; the issues with superrationality are far simpler
>> than anything Godelian in nature...
>
> Okie, thanks. I wasn't thinking about any specific issues, it was more
> of "If taking consistancy itself as an explicit axiom can break a
> system that was consistent, and if superrationality works by playing
> around explicitly with the consiquences of the idea of rationality
> being consistent, then would that open up the possibility for various
> issues?"
"Consistency" in the Godelian sense means that the formal system never
proves both P and ~P.
Here we mean "consistency" simply in the sense of rationalists who make
a choice expecting similar rationalists to make the same choice, whether
or not that choice is correct.
A formal system that proves P, and is sufficiently powerful, can readily
prove "This formal system proves 'P'." It suffices simply to exhibit
the proof. The Godelian difficulty lies in proving "This formal system
will never prove '~P'."
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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