**From:** Charles D Hixson (*charleshixsn@earthlink.net*)

**Date:** Wed May 10 2006 - 14:28:44 MDT

**Next message:**Eliezer S. Yudkowsky: "Re: Changing the value system of FAI"**Previous message:**Ben Goertzel: "Re: Changing the value system of FAI"**In reply to:**Ben Goertzel: "Re: Changing the value system of FAI"**Next in thread:**Eliezer S. Yudkowsky: "Re: Changing the value system of FAI"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Ben Goertzel wrote:

*>> > Godel's Theorem places limitations on self-understanding,
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*>> > self-optimization and goal-directed self-modification, but it
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*>> > certainly does not prevent these things
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*>>
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*>> Ben, would you care to state what limitations you believe Godel's
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*>> Theorem places?
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*>
*

*> Well, Godel's Theorem shows that for any reasonably powerful and
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*> consistent formal system, there are some statements that cannot be
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*> proved either true or false within that system. Furthermore, many of
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*> the examples of this kind of undecidable statement happen to be
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*> "meta-statements" that pertain to the formal system as a whole.
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*> ...
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*> One question is whether any of these statements will be ones that are
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*> of any meaning for practical self-modification of a system. I.e.,
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*> will a self-modifying system ever run into a situation where it says:
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*> "Hmmm.... I would like to make a certain change to myself, but I find
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*> that I am intrinsically unable to prove whether or not this change
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*> will be good or bad, because the goodness or badness of this change is
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*> undecidable relative to the formal system that I embody"?
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*> ...
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*> -- Ben
*

In that context, consider Euclid's parallel postulate. Three different

answers to that one have *each* proven consistent...after the fact.

None of them (except Euclid's) were believed to be consistent until

people started just assuming that they might be true.

Geometry is a LOT simpler than the physical world, or even just the

simplified model of it that I use to walk across the room.

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