From: Charles D Hixson (charleshixsn@earthlink.net)
Date: Wed May 10 2006 - 14:28:44 MDT
Ben Goertzel wrote:
>> > Godel's Theorem places limitations on self-understanding,
>> > self-optimization and goal-directed self-modification, but it
>> > certainly does not prevent these things
>>
>> Ben, would you care to state what limitations you believe Godel's
>> Theorem places?
>
> Well, Godel's Theorem shows that for any reasonably powerful and
> consistent formal system, there are some statements that cannot be
> proved either true or false within that system. Furthermore, many of
> the examples of this kind of undecidable statement happen to be
> "meta-statements" that pertain to the formal system as a whole.
> ...
> One question is whether any of these statements will be ones that are
> of any meaning for practical self-modification of a system. I.e.,
> will a self-modifying system ever run into a situation where it says:
> "Hmmm.... I would like to make a certain change to myself, but I find
> that I am intrinsically unable to prove whether or not this change
> will be good or bad, because the goodness or badness of this change is
> undecidable relative to the formal system that I embody"?
> ...
> -- 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.
This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:00:56 MDT