From: "Phil Roberts, Jr." 
Subject: Re: Robot Evolution
Date: Tue, 26 Dec 2006 00:18:54 -0500 (EST)

Kent Paul Dolan wrote:

> Goedel was more than willing to admit that some
> theorem unprovable in one system of arithmetic might
> well be provable under a stronger set of axioms, but
> he then showed that the stronger set of axioms would
> form a system for which exactly the same sort of
> unprovable sentence could again be written.

Yes.  Lucas addressed this issue, in response to
Whitely and Bannaceraf as I recall:

   Banacerraf protests that "It is conceivable that
   another machine [or formal system] could do that
   as well."  Of course.  But that other machine was
   not the machine that the mechanist was claiming
   that I was.  It is the machine that I am alleged
   to be that is relevant: and since I can do
   something that it cannot, I cannot be it.  Of
   course It is still open for the mechanist to
   alter his claim and say, now, that I am that
   other machine which, like me, could do what the
   first machine could not.  Only, if he says that,
   then I shall ask him "Which other machine?" and
   as soon as he has specified it, proceed to find
   something else which that machine cannot do and
   I can.  I can take on all comers, provided only
   they come one by one in the sense of each being
   individually specified as being the one that it
   is:  and therefore I can claim to have tilted at
   and laid low all logically possible machines.
   An idealized person, or mind, may not be able to
   do more than all logically possible machine can,
   between them, do:  but for each logically
   possible machine there is something which he can
   can do and it cannot; and therefore he cannot be
   the same as any logically possible machine.
   (J. R. Lucas, 'The Monist', vol 52, pp 145-158)

> So, all you've proved is that the human mind _may_
> employ a stronger set of axioms, not that it is
> somehow different in kind.

Or maybe no axioms at all, at least not in any strict
sense of the terms.  Perhaps "all forms of reasoning
are nothing but comparing", as Hume has maintained
and, as such, actually ANAlogical (nonlogical):

     One should not think of analogy-making as a special
     variety of reasoning (as in the dull and uninspiring
     phrase "analogical reasoning and problems solving,"
     a long-standing cliche in the cognitive science world),
     for that is to do analogy a terrible disservice.  After
     all, reasoning and problem-solving have (at least I
     dearly hope!) been at long last recognized as lying
     far indeed from the core of human thought.  If analogy
     were merely a special variety of something that in
     itself lies way out on the peripheries, then it would
     be but an itty bitty blip in the broad blue sky of
     cognition.  To me, however, analogy is anything but
     a bitty blip -- rather, ITS THE VERY BLUE THAT FILLS
     (Douglas Hofstadter) [emphasis mind].