Re: Robot Evolution

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 cliché 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
THE WHOLE SKY OF COGNITION -- ANALOGY IS EVERYTHING...
(Douglas Hofstadter) [emphasis mind].



PR
www.rationology.net


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Relevant Pages

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