From: Tim Tyler 
Subject: Re: Robot Evolution
Date: Thu, 21 Dec 2006 13:23:11 -0500 (EST)

Phil Roberts, Jr. wrote:
>> Tim Tyler wrote:
>>> My impression is that the only folk who reject the fundamentals
>>> of the brain-computer analogy are people like Roger Penrose
>>> and John Searle - i.e. those whose world view in the area is
>>> totally muddled.  [...]
> I have always thought the Godel argument constitutes a pretty
> good ARGUMENT against a computational view of the mind.  Where
> I think Lucas went wrong was in his claim that Godel constitutes
> a PROOF against computationalism.  You can't prove empirical
> assertions, you can only marshall evidence.  That's why all
> scientific theories are tentatively true until the next
> revision.
> I can't recall to what
> extent Penrose claimed Godel as a proof rather than an argument
> against computationalism.  But as an argument, I am definitely
> in the Lucas/Penrose camp.  Can you provide a brief overview of
> why you consider Penrose "totally muddled" on this issue?

John Lucas's 'Godel' argument has been much-criticized - and
Penrose's views in this area are essentially a variation on it.

Brief version of what's wrong:

``A mathematician often makes judgments about what
   mathematical statements are true. If he or she is not more
   powerful than a computer, then in principle one could write
   a (very complex) computer program that exactly duplicated
   his or her behavior. But any program that infers
   mathematical statements can infer no more than can be proved
   within an equivalent formal system of mathematical axioms
   and rules of inference, and by a famous result of Godel,
   there is at least one true statement that such an axiom
   system cannot prove to be true. "Nevertheless we can (in
   principle) see that P_k(k) is actually true! This would seem
   to provide him with a contradiction, since he aught to be
   able to see that also."

   This argument won't fly if the set of axioms to which the
   human mathematician is formally equivalent is too complex
   for the human to understand. So Penrose claims that can't be
   because "this flies in the face of what mathematics is all
   about! ... each step [in a math proof] can be reduced to
   something simple and obvious ... when we comprehend them
   [proofs], their truth is clear and agreed by all."

   And to reviewers' criticisms that mathematicians are better
   described as approximate and heuristic algorithms, Penrose
   responds (in BBS) that this won't explain the fact that "the
   mathematical community as a whole makes extraordinarily few"

   These are amazing claims, which Penrose hardly bothers to
   defend. Reviewers knowledgeable about Godel's work, however,
   have simply pointed out that an axiom system can infer that
   if its axioms are self-consistent, then its Godel sentence
   is true. An axiom system just can't determine its own self-
   consistency. But then neither can human mathematicians know
   whether the axioms they explicitly favor (much less the
   axioms they are formally equivalent to) are self-consistent.
   Cantor and Frege's proposed axioms of set theory turned out
   to be inconsistent, and this sort of thing will undoubtedly
   happen again.''


I see there's also this:

As to what this has to do with evolution - if humans can
do things no machine can do - or will ever be able to do -
that may impact the hypothesis that machine-based organisms
may replace humans as the dominant life form on earth over
the next century or so.

However, this particular argment for the qualitative
superiority of humans is simply wrong - and (IMO) rather
obviously so for anyone who knows anything about Godel's

Tim Tyler