Re: Robot Evolution

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"
mistakes.

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.''

- http://hanson.gmu.edu/penrose.html

I see there's also this:

http://www.paul-almond.com/RefutationofPenroseGodelTuring.htm

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
work.
--
__________
|im |yler http://timtyler.org/ tim@xxxxxxxxxxx Remove lock to reply.

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Relevant Pages

  • Re: Penroses reply to Chalmers
    ... you have to identify which of the axioms are wrong. ... >Penrose thinks we can see the axioms are true for humans. ... and I'm saying that Penrose is in exactly the same boat ... >> Clearly a computer program could have produced those pages. ...
    (sci.logic)
  • Re: Contradicrtion-free mathemattics (The new nonstandard analysis
    ... >of inference are not well-defined by the axioms. ... >specific to the mathematical space and well-defined by its axioms. ... When you learn how to speak like a mathematician, ... You believe that because you got your results published in journals ...
    (sci.math)
  • Re: Penroses reply to Chalmers
    ... >> it doesn't satisfy Chalmers' axioms (which are actually ... >But I think with the axioms I gave the Godel argument goes through. ... Penrose believes that he is sound. ...
    (sci.logic)
  • Re: Penroses reply to Chalmers
    ... >>But I think with the axioms I gave the Godel argument goes through. ... > I'm saying that my B *doesn't* satisfy your axioms. ... Penrose believes that he is sound. ...
    (sci.logic)
  • This is just a totally bullshit reply
    ... For some reason AK is wilfully hell-bent on never ... EVERY mathematician KNOWS WHAT A PROOF is! ... when I said that PA only had 3 axioms, ... the existence of operators like multiplication and addition, ...
    (sci.logic)
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