From: Ben Goertzel (email@example.com)
Date: Fri Oct 08 2004 - 21:53:56 MDT
One more comment:
So, it's not true that Penrose misinterprets Godel's Theorem. Not at all.
What he does is to make physics hypotheses that are completely unmotivated
by any data in contemporary physics, or any theoretical ideas in
contemporary physics -- but are motivated *solely* by the consequences that
these physics hypotheses would have for the philosophy of mind. Not even
for cognitive psychology in terms of predicting the results of any
experiments on human beings -- purely for the philosophy of mind.
I think this is a pretty bad way to go about generating physics hypotheses.
My view is, if your philosophy of mind contradicts physics, probably it's
your philosophy that's wrong rather than the physics.
But in a sense, Penrose's hypothesis is legitimate science, in the sense
that Penrose would consider himself refuted if someone came up with
a) an elegant, unifying theory of quantum gravity, that did not involve
b) a detailed theory of neurodynamics in terms of the physics in a)
So his hypothesis is falsifiable, not by particular experiments but via the
conception of certain sorts of theories ;-)
> The problem with Penrose's argument is pretty simple. He argues
> as follows:
> Premise 1) FOR EACH computer, THERE EXISTS some problem which
> that computer
> can't solve
> Premise 2) NOT [ FOR EACH human, THERE EXISTS some problem which
> that human
> can't solve ]
> Conclusion) Therefore, humans are not computers
> The problem is that his premise 2 is false
> Now, I can't prove that his premise 2 is false. So I can't prove he's
> On the other hand, he doesn't give any kind of reasonable
> argument that his
> premise 2 is true, either.
> Note that both premise 1 and premise 2 are based on
> idealizations. Neither
> of them is based on an argument about some particular physical system
> carrying out particular actions -- if so, they'd have to be weaker
> statements like "FOR EACH human, THERE EXISTS some problem which
> that human
> will never solve in practice during its life, no matter how long." These
> weaker statements are less interesting. So both of Penrose's premises are
> based on making idealized models of certain systems -- idealized abstract
> computers and humans -- and then making statements about these. We have
> standard and well-accepted ways of talking about idealized, abstract
> computers (Turing machines, combinatory logic, whatever,...), but we don't
> really have standard and well-accepted ways of talking about idealized
> abstract humans....
> One way to talk about idealized, abstract humans is to talk about
> them as a
> special case of idealized, abstract physical systems -- but then you get
> into the problems with current theories of physics. Physicists
> don't quite
> agree on how to formalize the notion of an idealized abstract physical
> system, so Penrose is left with the possibility of saying "hey --
> maybe once
> the correct physics theory is found, it'll involve an idealization of
> abstract humans that will validate my Premise 2. In effect, what
> this will
> require is that some future physics theory says that humans are *infinite
> systems* (infinite in the sense of algorithmic information)
> whereas physical
> digital computers are finite systems (again in the sense of algorithmic
> information). It's hard to say this is *impossible*, but it's clearly the
> case that Penrose has no particular reason to believe this, except his
> intuitive feeling that his Premise 2 should be true.
> -- Ben G
> > -----Original Message-----
> > From: firstname.lastname@example.org [mailto:email@example.com]On Behalf Of Bill
> > Hibbard
> > Sent: Friday, October 08, 2004 6:06 PM
> > To: firstname.lastname@example.org
> > Subject: Re: Human mind not Turing computable according to Eliezer?
> > Hi Christian,
> > > . . .
> > > You must refute the *original proof*.
> > You are right that I do not demonstrate a mathematical
> > error in Penrose. Rather, his overall argument is wrong,
> > based on an unrealistic model of human brains. They are
> > properly modeled by finite state machines. I think the
> > inability of Penrose's argument to work using finite
> > state machines indicates that he has just uncovered a
> > property of infinite sets that is not relevant to human
> > brains.
> > Cheers,
> > Bill
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