From: Ben Goertzel (ben@goertzel.org)
Date: Fri Oct 08 2004 - 20:56:36 MDT
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
wrong.
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: owner-sl4@sl4.org [mailto:owner-sl4@sl4.org]On Behalf Of Bill
> Hibbard
> Sent: Friday, October 08, 2004 6:06 PM
> To: sl4@sl4.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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