Re: Raatikainen's critique of Chaitin

From: Eray Ozkural exa (erayo_at_bilkent.edu.tr)
Date: 09/03/04 

Date: 2 Sep 2004 16:51:58 -0700

[In which I give an argument for computational minds]

daryl@atc-nycorp.com (Daryl McCullough) wrote in message news:<ch7has0bv0@drn.newsguy.com>...
> Craig Feinstein says...
> >
> >I'll ask a question to the people who criticize Chaitin's work. What
> >in general about Chaitin's work, which I happen to think is some of
> >the best mathematics of the past century, bothers you so much?
>
> Well, his way of proving incompleteness is an interesting alternative to the
> usual approach, but I think he is greatly exaggerating the philosophical
> consequences.

I think he is not merely re-proving incompleteness, he is proving a
stronger form of incompleteness based on algorithmic randomness. His
contribution is surely not limited to his unique proof of Godel's
first incompleteness theorem.

Perhaps, you do not appreciate why I brought the discussion from Godel
to Chaitin. It's about the disjunctive proposition in the Gibbs
lecture (which Chaitin has read and commented at least about the
similarity of mathematics to physics) that:
    either the mind is infinitely more powerful than a computer, or
there are such propositions that are absolutely unsolvable by a
computer.

>From my review:
http://www.amazon.com/exec/obidos/tg/detail/-/3764353104/102-2022094-7896904?v=glance

Or in Godel's words:
"Either mathematics is incompletable in this sense, that its evident
axioms can never be comprised in a finite rule, that is to say, the
human mind (even within the realm of pure mathematics) infinitely
surpasses the powers of any finite machine, or else there exist
absolutely unsolvable diophantine problems of the type specified."

http://users.ox.ac.uk/~jrlucas/Godel/implgoed.html

According to Lucas, Godel thought the second disjunct is false.

Chaitin's work is a good model for the second disjunct, therefore the
mind is not infinitely more powerful than a computer, according to
Godel's philosophy.

How remarkable is that?

Regards, 

--
Eray Ozkural
PS: Please note that I am not saying that:
  Chaitin thinks the disjunctive proposition is true.
  I think the disjunctive proposition is true.

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