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From: jwl@ucbvax.ARPA (James Wilbur Lewis)
Newsgroups: net.philosophy,net.math
Subject: Re: Sc--nce Attack (really on minds and computers)
Message-ID: <10700@ucbvax.ARPA>
Date: Fri, 18-Oct-85 05:21:54 EDT
Article-I.D.: ucbvax.10700
Posted: Fri Oct 18 05:21:54 1985
Date-Received: Sun, 20-Oct-85 04:38:44 EDT
References: <299@umich.UUCP> <10699@ucbvax.ARPA>
Reply-To: jwl@ucbvax.UUCP (James Wilbur Lewis)
Distribution: net
Organization: University of California at Berkeley
Lines: 56
Keywords: Turing machines vs. the mind
Xref: watmath net.philosophy:2883 net.math:2385

In article <10699@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes:
>
>No, I don't get the point. The complexity of the statement is not
>the issue. The issue is that humans seem to recognize that certain
>be proved within the system. This mysterious ability to recognize
>such things being something lacking in deterministic machines,
>I claim there is a distinction between the human mind and any
>Turing machine.
>
>Of course, I may be wrong in believing that these formal
>systems are consistent. 

Your points seem to be:

(1) Humans can recognize consistency of certain formal systems, and
    machines lack this ability .
(2) There is something mysterious about this ability, and nondeterminism
    has something to do with it; therefore
(3) no Turing machine can be equivalent to a human mind.

You are confusing two issues: reasoning *within* a formal system, and
reasoning *about* a formal system. What is so mysterious about the
latter kind of reasoning? All one needs to do is define a more powerful
system, and then by reasoning within the new system you can show the
incompleteness/inconsistency/whatever of the weaker system.

Of course, the formal system for any given Turing machine is fixed, and
that machine will be unable to 'jump out of the system' to reason
about its own properties.  But we can always design a more powerful 
machine which *will* be able to reason about the weaker one.

Humans are subject to these constraints, too. Consider:
"Tom Tedrick cannot consistently assert this proposition."

I can prove it, but you can't do so and remain consistent.  Does that
make my mind more powerful than yours?  Of course not, because
you can exhibit the obvious proposition which *you* can prove but
*I* can't (assuming I'm consistent! :-) 

Your mention of determinism is irrelevant; humans are just as deterministic
as machines. Unpredictable, perhaps...since we are orders of magnitude more
complex than any machines we know how to build....but subject to the same
laws of physics.

For a fascinating presentation of this and many other topics, check out
any book by Douglas Hofstadter, especially "Godel, Escher, Back: An 
Eternal Golden Braid".

Cheers,

-- Jim 'down with human chauvinism' Lewis
   U. C. Berkeley
   ...!ucbvax!jwl        jwl@ucbernie.BERKELEY.EDU

"Lately it occurs to me
  What a long, strange trip it's been..."