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From: minsky@media.mit.edu (Marvin Minsky)
Subject: Re: Lucas & Penrose's use of Godel
Message-ID: <1995Jul4.165329.16706@media.mit.edu>
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Date: Tue, 4 Jul 1995 16:53:29 GMT
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In article <3takca$bn3@aurora.cs.athabascau.ca> burt@cs.athabascau.ca (Burt Voorhees) writes:

>The point in the argument from
>godel, as it is given by Penrose,
>is that he claims that we use specifically non-computational
>methods to "see" mathematical truth.  Insigit, or intuition.
>People such as Minsky who support strong AI make the claim
>that such things as mathematical intuition are probably nothing
>more than unconscious computation.  Penrose wants to make the
>argument that minds are not machines, and he focuses attention
>on mathematics because it is something where one can be very
>precise.  His assertion is that if it can be shown that
>mathematical intuition is not computational then it is clear
>that minds are also not computational.  On the other hand, if
>intuition in mathematics is computational then there is good
>reason to fear that all thought is as well.
>I discuss this in a paper which is to appear in the journal
>Complexity at some point in the reasonably (I hope) near
>future.

I'd like to see the paper. The idea that mathematical intuition
involves unconscious processes was elaborated by Poincare many years
ago.  I would also emphasize the irrelevancy of logical consistency,
which I think is where Penrose goes most badly wrong.  Poincare
himself, no mean mathematician, complained that his mathematical
intuition was often badly wrong!  In other words what good
mathematicians learn to do is to make "good guesses" more than other
people do. This has some obvious implications:

1. Most present-day discussions of "computational" seem to ignore the
possibilities of programs that do a pretty good job of something but
are not "algorithms for X" in the sense of *always" doing the desired
job.  I have the impression that Penrose and similar thinkers tend
to muddle things by ignoring this sort of thing -- which obviously the
brain is good at.

2. In particular, given an inconsistent system like the brain's --
which is perfectly happy with things like the heterological paradox
until a Bertrand Russell notices the problem, all that discussion
about Godel theorems, completeness, consistency and, yes,
"non-computational" when it's used as a synonym for "recursive
enumerability" are entirely irrelevant to any philosophical discussion
of functional human psychology.

