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From: jqb@netcom.com (Jim Balter)
Subject: Re: Penrose and human mathematical capabilities
Message-ID: <jqbDBovDF.1wn@netcom.com>
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References: <[110q<3tue <3u0sin$7ou@nnrp.ucs.ubc.ca> <3u384f$lak@netnews.upenn.edu>
Date: Fri, 14 Jul 1995 04:34:27 GMT
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In article <3u384f$lak@netnews.upenn.edu>,
Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>Yes.  Your very paragraph!  The computer is going to evade Goedel's
>theorem by having some informal notion of knowledge?  Pfui.

Pfui.  That's Wiener's argument in a nutshell.  Computers evade Goedel's
theorem by having some informal notion of knowledge?  Pfui.  Humans evade
Goedel's theorem by having some informal notion of knowledge?  Of course, we
do it all the time.  It's an empirical observation.

>>					     It's not helpful to pretend 
>>that there are mathematically precise definitions of terms like 
>>"knowledge" and "mathematical intuition", and until there are,
>
>What pretend?  *WHATEVER* the machine does is susceptible to a precise
>formal specification.  And whatever it does, whether you give it a name
>or not, is apparently incomplete with respect to a certain human ability.

What machines do is susceptible to precise formal specification, but our
*interpretions* of what they do is not.  Whether a machine or a human
has "seen" a mathematical truth is a matter of *interpretation*,
not a matter of fact.

-- 
<J Q B>

