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From: jqb@netcom.com (Jim Balter)
Subject: Re: Penrose and human mathematical capabilities
Message-ID: <jqbDBq6p3.ILK@netcom.com>
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References: <3ts4di$aa3@netnews.upenn.edu> <3u376p$lak@netnews.upenn.edu> <jqbDBouru.13C@netcom.com> <3u5on1$oba@netnews.upenn.edu>
Date: Fri, 14 Jul 1995 21:36:39 GMT
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In article <3u5on1$oba@netnews.upenn.edu>,
Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>In article <jqbDBouru.13C@netcom.com>, jqb@netcom (Jim Balter) writes:
>>In article <3u376p$lak@netnews.upenn.edu>,
>>Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>>>>Ummm... Why? Or are you claiming that your knowledge system is fully
>>>>self-consistent? Among the human beings I know that is a very big stretch.
>
>>>Really?  You know of any mathematicians who claim both P and not-P
>>>are true, P some mathematical statement?
>
>>If any mathematician has ever, due to an error, reached a false conclusion,
>>then that mathematician has held formally inconsistent beliefs.  Live with it.
>
>Don't be obtuse.  (Oops, wrong person.)  Thinking one has a proof and
>claiming that something really is true are different phenomena.

Which is why Goedel does not apply to "claiming that something is really
true".  (Except when the latter is formalizable, making them not such
different phenomena after all.)

And of course we were talking of fully self-consistent knowledge systems.
People quite convinced of the truth of things that are in fact false
do not qualify.

By the way, Matthew, by implying that I'm consitutionally obtuse, rather than
merely mistaken, you undermine your argument in the minds of many.  And I'd
rather you didn't do that, since the validity of arguments should stand on
their own.  For instance, some of the people who keep trying to evade the
application of Goedel to formal proof procedures by recourse to simulation,
multiple levels, etc., might miss the validity of your criticisms when they
are couched in such arrogant terms.  As your buddy Mikhail says, vituperation
and obloquy are no substitute for rational discourse (I guess he learned this
the hard way, after much practice with the former).

-- 
<J Q B>

