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From: jqb@netcom.com (Jim Balter)
Subject: Re: Penrose and human mathematical capabilities
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References: <3ts4di$aa3@netnews.upenn.edu> <3ttstt$fo7@netnews.upenn.edu> <3u0k8q$3d3@cnn.Princeton.EDU> <3u376p$lak@netnews.upenn.edu>
Date: Fri, 14 Jul 1995 04:21:30 GMT
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In article <3u376p$lak@netnews.upenn.edu>,
Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>In article <3u0k8q$3d3@cnn.Princeton.EDU>, schechtr@flagstaff (Joshua B. Schechter) writes:
>>In article <3ttstt$fo7@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:
>>>In article <3tsmsj$ctr@menudo.uh.edu>, math0@menudo (Siemion Fajtlowicz) writes:
>>>>					   The list at any moment might
>>>>contain statements of the form P and not P, but I never made a claim
>>>>that list would be consistent.
>
>>>Then your algorithm is rejected a priori as a candidate for "knowledge".
>
>>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.

It is so obvious (to anyone other than certain mathematicians, apparently)
that mathematicians unknowlingly hold inconsistent beliefs, but it is also
possible to knowingly hold inconsistent beliefs.  A classic one in the
literature is that if one proof-reads a thousand page manuscript, one can
believe, for each page of the manuscript, that all the errors on that page
were found, and still believe that the manuscript contains errors.

>The whole point of the form of the Lucas/Penrose argument is to concentrate
>on just these narrow kinds of questions, one to which mathematical rigor can
>be applied to a substantial part.

The whole point is to misrepresent the human endeavor.
(Well, that's not the point, or intent, but that's the result.)

-- 
<J Q B>

