Newsgroups: comp.ai.philosophy,sci.logic
Path: cantaloupe.srv.cs.cmu.edu!bb3.andrew.cmu.edu!nntp.sei.cmu.edu!news.psc.edu!hudson.lm.com!godot.cc.duq.edu!news.duke.edu!news-feed-1.peachnet.edu!usenet.eel.ufl.edu!usenet.cis.ufl.edu!caen!spool.mu.edu!news.moneng.mei.com!uwm.edu!vixen.cso.uiuc.edu!howland.reston.ans.net!ix.netcom.com!netcom.com!jqb
From: jqb@netcom.com (Jim Balter)
Subject: Re: Penrose and human mathematical capabilities
Message-ID: <jqbDBq5sJ.H02@netcom.com>
Organization: NETCOM On-line Communication Services (408 261-4700 guest)
References: <3ts4di$aa3@netnews.upenn.edu> <3u376p$lak@netnews.upenn.edu> <3u3v6t$7mm@Bayou.UH.EDU> <3u5u5c$b81@hamilton.maths.tcd.ie>
Date: Fri, 14 Jul 1995 21:17:07 GMT
Lines: 30
Sender: jqb@netcom7.netcom.com
Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:30208 sci.logic:12422

In article <3u5u5c$b81@hamilton.maths.tcd.ie>,
Timothy Murphy <tim@maths.tcd.ie> wrote:
>math0@Bayou.UH.EDU (siemion fajtlowicz,) writes:
>
>>Not at the same time,   so that's  how the algorithm could be extended:
>>Each time P and not P appears on the list, it should form two lists, one 
>>containing P, other not P, and both including everything else. One of the
>>list might be later discarded, for a number of reasons, one of which 
>>could be a possibility of contradiction. Other reasons might include
>>its mathematical utility.
>
>This seems to me just a play on the word "true".
>As far as I can see, at any moment you would have certain propositions
>you have proved true, others you have proved false,
>and the rest, which you will say are "true, but may later be proved false".
>This last phrase seems to me just a misleading synonym for "unproved".

As is "can see the truth of".  Fermat saw the truth of FLT.  But did he
really, or did he believe it true for the wrong reasons?  What if he had seen
it to be true, and it later had turned out to be false?  Not likely at this
point, but there are other examples or "seeing the truth of" false statements.
Thousands of mathematicians saw the truth of the "fact" that there is no
advantage to switching doors with Monty Hall, and "vigorously defended" this
sight, referring to Martin Gardner and others as "retards", "morons", and
worse.  The mathematical intuition of these mathematicians is obviously not a
"knowably sound algorithm".  That is, Penrose's G is trivially true, just as
Turing held.
-- 
<J Q B>

