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From: jqb@netcom.com (Jim Balter)
Subject: Re: Penrose and human mathematical capabilities
Message-ID: <jqbDBK89s.3xF@netcom.com>
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References: <3t6tcv$nca@netnews.upenn.edu> <3tra4b$em9@netnews.upenn.edu> <3tsi61$t7g@nnrp.ucs.ubc.ca> <3tu382$av2@hamilton.maths.tcd.ie>
Date: Tue, 11 Jul 1995 16:25:03 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:29936 sci.logic:12185

In article <3tu382$av2@hamilton.maths.tcd.ie>,
Timothy Murphy <tim@maths.tcd.ie> wrote:
>constab@unixg.ubc.ca (Adam Constabaris) writes:
>
>>: Easily?  As in, you write a table that says "belief in Con(ZF)"?  Well,
>>: that's cheating.
>
>>No, by writing a table that says, "if ZF works, and you can't derive a 
>>contradiction from ZF, then believe Con(ZF)"
>
>How does the machine determine that it can't derive a contradiction?
>It will spend quite a lot of time going through all the deductions from ZF.

Well, it will fail to derive a contradiction in practice, which is all Adam
asked for.  However, as he already realized, the same applies to ~Con(ZF).
So, we can add a Ockhamish rule, that says to believe in consistency unless it
is explicitly contradicted.  Of course, this will lead to having an
inconsistent set of beliefs, since some things will believed to be consistent
simply because the machine hasn't noticed the contradiction yet.  Which is
exactly the way it works in human beings.
-- 
<J Q B>

