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From: jqb@netcom.com (Jim Balter)
Subject: Re: Penrose and human mathematical capabilities
Message-ID: <jqbDBMIA5.4LL@netcom.com>
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References: <3t6tcv$nca@netnews.upenn.edu> <3tu382$av2@hamilton.maths.tcd.ie> <jqbDBK89s.3xF@netcom.com> <3u0g1q$44@netnews.upenn.edu>
Date: Wed, 12 Jul 1995 21:56:28 GMT
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In article <3u0g1q$44@netnews.upenn.edu>,
Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>In article <jqbDBK89s.3xF@netcom.com>, jqb@netcom (Jim Balter) writes:
>>In article <3tu382$av2@hamilton.maths.tcd.ie>,
>>Timothy Murphy <tim@maths.tcd.ie> wrote:
>>>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.
>
>Exactly?
>
>Not at all.
>
>Belief regarding the infinite tends towards accepting consistency.

That's the Ockhamish rule I just stated.

>There
>are individuals who lean the other way, but I believe no one who is schizoid
>on such matters.

Yes, so?  One who was schizoid presumably would be one who believed two
propositions that s/he *noticed* as being contradictory.  Perhaps you are
suffering from a reading comprehension problem.

-- 
<J Q B>

