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From: zeleny@oak.math.ucla.edu (Michael Zeleny)
Subject: Re: Penrose's new book
Message-ID: <1994Oct26.174127.23746@math.ucla.edu>
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References: <385oqf$b32@lyra.csx.cam.ac.uk> <1994Oct21.210340.28435@math.ucla.edu> <Cy9tru.D2u@lincoln.gpsemi.com>
Date: Wed, 26 Oct 94 17:41:27 GMT
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In article <Cy9tru.D2u@lincoln.gpsemi.com> 
whipp@roborough.gpsemi.com (David Whipp.) writes:

>In article <1994Oct21.210340.28435@math.ucla.edu>, 
>zeleny@oak.math.ucla.edu (Michael Zeleny) writes:

>[in the context of Goedel]

>>>Logic is largely irrelevant to intelligence, consciousness
>>>and what makes us human in general. Get it straight - we evolved by natural 
>>>selection - we weren't designed, verified, or guaranteed to be consistent.
>>>No one ever contemplated or proved the validity of the algorithms
>>>that are us. There is no proof that our algorithms work, terminate, halt
>>>or are free from error. But so what? They helped us survive anyway!

>>Consider a total mathematical model of human performance -- guaranteed
>>to be consistent, for the simple reason that you cannot do and not do
>>P at once.

>But will this mathematical model form a complete system? Surely a model
>of the brain (or any intelligence) must include interaction with its
>environment, and so does not form a closed system. If the entire universe
>is included in the model then you will find that the brain can 'know' P
>to be true, when in fact it is false.

This is a good point -- the first such that I have come across in this
entire thread.  Suppose then that the entire universe is closed in the
above sense.  Then, since it includes a knowing subject (in principle)
capable of understanding any and all of its parts, you can diagonalize
the grand universal theory of everything (which exists by closure),
presenting him with a proposition he can know as true yet unprovable.

The moral of the story, as I see it: The postulation of closure with
respect to potential knowledge is a plausible epistemic hypothesis,
replete with strong metaphysical implications.  While it is likely
that no individual can know everything (compare the Montague-Kaplan
diagonal "paradox of the knower"), the imposition of a finite bound on
individual or communal cognitive potential is highly counterintuitive.

>-- 
>                    David P. Whipp.            <whipp@roborough.gpsemi.com>
>Not speaking for:   -------------------------------------------------------
> G.E.C. Plessey     Due to transcription and transmission errors, the views
> Semiconductors     expressed here may not reflect even  my  own  opinions!

cordially,                                                    don't
mikhail zeleny@math.ucla.edu                                  tread
writing from the disneyland of formal philosophy                 on
"Le cul des femmes est monotone comme l'esprit des hommes."      me
