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Article 5891 of comp.ai.philosophy:
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>From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: penrose
Message-ID: <1992May25.164314.19628@guinness.idbsu.edu>
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Organization: Boise State University Math Dept.
References: <1992May18.194416.27171@hellgate.utah.edu> <27@tdatirv.UUCP> <atten.706786286@groucho.phil.ruu.nl>
Date: Mon, 25 May 1992 16:43:14 GMT
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In article <atten.706786286@groucho.phil.ruu.nl> atten@phil.ruu.nl (Mark van Atten) writes:
>sarima@tdatirv.UUCP (Stanley Friesen) writes:
>
>>In article <1992May18.194416.27171@hellgate.utah.edu> tolman%asylum.utah.edu@cs.utah.edu (Kenneth Tolman) writes:
>>|Algorithms are fundamentally incomplete.  Turing machines are fundamentally
>>|incomplete.  Think.
>
>>Right, but why assume *human* *thought* is complete (in this sense)?
>>Is ti really certain that we can *always* jump the rails, so to speak,
>>and arrive at the truth.
>
>>This is what Penrose' argument requires, and I find it extremely unlikely.
>
>No, Penrose's argument does not require that we cab *always* jump the rails,
>he just argues that there is at least one case where we can (i.e. Goedel's
>argument). (Why are so many - including me - always typing cab instead of cab ; see what I mean ? :) )
>
>Best wishes,
>Mark.

And this kills Penrose's argument; where any particular formal system
runs into trouble, there is another _formal system_ which can "jump
the rails" for the particular problem (for example, there is a
stereotyped way to deal with Godel's basic construction -- add to the
original system axioms asserting that "P is provable" implies P for
each sentence P (where "P is provable" is defined via a Godel coding)
-- notice that the notion of provability is the notion of the original
system -- the notion of provability of the extended system is
different, and so a new Godel sentence appears, and the process can be
repreated...  (this particular rail-jumping technique can be
formalized!))).  Penrose's argument does depend on human beings
_always_ being able to jump the rails, or he has not succeeded in
showing that humans are not formal systems (which he can't, since we
are, insofar as we make sense).
-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu


