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Article 5910 of comp.ai.philosophy:
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>From: atten@phil.ruu.nl (Mark van Atten)
Subject: Re: penrose
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Organization: Department of Philosophy, University of Utrecht, The Netherlands
References: <1992May18.194416.27171@hellgate.utah.edu> <27@tdatirv.UUCP> <atten.706786286@groucho.phil.ruu.nl> <1992May25.164314.19628@guinness.idbsu.edu>
Date: Tue, 26 May 1992 10:07:34 GMT
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holmes@opal.idbsu.edu (Randall Holmes) writes:

>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).
>

Penrose maintains that the rail-jumping cannot be formalized, because
the construction of a new Goedel sentence cannot be formalized. See his
article in Behavioral and Brain Sciences, 1991.

Best wishes,
Mark. 


