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Article 1373 of comp.ai.philosophy:
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>From: costello@CS.Stanford.EDU (Tom Costello)
Newsgroups: comp.ai.philosophy
Subject: Re: Chinese Room Variant
Message-ID: <1991Nov18.114641.964@CSD-NewsHost.Stanford.EDU>
Date: 18 Nov 91 11:46:41 GMT
References: <1991Nov8.170856.21527@psych.toronto.edu> <1991Nov12.131428.4850@osceola.cs.ucf.edu> <1991Nov14.163630.20597@spss.com> <1991Nov17.163705.5540@husc3.harvard.edu>
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Organization: Computer Science Department, Stanford University
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In article <1991Nov17.163705.5540@husc3.harvard.edu>, zeleny@brauer.harvard.edu (Mikhail Zeleny) writes:
|> In article <1991Nov14.163630.20597@spss.com> 
|> markrose@spss.com (Mark Rosenfelder) writes:
|> 
|> >In article <1991Nov12.131428.4850@osceola.cs.ucf.edu> 
|> clarke@next1 (Thomas Clarke) writes:
|> 
|> TC:
|> >>That is, the bare rules of computation plus any finite set of additional 
|> >>usage/correspondence rules are not sufficient for an understanding of number. 
|> 
|> MR:
|> >What is sufficient, then?  An infinite set of rules?  Or, if something else
|> >entirely is needed, what is it?
|> 
|> In effect, on the syntactical level, infinitely many rules are required in
|> order to characterize the standard model of the natural numbers.  This is a
|> direct consequence of G\"odel's Second Incompleteness Theorem.

While it is very flattering to see Mikhail repeat something that I explained
to him just recently on sci.philosophy.tech, I should point out that the
theorem is Godel first incompleteness theorem.   Also, infinitely many rules
is not a correct characterisation.  It should be, and I quote from
Godel Collected Work's, editor Fefermann.
1. The class of axioms and rules of inference(that is, the relation "immediate
consequence") are recursively definable ( as sonn as we replace the primitive signs in some way by natural numbers).
2. Every recursive relation is definable in the system

The first part is the condition that the system must be weaker than for
the result to apply, the second, a condition that the system must be as 
strong as.


|> 
|> '`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`
|> `'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
|> : Qu'est-ce qui est bien?  Qu'est-ce qui est laid?         Harvard   :
|> : Qu'est-ce qui est grand, fort, faible...                 doesn't   :
|> : Connais pas! Connais pas!                                 think    :
|> :                                                             so     :
|> : Mikhail Zeleny                                                     :
|> : 872 Massachusetts Ave., Apt. 707                                   :
|> : Cambridge, Massachusetts 02139                                     :
|> : (617) 661-8151                                                     :
|> : email zeleny@zariski.harvard.edu or zeleny@HUMA1.BITNET            :
|> :                                                                    :
|> '`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`
|> `'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'


Tom


