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Article 1375 of comp.ai.philosophy:
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>From: zeleny@osgood.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy
Subject: Re: Chinese Room Variant
Message-ID: <1991Nov18.094715.5563@husc3.harvard.edu>
Date: 18 Nov 91 14:47:14 GMT
References: <1991Nov14.163630.20597@spss.com> <1991Nov17.163705.5540@husc3.harvard.edu> <1991Nov18.114641.964@CSD-NewsHost.Stanford.EDU>
Organization: Dept. of Math, Harvard Univ.
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Nntp-Posting-Host: osgood.harvard.edu

In article <1991Nov18.114641.964@CSD-NewsHost.Stanford.EDU> 
costello@CS.Stanford.EDU (Tom Costello) writes:

>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?

MZ:
>|> 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.

TCos:
>While it is very flattering to see Mikhail repeat something that I explained
>to him just recently on sci.philosophy.tech,

yeah, sure.

TCos:
>                                             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

Had your grade school teachers been more attentive to your development, you
might have learned to read; then you would be able to distinguish a
consequence from a quotation (not that you really deliver on your promise
to present the latter).  Had you taken the time to read the Feferman
edition you are citing, you might have discovered that G\"odel never
published a proof of the Second Incompleteness Theorem.  All interested
parties are referred to Bell and Machover, or Smorynski's article in the
"Handbook of Mathematical Logic".

TCos:
>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.

Um, Tom, do you think you could try writing complete English sentences the
next time around?  You know, the ones you might have found in-between the
algebraic formulae over the two decades of your study of the subject...

>Tom


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: Mikhail Zeleny                                                     :
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