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Article 1388 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: <1991Nov19.001943.9064@CSD-NewsHost.Stanford.EDU>
Date: 19 Nov 91 00:19:43 GMT
References: <1991Nov14.163630.20597@spss.com> <1991Nov17.163705.5540@husc3.harvard.edu> <1991Nov18.114641.964@CSD-NewsHost.Stanford.EDU> <1991Nov18.094715.5563@husc3.harvard.edu>
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Organization: Computer Science Department, Stanford University
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In article <1991Nov18.094715.5563@husc3.harvard.edu>, zeleny@osgood.harvard.edu (Mikhail Zeleny) writes:
|> 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.

The following is a quotation, I'll put in quotation marks so 
it's even more obvious. 
 "
|> >1. The class of axioms and rules of inference(that is, the relation "immediate
|> >consequence") are recursively definable ( as soon 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).

The above is a quotation.  It concerns the conditions necessary for 
the application of Godel's First Incompleteness Theorem.

|>  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.

Ok, this is false, here is a claim that he did, in Godel's words;
"Satz XI.  Sei k eine beliebige rekursive widerspruchsfrie Klasse
von FORMELEN, dann gilt.  Die SATZFORMEL, welche besagt, dass k
 wider-spruchsfrei ist, ist nicht k-BEWEISBAR; insbesondere ist die
 Widerspruchs-freiheit von P in P unbweiesbar, vorausgesetzt, dass P
 widerspruchsfrei ist ( im entgegengesetzten Fall ist naturlich jede
 Aussage beweisbar).
 Der Beweis ist ( in Umrissen skizziert) der folgende: .. "
And in translation;
Theorem 11.  Let k be any recursive consistent class of FORMULAS; then the SENTENTIAL FORMULA stating that k is consistent is not k-PROVABLE; in particuylar the consistency of P is not provable in P, provided P is consistent ( in the opposite case, of cou
rse, every proposition is provable [in P]).
The proof (briefly outlined) is as follows:...

All of the above is taken from the aforementioned volume.

|>  All interested
|> parties are referred to Bell and Machover, or Smorynski's article in the
|> "Handbook of Mathematical Logic".

At least this interested party will read the original.  Godel second 
incompleteness theorem, is the final theorem, Theorem XI of section 4
of Godel 1931.  Misha, read the originals, sometimes commentators
get it wrong.
|> 
|> 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...
|> 

"The first part" subject, "is" verb, "the condition", object, "..."
a clause modifying the object, "the second" secondary subject, "a condition"
secondary object, ".." a modifier of the secondary object;
These are the parts of speech that the various parts of the sentence
are.  It is perfectly grammatical, though some would find ending a
sentence with "as", behaviour up with which they would not put.


 
|> >Tom
|> 
|> 
|> '`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`
|> `'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
|> : 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


