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Article 1655 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: rec.arts.books,sci.philosophy.tech,comp.ai.philosophy
Subject: Re: The Philosophical Foibles of John McCarthy
Message-ID: <1991Nov26.211349.5938@husc3.harvard.edu>
Date: 27 Nov 91 02:13:47 GMT
References: <JMC.91Nov24203029@SAIL.Stanford.EDU> <1991Nov25.180643.5898@husc3.harvard.edu> <443@trwacs.UUCP>
Organization: Dept. of Math, Harvard Univ.
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Nntp-Posting-Host: zariski.harvard.edu

In article <443@trwacs.UUCP> 
erwin@trwacs.UUCP (Harry Erwin) writes:

>I'm bothered by some aspects of this argument. The distinction between
>"facts" and "formal models" becomes fuzzy when you start looking at the
>foundations of mathematics. It is true that there are true statements that
>are not provable in the model that Goedel defined.

I am not aware of the notion `provable in a model'; furthermore, are you
referring to the incompleteness results, or to the later proof that AC and
GCH are compatible with the rest of ZFC?  On a more fundamental issue, I'll
add that McCarthy himself argues in his 1977 IJCAI article that realism
yields the right perspective for an AI program.  Normally I would offer an
argument that Platonism is the correct philosophy of mathematics; thanks to
McCarthy's stated views, I feel justified in assuming the truth of
Platonism for the present purposes.

>                                                   But there are also
>non-standard models that are equivalent to the standard model for most
>interesting problems, but that define additional statements to be true or
>false. The point is that these non-standard models are equivalent in terms
>of our intuitive sense of "truth" to the standard model and only differ in
>areas where we have no way of telling the truth or falsity of the system.
>See Cohen's work plus the later work from the University of Pennsylvania.

On the contrary, the interest of Cohen's work lies exactly in the way he
utilizes the non-standard generic model in order to "make" certain
propositions come out true or false.  What UPenn work are you alluding to? 

>Those arguments convinced me that Platonism is invalid, since ideal
>objects appear not to be definable.

Most real numbers are not definable.  What's your point?

>Cheers,
>-- 
>Harry Erwin
>Internet: erwin@trwacs.fp.trw.com

Regards,
MZ

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: Mikhail Zeleny                                                     :
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