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Article 5161 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: Peano and the commerce of ideas and representatio
Message-ID: <1992Apr20.211210.11342@husc3.harvard.edu>
Date: 21 Apr 92 01:12:07 GMT
Article-I.D.: husc3.1992Apr20.211210.11342
References: <kv3lf9INNe8g@exodus.Eng.Sun.COM>
Organization: Dept. of Math, Harvard Univ.
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Nntp-Posting-Host: zariski.harvard.edu

In article <kv3lf9INNe8g@exodus.Eng.Sun.COM> 
silber@orfeo.Eng.Sun.COM (Eric Silber) writes: 

ES:
>Assert for the purpose of disputation that "real mathematical objects"
>exist independent of the physical world.
>
>Hence  Integer-3 for which "3" is a physical representation, exists
>independent of the physical world.
>
> Does Integer-3 know that it is an integer?
> Does Integer-3 know what its successor is?
>
> It would seem evident that in order for the abstract real mathematical
> object Integer-3 to be able to "answer" these questions, it must be
> EMBEDDED IN A REPRESENTATION.  But such a representation, that is to say
> "structure" would pose a contradiction,
> for if the abstract non-material world of the
> platonic forms admits of structures , they too must be nonmaterial,
> and in that abstract nonmaterial world, there are no bounds to these
> nonmaterial representations, hence there can only be
> one grand-unified all-and-everything structure in the "abstract world"
> (were it otherwise, then Integer-3 would be: 
> not only itself, but every integer,
> and the essence of all integers, and every theorem about integers.
> If this were so, it would be so for every integer, and hence all
> integers would be identical and indistinguishable from one another)

This is false, as you are neglecting the distinction between an extensional
set and an ordered structure.  In any case, there is a difference between
an integer and a concept thereof; your reasoning may only apply to the
latter, if at all.  Of course, the concept may possess any sort of
structure, in the presence of which extensional identity will surely fail.

> Peano's axioms, for example, esatblish an inductive representation
> which gives meaning to the notion "integer".
> Things are NOT the other way around, disembodied "real mathematical
> objects" DO NOT supply "meaning" to physical representations, rather they
> derive meaning from representations.

Sounds like a profession of faith.  Too bad Frege refuted mathematical
empiricism over a century ago.


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