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Article 5149 of comp.ai.philosophy:
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>From: silber@orfeo.Eng.Sun.COM (Eric Silber)
Newsgroups: comp.ai.philosophy
Subject: Peano and the commerce of ideas and representations
Message-ID: <kv3lf9INNe8g@exodus.Eng.Sun.COM>
Date: 19 Apr 92 20:19:53 GMT
Organization: Sun Microsystems, Mt. View, Ca.
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NNTP-Posting-Host: orfeo

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)
 
 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.
 


