From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!utgpu!cs.utexas.edu!uunet!trwacs!erwin Wed Apr 22 12:04:21 EDT 1992
Article 5176 of comp.ai.philosophy:
Xref: newshub.ccs.yorku.ca comp.ai.philosophy:5176 sci.philosophy.tech:2576
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!utgpu!cs.utexas.edu!uunet!trwacs!erwin
>From: erwin@trwacs.fp.trw.com (Harry Erwin)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: Peano and the commerce of ideas and representatio
Message-ID: <556@trwacs.fp.trw.com>
Date: 21 Apr 92 17:46:22 GMT
References: <kv3lf9INNe8g@exodus.Eng.Sun.COM> <1992Apr20.211210.11342@husc3.harvard.edu>
Followup-To: comp.ai.philosophy
Organization: TRW Systems Division, Fairfax VA
Lines: 19

There was an enjoyable book published many years ago titled "Arithmetic
Made Complicated" (or something similar), which took a category- theoretic
view of "simple" arithmetic, introducing such concepts as universal
objects and commutative diagrams. Much of what has passed on this board is
passe' for the category theorists, which is why I invite one to join this
discussion. The existence of the universal object "3" is a consequence of
the Axiom of Choice. Cohen's demonstration that the Axiom of Choice is in
the same category as Euclid's 5th Postulate, i.e., independent of the
remaining axioms, undermined my belief in Platonic ideals, particularly
after Robinson demonstrated that there were non-standard models of
arithmetic where the Axiom of Choice did not hold. Thus I've regarded much
of what has passed on this board as being insufficiently grounded in the
Foundations of Mathematics.

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



