From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/331 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: Intuitionism's (read "Philosophy's") Limits Date: Wed, 5 Mar 1997 17:19:30 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016896 25222 80.91.229.2 (29 Apr 2009 14:54:56 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:54:56 +0000 (UTC) To: categories Original-X-From: cat-dist Wed Mar 5 17:20:12 1997 Original-Received: by mailserv.mta.ca; id AA06945; Wed, 5 Mar 1997 17:19:30 -0400 Original-Lines: 59 Xref: news.gmane.org gmane.science.mathematics.categories:331 Archived-At: Date: Wed, 5 Mar 1997 11:27:42 -0500 (EST) From: James Stasheff this seems to ignore the distinction between neighbors (aka comrades) and parts (elements) The group of rational integers, with its non-identity automrophisms can, i thought, be distinguished from the Thom space of the > tangent bundle of some exotic manifold with its non-identity automrophisms without comparison to other sets of `numbers' or less exotic manifolds .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds May 15 - August 15: 146 Woodland Dr Lansdale PA 19446 (215)822-6707 On Wed, 5 Mar 1997, categories wrote: > Date: Wed, 05 Mar 1997 00:56 -0500 (EST) > From: Fred E J Linton <0004142427@mcimail.com> > > Any philosophy category theory may have would have at its core, I think, > the notion that mathematical objects are known *not* in isolation but > in the context of their comrades. The group of rational integers, > accompanied *only* by its identity map, and the Thom space of the > tangent bundle of some exotic manifold, accompanied once again *only* > by its identity map, are, as categories, indistinguishable. > > Plucked out of their original contexts, there is no longer any social setting > where one can find any difference between them that really *makes* a > difference. > > According to some other views of mathematics, the group of rational integers, > that particular Thom space, the real number {pi}, and my current left shoe, > all have unique mathematical personalities that let them be "obviously" > distinguished one from another, without any reference even to what I would > call their "natural ambient environments". > > >From my perspective, admittedly that of a categorist, these views result > from a simple failure to recognize that what passes for the "intrinsic > structure" of a mathematical object is in fact nothing more (nor less) > than a clear understanding of its relations with its mates, of roughly > similar character, in some category (that "went without saying") they all > jointly inhabit -- even the phrase "roughly similar character" is justifiable > *only* by virtue of the fact that they *do* all inhabit some same category. > > I hope I'm actually making myself clear, and not just preaching to the converted. > > -- Fred > > >