From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1841 Path: news.gmane.org!not-for-mail From: Charles Wells Newsgroups: gmane.science.mathematics.categories Subject: Inevitability of ordering products Date: Thu, 08 Feb 2001 10:48:43 -0800 Message-ID: <4.1.20010208103452.00af4d30@mail.oberlin.net> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" X-Trace: ger.gmane.org 1241018143 753 80.91.229.2 (29 Apr 2009 15:15:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:15:43 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Feb 10 17:24:16 2001 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f1AKfXj07102 for categories-list; Sat, 10 Feb 2001 16:41:33 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: cwells@mail.oberlin.net X-Mailer: QUALCOMM Windows Eudora Pro Version 4.1 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 23 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:1841 Archived-At: Vaughn Pratt made some valid points about my earlier remarks on the inevitably of binary product projections being ordered. For the most part, I agree with him (but see below), since my (unclearly made) point was that it is inevitable in our current mathematical culture, not that it was mathematically inevitable. However, I am stuck on one point: Sometimes one needs to refer to one of the projections, and that involves giving the projections names. I mentioned "red" and "blue" as examples of names that do not introduce a spurious ordering. But in practice, we must occasionally give names. This is not only for computation, either. For example, one sometimes needs to assume that an n-ary operation factors through one of the projections, and then deduce consequences from that (Peter Johnstone did something like that in his study of varieties that are ccc's). In the proof one must give a name to the projection it factors through. So I argue that naming the projections is sometimes a practical necessity, and given current mathematical habits the names are likely to have some intrinsic (culturally intrinsic!) ordering. But we could use red and blue. Or vanilla and chocolate. Charles Wells, 105 South Cedar St., Oberlin, Ohio 44074, USA. email: charles@freude.com. home phone: 440 774 1926. professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.oberlin.net/~cwells/index.html NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm