From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1837 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Why binary products are ordered Date: Thu, 8 Feb 2001 12:44:59 -0500 (EST) Message-ID: References: <200102080117.RAA13130@coraki.Stanford.EDU> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018136 711 80.91.229.2 (29 Apr 2009 15:15:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:15:36 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Feb 9 15:20:20 2001 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f19Iac129963 for categories-list; Fri, 9 Feb 2001 14:36:38 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs X-Sender: barr@triples.math.mcgill.ca In-Reply-To: <200102080117.RAA13130@coraki.Stanford.EDU> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 19 Original-Lines: 31 Xref: news.gmane.org gmane.science.mathematics.categories:1837 Archived-At: As I said in an earlier post, the whole thing is a figment of the linear way we write (and speak, for that matter). Products are over unordered sets and any ordering is purely irrelevant. On Wed, 7 Feb 2001, Vaughan Pratt wrote: ... > I confess to some confusion as to what Charles is insisting is inevitable > here. A binary product in C is a limit of a diagram 1+1->C (1+1 the > two-object discrete category), and 1+1 has two automorphisms. This much > and its mathematical consequences are surely inevitable. > > But woven into Charles' argument is what Bill has called the "totally > arbitrary singleton operation of Peano." It appears implicitly at the > beginning when Charles names the projections, and then (after an indirect > reference to the automorphisms of the binary product) more explicitly > when he collects the names as a set. > > Surely anyone insisting on names like 1 and 2 or red and blue for the > projections of binary product is backsliding into the ZFvN tarpit of > spurious rigidified membership. If this backsliding really is inevitable > as Charles seems to be saying, how does one reconcile this with Bill's > view of "rigidified membership" as "mathematically spurious"? > > Must mathematics accept the spurious, in this or any other case? > > Vaughan >