From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7312 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: The Idea of Structure as Data and Conditions Date: Sun, 27 May 2012 16:25:35 -0700 Message-ID: References: Reply-To: Vaughan Pratt NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1338245667 23714 80.91.229.3 (28 May 2012 22:54:27 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 28 May 2012 22:54:27 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Tue May 29 00:54:26 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1SZ8pW-0005Ni-Gm for gsmc-categories@m.gmane.org; Tue, 29 May 2012 00:54:26 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45172) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SZ8p3-0007vS-6r; Mon, 28 May 2012 19:53:57 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SZ8p4-0004FQ-TE for categories-list@mlist.mta.ca; Mon, 28 May 2012 19:53:58 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7312 Archived-At: The proposition that "mathematical structure is given by data and conditions" is so broad as to be vacuous from a foundational standpoint. While there may be disagreement between mathematical camps over whether algebraic frameworks rest on logical or vice versa, common to both is the idea that one starts with a (non-logical) language and equips it with a theory. I don't see how "data and conditions" can be interpreted as giving undue weight to either the equational or first-order starting points. The sentiment could just as validly preface a graduate course on first order model theory. Vaughan Pratt On 5/25/2012 3:09 PM, Ellis D. Cooper wrote: > I was permitted to audit a graduate course on category theory guided > by Sammy at Columbia University in the early 1960s. > I recall his insistence that mathematical structure is given by data > and conditions. Is that idea > implicit or explicit in Bourbaki? Has that idea been superceded? How > does it relate to the > development of algebraic theories as understood by Lawvere, Linton, > Barr-Wells, the Elephant, and so on? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]