From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3153 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: One-stop version of my postings Date: Thu, 23 Mar 2006 20:31:47 -0800 Organization: Stanford University Message-ID: Reply-To: pratt@cs.stanford.edu NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019124 7466 80.91.229.2 (29 Apr 2009 15:32:04 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:32:04 +0000 (UTC) To: cat group Original-X-From: rrosebru@mta.ca Sat Mar 25 00:47:19 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 25 Mar 2006 00:47:19 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FN0XW-0004pQ-0x for categories-list@mta.ca; Sat, 25 Mar 2006 00:38:14 -0400 User-Agent: Mozilla Thunderbird 0.9 (Windows/20041103) X-Accept-Language: en-us, en Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 99 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:3153 Archived-At: Robert J. MacG. Dawson wrote: > ...fatally flawed. (Why do the circles in Euc.I.1 intersect? None of his > axioms assert that any pair of circles whatsoever do so.) In axiomatic mathematics, everything that is not forbidden is permitted. Circles can climb trees and drape themselves over branches in Dali's axiomatization of geometry, not because he says they can but because he is not the strict disciplinarian that Euclid is. Euclid insists that his circles shape up or else. This creates many problems for the circles but few problems for mathematicians as their managers. Dali runs a looser ship, which lets the circles lead a less structured life while creating more problems for mathematicians. This is a win-win situation: the circles end up with fewer neuroses while the mathematicians thrive, problems being their lifeblood. Thank god for Lobachevsky and the others we can't remember because Tom Lehrer didn't. Vaughan Pratt