From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5949 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: The humility topos Date: Fri, 02 Jul 2010 12:03:47 -0300 Message-ID: References: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.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 1278261259 21591 80.91.229.12 (4 Jul 2010 16:34:19 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 4 Jul 2010 16:34:19 +0000 (UTC) Cc: Michael Barr ,Categories list To: Dusko Pavlovic Original-X-From: categories@mta.ca Sun Jul 04 18:34:18 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OVS91-0000tc-Rc for gsmc-categories@m.gmane.org; Sun, 04 Jul 2010 18:34:16 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OVRii-00072h-CY for categories-list@mta.ca; Sun, 04 Jul 2010 13:07:04 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5949 Archived-At: Grothendieck introduced the term "topos" simply out of "topology" and "topological space". we should wonder who and why introduced "topology" and "topological space". Dusko Pavlovic wrote: > It might be fair to remember that "Topoi" is the title of 6th book or > Aristotle's Organon. "On Categories" is the title of the 1st book of > Organon. > > Both concepts were very actively used by scolastic philosophers. Maybe > we are their heirs of some sort ;) > > It would be interesting to know about the motivations of people who introduced these terms into mathematics. I think that MacLane said at one point that there was a terminological link through Rudolf Carnap, thus through neokantians. The notion of categories plays a prominent role in Kant's first Critique. But it is even more interesting if the term topos was introduced with an intentional reference to *dialectics*, which is what that part of Organon is about. > > -- dusko [For admin and other information see: http://www.mta.ca/~cat-dist/ ]