From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6149 Path: news.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Re: Evil in bicategories Date: Mon, 13 Sep 2010 09:46:04 +0930 Message-ID: References: Reply-To: David Roberts NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1284402370 19655 80.91.229.12 (13 Sep 2010 18:26:10 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 13 Sep 2010 18:26:10 +0000 (UTC) Cc: categories To: JeanBenabou Original-X-From: majordomo@mlist.mta.ca Mon Sep 13 20:26:08 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OvDjD-0005RD-AD for gsmc-categories@m.gmane.org; Mon, 13 Sep 2010 20:26:07 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:57791) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OvDhs-000816-Eo; Mon, 13 Sep 2010 15:24:44 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OvDhn-00007E-Nq for categories-list@mlist.mta.ca; Mon, 13 Sep 2010 15:24:39 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6149 Archived-At: Dear Jean, You wrote: > Maybe my english isn't so "beautiful", but in all cases where "evil" has > been used, what is wrong with "wrong" instead? I'm not so enamoured with the use of the word 'evil', but it seems to be more entrenched than perhaps it was intended, namely as a joke. Regardless of my personal convictions, I like to remain a mathematical agnostic, so 'wrong' seems to me to be too strong. In my everyday mathematical work I use choice and excluded middle and equality at will, but I know that these foundational ideas ('evil' in categories, constuctivism etc) exist and are useful and interesting. Unfortunately I don't have any decent alternatives to offer, but the philosophy boils down to, in my opinion, a structuralist view of foundations (as opposed to the standard ZF with 'member of' foundations) combined with (even a simple grasp of) type theory. The former is essentially the 'sets are bags of points' approach and the latter is the 'you can't ask: is \pi = (sin:R \to [-1,1])?' idea. Perhaps readers of this list with the inclination and an eye for nomenclature will suggest some words. Toby Bartels calls categories where one is not allowed to test for equality between arbitrary objects 'weak' and those where one can do so 'strict' (most often these latter are internal categories in some version of Set, or perhaps using universes). This reflects thinking about higher categories (and completely exemplified by Makkai's approach via FOLDS). This terminology takes the 'moral dimension' out of talking about serious foundational ideas. But we don't have a word that replaces 'evil' in this context that conveys the sort of mild disdain for attempting to make the naive mistake of trying to ask if a scalar is contained in a vector, as one can do in traditional foundations (note that the answer depends on how one defines tuples). That's my two cents, for what it's worth. David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]