From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6167 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: Evil in bicategories Date: Wed, 15 Sep 2010 08:32:27 +1000 Message-ID: References: Reply-To: Richard Garner NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1284506099 7355 80.91.229.12 (14 Sep 2010 23:14:59 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 14 Sep 2010 23:14:59 +0000 (UTC) Cc: JeanBenabou , categories To: David Roberts Original-X-From: majordomo@mlist.mta.ca Wed Sep 15 01:14:57 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OveiG-0001Rx-Ot for gsmc-categories@m.gmane.org; Wed, 15 Sep 2010 01:14:57 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:32966) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Oveh2-0004vI-CM; Tue, 14 Sep 2010 20:13:40 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Ovegx-0002nA-V0 for categories-list@mlist.mta.ca; Tue, 14 Sep 2010 20:13:36 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6167 Archived-At: Two that spring to mind are "inflexible" (after Kelly) or "impersistent" (after Par=E9). On 13 September 2010 10:16, David Roberts w= rote: > Dear Jean, > > You wrote: >> Maybe my english isn't so "beautiful", but in all cases where "evil" ha= s >> 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 =3D (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/ ]