From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6215 Path: news.gmane.org!not-for-mail From: =?ISO-8859-1?Q?Mattias_Wikstr=F6m?= Newsgroups: gmane.science.mathematics.categories Subject: =?UTF-8?B?UmU6IElzIGVxdWFsaXR5IGV2aWw/4oCP?= Date: Fri, 24 Sep 2010 17:30:15 +0200 Message-ID: Reply-To: =?ISO-8859-1?Q?Mattias_Wikstr=F6m?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1285374243 25837 80.91.229.12 (25 Sep 2010 00:24:03 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 25 Sep 2010 00:24:03 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sat Sep 25 02:24:02 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 1OzIYZ-00027p-9d for gsmc-categories@m.gmane.org; Sat, 25 Sep 2010 02:23:59 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51116) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OzIXl-0007cz-0V; Fri, 24 Sep 2010 21:23:09 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OzIXh-00029s-LW for categories-list@mlist.mta.ca; Fri, 24 Sep 2010 21:23:05 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6215 Archived-At: Toby Bartels wrote: > Right. I would prefer to use no identity types at all. > If there is a particular predicate (on some particular type) > that you would like to think of as equality (on that type), > then write down its definition and introduce a symbol for it. If any (well-behaved) equivalence relation can be thought of as equality then it would seem to follow that equality is relative. That is: 1) A and B may be the same thing from one point of view and two different things from another point of view, 2) the cardinality of {A, B} may be either 1 or 2 depending on what point of view one takes, and 3) it may be that from one point of view there is no property that distinguishes A from B while from another point of view there is a property P that distinguishes A from B (for consistency I guess one has to say that relative to the first viewpoint, not only does P not exist, but the second viewpoint also fails to exist). In the philosophical literature the idea that equality/identity is relative is credited to philosopher Peter Geach (I can give a list of references if anyone is interested). It has few adherents, but maybe category theory can make it popular. Best regards, Mattias [For admin and other information see: http://www.mta.ca/~cat-dist/ ]