From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7316 Path: news.gmane.org!not-for-mail From: Colin McLarty Newsgroups: gmane.science.mathematics.categories Subject: Re: The Idea of Structure as Data and Conditions Date: Tue, 29 May 2012 09:28:42 -0400 Message-ID: References: <043qeCDoI7392S02.1338261334@web02.cms.usa.net> Reply-To: Colin McLarty NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1338314204 1365 80.91.229.3 (29 May 2012 17:56:44 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 29 May 2012 17:56:44 +0000 (UTC) Cc: Florian Lengyel , categories@mta.ca To: "Fred E.J. Linton" Original-X-From: majordomo@mlist.mta.ca Tue May 29 19:56:43 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1SZQex-0001VM-1C for gsmc-categories@m.gmane.org; Tue, 29 May 2012 19:56:43 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45388) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SZQeN-00022r-HE; Tue, 29 May 2012 14:56:07 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SZQeO-0008QZ-6Y for categories-list@mlist.mta.ca; Tue, 29 May 2012 14:56:08 -0300 In-Reply-To: <043qeCDoI7392S02.1338261334@web02.cms.usa.net> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7316 Archived-At: Something has gone entirely wrong here. The axiom of regularity forbids x\in x. colin On Mon, May 28, 2012 at 11:15 PM, Fred E.J. Linton wrot= e: > On Mon, 28 May 2012 07:25:19 PM EDT, Florian Lengyel > , protesting my assertion that > >>> Virtually no one ever wants to restrict attention to functions that > respect >>> (preserve or reflect) membership (other than "preserve" between ordinal= s). > > remonstrated that > >> Within set theories that satisfy the axiom of regularity, one's attentio= n >> is restricted to functions that both preserve and reflect self-membershi= p. >> >> f(x) \in f(x) iff x\in x > > Hereto, I in turn ask: Why only self-membership? why not membership outri= ght > > -- f(x) \in f(y) if (and/or only if) x \in y -- ? > > And how often, really, do we actually impose either of those restrictions= ? (Or > > did FL inadvertently omit a "sometimes" between "is" and "restricted" :-)= =A0?) > > Cheers, -- Fred > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]