From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7314 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: The Idea of Structure as Data and Conditions Date: Mon, 28 May 2012 23:15:34 -0400 Message-ID: <043qeCDoI7392S02.1338261334@web02.cms.usa.net> Reply-To: "Fred E.J. Linton" 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 1338285341 16102 80.91.229.3 (29 May 2012 09:55:41 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 29 May 2012 09:55:41 +0000 (UTC) Cc: To: Florian Lengyel , FEJ Linton Original-X-From: majordomo@mlist.mta.ca Tue May 29 11:55:38 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 1SZJ9G-0002Ak-Gs for gsmc-categories@m.gmane.org; Tue, 29 May 2012 11:55:30 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45259) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SZJ8M-0004lk-7e; Tue, 29 May 2012 06:54:34 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SZJ8L-0006sC-ON for categories-list@mlist.mta.ca; Tue, 29 May 2012 06:54:33 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7314 Archived-At: 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 ordina= ls). remonstrated that > Within set theories that satisfy the axiom of regularity, one's attenti= on > is restricted to functions that both preserve and reflect self-membersh= ip. > = > 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" :-)= ?) Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]