From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8549 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: Category without objects Date: Sun, 15 Mar 2015 12:34:44 -0300 Message-ID: References: , Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1426510478 32318 80.91.229.3 (16 Mar 2015 12:54:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 16 Mar 2015 12:54:38 +0000 (UTC) To: Tadeusz Litak , Vaughan Pratt , categories Original-X-From: majordomo@mlist.mta.ca Mon Mar 16 13:54:30 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1YXUXM-0006AO-KN for gsmc-categories@m.gmane.org; Mon, 16 Mar 2015 13:54:28 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:40842) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YXUWi-0002rD-QH; Mon, 16 Mar 2015 09:53:48 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YXUWh-0004zJ-9s for categories-list@mlist.mta.ca; Mon, 16 Mar 2015 09:53:47 -0300 User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.10; rv:31.0) Gecko/20100101 Thunderbird/31.5.0 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8549 Archived-At: Redundancy is not the same that lack of simplicity, in fact, most of the time is the other way around. Unnatural elimination of redundancy makes things very difficult to understand. On 11/3/15 21:42, Tadeusz Litak wrote: > > On 11/03/15 05:20, Vaughan Pratt wrote: >> >> >> Quine wrote "Word and Object". Reasoning analogously as above, what a >> category theorist would call an object, Quine would call a word. > > > There is actually a (perhaps) more direct reference to Quine in the > context of this discussion. > > In the entry "Mathematosis" of his "Quiddities: An Intermittently > Philosophical Dictionary", he wrote: > >> There has been a tendency of late to sacrifice simplicity at the >> altar of model theory. For instance we find a group defined as >> an ordered pair (A, f) where A is a class and f is a FUNCTION, >> q.v., whose arguments and values comprise A and fulfill certain >> axioms that I shall not pause over. This dragging in of a class >> A, and therewith of an ordered pair, is a gratuitous conformity >> to model-theoretic fashion; the function f is enough by itself, >> since A is definable in terms of f as the class of its arguments >> and values. > > One can see here an analogy to the redundancy of objects in category > theory. > > However, the entry "Function" in the same book makes it clear that Quine > thinks of functions in entirely set-theoretic > terms: as collections of ordered pairs. > > t. > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]