From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5009 Path: news.gmane.org!not-for-mail From: Martin Escardo Newsgroups: gmane.science.mathematics.categories Subject: Re: no fundamental theorems please Date: Tue, 23 Jun 2009 10:28:04 +0100 Message-ID: Reply-To: Martin Escardo NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1245763645 25261 80.91.229.12 (23 Jun 2009 13:27:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 23 Jun 2009 13:27:25 +0000 (UTC) To: categories , Paul Taylor Original-X-From: categories@mta.ca Tue Jun 23 15:27:19 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MJ61u-0002Fw-L9 for gsmc-categories@m.gmane.org; Tue, 23 Jun 2009 15:27:18 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MJ5Qj-0005nx-FZ for categories-list@mta.ca; Tue, 23 Jun 2009 09:48:53 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5009 Archived-At: I am sure several other readers of this list will have the same reply to this specific point of Paul's message: Paul Taylor wrote: > For example, there is Cantor's "theorem" about a powerset being > strictly bigger than a set. This belongs entirely to the dogma > of set theory. When set theory is overturned, this miserable > and wholely misguided "theorem" will go in the dustbin of > mathematical history with it. There is a very nice paper by Lawvere that shows that the essence of Cantor's theorem is fundamental and beautiful: Originally published in: Diagonal arguments and cartesian closed categories, Lecture Notes in Mathematics, 92 (1969), 134-145. Reprinted in TAC: http://www.tac.mta.ca/tac/reprints/articles/15/tr15abs.html There is also a post by Andrej Bauer in his Mathematics and Computation blog: http://math.andrej.com/2007/04/08/on-a-proof-of-cantors-theorem/ Martin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]