From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5217 Path: news.gmane.org!not-for-mail From: Andre Joyal Newsgroups: gmane.science.mathematics.categories Subject: pragmatic foundation Date: Fri, 6 Nov 2009 16:14:18 -0500 Message-ID: Reply-To: Andre Joyal NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1257558268 28846 80.91.229.12 (7 Nov 2009 01:44:28 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 7 Nov 2009 01:44:28 +0000 (UTC) To: Original-X-From: categories@mta.ca Sat Nov 07 02:44:21 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 1N6aLl-0005RZ-1M for gsmc-categories@m.gmane.org; Sat, 07 Nov 2009 02:44:21 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1N6ZoS-0007Qt-OV for categories-list@mta.ca; Fri, 06 Nov 2009 21:09:58 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5217 Archived-At: Dear category theorists, I invite everyone to read the interesting interview of Yuri Manin=20 published in the November issue of the Notices of the AMS: http://www.ams.org/notices/200910 http://www.ams.org/notices/200910/rtx091001268p.pdf One the ideas discussed by Manin is that of a "pragmatic foundation" of mathematics as opposed to a "normative foundation" by logicists or = constructivists.=20 He attributes the former to Bourbaki. I disagree. The foundational framework of Bourbaki is very much in the tradition=20 of Zermelo-Fraenkel, Godel-Bernays and Russell. I am aware that Bourbaki was more interested in the development of=20 mathematics than in its foundation.=20 My guess is that the foundation was too problematic to be given a = proeminent place=20 in the treaty, not for logical reasons but for conceptual reasons. I claim that nobody truly understand set theory, even today! The emperor has no clothes! I mean that the hierarchy of infinite cardinals is so profoundly = mysterious=20 that it looks pathological. What is the value of a theory if it leads to meaningless problems and = structures?=20 Having no good answer to offer, Bourbaki decided to diminish the = importance of=20 foundation rather than leaving it open.=20 It may explain why category theory was not incorporated in the = foundation later. In the interview, Manin also said that: >And so I don=92t foresee anything extraordinary=20 >in the next twenty years. Probably, a rebuilding of=20 >what I call the =93pragmatic foundations of math-=20 >ematics=94 will continue. By this I mean simply a=20 >codification of efficient new intuitive tools, such=20 >as Feynman path integrals, higher categories, the=20 >=93brave new algebra=94 of homotopy theorists, as=20 >well as emerging new value systems and accepted=20 >forms of presenting results that exist in the minds=20 >and research papers of working mathematicians=20 >here and now, at each particular time.=20 Any comments? AJ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]