From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5247 Path: news.gmane.org!not-for-mail From: Andre.Rodin@ens.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: pragmatic foundation Date: Thu, 12 Nov 2009 10:07:05 +0100 Message-ID: References: Reply-To: Andre.Rodin@ens.fr 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 1258047237 21282 80.91.229.12 (12 Nov 2009 17:33:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 12 Nov 2009 17:33:57 +0000 (UTC) To: "Eduardo J. Dubuc" , categories@mta.ca Original-X-From: categories@mta.ca Thu Nov 12 18:33:50 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 1N8dYL-0004hv-J3 for gsmc-categories@m.gmane.org; Thu, 12 Nov 2009 18:33:49 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1N8d1W-0000Zy-Bm for categories-list@mta.ca; Thu, 12 Nov 2009 12:59:54 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5247 Archived-At: I agree with WHAT Yuri Ivanovitch Manin says about foundations of mathema= tics but DISagree when he calls these foundations "pragmatic". I might be mist= aken (in this case, I hope, Yuri Ivanovitch will correct me) but I don't think= that in the given context the word "pragmatic" is supposed to be understood wi= th a philosophical seriousness. In the given context "pragmatic" is rather synonymous to "practical" as opposed to "theoretical" - and perhaps also = to "purely mathematical" as opposed to "philosophical". I fully share with Y= uri Ivanovitch his disappointment about what he calls the "normative foundati= ons that logicists or constructivists tried to impose". But I see a solution = in a new dialectical philosophy of foundations (tightly connected to mathemati= cal practice), NOT in developing foundations purely "pragmatically" without theoretical and philosophical grounds. The history teaches us that philosophical thinking is crucial for what Yuri Ivanovitch calls the "rebuilding" of foundations, and I don't see any reason why this might ce= ase to be true today. On the contrary, I think that the acceleration of mathematical progress necessitates the acceleration of rebuilding of foundations - and this mak= es philosophy more relevant to mathematical research than ever. "Logicists a= nd constructivists" don't have centuries to come to eternalise their finding= s by establishing a new Scholastic tradition in philosophy - even if some of t= hem would wish it. Andrei [For admin and other information see: http://www.mta.ca/~cat-dist/ ]