From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/335 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: Intuitionism's Limits Date: Thu, 6 Mar 1997 13:29:47 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016898 25234 80.91.229.2 (29 Apr 2009 14:54:58 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:54:58 +0000 (UTC) To: categories Original-X-From: cat-dist Thu Mar 6 13:31:31 1997 Original-Received: by mailserv.mta.ca; id AA26186; Thu, 6 Mar 1997 13:29:47 -0400 Original-Lines: 35 Xref: news.gmane.org gmane.science.mathematics.categories:335 Archived-At: Date: Wed, 05 Mar 1997 22:36:19 -0800 From: Vaughan Pratt Date: Tue, 4 Mar 1997 18:19:51 +1030 (CST) From: William James (I grant you the original question would have been more recognisable given better use of language: "...philosophies of constructive mathematics and *of* category theory...") Your original question was "Which view should dominate?", where "the category theoretic view" was one of your options. (You had several questions but this one seemed the most central.) If you are asking whether the primary expression of structure should be in terms of relations between elements or transformations of objects, then I would answer this as follows. The analogous question for physics is whether energy and matter consist of particles or waves. The consensus in physics today is that both energy and matter can be viewed more or less equally accurately, if not equally insightfully, as either particles or waves. Which offers more insight depends on the circumstances. The corresponding position for mathematics would be that structure can be expressed more or less equally well in elementary or transformational terms, and that which approach gives more insight depends on the circumstances. The extent to which this is not the consensus in mathematics today is less a reflection on either approach than on the conceptual health of mathematics relative to that of physics. Vaughan Pratt