From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2311 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: Topos logic arises naturally Date: Sun, 1 Jun 2003 09:05:31 -0700 Message-ID: <20030601160531.GH20845@math-rs-n01.ucr.edu> References: <3ED34194.9050005@informatik.uni-bremen.de> <002801c326a1$05dc0000$f112fea9@essex.ac.uk> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241018566 3491 80.91.229.2 (29 Apr 2009 15:22:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:22:46 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Mon Jun 2 17:35:29 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 02 Jun 2003 17:35:29 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19Mvzh-0004bG-00 for categories-list@mta.ca; Mon, 02 Jun 2003 17:33:25 -0300 Content-Disposition: inline In-Reply-To: <002801c326a1$05dc0000$f112fea9@essex.ac.uk> User-Agent: Mutt/1.4i Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 1 Original-Lines: 18 Xref: news.gmane.org gmane.science.mathematics.categories:2311 Archived-At: Elwood Wilkins wrote: >Isabelle's internal logic is not constructive. The existential clause of the >BHK-interpretation is violated so that a consquence of "all unicorns have >horns" is that "some unicorn has a horn". The moral (biased towards >theorists): software engineering considerations are not enough, a coherant >philosophy of mathematics is also needed. Is this a failure of constructivism as such, or just a bug? No doubt that a coherent philosophy of mathematics helps to avoid such mistakes, but would anybody ever claim that it's *not* a mistake? -- Toby