From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5983 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Are mathematical proofs incomparable with proofs in other disciplines? Date: Fri, 9 Jul 2010 10:10:18 -0400 (EDT) Message-ID: References: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1278765749 3459 80.91.229.12 (10 Jul 2010 12:42:29 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 10 Jul 2010 12:42:29 +0000 (UTC) Cc: categories list To: Vaughan Pratt Original-X-From: categories@mta.ca Sat Jul 10 14:42:27 2010 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 4.69) (envelope-from ) id 1OXZNy-00011m-2y for gsmc-categories@m.gmane.org; Sat, 10 Jul 2010 14:42:26 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OXYt4-0003k7-FN for categories-list@mta.ca; Sat, 10 Jul 2010 09:10:30 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5983 Archived-At: On Wed, 7 Jul 2010, Vaughan Pratt wrote: > My questions are > > 1. Is mathematical proof so different from say legal proof that the two > notions should be listed on a disambiguation page as being unrelated > meanings of the same word, or should they be treated as essentially the > same notion modulo provenance of evidence and strictness of sufficiency, > both falling under the definition "sufficient evidence of the truth of a > proposition." Let me begin my answer with an aphorism. I don't know who said it first, but I heard it from Charles Wells. In principle, there is no difference between principle and practice, but in practice... If mathematical proof were simply logical deductions, there would never be mistaken proofs published. On the other hand, if proofs weren't logical deductions, we could never find errors in proofs, only in their consequences. Nonetheless, the biggest difference between mathematical proof and, say, legal proof, is that the latter depends on real world evidence. Legal terms do not have definitions that can be understood without reference to the real world. we believe that, in principle, every proof we publish is a surrogate for a formal logical deduction, but I once tried that for a simple argument and gave up after I had filled a couple pages with indecipherable chicken scratchings (cf. Russell & Whitehead). > > 2. Gandalf61 evidently feels his sources, Krantz and Bornat, prove the > notions are incomparable. Are there suitable sources for the opposite > assertion, that they are comparable? > I agree, however, that they are incomparable. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]