From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5990 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Are mathematical proofs incomparable with proofs in other disciplines? Date: Thu, 15 Jul 2010 00:31:06 -0700 Message-ID: References: Reply-To: Vaughan Pratt NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1279291979 20331 80.91.229.12 (16 Jul 2010 14:52:59 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 16 Jul 2010 14:52:59 +0000 (UTC) To: categories list Original-X-From: categories@mta.ca Fri Jul 16 16:52:57 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 1OZmHY-0007PZ-OU for gsmc-categories@m.gmane.org; Fri, 16 Jul 2010 16:52:56 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OZlf3-0002MC-Vy for categories-list@mta.ca; Fri, 16 Jul 2010 11:13:10 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5990 Archived-At: On 7/9/2010 12:55 PM, Joyal, Andr=E9 wrote: > I agree with your definition: > > "A proof is sufficient evidence for the truth of a proposition," Meanwhile the existence of some who prefer adding "or argument" to=20 "evidence" seems to have been established. Maybe one day they'll=20 surrrender, but this is not my highest priority. Higher is to make the=20 following title changes on Wikipedia: Proof (truth) ---> Proof Proof ---> Proof (disambiguation) The first is the article on proof, the second is the Wikipedia=20 disambiguation or dab page that takes you to other meanings such as=20 "alcoholic proof" (an obsolete term even in the US, having been replaced=20 by "alcohol by volume" or ABV) and proofreading. The suggested change=20 would make the article on proof the primary topic (a Wikipedia concept)=20 having a so-called hatnote (note at the head of the article) pointing to=20 a disambiguation page for the lesser meanings. So far no but myself and=20 one or two people have spoken up for this; until they do nothing will=20 change. > The article > > http://en.wikipedia.org/wiki/Proof > > does not discuss the idea (of Paul Lorenzen) that a mathematical proof > is essentially a winning strategy in a formal game. > I first learned the idea from Andreas Blass > who introduced the game semantic of linear logic, > > http://arxiv.org/abs/math/9310211 > > A proof can be viewed as an argumentation to convince others of the val= idity of a statement. > In mathematics, the argumentation must be solid enough to resist > any conter-argumentation by an ideal opponent. I would divide proofs into two kinds, those where the intended audience=20 can argue back, as in a courtroom or ordinary conversation, and those=20 where they can't, for example the subscribers to a journal. What you=20 describe does cover both, but for the latter the game is very short. In computation this distinction is that between alternating computation=20 and nondeterministic computation. Alternation computation is an=20 on-going game, in non-deterministic computation one player makes one=20 choice and the game ends. Interestingly the notion of nondeterministic=20 computation preceded that of alternating computation under that name by=20 some 15 years or so. But Fra=EFss=E9's alternation preceded both by a=20 decade, although it took a decade for Ehrenfeucht to cast Fra=EFss=E9's=20 approach as a game (1961). Vaughan [For admin and other information see: http://www.mta.ca/~cat-dist/ ]