From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7118 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: __?__ Date: Fri, 16 Dec 2011 00:56:28 -0800 Message-ID: References: Reply-To: Vaughan Pratt NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1324042668 22321 80.91.229.12 (16 Dec 2011 13:37:48 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 16 Dec 2011 13:37:48 +0000 (UTC) To: Categories Original-X-From: majordomo@mlist.mta.ca Fri Dec 16 14:37:39 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpz.mta.ca ([138.73.1.187]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RbXyk-0002Jx-C8 for gsmc-categories@m.gmane.org; Fri, 16 Dec 2011 14:37:38 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:54531) by smtpz.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1RbXxZ-0003Wp-Tr; Fri, 16 Dec 2011 09:36:25 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RbXxa-0002jf-QQ for categories-list@mlist.mta.ca; Fri, 16 Dec 2011 09:36:26 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7118 Archived-At: On 12/14/2011 1:35 PM, Eduardo J. Dubuc wrote: > Is the following nonsense ? > > http://arxiv.org/abs/1112.2141 The concluding paragraph of the conclusion, on page 37, reads as follows. "Kurt G=F6del provided innovative but convoluted proofs of some normal=20 properties of a simple recurrence relation, accompanied by spectacular=20 misinterpretations. G=F6del=92s incompleteness conjectures have beguiled=20 generations of readers lost in the sea of his complex proofs; his=20 unwarranted conclusions have smashed mathematical reason against the=20 petrified relics of ancient misunderstandings. But other thinkers have=20 seen more clearly; most importantly George Boole, whose brilliant=20 synthesis of algebra and logic has shown the way to modern computer=20 science. Perhaps it is time to raise the lamp in Boole=92s lighthouse, an= d=20 to let the beacon of unified mathematics and logic guide a renewed quest=20 for the rational understanding of our world." Let's go through this point by point. 1. "...convoluted proofs..." G=F6del's 1931 paper was 25 pages.=20 Norman's is 48. Sounds like a pot calling the kettle black. 2. "G=F6del=92s incompleteness conjectures have beguiled generations of=20 readers lost in the sea of his complex proofs..." Evidently Norman is=20 one of those readers, since he appears to have mistaken a legitimate=20 proof for a conjecture. 3. "But other thinkers have seen more clearly; most importantly George=20 Boole, whose brilliant synthesis of algebra and logic has shown the way=20 to modern computer science." Since Boole's book predated G=F6del's proof= =20 by 77 years, Norman's implication would seem to be that logicians=20 including G=F6del had failed to grasp Boole's deep insights throughout=20 that period, and furthermore throughout the following 80 years up to the=20 present, obliging Norman to bring them to light. Similar logic would show that Newton invented quantum mechanics on the=20 basis of his corpuscular theory of light. If there is any legitimate point in Norman's article, it would be along=20 the lines of Kripke's semantics of the liar paradox (to which Haim=20 Gaifman had a nice follow-up). Norman may well have rediscovered=20 Kripke's insight, but in that case he should either discuss the=20 connection or explain why his references make a reference to Kripke=20 unnecessary. Boole himself is not sufficient for that purpose because=20 arithmetic mod 2 did not occur to him as a model of his axioms. Vaughan Pratt [For admin and other information see: http://www.mta.ca/~cat-dist/ ]