From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8423 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Achieving "neither P nor not P" Date: Sat, 13 Dec 2014 04:19:10 -0500 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1418510536 22431 80.91.229.3 (13 Dec 2014 22:42:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 13 Dec 2014 22:42:16 +0000 (UTC) To: "categories" Original-X-From: majordomo@mlist.mta.ca Sat Dec 13 23:42:11 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1XzvO6-0006Tg-Tm for gsmc-categories@m.gmane.org; Sat, 13 Dec 2014 23:42:11 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:45059) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XzvNS-0006LN-GZ; Sat, 13 Dec 2014 18:41:30 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XzvNT-0004Ll-GS for categories-list@mlist.mta.ca; Sat, 13 Dec 2014 18:41:31 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8423 Archived-At: Here's a thought that may seem a bit off-topic, having more to do, = at first glance, with "paradoxical" logic than with categories. Eleven years ago, for a conference in Bangalore [1], I was trying to = present natural-seeming examples of statements P each illustrating = another of the four distinct, mutually exclusive, jointly exhaustive, = and individually indispensable "logical possibilities" thought available = for P in the logic of the Hindu catuskoti, or Tetralemma principle: that,= given P, one have either P, or ~P, or both P and ~P, or neither P nor ~P.= (Note that an Aristotelean would hold that already P and ~P are mutually = exclusive and jointly exhaustive, so that the last two are simply false, hence utterly dispensable.) The only illustrations I could come up with back then for a P with = "neither P nor ~P" always struck me as somewhat artificial; so that = I was greatly heartened, recently, to stumble on a far more natural = illustration as outgrowth of a discussant's sardonic comment, concluding = his remarks on how contemporary web page design strategies needed to be = modified to take into account the fact that *touch* is more and more = replacing *mouse cursor and click* as the user interface of choice: = "Change is good." Well, he didn't mean it, of course: he said it entirely tongue-in-cheek. = But it hit me: that's a superb illustration of a P with "neither P nor ~P= ": for, in fact (in my view), such "change" is neither good nor not good -- = it = just is, and may need to be accommodated :-) ). Enjoy! And cheers, -- Fred --- [1] pp. 62-73 of ISBN 81-85931-58-5, www.hindbook.com, 2005 (esp. pp. 70-= 71); cf. http://www.hindbook.com/images/book_content/Emch.pdf ; or www.hindbook.com/index.php/contributions-to-the-history-of-indian-mathema= tics [For admin and other information see: http://www.mta.ca/~cat-dist/ ]