From lojban-out@lojban.org Wed Jul 12 16:33:49 2006 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (qmail 89704 invoked from network); 12 Jul 2006 23:22:25 -0000 Received: from unknown (66.218.67.36) by m31.grp.scd.yahoo.com with QMQP; 12 Jul 2006 23:22:25 -0000 Received: from unknown (HELO chain.digitalkingdom.org) (64.81.49.134) by mta10.grp.scd.yahoo.com with SMTP; 12 Jul 2006 23:22:24 -0000 Received: from lojban-out by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G0o21-0001BW-58 for lojban@yahoogroups.com; Wed, 12 Jul 2006 16:22:13 -0700 Received: from chain.digitalkingdom.org ([64.81.49.134]) by chain.digitalkingdom.org with esmtp (Exim 4.62) (envelope-from ) id 1G0nzm-000198-Nv; Wed, 12 Jul 2006 16:19:57 -0700 Received: with ECARTIS (v1.0.0; list lojban-list); Wed, 12 Jul 2006 16:19:46 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G0nzJ-00018v-Dn for lojban-list-real@lojban.org; Wed, 12 Jul 2006 16:19:25 -0700 Received: from simba.math.ucla.edu ([128.97.4.125]) by chain.digitalkingdom.org with esmtps (TLS-1.0:DHE_RSA_AES_256_CBC_SHA1:32) (Exim 4.62) (envelope-from ) id 1G0nzF-00018o-MY for lojban-list@lojban.org; Wed, 12 Jul 2006 16:19:25 -0700 Received: by simba.math.ucla.edu (Postfix, from userid 500) id DA67E3BADA; Wed, 12 Jul 2006 16:19:19 -0700 (PDT) Received: from localhost (localhost [127.0.0.1]) by simba.math.ucla.edu (Postfix) with ESMTP id B9BE83BAD4 for ; Wed, 12 Jul 2006 16:19:19 -0700 (PDT) Date: Wed, 12 Jul 2006 16:19:19 -0700 (PDT) In-Reply-To: <925d17560607121113y4d0be37y1fe4757a46c030f4@mail.gmail.com> Message-ID: References: <20060711233003.36140.qmail@web81310.mail.mud.yahoo.com> <925d17560607120531v7de5bfefwa96db493b274fbdf@mail.gmail.com> <925d17560607121113y4d0be37y1fe4757a46c030f4@mail.gmail.com> MIME-Version: 1.0 Content-Type: MULTIPART/MIXED; BOUNDARY="1635810564-1773356151-1152746359=:20555" X-Spam-Score: -2.6 (--) This message is in MIME format. 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X-archive-position: 12159 X-ecartis-version: Ecartis v1.0.0 Errors-to: lojban-list-bounce@lojban.org X-original-sender: jimc@math.ucla.edu X-list: lojban-list X-Spam-Score: -2.6 (--) To: lojban@yahoogroups.com X-Originating-IP: 64.81.49.134 X-eGroups-Msg-Info: 1:0:0:0 X-eGroups-From: Jim Carter From: Jim Carter Reply-To: jimc@math.ucla.edu Subject: [lojban] Re: A (rather long) discussion of {all} X-Yahoo-Group-Post: member; u=116389790; y=pqghDCfxGgn9_HM5oz9jGeujaeBzMh4nVUl22Ycr9qjZBkRrVQ X-Yahoo-Profile: lojban_out X-Yahoo-Message-Num: 26586 --1635810564-1773356151-1152746359=:20555 Content-Type: TEXT/PLAIN; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable On Wed, 12 Jul 2006, Jorge Llamb=EDas wrote: > On 7/12/06, Maxim Katcharov wrote: >=20 > > No, I want to know how you explain why the singular is the only one > > that is not subject to collectivity. >=20 > You need at least two things before you can have a distinction between > distributing or not distributing something among them. Isn't that obvious= ? No. I can't help jumping in here... > Because there is no distinction to be made. Why does it not make > any difference to order a set of numbers from smallest to largest or > from largest to smallest when the set contains a single number? > Same thing with distributivity, if there is only one thing, distributive > and non-distributive give identical results. In a database query you often sort (order) the result, and it's important=20 to do so, even if you don't know in advance whether the result will have=20 zero, one or multiple members, and any of those outcomes happen often. You= =20 expect to be able to produce an ordered set with no irrelevant complaints=20 about the lack of plurality. Another example: "An Army of One". Usually battle involves teams of=20 soldiers, but it happens, often enough to mention and often enough to try=20 to give the soldiers some training, that the outcome hinges on the actions= =20 of a team of one soldier. The relation between the circumstances of battle= =20 and the teams are the same, regardless of how many people are in them. Yet another example: One formalism for defining the integers goes like=20 this: if a 1-1 relation exists between 2 sets they are said to have the=20 "same count" (or cardinality), and this is an equivalence relation, so that= =20 each set is in exactly one of the equivalence classes of equal count sets. = =20 The equivalence classes are the integers. Bertrand Russell proved back in= =20 the 1950's (or earlier?) that a particular list of examples had a unique=20 member in every equivalence class, and thus was a representation of the=20 integers. The list member for 0 is the empty set (represented {}; all the= =20 members of the set can be viewed between the brackets). The member for 1=20 is {{}} (set containing the empty set). The member for 2 is {{} {{}}} (set= =20 containing the list member for each smaller integer (1 and 0 follow the=20 same definition)), and so on recursively. The point is, each of these is a= =20 set, and it doesn't work if you elide the set nature of the non-plural=20 {{}}, which cannot be taken to be "the same as" its unique member {}. And= =20 similarly it's important that procedures work correctly when applied to all= =20 the members of the empty set (look up St. Anselm's ontological proof of the= =20 existence of God). So distributing a relation over all the one or zero members of the smaller= =20 sized sets is important and needs to be supported in the language. James F. Carter Voice 310 825 2897 FAX 310 206 6673 UCLA-Mathnet; 6115 MSA; 405 Hilgard Ave.; Los Angeles, CA, USA 90095-1555 Email: jimc@math.ucla.edu http://www.math.ucla.edu/~jimc (q.v. for PGP k= ey) --1635810564-1773356151-1152746359=:20555--