From nobody@digitalkingdom.org Wed Jul 12 16:55:17 2006 Received: with ECARTIS (v1.0.0; list lojban-list); Wed, 12 Jul 2006 16:55:17 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G0oXh-0001Zr-Es for lojban-list-real@lojban.org; Wed, 12 Jul 2006 16:54:57 -0700 Received: from web81302.mail.mud.yahoo.com ([68.142.199.118]) by chain.digitalkingdom.org with smtp (Exim 4.62) (envelope-from ) id 1G0oXf-0001Zk-D0 for lojban-list@lojban.org; Wed, 12 Jul 2006 16:54:57 -0700 Received: (qmail 76365 invoked by uid 60001); 12 Jul 2006 23:54:46 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=sbcglobal.net; h=Message-ID:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding; b=iFxl89s8g9XVKblot4l3YV3GSYSXrLZDXXIcElRoN5m6f2Q+ySIsU3AmEU5EWGunMHGu6xdK9pdJtg9rUoe9P65s1wqYwtNjNopbAP5ce9KjMRzJgtMGhgUHTXTO82/llruXt3UkDLGleILosNLWdwVjtubBD5L5KW4sxsaa82I= ; Message-ID: <20060712235446.76363.qmail@web81302.mail.mud.yahoo.com> Received: from [70.237.228.212] by web81302.mail.mud.yahoo.com via HTTP; Wed, 12 Jul 2006 16:54:46 PDT Date: Wed, 12 Jul 2006 16:54:46 -0700 (PDT) From: John E Clifford Subject: [lojban] Re: A (rather long) discussion of {all} To: lojban-list@lojban.org In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Spam-Score: -0.7 (/) X-archive-position: 12160 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: clifford-j@sbcglobal.net Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list --- Jim Carter wrote: > On Wed, 12 Jul 2006, Jorge Llamb�as wrote: > > On 7/12/06, Maxim Katcharov wrote: > > > > > No, I want to know how you explain why the singular is the only one > > > that is not subject to collectivity. > > > > 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 > to do so, even if you don't know in advance whether the result will have > zero, one or multiple members, and any of those outcomes happen often. You > expect to be able to produce an ordered set with no irrelevant complaints > about the lack of plurality. > > Another example: "An Army of One". Usually battle involves teams of > soldiers, but it happens, often enough to mention and often enough to try > to give the soldiers some training, that the outcome hinges on the actions > of a team of one soldier. The relation between the circumstances of battle > 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 > this: if a 1-1 relation exists between 2 sets they are said to have the > "same count" (or cardinality), and this is an equivalence relation, so that > each set is in exactly one of the equivalence classes of equal count sets. > The equivalence classes are the integers. Bertrand Russell proved back in > the 1950's (or earlier?) that a particular list of examples had a unique > member in every equivalence class, and thus was a representation of the > integers. The list member for 0 is the empty set (represented {}; all the > members of the set can be viewed between the brackets). The member for 1 > is {{}} (set containing the empty set). The member for 2 is {{} {{}}} (set > containing the list member for each smaller integer (1 and 0 follow the > same definition)), and so on recursively. The point is, each of these is a > set, and it doesn't work if you elide the set nature of the non-plural > {{}}, which cannot be taken to be "the same as" its unique member {}. And > similarly it's important that procedures work correctly when applied to all > the members of the empty set (look up St. Anselm's ontological proof of the > existence of God). > > So distributing a relation over all the one or zero members of the smaller > 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 key) To unsubscribe from this list, send mail to lojban-list-request@lojban.org with the subject unsubscribe, or go to http://www.lojban.org/lsg2/, or if you're really stuck, send mail to secretary@lojban.org for help.