From lojban+bncCJ2UzZHuDRDUlLfyBBoEp96H1Q@googlegroups.com Thu Aug 18 19:28:49 2011 Received: from mail-vw0-f61.google.com ([209.85.212.61]) by chain.digitalkingdom.org with esmtp (Exim 4.72) (envelope-from ) id 1QuEpD-0000L1-1x; Thu, 18 Aug 2011 19:28:49 -0700 Received: by vwe42 with SMTP id 42sf2884804vwe.16 for ; Thu, 18 Aug 2011 19:28:40 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=beta; h=x-beenthere:received-spf:mime-version:in-reply-to:references:date :message-id:subject:from:to:x-original-sender :x-original-authentication-results:reply-to:precedence:mailing-list :list-id:x-google-group-id:list-post:list-help:list-archive:sender :list-subscribe:list-unsubscribe:content-type :content-transfer-encoding; bh=8wocqybhiyDB2bjTcV/WE5k3eQeaobUB6Dz0zF2qeVc=; b=buEjKJbmABNAb6lpthQIVlcl7CNWo6bhSCTDdPiNXJb1NM2Wp1e+09ZJaEhRPftA/0 tUvlyup3UcQzesB0arMZbK1wq4RSUwcYdibqu5qVudiAZIRX4Jaf7CCT1UBbaESRMtGc t+01MjO/6n4aB74GxdcMyDx6VV0EgE62q5fdw= Received: by 10.220.169.193 with SMTP id a1mr450689vcz.37.1313720916707; Thu, 18 Aug 2011 19:28:36 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.220.200.10 with SMTP id eu10ls27686vcb.3.canary; Thu, 18 Aug 2011 19:28:36 -0700 (PDT) Received: by 10.52.95.50 with SMTP id dh18mr1597529vdb.25.1313720915974; Thu, 18 Aug 2011 19:28:35 -0700 (PDT) Received: by 10.52.95.50 with SMTP id dh18mr1597528vdb.25.1313720915966; Thu, 18 Aug 2011 19:28:35 -0700 (PDT) Received: from mail-vw0-f46.google.com (mail-vw0-f46.google.com [209.85.212.46]) by gmr-mx.google.com with ESMTPS id t2si7837369vdv.2.2011.08.18.19.28.35 (version=TLSv1/SSLv3 cipher=OTHER); Thu, 18 Aug 2011 19:28:35 -0700 (PDT) Received-SPF: pass (google.com: domain of jjllambias@gmail.com designates 209.85.212.46 as permitted sender) client-ip=209.85.212.46; Received: by vws1 with SMTP id 1so2044411vws.19 for ; Thu, 18 Aug 2011 19:28:35 -0700 (PDT) MIME-Version: 1.0 Received: by 10.52.22.162 with SMTP id e2mr1632768vdf.299.1313720915509; Thu, 18 Aug 2011 19:28:35 -0700 (PDT) Received: by 10.52.101.170 with HTTP; Thu, 18 Aug 2011 19:28:35 -0700 (PDT) In-Reply-To: <20110819002533.GG6674@gonzales> References: <1313511086.45473.YahooMailRC@web81308.mail.mud.yahoo.com> <20110817114634.GE6674@gonzales> <1313593494.36002.YahooMailRC@web81306.mail.mud.yahoo.com> <20110819002533.GG6674@gonzales> Date: Thu, 18 Aug 2011 23:28:35 -0300 Message-ID: Subject: Re: [lojban] xorlo and masses From: =?ISO-8859-1?Q?Jorge_Llamb=EDas?= To: lojban@googlegroups.com X-Original-Sender: jjllambias@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of jjllambias@gmail.com designates 209.85.212.46 as permitted sender) smtp.mail=jjllambias@gmail.com; dkim=pass (test mode) header.i=@gmail.com Reply-To: lojban@googlegroups.com Precedence: list Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com List-ID: X-Google-Group-Id: 1004133512417 List-Post: , List-Help: , List-Archive: Sender: lojban@googlegroups.com List-Subscribe: , List-Unsubscribe: , Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable On Thu, Aug 18, 2011 at 9:25 PM, Martin Bays wrote: > * Wednesday, 2011-08-17 at 08:04 -0700 - John E Clifford : > > From this and your other mails, I am understanding that want to base > Lojban on Lesniewskian mereology. > > I'm hazy on exactly what this would mean, but allow me to guess. > > Our universe consists of Wholes, and is partially ordered by the "part > of" relation. All the things we would usually consider as individuals in > our universe are Wholes. In addition, we have mereological sums, i.e. > supremums with respect to the "parthood" partial order, of arbitrary > sets of Wholes. > > The interpretation of an ordinary sumti is a Whole; selbri are > interpreted as relations on our universe of Wholes. > > Presumably {me} is interpreted as the parthood relation. > > A unary predicate P is 'distributive' iff > =A0 =A0\forall x,y. ( ( x Part y /\ P(y) ) --> P(x) ). > > To handle quantification, I suppose it is necessary to assume that every > whole is the sum of atoms - quantification is then over those atoms. You can still have quantification without assuming that every whole is the sum of atoms. You just used quantification over wholes to define 'distributive'. >> In my xorlo, terms and quantifiers all assume plurality, >> with singularity as a limit case. > - does this mean that you want {ro da} to be a plural quantifier rather > than the singular quantifier (i.e. quantifying over atoms) it would be > in the above account? Does this mean you don't want to assume we're > working in an atomic Boolean algebra? If not, how to deal with {re da}? I think you can still define "re da" in the usual way. The only thing is that without atoms "re da broda" will always be false for any distributive broda. So most predicates would not be *fully* distributive. But I think you can define a more useful "relative distributivity". Something like: A predicate P is 'distributive with respect to Q' iff =A0\forall x,y. ( ( Q(x) /\ x Part y /\ P(y) ) --> P(x) ). Would that work? mu'o mi'e xorxes --=20 You received this message because you are subscribed to the Google Groups "= lojban" group. 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