From lojban+bncCOTEtqyUDhCr7LjyBBoEdlfU6g@googlegroups.com Fri Aug 19 03:20:26 2011 Received: from mail-gw0-f61.google.com ([74.125.83.61]) by chain.digitalkingdom.org with esmtp (Exim 4.72) (envelope-from ) id 1QuMBa-0008V5-Kg; Fri, 19 Aug 2011 03:20:25 -0700 Received: by gwb11 with SMTP id 11sf3025927gwb.16 for ; Fri, 19 Aug 2011 03:20:16 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=beta; h=x-beenthere:received-spf:date:from:to:subject:message-id:references :mime-version:in-reply-to:x-pgp-key:x-pgp-keyid:user-agent :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-disposition:content-transfer-encoding; bh=t0JkhZhAwEaWvoKLvgUTGScEDn88hTa9ewwGwuKC/rk=; b=ig6VuDuzkUnsM4KjXsXOKvEHQrICyOlEnDyt+tbY8RhXLbT9ESHpn3Awr4o1YMi/cM 4d0hilpD9ZZgr3q7KEMor5/vDAV12m0GuAJtvK2EEUyCZik+ljSMYx2d1HfTPpErdoHT fWqyAztEQv+x+Kq36HwXMEq+Ia/Uj62RNJfsA= Received: by 10.100.216.13 with SMTP id o13mr320704ang.4.1313748523888; Fri, 19 Aug 2011 03:08:43 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.101.168.35 with SMTP id v35ls11064802ano.3.gmail; Fri, 19 Aug 2011 03:08:41 -0700 (PDT) Received: by 10.100.173.14 with SMTP id v14mr1773903ane.22.1313748521913; Fri, 19 Aug 2011 03:08:41 -0700 (PDT) Received: by 10.100.173.14 with SMTP id v14mr1773902ane.22.1313748521895; Fri, 19 Aug 2011 03:08:41 -0700 (PDT) Received: from sdf.lonestar.org (mx.sdf.org [192.94.73.19]) by gmr-mx.google.com with ESMTPS id kr11si7847119pbb.1.2011.08.19.03.08.40 (version=TLSv1/SSLv3 cipher=OTHER); Fri, 19 Aug 2011 03:08:40 -0700 (PDT) Received-SPF: pass (google.com: best guess record for domain of mbays@sdf.org designates 192.94.73.19 as permitted sender) client-ip=192.94.73.19; Received: from sdf.org (mbays@sverige.freeshell.org [192.94.73.4]) by sdf.lonestar.org (8.14.4/8.14.3) with ESMTP id p7JA8ebi026839 for ; Fri, 19 Aug 2011 10:08:40 GMT Received: (from mbays@localhost) by sdf.org (8.14.4/8.12.8/Submit) id p7JA8elx001598 for lojban@googlegroups.com; Fri, 19 Aug 2011 10:08:40 GMT Date: Fri, 19 Aug 2011 10:08:40 +0000 From: Martin Bays To: lojban@googlegroups.com Subject: Re: [lojban] xorlo and masses Message-ID: <20110819100840.GA27065@SDF.ORG> References: <1313511086.45473.YahooMailRC@web81308.mail.mud.yahoo.com> <20110817114634.GE6674@gonzales> <1313593494.36002.YahooMailRC@web81306.mail.mud.yahoo.com> <20110819002533.GG6674@gonzales> MIME-Version: 1.0 In-Reply-To: X-PGP-Key: http://mbays.freeshell.org/pubkey.asc X-PGP-KeyId: B5FB2CD6 User-Agent: Mutt/1.5.21 (2010-09-15) X-Original-Sender: mbays@sdf.org X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: best guess record for domain of mbays@sdf.org designates 192.94.73.19 as permitted sender) smtp.mail=mbays@sdf.org 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-Disposition: inline Content-Transfer-Encoding: quoted-printable * Thursday, 2011-08-18 at 23:28 -0300 - Jorge Llamb=EDas : > 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 i= n > > 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 ever= y > > whole is the sum of atoms - quantification is then over those atoms. >=20 > You can still have quantification without assuming that every whole is > the sum of atoms. You just used quantification over wholes to define > 'distributive'. >=20 > >> 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}? >=20 > 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: >=20 > A predicate P is 'distributive with respect to Q' iff > =A0\forall x,y. ( ( Q(x) /\ x Part y /\ P(y) ) --> P(x) ). >=20 > Would that work? Do you mean that we could then talk not about global atoms but about "P-atoms", by which I mean the x which are minimal such that P(x)? And so have {re P cu broda} mean that two of the P-atoms broda? That seems plausible... Martin --=20 You received this message because you are subscribed to the Google Groups "= lojban" group. To post to this group, send email to lojban@googlegroups.com. To unsubscribe from this group, send email to lojban+unsubscribe@googlegrou= ps.com. For more options, visit this group at http://groups.google.com/group/lojban= ?hl=3Den.