From lojban+bncCJ2UzZHuDRCe4L3eBBoEvzta3g@googlegroups.com Wed Apr 21 14:37:59 2010 Received: from mail-vw0-f61.google.com ([209.85.212.61]) by chain.digitalkingdom.org with esmtp (Exim 4.71) (envelope-from ) id 1O4hcJ-0004F5-VX; Wed, 21 Apr 2010 14:37:59 -0700 Received: by vws20 with SMTP id 20sf2218260vws.16 for ; Wed, 21 Apr 2010 14:37:49 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=beta; h=domainkey-signature:received:x-beenthere:received:received:received :received:received-spf:received:mime-version:received:in-reply-to :references:date:received:message-id:subject:from:to :x-original-authentication-results:x-original-sender:reply-to :precedence:mailing-list:list-id:list-post:list-help:list-archive :sender:list-subscribe:list-unsubscribe:content-type :content-transfer-encoding; bh=t2iI/YIspWq5Of0rGLxvctF9LRR3T2A80dnVgsVkyJg=; b=kJ/smdvdiR02zF6Z8mGNpB23evdT6fisRH6AsJ3XowiTq2o43p5vIqd1iJ2wzfpMaC Qi8kvDbxW32/B+FzkF2mQ044waVl734oF/b1p34l8lwTseIx+0uEbAT4sNB4LtztDn3Q WyVhCG2zQxH0QlA2Qm8WtO+f8SiuBA1DpVR7g= DomainKey-Signature: a=rsa-sha1; c=nofws; d=googlegroups.com; s=beta; h=x-beenthere:received-spf:mime-version:in-reply-to:references:date :message-id:subject:from:to:x-original-authentication-results :x-original-sender:reply-to:precedence:mailing-list:list-id :list-post:list-help:list-archive:sender:list-subscribe :list-unsubscribe:content-type:content-transfer-encoding; b=xp2paejH6NFQU+3FgCl0bmLlcUAZtPCDPg8vBCHmELGBCq52MRlTTTjQ0lufgkU5ua Cg6k0Ak2FOTjDAR100kY2Gvbek17+zwtssZqj7ppBt8Tkgrk4honJ8WqdZprZ46wLrni 2MCtYLHe/gSHL4fimp8kdUEi7ezUMLU08rgyE= Received: by 10.220.47.158 with SMTP id n30mr723748vcf.17.1271885854214; Wed, 21 Apr 2010 14:37:34 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.220.66.74 with SMTP id m10ls21216024vci.4.p; Wed, 21 Apr 2010 14:37:33 -0700 (PDT) Received: by 10.220.165.8 with SMTP id g8mr1938721vcy.1.1271885852374; Wed, 21 Apr 2010 14:37:32 -0700 (PDT) Received: by 10.220.165.8 with SMTP id g8mr1938720vcy.1.1271885852342; Wed, 21 Apr 2010 14:37:32 -0700 (PDT) Received: from mail-qy0-f179.google.com (mail-qy0-f179.google.com [209.85.221.179]) by gmr-mx.google.com with ESMTP id b14si703301vcx.5.2010.04.21.14.37.31; Wed, 21 Apr 2010 14:37:31 -0700 (PDT) Received-SPF: pass (google.com: domain of jjllambias@gmail.com designates 209.85.221.179 as permitted sender) client-ip=209.85.221.179; Received: by mail-qy0-f179.google.com with SMTP id 9so10000153qyk.1 for ; Wed, 21 Apr 2010 14:37:31 -0700 (PDT) MIME-Version: 1.0 Received: by 10.229.79.75 with HTTP; Wed, 21 Apr 2010 14:37:30 -0700 (PDT) In-Reply-To: <225049.90411.qm@web81306.mail.mud.yahoo.com> References: <6a2c862a-91f0-452e-9a31-0064620d5d06@g11g2000yqe.googlegroups.com> <102923.48908.qm@web81306.mail.mud.yahoo.com> <75805.51342.qm@web81301.mail.mud.yahoo.com> <934390.40893.qm@web81308.mail.mud.yahoo.com> <391970.26672.qm@web81302.mail.mud.yahoo.com> <225049.90411.qm@web81306.mail.mud.yahoo.com> Date: Wed, 21 Apr 2010 18:37:30 -0300 Received: by 10.229.213.140 with SMTP id gw12mr1309450qcb.96.1271885850903; Wed, 21 Apr 2010 14:37:30 -0700 (PDT) Message-ID: Subject: Re: [lojban] About plural 'ro' From: =?ISO-8859-1?Q?Jorge_Llamb=EDas?= To: lojban@googlegroups.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of jjllambias@gmail.com designates 209.85.221.179 as permitted sender) smtp.mail=jjllambias@gmail.com; dkim=pass (test mode) header.i=@gmail.com X-Original-Sender: jjllambias@gmail.com Reply-To: lojban@googlegroups.com Precedence: list Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com List-ID: 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 Wed, Apr 21, 2010 at 4:31 PM, John E Clifford wro= te: > From: Jorge Llamb=EDas >> >> Right, the corresponding inference when you have a singular quantifier >> 'Ax' and a plural term 'a' is: >> >> "AxFx, therefore if a is one, Fa" > > [[[Where did the "if a is one come from? =A0It is not anywhere in the for= mula above. That's why it's the *corresponding* inference. The inference rule you gave was for singular quantifier to singular term, or for plural quantifier to plural term. It is obvious why you need to add the "if a is one" when going from singular quantifier to plural term, isn't it? >=A0And, of course, it won't help in the reverse case, even if it does here= . =A0But it doesn't of course, because a ios not one but plural ex hypothes= i]]] What is the reverse case? Existential generalization? The corresponding rule would be: "Fa, therefore if a is one, ExFx" If the reverse case was from plural quantifier to singular term, then neither rule need modification: "AxFx, therefore Fa" "Fa, therefore ExFx" both work with singular 'a' and plural 'Ax' or 'Ex'. > Suppose a piano (or something) ways a ton and a half. =A0Then, "all the = people who carried the whatever will be rewarded" is going to be either eit= her vacuously false or vacuously true, even though the piano got carried (i= f we are going by singulars) or either nobody gets a reward or everybody ge= ts several (if we go by plurals). =A0Since both plural reference of at leas= t the latter sort and plural quantification (which follows) seems > =A0useful, some trick is needed. =A0And one that can be reliably and cons= istently used,]]] ro lo prenu poi bevri lo co'e cu ba se cnemu =3D ro da poi me lo prenu poi bevri lo co'e zo'u da ba se cnemu "Each of (the people who carried the whatever) will be rewarded." "For each x, such that x is one of (the people who carried the whatever): x will be rewarded." (Reward for each participant in the carrying.) ro lo prenu ku poi bevri lo co'e cu ba se cnemu =3D ro da poi me lo prenu zi'e poi bevri lo co'e zo'u da ba se cecmu "Each of (the people) who carried the whatever will be rewarded." "For each x, such that x is one of (the people) and x carried the whatever: x will be rewarded." (Only Superman gets reward.) Neither of those two, however, involve plural quantification. Using "roro" as the plural quantifier: roro lo prenu poi bevri lo co'e cu ba se cnemu roro da poi me lo prenu poi bevri lo co'e zo'u da ba se cnemu "Any one or more of (the people who carried the whatever) will be rewarded." "For any X, such that X is one or more of (the people who carried the whatever): X will be rewarded." (Lots of rewards for anybody involved.) roro lo prenu ku poi bevri lo co'e cu ba se cnemu roro da poi me lo prenu zi'e poi bevri lo co'e zo'u da ba se cecmu "Any one or more of (the people) who carried the whatever will be rewarded." "For any X, such that X is one or more of (the people) and X carried the whatever: X will be rewarded." (Any teams that carried it gets reward.) mu'o mi'e xorxes --=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.