From jjllambias@hotmail.com Wed Mar 13 15:27:17 2002 Return-Path: X-Sender: jjllambias@hotmail.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 13 Mar 2002 23:27:17 -0000 Received: (qmail 23297 invoked from network); 13 Mar 2002 23:27:16 -0000 Received: from unknown (216.115.97.167) by m2.grp.snv.yahoo.com with QMQP; 13 Mar 2002 23:27:16 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.143) by mta1.grp.snv.yahoo.com with SMTP; 13 Mar 2002 23:27:16 -0000 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Wed, 13 Mar 2002 15:27:16 -0800 Received: from 200.69.2.52 by lw8fd.law8.hotmail.msn.com with HTTP; Wed, 13 Mar 2002 23:27:16 GMT To: lojban@yahoogroups.com Bcc: Subject: Re: [lojban] More about quantifiers Date: Wed, 13 Mar 2002 23:27:16 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 13 Mar 2002 23:27:16.0779 (UTC) FILETIME=[9CF6BFB0:01C1CAE6] From: "Jorge Llambias" X-Originating-IP: [200.69.2.52] X-Yahoo-Group-Post: member; u=6071566 X-Yahoo-Profile: jjllambias2000 la pycyn cusku di'e > > What do you mean by "actual quantification"? > > >Quantity and quality (universal-particular, affirmative-negative) as well >as >import. So, in: ro broda su'o brode cu brodi = no broda me'iro da poi brode cu brodi What is the "actual quantification" of broda and brode? I can tell what the actual import is: - for broda and + for brode in my system, ++ in yours. But what is the "actual quantification"? > > >All + with the assumption that all classes mentioned as subject are >non-null >(and maybe a few less certain things as well). That sounds exactly like (A-,E-,I+,O+) with the assumption that all classes mentioned as subject are non-null. Indeed, with that assumption we can drop the +/- distinction, as it becomes irrelevant. >Well, I didn't read the whole book, just a few sections that talked about >restricted quantification. I never saw any evidence that it was developed >as >a separate system. This is where he defines things: http://www.wabash.edu/depart/Phil/classmaterials/Phil3F99/Phil3txt/Phil3txt7/Phil3txt72/Phil3txt723.html >Obversion is just a device for making >"not every" a bit more readable, as I read him. But for "not every" to be equivalent to "some not", "every" and "some" must have opposite import. >But I will look at some more >(and of course it works for an all positive set as well -- under the >standard >condition -- no empty subjects). Of course. Under that condition, the +/- distinction is pointless. >Of course, the restricted quantifier is -, since it just is the ultimate >form >in a minorly gussied up way. Part of the gussying is, alas, to hide the >real >subject of the of the final quantifier, namely the universal class. Do you agree or disagree that in Lojban these are equivalent: 1. ro da poi broda cu brode =||= ro da zo'u ganai da broda gi da brode 2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode They have to be defined that way if obversion is to work for the {poi} forms. And that gives A- and I+ for the {poi} forms. >Every universal quantifier (in a non-empty universe) entails every instance >of its matrix, every matrix with a free term entails its particular >closure >on that term: >AxFx therefore Fa therefore ExFx. That is about as thorough a working out >as >I can think of. Assuming a non-empty universe (and you are assuming it by bringing up a), I have no problem with that. But of course that does not mean that {ro da zo'u ganai da broda gi da brode} entails {su'o da zo'u ge da broda gi da brode}. It does not. So, if, as I believe, these hold: 1. ro da poi broda cu brode =||= ro da zo'u ganai da broda gi da brode 2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode then we cannot say that {ro da poi broda cu brode} entails {su'o da poi broda cu brode}. You may not like 1. and 2. as definitions, but they seem to me fairly standard. At least they are presented as valid in the page I found (from a random search I did for "restricted quantification"). mu'o mi'e xorxes _________________________________________________________________ Join the world’s largest e-mail service with MSN Hotmail. http://www.hotmail.com