From a.rosta@lycos.co.uk Fri Nov 08 16:06:02 2002 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_2_3_0); 9 Nov 2002 00:06:02 -0000 Received: (qmail 69479 invoked from network); 9 Nov 2002 00:06:02 -0000 Received: from unknown (66.218.66.216) by m7.grp.scd.yahoo.com with QMQP; 9 Nov 2002 00:06:02 -0000 Received: from unknown (HELO digitalkingdom.org) (204.152.186.175) by mta1.grp.scd.yahoo.com with SMTP; 9 Nov 2002 00:06:02 -0000 Received: from lojban-out by digitalkingdom.org with local (Exim 4.05) id 18AJ8U-0006f1-00 for lojban@yahoogroups.com; Fri, 08 Nov 2002 16:06:02 -0800 Received: from digitalkingdom.org ([204.152.186.175] helo=chain) by digitalkingdom.org with esmtp (Exim 4.05) id 18AJ8L-0006eh-00; Fri, 08 Nov 2002 16:05:53 -0800 Received: with ECARTIS (v1.0.0; list lojban-list); Fri, 08 Nov 2002 16:05:52 -0800 (PST) Received: from mrin02.spray.se ([212.78.193.8] helo=mrin02.st1.spray.net) by digitalkingdom.org with esmtp (Exim 4.05) id 18AJ8G-0006eS-00 for lojban-list@lojban.org; Fri, 08 Nov 2002 16:05:48 -0800 Received: from lmin04.st1.spray.net (lmin04.st1.spray.net [212.78.202.104]) by mrin02.st1.spray.net (Postfix) with ESMTP id DC98C24BD79 for ; Sat, 9 Nov 2002 01:05:02 +0100 (CET) Received: from oemcomputer (host213-121-66-55.surfport24.v21.co.uk [213.121.66.55]) by lmin04.st1.spray.net (Postfix) with ESMTP id 562A81C0BE for ; Sat, 9 Nov 2002 01:05:01 +0100 (MET) To: Subject: [lojban] quantifying over imaginaries (was: Re: partial recantation in favour of solomonics Date: Sat, 9 Nov 2002 00:06:53 -0000 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook IMO, Build 9.0.2416 (9.0.2910.0) Importance: Normal In-Reply-To: <20021108154944.I36803-100000@granite.thestonecutters.net> X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 X-archive-position: 2561 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: a.rosta@lycos.co.uk Precedence: bulk X-list: lojban-list From: "And Rosta" Reply-To: a.rosta@lycos.co.uk X-Yahoo-Group-Post: member; u=122260811 X-Yahoo-Profile: andjamin xod: > On Fri, 8 Nov 2002, And Rosta wrote: [...] > > How do we say "99% of Lojbanists are male"? I don't know, but > > it ought to be doable along the same lines of so'e, "most", > > which also expresses a fraction of a total extension. {so'e} makes > > sense only with {so'e broda} and {so'e da poi broda} -- these > > can't be paraphrased with unrestricted da > > > > What are the truth conditions of "99% of Lojbanists are male"? > > At the least they seem to require that there are at least > > 100 Lojbanists (or at least 2 Lojbanists, if the claim was > > that 50% of Lojbanists were male). So n% would seem to be > > importing. But I think we also would like to be able to say > > truthfully that "50% of unicorns are male". So it seems desirable > > that we should be able to mark n% quantifiers as either > > importing or nonimporting. Jorge already suggested a way to do > > that: by adding ma'u/ni'u with no default when it is omitted, > > and letting it be glorked from context when not used. This would > > naturally extend to "100% of", which is equivalent to {ro}. I > > therefore conclude that for all fractional quantifiers, including > > {ro} and {so'e}, we want both importing and nonimporting versions, > > and xorxes's suggestion is the best way to effect it > > > > Is this something everyone could live with? > > I don't like overloading the meanings of ma'u and ni'u. I don't like > leaving it to context when it's not expressed. And you should probably > read and meditate on what I closed message 17044 with, which shows why > "50% of unicorns are male" is always a valid statement Okay. I was going to throw up my hands and give up, but I'll try a different tack. It turns out that I agree with you (in 17044), but I think it means that John and pc are right about importingness.... Firstly, {pi mu lo(i) no pavyseljirna} really does seem nonsensical to me -- taking 0.5 of 0 is daft, and is really not at all what we mean to say when we say "50% of unicorns are male". I conclude from this that the inner cardinality must be su'o. Secondly, if we can talk about the set of Graces, lo'i cridrgreisa, it seems proper that we can note that there were three of them: {lo'i ci cridrgreisa}. I conclude from this: (i) fractional quantifiers entail cardinality su'o (ii) the cardinality of an imaginary category is or can be also imaginary Applied to the general debate, this leads to the following conclusions: (a) fractional quantifiers, including ro, are importing in the sense that they entail cardinality su'o: {ro broda} entails {ro lo su'o broda} (b) the truth or falsity of claims involving {ro pavyseljirna} and {lo ci cridrgreisu} depends on however we decide and signal whether the universe of discourse includes only the real world, or also imaginaries . (c) {ro lo in-not-necessarily-real-world su'o broda} entails {in-not-necessarily-real-world: da broda}, but not {in-necessarily-real-world: da broda}. The upshot is as follows: (d) {ro broda} IS importing (e) it is not false to talk about {ro pavyseljirna}, even in belief systems where these are purely imaginary. But it is false to talk about {ro in-necessarily-real-world pavyseljirna}. I was going to ask whether this at least could win agreement, but in fact I have (temporarily at least) convinced myself that my reasoning is actually correct, rather than merely a possible basis for compromise. --And.