From nobody@digitalkingdom.org Thu Oct 29 12:15:40 2009 Received: with ECARTIS (v1.0.0; list lojban-list); Thu, 29 Oct 2009 12:15:41 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.69) (envelope-from ) id 1N3aTE-0002vr-Am for lojban-list-real@lojban.org; Thu, 29 Oct 2009 12:15:40 -0700 Received: from mail-yw0-f204.google.com ([209.85.211.204]) by chain.digitalkingdom.org with esmtp (Exim 4.69) (envelope-from ) id 1N3aTB-0002vP-43 for lojban-list@lojban.org; Thu, 29 Oct 2009 12:15:40 -0700 Received: by ywh42 with SMTP id 42so2047034ywh.28 for ; Thu, 29 Oct 2009 12:15:30 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=/EvLNNhKPwCWC4vKHwxHRKKR9OAX+dthJw9f/Wu4JWY=; b=bWLRoDvFbo0Fa1RJkRJVbAzgTUPYWMpA1g29SGZBF29iqJf/M1ZCef1lQ6IYivl4xY ZpHWQGY4sl2KLxG9jaiu8vdXnxyFy9WyBK9dqVzBtglnTk+n0bUI3nudWMjhr93wmOxS IQC++yUb9e95YvUUn/Bx13g2IwwykcbyEWVIs= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=cFzo57oGK1cxvovAp0hPTYtQeYlSUJ4EPBHW8MDHsgexJRi/QOzQRDKt4WwL38p1fr ok0qCCfd+6iXu/QIW8GkzFMtOIPybVIzcgwADotbGq9cNqmj+4hScFDIhcPSLBcIbexb eqp6s+OFD4cfP6UYvg8fOWbRQAUVPbU9IPZb0= MIME-Version: 1.0 Received: by 10.90.40.37 with SMTP id n37mr1372244agn.74.1256843730801; Thu, 29 Oct 2009 12:15:30 -0700 (PDT) In-Reply-To: <4AE9DD03.7070401@fastmail.fm> References: <4AE71391.5090501@fastmail.fm> <925d17560910271000j10c5f931ga1f4d12f85c12651@mail.gmail.com> <4AE9DD03.7070401@fastmail.fm> Date: Thu, 29 Oct 2009 16:15:30 -0300 Message-ID: <925d17560910291215s49f2b043i8cfff957a2ec5e67@mail.gmail.com> Subject: [lojban] Re: xorlo and the expansion of bridi From: =?ISO-8859-1?Q?Jorge_Llamb=EDas?= To: lojban-list@lojban.org Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by Ecartis X-archive-position: 16413 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: jjllambias@gmail.com Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list 2009/10/29 Roman Naumann : > Thanks for your reply. > > Jorge Llambías wrote: >> >> (BTW, what does "B dogs exist" mean to you exactly? Is that the number >> of dogs alive at the time of the utterance, the number of dogs that >> have ever existed or will exist on this planet, or something else, >> depending on the context?) > > I'm not sure what it means, I just remember the 'old' lo implied existential > claims. I just wanted to point out that the 'old' meaning is not really that different from the new one, at least as far as it can be understood. The inner quantifier gives the number of referents that the sumti has. This was always the case. The old exposition seemed to assume that any given sumti headed with 'lo' has a certain number of referents independently of the context in which it is used, but that doesn't make a lot of sense. It is hard to come up with sumti that are so context independent. > What I meant to say was: {B da poi gerku zo'u A da vasxu} > But still, I don't see why you say the variable is being bound twice. In "A da vasxu", the variable "da" is bound by the quantifier "A". It is equivalent to "A da zo'u da vasxu". "B da poi gerku zo'u A da vasxu" is equivalent to B da poi gerku zo'u A da zo'u da vasxu", with apparently two bindings for the same variable. > According to the example from CLL:16, it should be locally requantified > instead of being bound again: > > ( 14.1)    ci da poi mlatu cu blaci .ije re da cu barda >    Three Xs which-are cats are white, and two Xs are big. > > What does Example 14.1 mean? In normal predicate logic, it's equivalent to "ci da poi mlatu cu blabi .ije re de cu barda". The two variables are independent of one another. In CLL-logic it means something else, but since Lojban is supposed to be based on predicate logic, I prefer to stick to that. The CLL-logic of quantifiers is not completely coherent or consistent. > The appearance of ``ci da'' quantifies ``da'' > as referring to three things, which are restricted by the relative clause to > be cats. The way I would say it is that the variable "da" takes values from the things that are cats, and (exactly) three of those values satisfy the predicate "blabi" (which also means all but three of those values don't satify it). If there is any reference going on here at all it is to all cats, not just to the three that do satisfy the predicate "blabi". If we were to say "no da poi mlatu cu blabi" then "da" again takes values from the same set of referents, but now the number of them that are said to satisfy blabi is zero. Would we say that "da" doesn't refer to anything in this case? > When ``re da'' appears later, it refers to two of the those three > things --- there is no saying which ones. That's the CLL story, yes. It's appealing in simple cases like this, but it doesn't work in general. (Or at least nobody has given any satisfactory account of how these "double quantifications" should work in general.) >>> How does {A lo B gerku cu vasxu} expand with xorlo? > > I should have been more specific about what kind of expansion I had in mind. > The thing I'm looking for is a canonical form of {A lo B cu broda} > with a proper prenex. "A lo B cu broda" or "A lo B cu broda"? Both are grammatical, at least if doesn't have another quantifier. I assume you want an expansion of "A lo B broda cu brode". The proper expansion would be: A da poi ke'a me lo B broda zo'u da brode >That canonical form should not contain {lo}. OK, but this is independent of the quantifiers. I expand "lo broda" to "zo'e noi ke'a broda". And an "inner quantifier", which is not a logical quantifier, can be expanded thus: "lo B broda" = "lo broda noi ke'a klani li B". Putting all three expansions together (which are all inependent of one another) we get: A lo B broda cu brode = A da poi ke'a me zo'e noi ke'a broda gi'e klani li B zo'u da brode We have shifted the outer quantifier A (a logical quantifieer) to a proper prenex, we have transformed the "inner quantifier" B to an ordinary number "li B" used as an ordinary argument, and we have got rid of "lo". B cannot be transformed into a proper prenexed quantifier because it was never a true quantifier to begin with, it's just a cardinality. >> A cu broda >> = A da poi me cu broda >> A of the referents of are broda. > > Isn't A an _inner_ quantifier here? No, an "inner quantifier" (which is not a logical quantifier) always goes after the gadri. An inner quantifier gives the number of referents of a sumti. It is only concerned with a sumti, not with a whole bridi. An outer quantifier binds a variable and quantifies a whole bridi, it says for how many values of the variable the bridi in which that variable appears is true. mu'o mi'e xorxes To unsubscribe from this list, send mail to lojban-list-request@lojban.org with the subject unsubscribe, or go to http://www.lojban.org/lsg2/, or if you're really stuck, send mail to secretary@lojban.org for help.