From nobody@digitalkingdom.org Thu Dec 15 17:28:08 2005 Received: with ECARTIS (v1.0.0; list lojban-list); Thu, 15 Dec 2005 17:28:08 -0800 (PST) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.54) id 1En4Ny-0001gL-QO for lojban-list-real@lojban.org; Thu, 15 Dec 2005 17:27:50 -0800 Received: from web81304.mail.mud.yahoo.com ([68.142.199.120]) by chain.digitalkingdom.org with smtp (Exim 4.54) id 1En4Nx-0001gD-TC for lojban-list@lojban.org; Thu, 15 Dec 2005 17:27:50 -0800 Received: (qmail 77514 invoked by uid 60001); 16 Dec 2005 01:27:43 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=sbcglobal.net; h=Message-ID:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding; b=h6ZPCYk89GFgLlhItBnM5APBb1FHG+2Kt5R50NFJvjVEW8T/tMDp5CFY67ULlzJPRt1eQxk73fgMpG8XS1CsaJriOnm++r7QDugXM9fAfShQkDJys/4lZVI67SZpGAEXD9c3X+ccNmNL51ooLaRBT3fwB1GxX8y6ENm4Img+KGs= ; Message-ID: <20051216012743.77512.qmail@web81304.mail.mud.yahoo.com> Received: from [70.230.168.167] by web81304.mail.mud.yahoo.com via HTTP; Thu, 15 Dec 2005 17:27:43 PST Date: Thu, 15 Dec 2005 17:27:43 -0800 (PST) From: John E Clifford Subject: [lojban] Re: A Proposed Explanation of {gunma} To: lojban-list@lojban.org In-Reply-To: <925d17560512151649w34dd7b5eg2cc377f310ef52e8@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Spam-Score: -0.1 (/) X-archive-position: 10907 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: clifford-j@sbcglobal.net Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list --- Jorge Llambías wrote: > On 12/15/05, John E Clifford > wrote: > > Looking over that chapter again, I note that > > McKay is doing a very different thing there. > He > > is arguing that plural > quantification/reference > > cannot be reduced to any singularist version > and > > that it does not require a singularist > > underpinning of any sort. All of which I > agree > > with; I am only saying that there are > singularist > > systems that are formally indistinguishable > from > > plural reference/quantification. > > Isn't that contradictory? If plural reference > cannot be reduced > to any singularist version, how can it be > equivalent to some > singularist system? They could have the same formal theorems without one being definable in the other. That is the situation I am contemplating. What is odd here is that the two (or more) isomorphic theories are also theories that apply to the same phenomena, but even this is not unprecedented (though I can't at the moment remember the classic examples). > After all, > > bunch theory does not *say* there is a bunch > that > > so and so, it just says that something is so > and > > so, leaving it open what that something > is/are: > > aF & bF & cF => [Ed]d-F regardless. Put > another > > way, McKay uses "plurality" and "plurals" in > ways > > that are to the naked eye not different from > the > > way a singularist uses "set" or "fusion" and > this > > is even more true in the formalism. I have admit though that my remarks about the fusion principle (the fusion of any two things exists) was a bit of singularist thinking. Even if there such a plurality exists in some sense, that does not mean that it is assigned to some variable or term and thus [Ax][Ay][Ez](x in z & y in z) is not true in every assignment and so not a theorem (the special case where all assignments are singular and individual shows that). Now the question is "What would be lost from bunches if that principle did not occur?" So far nothing else that I'm sure I want seems to be affected, but I haven't checked all that carefully. In particular, the break-down parts -- which seem to me more important that the build-up parts -- seem to work. But I am open to correction on even that. 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.