From mbays@sdf.lonestar.org Fri Apr 18 04:53:22 2003 Received: with ECARTIS (v1.0.0; list lojban-list); Fri, 18 Apr 2003 04:53:23 -0700 (PDT) Received: from ol.freeshell.org ([192.94.73.20] helo=sdf.lonestar.org ident=root) by digitalkingdom.org with esmtp (Exim 4.12) id 196UQd-00036K-00 for lojban-list@lojban.org; Fri, 18 Apr 2003 04:53:15 -0700 Received: from sdf.lonestar.org (IDENT:mbays@norge.freeshell.org [192.94.73.3]) by sdf.lonestar.org (8.12.8/8.12.8) with ESMTP id h3IBr17r011880 for ; Fri, 18 Apr 2003 11:53:01 GMT Received: (from mbays@localhost) by sdf.lonestar.org (8.12.8/8.12.8/Submit) id h3IBr12J022797; Fri, 18 Apr 2003 11:53:01 GMT Date: Fri, 18 Apr 2003 11:53:01 +0000 (UTC) From: Martin Bays X-X-Sender: mbays@norge.freeshell.org To: lojban-list@lojban.org Subject: [lojban] Re: materials needed for resumption of ju'i lobypli In-Reply-To: <20030417183836.GI26227@skunk.reutershealth.com> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-archive-position: 4827 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: mbaysATfreeshellDOTorg@flibble.INVALID Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list On Thu, 17 Apr 2003, John Cowan wrote: > > Martin Bays scripsit: > > > I was trying to figure that out the other day - what's the cardinality of > > the set of possible worlds? Or, more likely, is it a proper class? > > Aleph-one. Whether it is a private class depends on whether you think > classes belong to the world state or not. > Exactly aleph-one, or just at least? I'm afraid I didn't understand your second sentence. In case anyone else finds this interesting - here's a load of stuff about set-theoretical paradoxes applied to modal logic: http://www.hf.uio.no/filosofi/njpl/vol4no1/ruskap/node2.html One of the basic ideas seems to be that any set of possible worlds defines a possible world, so then you get a paradox by Cantor (the power set of A is strictly larger than A). --- #^t'm::>#shs>:#,_$1+9j9"^>h>" < v :>8*0\j" o'u" v" e'i" v".neta"^q> ;z,[; > > ^