From edward.cherlin.sy.67@aya.yale.edu Mon Jul 02 12:51:32 2001 Return-Path: X-Sender: Edward.Cherlin.SY.67@aya.yale.edu X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_2_0); 2 Jul 2001 19:51:32 -0000 Received: (qmail 18799 invoked from network); 2 Jul 2001 19:51:28 -0000 Received: from unknown (10.1.10.142) by l9.egroups.com with QMQP; 2 Jul 2001 19:51:28 -0000 Received: from unknown (HELO pltn13.pbi.net) (64.164.98.8) by mta3 with SMTP; 2 Jul 2001 19:51:23 -0000 Received: from mcp.aya.yale.edu ([216.103.90.93]) by mta7.pltn13.pbi.net (iPlanet Messaging Server 5.1 (built May 7 2001)) with ESMTP id <0GFV00J0I35M2C@mta7.pltn13.pbi.net> for lojban@yahoogroups.com; Mon, 02 Jul 2001 12:51:23 -0700 (PDT) Date: Mon, 02 Jul 2001 13:06:27 -0700 Subject: Re: [lojban] Not talking about imaginary worlds In-reply-to: <74.c89462b.2871f8f0@aol.com> X-Sender: cherlin@postoffice.pacbell.net To: lojban@yahoogroups.com Message-id: <5.1.0.14.0.20010702124522.02c8dea8@postoffice.pacbell.net> MIME-version: 1.0 X-Mailer: QUALCOMM Windows Eudora Version 5.1 Content-type: text/plain; format=flowed; charset=us-ascii From: Edward Cherlin At 09:18 AM 7/2/2001, pycyn@aol.com wrote: >In a message dated 7/2/2001 4:25:58 AM Central Daylight Time, >edward.cherlin.sy.67@aya.yale.edu writes: ... >by proposing a modal logical theory in which to carry on our discourse. >We're not too keen on hand-waving here, and we certainly don't agree on a >Lojbanic theory of modal logic sentence modifiers. This results in the >typical infinite regress so familiar from the Tortoise and Achilles, where >one of us says, "It's obvious!" and the other says, "No it isn't, it's >impossible, and even if it were possible, I still wouldn't believe it."> > >Which is why I am suggesting turning to a "uses of language" approach, rather >than trying to work this out in terms of other worlds, taking (almost) all >language as descriptive. OK. We agree in principle, and we can discuss the details. >absurdum (and excluded middle along with it) and use a somewhat limited >form of positive, even constructive logic. "Let us suppose X" says the >mathematician, physicist, or science fiction writer, "then ignoring the >obvious contradictions, what happens?"> > >Classically one or the other version of relevance logic or some sort of >paraconsistency, but I repeat that that is missing a useful alternative in >favor of a nearly useless formalism in descriptive language. References, please. This sounds promising. I think that we should have the *option* of specifying the logic we are using, just as some gismu have options for an ontology. At this point, I don't know what I might want to specify, but I want some rather general method for specifying it. For now, I will think about explicit methods of specification using existing grammar. Perhaps by the end of the grammar freeze, we will have something worth adding. ... >different logics simultaneously. Technically they are called first-order >and second-order logic. We don't have a good way of describing this >situation either in natural languages or in Lojban. If we did, I think it >would go a long way toward clarifying the grammar puzzles that are >exercising us today.> > >Well, Robinson's non-standard artihmetic does not involve second-order logic >explicitly (or, any more than ordinary arithmetic does). It is more a matter >of object language and metalanguage: The formulae look normal but what they >mean is something else (Goedel's proof shows this more clearly, since we get >interesting metalanguage readings of apparently uninteresting object language >formulae. Well, you get that in Robinson, too, but the metalnaguage readings >are a lot less clear). The object language is first-order, and the metalanguage must be at least second-order (although there must also be a non-formal language somewhere up the chain). First-order theories can talk about sets, and second-order theories can talk about sets of sets. Although this is rarely made explicit, it is necessary to change points of view constantly in developing non-standard arithmetic and analysis. Ordinary mathematical discourse discusses sets in a form that encompasses all levels of membership. This is not a well-defined concept, since it turns out that there are models of set theory with non-standard levels of nesting. >I don't think this has a lot to do with the present problem, though. Possibly. But "all progress depends on the unreasonable man", so I'll keep at it. >ourselves clumsily in the current language, and then invent a better one >when we have a better idea of what we are doing.> >Amen. Selah. Edward Cherlin Generalist "A knot! Oh, do let me help to undo it." Alice in Wonderland