From jjllambias@hotmail.com Sun Jun 25 19:26:09 2000 Return-Path: Received: (qmail 5722 invoked from network); 26 Jun 2000 02:26:07 -0000 Received: from unknown (10.1.10.26) by m3.onelist.org with QMQP; 26 Jun 2000 02:26:07 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.70) by mta1 with SMTP; 26 Jun 2000 02:26:07 -0000 Received: (qmail 64824 invoked by uid 0); 26 Jun 2000 02:26:06 -0000 Message-ID: <20000626022606.64823.qmail@hotmail.com> Received: from 200.32.23.11 by www.hotmail.com with HTTP; Sun, 25 Jun 2000 19:26:06 PDT X-Originating-IP: [200.32.23.11] To: lojban@egroups.com Subject: Re: [lojban] RE:Trivalent Logics Date: Sun, 25 Jun 2000 19:26:06 PDT Mime-Version: 1.0 Content-Type: text/plain; format=flowed From: "Jorge Llambias" X-Yahoo-Message-Num: 3232 la pycyn cusku di'e >The assignments of functions to terms looks about >right and the means of using the functors in different contexts does recall >much of the Aymara approach (so far as i understand it). I realized something else about those assignments after I posted it. The three assertions: cai (1,-1,-1) necessarily sai (1,0,0) probably ru'e (1,1,-1) possibly are the three that differ minimally from the simple assertion (1,0,-1). Maybe that is why they are useful and the easiest to understand. (The fourth minimal variation, (0,0,-1) is not an assertion, as it doesn't start with 1.) >I also haven't checked to see whether the system xorxes gives is minimal >(i.e., could we do it with fewer functors), but I suspect it is not -- as I >am sure that the Aymara system is not. It is not minimal. For example, {ru'e} is equivalent to {naicainai}. (Possible = not necessarily not.) But we don't want a minimal system because some functions become unusably cumbersome. >xorxes' system lacks one interesting >feature of Aymara, that negation is not a primitive functor, but, since >negation is a given in lb, that would be hard to recreate, in spite of the >interesting thoughts it brings to mind. I tried assigning (-1,1,0) to {nai} but it becomes too different from the binary meaning of {nai}. In any case, {cu'i} = (0,1,-1) is -1. What would that be? A counter-negation? >(In Aymara, negation is something >like "it is certain that it is controversial that," where certainty and >controversiality are primitive functors). Isn't (-1,1,0) just plain controversial? I think "necessarily controversial" is (-1,1,-1). With my proposal, "controversial", or trivalent negation, comes out as {naicu'i}, something like "doubtful that not". (-1,1,-1) is {cu'icai}, "necessarily doubtful". >lb does not provide any natural way of upgrading this to a system of binary >connectives unless the gi's that got us into trouble the last time around >can >be called to our aid. Maybe it does: do'egi ... gi ... vau >(I hope they -- or something else -- can be, since >being able to absorb a totally unexpected and odd system would be a nice >demonstration of some property or other than lb is supposed to have.) Yes, it is working out very nicely. co'o mi'e xorxes ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com