From @uga.cc.uga.edu:lojban@cuvmb.bitnet Tue Jun 20 00:23:58 1995 Received: from punt2.demon.co.uk by stryx.demon.co.uk with SMTP id AA3464 ; Tue, 20 Jun 95 00:23:56 BST Received: from punt2.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Mon, 19 Jun 95 14:44:00 GMT Received: from uga.cc.uga.edu by punt2.demon.co.uk id aa04667; 19 Jun 95 15:43 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 1227; Mon, 19 Jun 95 10:40:42 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 7021; Mon, 19 Jun 1995 10:34:48 -0400 Date: Mon, 19 Jun 1995 07:34:22 -0700 Reply-To: "John E. Clifford" Sender: Lojban list From: "John E. Clifford" Subject: pc answers X-To: lojban list To: Iain Alexander Message-ID: <9506191543.aa04667@punt2.demon.co.uk> Status: R Xorxes has adequately dealt with djer's comments about quantifier order. djer's other comment, about the number of non-identities needed, is correct in the real world, but logic does not know that relevant men and relevant dogs are mutually exclusive groups, so we have to separate them somehow. Admittedly, it would be shorter to put in "not: for some v1, both v1 is a relevant man and v1 is a relevant dog," but, as I said, the translation was made without thinking too much. Xorxes's Lojban versions are contentious. The logical forms involve only quantifiers, his involve descriptors as well. His translations presuppose the answer to the question that is being investigated, what situations are covered by what descriptors, without discussing the plausibilities of the claimed translations other than appeal to a (logically unjustified, as I have noted) rule about quantifiers inherent in descriptors. This is not to say that they are inaccurate, but, by calling them translations, xorxes appears to cut off the possibility that other expressions might also cover the same ground or that the lojban expressions might cover more ground than that it "translates." Xorxes call attention to a further problem also involved here, ci nanmu cu pencu ci gerku. The choices here are between one that involves three men and only three dogs and one that involves three men and as many as nine dogs, three for each man. The first starts like the _le_ case: for some six things, x,y,z,w,v,u, all distinct, x,y,z men, w,v,u dogs, and for all x1, if x1 is any of x, y, z then x1 touches w and x1 touches v and x1 touches u. This has the charm of being convertible to ci gerku cu se pencu ci ranmu. But it plays havoc with the underlying quantifiers in the Lojban form. They seem better represented by for some x,y,z, distinct and men, for all w, if w is one of these, then there are v,u,x1, distinct and dogs, such that w touches each of them (as above). This is the natural generalization of something like la djan cu pencu ci gerku. As usual the first reading entails the second, so, if we decide that the Lojban means the second, we have a cover for the first as well. But the issue then is, how do we say the first explcitly (short of spelling out the quantifiers, of course). Conversion will not help, since then we end up with three dogs but possibly nine men. Prenexing does not obviously help, since it does not seem likely that we can -- pace djer -- shift numerical quantifiers around even in prenex. I am tempted to propose another xV'V to indicate non-subordinate quantifiers, but I think that, as always, we need to try a few more formulations before we go to that point. For instance, if we make the first form be what the sentence means, how will we say the second, using the material we already have? pc >|83