From @uga.cc.uga.edu:lojban@cuvmb.bitnet Fri Jun 16 22:59:05 1995 Received: from punt2.demon.co.uk by stryx.demon.co.uk with SMTP id AA3442 ; Fri, 16 Jun 95 22:59:02 BST Received: from punt2.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Fri, 16 Jun 95 20:52:31 GMT Received: from uga.cc.uga.edu by punt2.demon.co.uk id aa23817; 16 Jun 95 21:52 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 5595; Fri, 16 Jun 95 16:50:14 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 6295; Fri, 16 Jun 1995 15:50:51 -0400 Date: Fri, 16 Jun 1995 12:49:37 -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: <9506162152.aa23817@punt2.demon.co.uk> Status: R Ok, what do you want to say? Let's take "Three men touched three dogs" into logic without thinking too much about it. That gives there are x,y,z,w,v,u, mutually distinct [actually a conjunction of 15 non-identities] and for all x1, x1 is a relevant man just in case x1 is x, y, or z and for all y1, y1 is a relevant dog just in case y1 is w, v, or u [so far we have that there are three men and three dogs of interest; now for the serious content, we have a choice among] 1. for every relevant man z1 and every relevant dog w1, z1 touched w1 2. for some relevant man z1 and every relevant dog w1, z1 touched w1 3. for some relevant dog w1 and every releant man z1, z1 touched w1 4. for every relevant man z1 and some relevant dog w1, z1 touched w1 5. for every relevant dog w1 and some relevant man z1, z1 touched w1 6. for some relevant man z1 and relevant dog w1, z1 touched w1. All of these can, of course, be expanded into disjunctions and conjunctions involving the original terms, x,...,u and such formulae would also provide relatively easy ways of saying things like "two of the men touched two dogs each while the third did nothing, but all three dogs got touched." We can skip these niceties for now, I hope. Clearly, if 1 is true, the _le_..._le_ form is justified, every man touches each of the dogs. But I think that the _le_ ... _le_ form is also appropriate when 4 and 5 are simultaneously true: every man touches at least one dog and every dog is touched by at least one man. That is, all the men were involved in the touching and so were all the dogs; only the exact distribution of labor is left open. Notice that, like 1, this form is symmetric (the order of the quantifiers, corresponding to the order of the sumti, is irrelevant), so that the _se_ form will mean the same thing. Since 2 entails 5 and 3 entails 4 (both are generally entailed by 1), we have to say that their conjunction is also appropriate for the _le_..._le_, though less obviously so. We have to work out that, once again, every man touches at least one dog and every dog gets touched by at least one man. We just get more information about the distribution of labor (and belabored). I suppose that mixtures, 2 and 4 or 3 and 5, would also fit in to this pattern although they are not really symmetric. But they do all guarantee that everyone in both group gets involved. However, none of 2-5 taken alone seem appropriate for the double _le_ form. They allow some man or some dog to escape participation in the whole complex event and that seems not to fit with the sense of _le_. It does fit with _le'i_ (? the _le_ style mass), however -- assuming that the the men and the dogs (as needed) have some reason to be together beyond this complex event (I agree with xorxes that we ought not mass things without some reason -- though keeping them in mind, under _le_, may be reason enough). Of course, any replacement of _le_ by _le'i_ will make a true claim in the cases discussed above, but now we get to cases where _le'i_ but not _le_ apply. The rule seems to be that the particular quantifier ("some") marks the _le'i_ here. So, 2 and 5 are _le'i_ men and _le_ dogs, 3 and 4 the reverse -- or, of course, all _le'i_. That last form is absolutely required for form 6, assuming that we can do this at all. Even if we allow that the two groups have some common ground for massification, it seems that too little has been done to really count for one mass touching the other. We might be inclined to say only "the men have started to touch the dogs" or some such thing indication a plan not yet much executed. I'm not quite clear about what parity of reasoning does for the intermediate cases, like "two of the three men touched the three dogs". Clearly _le_ is justified when both men each touch all three and I think it is when all are involved: each touches at least one dog and and each dog is touched by at least one man (and the more precise version of that, corresponding to 2 and 3). Whether we want to bother with _le'i_ here is less clear, especially with _le'i_re_le_ci_renma_ for some of the mixed cases. pc>|83