From LOJBAN%CUVMB.BITNET@uga.cc.uga.edu Sat Mar 6 23:00:40 2010 Received: from uga.cc.uga.edu by MINERVA.CIS.YALE.EDU via SMTP; Wed, 2 Dec 1992 08:20:58 -0500 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 5057; Wed, 02 Dec 92 08:17:30 EST Received: from UGA.BITNET by UGA.CC.UGA.EDU (Mailer R2.08 PTF008) with BSMTP id 6885; Wed, 02 Dec 92 08:17:29 EST Date: Wed, 2 Dec 1992 12:46:36 +0000 Reply-To: CJ FINE Sender: Lojban list From: CJ FINE Subject: Re: The Distribution Problem X-To: protin@usl.com To: Erik Rauch In-Reply-To: (null) Status: RO X-Status: X-From-Space-Date: Wed Dec 2 12:46:36 1992 X-From-Space-Address: @uga.cc.uga.edu:LOJBAN@CUVMB.BITNET Message-ID: On Tue, 1 Dec 1992 protin@com.usl wrote: > > The distributive property does not derive from the meanings of the > words being grouped but from the meaning(s) of the connectors. No, it doesn't. It derives from the meaning of tanru-modification. Consider the meaning of predication and tanru modification from the point of view of formal (Montagu) semantics. In this formulation, a selbri is a mapping from a tuple of possible sumti to {FALSE, TRUE} - in other words, a characteristic function on tuples of sumti (-referents). n b: S -> {T,F} [There are two different ways in which this function can be regarded as a set. Either, in the universal interpretation of mappings, it can be treated as a subset of the cross-product of the set of tuples and {T,F}; or more usefully it can be identified with that subset of the set of tuples which it maps to T. All these ways of describing it are equivalent]. Then giheks are the ordinary set operations on these functions, thus "gi'e" is the intersection of the functions (or their corresponding subsets). Since the functions are characteristic functions, the range of the resulting function is the intersection of the ranges of the selkanxe. A jek in the seltanru of a tanru, or a selbri which is not a tanru, works in the same way. But when we get to the tertanru, we have an entirely different semantic operation involved. Tanru modification is a restriction of the function (or its equivalent set). The nature of the restriction is (explicitly) not defined in the language - all that is defined is that the range of a tanru is a (not necessarily proper) subset of the range of its seltanru. This means that there is NO GENERAL SPECIFIABLE RELATION whatever between the range (characteristic set) of the tertanru, and that of the tanru. Given that there is no general relation, it is clearly unreasonable to expect the relation that happens to exist in particular cases to distribute over jek-connection. It may happen to do so - but that will depend on the meaning, not only of the particular terms used, but also of the tanru modification in the case. So where does this leave us? I believe that it is not in general valid to distribute a jek in the tertanru (it works in the seltanru). You are free to use cmalu je nixli ckule in a distributive sense, when the nature of the modification you intend lends itself to this; but I, as hearer, have as much freedom as in any tanru to interpret it differently. Note one implication of this: if you assume that jeks can be distributed, it appears to make sense to allow them to modify the seltanru in different ways. My argument shows that this in invalid. Thus cmalu ckule gi'e nixli ckule may certainly mean 'small school for girls', but I suggest that it is perverse to allow cmalu je nixli ckule to mean the same thing, because it is very hard to find a meaning to attach to the constituent "cmalu je nixli" that allow this. I suspect that this is a bigger problem for our use than the original point Iain made. Colin I haven't yet managed to work out, in this theory, why jeks do not work properly in selgadri. I will give it some more thought.