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--- In jboske@yahoogroups.com, "Jorge Llambías" <jjllambias@...> wrote: > > On 10/4/06, John E. Clifford <clifford-j@...> wrote: > > > There is probably an > > alternate way of doing this where all the ultimate nodes are the > > referent, but then the point of the nodes is somewhat lost. Of > > course, the nodes need have no reality other than as ways of speaking > > about the unltimate nodes, but we are not doing ontology here, just > > logical structure. > > Wheras for me there are no ultimate nodes (i.e. nodes that don't subsume > other nodes). I think there is a poit at which no matter how you slice it, the result of cutting is no longer a dog. To be sure, this is less likely with temporal cuts, so in that sense there may be no ultimate nodes. But there is a point where we pass over from dogs-by-distribution to dogs-personally and, while, these are not ultimat nodes they occupy a special place in the whole -- they are the real dogs, after all, even if parts of them are also. > > So far as I can tell, immediate descendent is always well defined -- > > each path is a well-ordering and so descrete -- neither dense nor > > continuous. > > Consider a dog, x, and x minus one hair, y. Is y an immediate > descendent of x? But then what about z, defined as x minus half > that hair? Wouldn't z be a descendant of x and have y as a > descendant? Interesting. I suppose you could set it up that way. I don't see any reason to do so at the moment, but if a reason comes along (even a philosophical one like this) we can accomodate. As far as I can see, the important features of the lattice are topological not metrical. Indeed, I noticed that the notion of levels does not work directly at all well. The level below a pluality node is all the pluralitis lacking one memner of the head, but it is also all those members individually, so that successors are already level mixing, if levels count. > > I think the move from one node to some of its decendents at least are > > quite common in object language talk: "I saw three dogs [level n]. One > > of them [level n-1, maybe n-2] ran to greet me. One of the others > > [level n-2 for the "one", n-1 for "the others"] ran away." and so on. > > Whereas for me, all of those are at the same level. For me > "x1 is/are among x2" is an object language relationship that holds > between brodas of the same metalinguistic level, it is not the > metalinguistic relationship between different level nodes, "x1 subsumes > x2", which is the relationship that sets up the lattice. Well, as I suspected, we are not in fact on the same page. In tthe model I presented, "among" is exactly the relation between a node and any node above it on a constantly upward path. In particular, each dog is among Mr. Dog. I hope you can explain what you thought I meant or, more exactly, what you did mean (and still do, I suppose).