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On 10/3/06, John E. Clifford <clifford-j@hidden.email> wrote:
What we have at the moment is a uniform definition for {lo broda) = a node on the lattice. Two brodas {lo re broda} is then a node with cardinality two.
I would say that the referents of {lo broda} in a given context are one or more same-level nodes of the lattice, so {lo re broda} would make reference to two nodes rather than one node with cardinality two. Perhaps the two formulations can be made equivalent, I don't know.
I suppose this means that the immediate descendants of this node are two things at the next lower level. I think we can set this up so that there are no nodes which mix levels -- indeed, that is what I envisioned until you noted the other possibility.
Is "immediate descendant" always well defined? I suppose it's something like "x is an immediate descendant of y if x is a descendant of y and there is no z such that x is a descendant of z and z is a descendant of y", but do we know that nodes in general have immediate descendants? (I would guess in general they don't.)
The only problem cases seem to be cases of a whole dog and a dog minus one hair (or whatever), which seem to be at different levels but together count as two dogs for most purposes. That is, the strict hierarchy seems to break down in that vague central area of things that are brodas personally, not merely distributively.
The way I'm picturing this, all nodes are brodas personally. The Dog is a dog, The Golden Retriever is a dog, Spot is a dog, puppy Spot is a dog, and so on. But in a given context, there is normally only one level in the domain of discourse. We can refer to several dogs/nodes from one level with a single expression, but that does not take us to a higher level of the lattice.
I suppose we can declare this area as a single "level" and allow "mixed" nodes. But we need to retain the p[otential separation, since there are times -- as you note -- where a dog and the same dog minus a hair will count as two dogs. I haven't though this out at all, but I expect there is a way to do this.
The proscription against mixing levels probably cannot be absolute, otherwise we couldn't be having this conversation for example, but when we mix levels, the discussion becomes in some sense metalinguistic or metaphysical. It's no longer about relationships between dogs and other things, but about what counts as a dog in a given context. If nodes from more than one level need to be referrenced, then the way to go is to switch lattices so that the two levels of the original lattice now each correspond to a single level of a new lattice.
Well, there clearly is the distinction between levels that are dogs distributively and those that are dogs personally. We do not have at the moment words for the various levels, so we can't at the moment use the type-token distinction, which is not a complete solution in any case, given that they are merely relative terms. There are probably -- now that I start to think about it -- other mixed levels as well: Dalmatians and Golden Retrievers are probably at different levels as things are set up now, but we do need a level for breeds as such in the dog lattice -- quite independent of the sizes of the various breed populations (and probably for show classes and the like as well).
I'd say the size of a breed population would never determine a level.
But once we start down that road, it is hard to see how to prevent all kinds of mixed levels. Perhaps the answer is that dog breeds, for example, {lo se gerku} are just a different lattice from dogs and that, although all the nodes in the breeds lattice are also nodes in the dog lattice, they are differently connected.
Yes, dog breeds would constitute a different lattice from dogs. And one would need to introduce that lattice if it was not clear which level of the dog lattice we were talking about. mu'o mi'e xorxes