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On 9/29/06, John E. Clifford <clifford-j@hidden.email> wrote:
Y'mean this is what you have meant! Lord, I wish you had said so earlier. I wouldn't have liked it any better, but at least I would have understood it, whereas Mr.Broda and broda types snf thre like are just obscure, evern (or especially) when you spell out (more or less) what they are supposed to do.
I wasn't going to mention this, but Mr Broda is of course the topmost node of the broda lattice, the ultimate subsumer. :)
On the other hand, I do't suppose you could have said this before all the stuff about bunches and plural quantification (and collective and distributive predication) came to light.
I think plural quantification is somewhat orthogonal to this. Plural quantification concerns something we do in the object language, within a horizontal level of the lattice. The vertical organization of the lattice is mostly metalinguistic, useful for comparing different models, but normally not relevant within a model.
Indeed, I set what comes to this out earlier but you rejected it, largely, I think, because we were still working with C-sets in those days and doing this in terms of C-sets is not very plausible looking.
I think most of my rejections came about because we ended up mixing the object language with the metalanguage. Just because the upper levels of the lattice are more abstract (metalinguistically speaking) that does not mean that some dogs are more abstract than other dogs (in the object language). In the object language model, dogs are dogs, not abstract things, no matter from what level of the metalinguistic lattice they came from.
"Among" was McKay's term for the relation between a subbunch (including an individual) and a superbunch of any size. I am just following along.
Yes. What I meant is that McKay's "among" relationships holds horizontally in the lattice, not vertically, and it is a relationship used within the object language. What I would like to call the subsumption relationship holds vertically, and is normally just metalinguistic. It joins objects that enter in different models, it won't normally be used to make claims in the object language.
"Part-whole" is traditional for Mereology, the original bunches. It also proceeds below the level of individuals (well the misty band across the middle of lattice); but that may not be an advantage, since what happens from individuals on down is spotty: a dog with a leg cut off is still a dog, but the leg is not. "Subsume", like "pervade," tends to be associated with intensional hierarchies (properties, especially) and this is extensional, so far as I can tell (I'm a little worried about identities).
It is extensional in the metalanguage, but the relationship does not normally get pulled in into the object language. In a given model only one horizontal level of the lattice will be present. (Lojban being a general purpose language, it will sometimes be used metalinguistically, but then we are forced to use different predicates to clarify the different levels of the lattice, just as in English, be that as "type" vs "token", or "event" vs "occurrence", or "species" vs "specimen", or "individual" vs "stage" or what have you.) mu'o mi'e xorxes