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--- In jboske@yahoogroups.com, "Jorge Llambías" <jjllambias@...> wrote: > > On 9/29/06, John E. Clifford <clifford-j@...> 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. :) Fine: I can under5stand that in terms of this lattice, but it was hard (indeed, impossible) to get to this latticre from Mr. Broda talk. > > 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. Remember that one interpretation of bunch talk just is plural quantification. Pluralities of different sizes are just different levels in the lattice (though talk of levels and horizontal planes is not officially proper -- the lattice does not offer comparisons between items at the same "level" except immediate successors of the same node). That is, "among" or whatever holds between an object at whatever level and all the objects linearly above it, all the way back to Mr. Broda (assuming that the parts of individuals that are not brodas are dropped). > > 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. Nothing in this lattice is abstract -- or at least has to be. In the broda lattice, there are nothing but brodas, more and more of them as you go up a single path (or more complete ones going up the lower levels). You can take the L-set reading of bunches, but then again nothing is more abstract than any other -- all are L-sets, just bigger or smaller. And L-sets are barely abstract at all. To be sure, we don't talk about the lattice in the object language as such, but its tructure determines what we can say truly in the object language -- so, in particular, all the axioms for lattices (transitivity, antisymmetry, reflexivity, and so on) are universal truths in the object language. > > "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. No, "among" holds vertically but not horizontally -- the lattice defines no horizontal relations. "Among" is just the same as "subsumption." > > "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.) I don't understand this at all. If this is to work, all levels of the lattice are available all the time and are treated in the object language as equals: Mr. Dog is the same sort of thing as the earless dog, something that is distributively a dog. The various predicate pairs you give are a mixed bag: property and extension (well, up and down), class and member, whole and part and so on. To be sure, they all have about the same logic and so in the object language we can't readily tell them apart (though Lojban does have different words for some of them -- property and extension, and class and member). Some of them may be ways to read the relation here, but some of them are clearly not.