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--- In jboske@yahoogroups.com, "Jorge Llambías" <jjllambias@...> wrote:
>
> On 10/3/06, John E. Clifford <clifford-j@...> 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.
Well, most nodes will not be dogs personally and I take it that the
cardinality involved -- in the dog simpliciter lattice -- is that of
dogs, but the dogs involved are in a sense on the next level down.
Indeed, as things are set up here, the referent of {lo broda} will
always be a single node first of all and its immediate descendentts
(ANnd theirs and so on down) only secondarily. There si probably an
alternate way of doing this where all the ultimate nodes atrre 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.
> > 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.)
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. Further, down to a certain level -- somewhwere below the
level of dogs, every node has an immediate successor, then some become
terminal. Actually, I have not thought about the case of collective
predications, where terminal nodes come fairly high up since we get
usually before the level of individuals a level that no longer ssfies
the predicate in the appropriate way.
> > 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.
Well, you do say this but I can't understand it. Mr.Dog is a dog
distributively but not personally. He has very few -- if any-
characteristics of a dog: no legs, no tail, not even spatiotemporally
continuous and discrete. Only a dog is [personally]a dog, satisfies
the predicate {gerku} say. Spot and puppy spot are in; Mr. Dog and
The Golden Retriever are not.
> 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.
Well, as set up, logically it does. Ontologically it need not.
"Bunch" may be, after all, just a fac,on de parler. Of course, some
levels (and nodes along some paths at every level) commit us to there
being nodes representing only possible critters relative to a given
world, but that is clearly a different sort of ontological problem.
> > I suppose we can declare this area as a single
> > "level" and allow "mixed" nodes. But we need to retain the potential
> > 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.
I think the move from one node to some of its decendents atleast 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.
It may be better to define levels bottom up rather than top down (as
here). But then I am not sure where the first level is (an
instantaneous viable dog chunk?).
>
> > 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.
I think this is clearly correct and I suspect that the relationship
between the two related lattices would not generally be too clear.
Except, of coure, that each nod in the breed lattice is a node in the
dog lattice and with the same immediate descendents (or maybe not
quite, depending on, for example, the rules about offsprings of
various sorts).