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On 9/29/06, John E. Clifford <clifford-j@hidden.email> wrote:
Herewith an attempt to make some systematic sense of your idea. I
think you have rejected this proposal earlier, but what we have
learned since them -- not least of all improved terminology -- may
make it more acceptable. I think this will work. I also think it is
a lousy analysis of the situation, not something that serves the cause
of Logic at all well.
{lo broda} refers in a given context to a contextually defined bunch
of brodas. This may range feom a single broda to all possible brodas
(probably including some impossible ones). These bunches are arranged
in the lattice by the part-whole relation (or the "among" relation).
Minor terminological note: I would reserve "among" for the object language relationship between each or some of the brodas in the bunch and some or all of the brodas in the bunch (which are all at the same level in the lattice). "The dog I mean is one among the three dogs we were talking about". I don't find "part-whole" especially illuminating either. I think "subsumes" was a nice word for the (metalinguistic) vertical relationship in the lattice, why don't you like it?
In any case, the lattice can continue below the level of individual brodas by a more literal part-whole relationship (although not all parts of a broda -- especially cut across spatial axes -- count as brodas).
At any given level, each broda will count as an individual in the object language. Your metalinguistic identification of one level of the lattice as "the level of individual brodas" may not always be easy to define. For example, what does the level of individual words contain, individual word tokens or individual word types?
In the case of {djica} and at least some other opaque contexts, the
intended bunch is either the maximal one (narrow scope) or a
particular bunch (broad scope). The maximal bunch is OK for Leibniz's
Law, since there is not anything identical with that bunch
(essentially by definition). Particular bunches, since they are
externalized by their particularity are probably also OK in this
extensional interpretation. As for the generalization, {mi djica lo
broda} entails {da poi [distributive] broda zo'u mi djica da}
regardless of which bunch is intended (for single brodas, the
distributive is the same as the personal).
The one charm of this approach is that it makes a sort of sense of the
usual "any one will do," since "any" in a secondary context always
comes out as a primary universal, here over the constituents of the
bunch.
Sounds right.
This will impose a restriction on models, namely that anything that is a broda in some world is a broda in every world in which it occurs (otherwise you could have something that was a possible broda in a world but in that world was actually something incompatible with being a broda. That is ^\F(F(a)), the individual concept of a, is either a constant partial function on worlds or a two state total function: one state being whatever it is in some world in which a is and the other being the null for worlds which lack a. This is not much of a restriction, since it is just what is required to make sense of the idea of adding a broda to a model.
I can't say I follow all that, but as long as it's not much of a restriction... [...]
As noted, some items toward the lower end of the lattice don't seem to me to be brodas any more, just broda parts: a dog's foot is not a dog, though a temporal segment of a dog is.
I wouldn't count a dog's foot as a dog in most contexts (although it would count as dog stuff). But some dog parts (say a dog minus one of it's ears) does still count as a dog in most contexts.
> {tu'a} might be a marker that indicates a higher node up the lattice
than might
> be expected (as described in the lattice scheme). But from my point
of view
> an absence of {tu'a} ought not to be used to mark anything.
I think marking higher nodes might be useful in some cases -- we do in
fact distinguish the two cases for opaque contexts (the opaque one and
the non-opaque, as it were) and using {tu'a} to mark the maximal bunch
reading might be a kindness, though not strictly required as this
might be set up.
In fact I like this meaning of {tu'a} much more than the official one that
introduces for {tu'a ko'a} some unmentioned realationship in which ko'a
takes part. Here we don't introduce any unknown relationships, we just
move up the abstraction axis. (I suppose {tu'anai} could be used for going
in the other direction, although it's currently ungrammatical.)
mu'o mi'e xorxes