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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).
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).
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.
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.
--- In jboske@yahoogroups.com, "Jorge Llambías" <jjllambias@...> wrote:
>
> On 9/28/06, John E. Clifford <clifford-j@...> wrote:
> > --- In jboske@yahoogroups.com, "Jorge Llambías" <jjllambias@> wrote:
> > >
> > > Do you remember the subsumption tree you introduced for events?
> > > If you can generalize that idea to other objects besides events,
I think
> > > you can get the gist of what I mean.
> >
> > Well, I apologize for calling them trees when they are strictly
> > lattices -- each node my be under more than one other node where these
> > higher nodes are not placed relative to one another(we might say they
> > are all on the same level, but the notion of level doesn't make sense
> > in potentially infinite arrays (though I think all these matrices have
> > both a highest and a large number of lowest members)).
>
> That sounds right, except perhaps about the lowest members. For
> example, let's take the event of my going to the market. I guess
> you would take one particular instance of my going to the market
> (let's say one that occurred this morning) as a lowest member. But,
> suppose John saw me going to the market from the window of his
> house, and Mary saw me going to the market from the window of her
> house. In one sense, we can say that they both saw the same thing.
> In another sense, we can say that what Mary saw was different from
> what John saw. I would allow my going to the market as seen by John
> and my going to the market as seen by Mary to be (in some contexts)
> two different members of the lattice, lower than and subsumed by the
> one we had taken to be a lowest member. Or, if my going to te market
> lasted from 9:16 to 10:07, then I would count an event that was just
> like it but that lasted from 9:17 to 10:08 to also count as my going to
> the market, and a whole lot of other slightly shifted events like these
> would all be subsumed by the one event of my going to the market that
> occured this morning.
Well, it is hard to specify exactly the boundaries of an event like
going to the market (what counts as beginning and what as ending).
And, of course, there are a range of possible my-going-to-the-market-
this-mornings, only one (or a relatively small set) actualized. Of
course, outside of opaque contexts, presumably not all the
possibilities are called up.
I don't much like calling the ordering relation "subsumption;" that is
moreintensional than this notion calls for.
> In a given model {lo nu mi klama le zarci} might pick a single node
> of the lattice, several (same-level) nodes, or we might not be able
> to tell nor care whether it picks several same-level nodes or the one
> node that subsumes them, or some nodes in some other intermediate
> level. If we cannot tell what exactly it picks, and we do care to tell,
> we need to ask the speaker to be more precise.
>
> > That said, I don't see how this fits into the present problem exactly.
> > I suppose you mean that {lo broda}in the "want" context stands for
> > some node or the nodes in some segment of some such lattice (the broda
> > one? the thing one? the Being one?)and that what we want is one of
> > these nodes (or, probably, the realization of one of these nodes,
> > since we usually really want (to have) brodas, not abstract nodes).
>
> Of course none of the nodes will be called nodes in the object language.
> In the object language any node at any level will count as a broda.
> {lo nu mi klama le zarci} will always count, in the object language, as
> an event or several events of my going to the market, never as a node
> in a lattice. The lattice is just a metalinguistic tool.
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
> > suppose that this can be fleshed in such a way as to do the trick, but
> > I don't see the need for all the apparatus. Surely it is enough to
> > use the (already needed) sense of (the event of having)a unicorn. But
> > whatever it is we mean here, my point remains that we ought to say
> > what we are using to block misunderstanding.
>
> We ought to say as much as we need in a given context, and no more
> than we need, yes.
>
> > To be sure, if saying it
> > gets too complex, we might drop that suggestion, but it seems we can
> > find something short enough to be practicable. We would also like to
> > leave enough of the old English appearance to show just how we have
> > avoided the problem. In short, using {tu'a lo broda} for the narrow
> > scope version and {lo broda} for the broad scope version seems a very
> > efficient way to deal with the issue. We can worry about just what
> > {tu'a} means later (and, indeed, we already have a good deal of
> > latitude on that).
>
> {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.