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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. 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. 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.
--- In jboske@yahoogroups.com, "Jorge Llambías" <jjllambias@...> wrote:
>
> On 9/29/06, John E. Clifford <clifford-j@...> 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?
"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. "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).
> > 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?
Insofar as I understand token and type, these would be two different
levels. I don't see the same problem with dogs, though the "level" of
individuals is more an areas, since some parts of individuals are
still individuals of the same sort (your dog minus one hair, e.g.).
But this is different in kind, it seems to me, from a token-type
distinction in the usual way of things.
> > 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.
Yeah; that's why I hedged that remark. It is a nice philosophic
enterprize (so one we don't have to think about) to figure just what
makes a part be or not be the same sort of thing as the whole -- it is
relatively easy for animals, but after 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.
>
> 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.)
Well, in the logic we had going (and which, by the way, I still think
is the more informative way to go -- this is just a cute trick to
achieve a dubious end))it made a lot of sense: with intensional
events, those foggy one subsume a lot of more specific one, where we
don't want to or can't be more specific about what event involving lo
broda we have in mind. Outside that logic -- which seems to be where
we are, wvwen without this dodge -- it looks very lame indeed.