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BPFK Section: Inexact Numbers

posts: 2388


wrote:

>
> pc:
> > So, {me lo broda} means "is a referent of {lo
> > broda}" and what we disagree about then is
> what a
> > referent of {lo broda} might be>
>
> That appears to be the situation, yes.
>
> > I say that the
> > only referent of {lo broda} is a group of
> broda
> > and you say — against the odds — that it is
> one
> > or several broda.
>
> Against what odds?
I break in here to apologize for being stupid: I
have been uncomfortable with this presentation
for a long time but have not been able to find
the root source of the problem, so have picked
away half-heartedly at the individual oddities.
The new definition of {me}, in terms of
reference, finally clicked to show me a more
fundamental underlying problem. Reference is a
function; that is, each sucessful referring
expression refers to exactly one thing (on a
given occasion, yada yada all the pragmatic
stuff). It is variance from this principle that
seems to me now to underlie all the difficulties
with this raft of proposals. Since so many of
the are explicitly about reference, I have to
asume that xorxes is using "refer" in some
nonstandard way. Two possibilities occur to me
so far. 1) He is using plural semantics (already
nonstandard) at least occasionally. Or 2), he
means by "'sumti' refers to a" something like "a
is one of the things whose behavior we have to
check in order to determine the truth of a
sentence containing 'sumti'." Since xorxes is as
familiar witrh plural reference theory as I am, I
assume this is not what is happening, leaving —
until some better suggestion comes along — 2. I
skimmed CLL and did not find any uses of
"reference" or "refer" that fit this pattern, but
I did find some cases of "mean" and "meaning"
which might be the source of the problem. In any
case, working with this new assumption, I am
going back over the previously troubling
positions to see whether they now work. As you
might expect, I have not yet found one that
didn't; xorxes stuff tends to cohere. And, since
in the case of sets, anyhow, the ordinary
referent is the only thing one has has to
consider, the generalization about what the
various quantifiers quantify works pretty well.
The {loi/lei/lai} case is problematic, since it
could be argued that we do have to consider the
behavior of each member of the group to determine
truth. But it could also be argued that we
consider each member only insofar as it is a
member of the group and contributes to the whole,
thus making the group in this case (unlike the
{lo/le/la} case, the correct unit for evaluation.
I still don't quite get half an apple, but a
bunch of apple halves is looking more resonable
(for coherence, not for usefulness).


> > Thus, I come up with a smaller
> > group of broda (as in English) and you come
> up
> > with a fraction of one broda (as in no known
> > laguage, apparently).
>
> I agree excluding the parentheticals.
>
> > So, yes, your position is
> > coherent, just very strange, at leas in this
> > case. What, by the way, happened to {me}
> meaning
> > "is an instance / example of," which talked
> about
> > lo broda, not {lo broda}?
>
> That will work for lo/loi/lo'i, but not for
> le/la/lei/lai/le'i/la'i. Identifying {me} with
> McKay's "Among" gives a definition that works
> in
> all cases.

Except, of course, that "among" is about
plurality and here we have groups and sets and
what not. To be sure, the crucial relation in
each of these cases is formally the same as
"among," but is not the same relation (nor is the
one for groups the same as that for sets) so this
reduction does not quite work. Unless we really
are going over to plurals after all, in which
case the groups at least drop out.


> There is no need to talk about {lo broda},
> we can just say: {me ko'a} = "x1 is/are among
> ko'a".
> When ko'a is an apple or several apples, x1 is
> an
> apple or several apples, when ko'a is a set, x1
> is
> a set.

This is new and opaque. {ko'a} doesn't "refer"
(or refer, for that matter) to anything until it
has been assigned somehow, so how does it come to
"refer" an apple or a bunch of apples. I suppose
this is contextual. And, of course, {me ko'a},
even with {ko'a} "referring" to apples does not
do away with the need for {lo plise} or any other
{lo} expression. And certainly not in a way that
distinguishes {lo} from {le}.

The subsequent stuff about fractions of the
"referents" of various expressions I witrhdraw
from, since my remarks were based on reference
not "reference."

> > So, {so'i le pa broda} is also nonsensefor
> the
> > same reason,
>
> Right.
>
> > but {piso'i lei ro broda} would also
> > be nonsense again for that reason.
>
> No, that one is meaningful:
>
> piso'i lei ro broda
> (= piso'i lo gunma be le ro broda)
>
> "A large fraction of the group that consists of
> all the brodas".
>
> > > > It starts to look as though
> > > > these {pi} with nonnumeric quantifiers
> are just
> > > > redundant.
> > >
> > > I think they are. I wouldn't want to define
> > > them if they weren't
> > > already there.
> >
> > How would you replace them, since by you they
> do
> > have non-redundant uses: how do {piso'i le
> broda}
> > without {piso'i}? I take using {fu'i}
> somehow as
> > a cheat.
>
> I would have lo/le/la as the only gadri.
> I would say {lo so'i le broda} for "many of the
> broda" when
> not taken distributively.
>
How do we know nondistributively? We could do
this, assuming we had some other way of showing
wen predication was distributive and when not and
assuming that we never wanted sets (except under
the rubric {le selcmi be}) This is getting
formally very close to plurals again (or, rather,
still) when the groups disappear.

Ahah! I just got it: unquantified descriptions
(or at least {lo}) are inherently collective, but
external quantifiers (at least numerical ones)are
inherently distributive. so, {so'i} distributes
and allows for a non-fractional quantification,
and then {lo} collects the result again. This
would work, but seems unduly complex, requiring a
quantifier for every distributive use (and they
do seem to be the most common). So, I suspect I
have missed something. And, of course, we don't
have plurality logic going yet (I think). On the
whole it still seems that leaving distributive as
(linguistically — though not logically)
fundamental and then marking collectives somehow
is going to be most efficient — if we are going
to introduce these notions at all (which, if we
do, why not go to plural logic altogether, since
then at least we are up front about what is going
on, which is mightily unclear now).