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BPFK Section: Inexact Numbers

posts: 2388


wrote:

>
> pc:
> > As for the rest, your remarks suggest
> > that you either think {pa lo'i broda} is some
> > unspecified set of brodas, like {pa lo selcmi
> be
> > lo broda}
>
> Not exactly, but along those lines, yes.
>
> Strictly speaking, {pa sumti} is a
> quantified term,
> so it does not refer to anything, so it is not
> some
> unspecified thing. What the quantifier does is
> tell us
> that (exactly) one thing from those that are
> referents of
> the sumti satisfies the selbri for which it is
> an argument.
> I know you already know that, please don't take
> it as
> lecturing. I'm just writing it down mainly to
> clarify
> for myself.

Good. So, in place of "refer to" we can use "is
satisfied by" or some such locution.

> > or you think that {pa lo selcmi be lo
> > broda} is a one-membered subset or is one
> broda,
> > like {pa lo'i broda}.
>
> No, I do not think that. I think that outer
> quantifiers
> are always true quantifiers. That would not
> count as a true
> quantifier.

So, what satisfies {pa lo'i broda}? It can't
mean "one of the things that satisfy {lo'i
broda}", since that would always just be {lo'i
broda} again — and {re lo'i broda} would always
be meaningless. Or do you think that {lo'i
broda} is as inherently plural as {lo broda},
rather than being absolutely singular?

> > Either way you violate
> > your uniformity rule and need special, either
> for
> > {lo'i} among the gadri or {selcmi} among
> > predicates.
>
> Could you please elaborate. In both cases, the
> referent of the
> sumti is a set, and {pa} quantifies over those
> referents.
No, in one case the referent is a set, in the
other it is (a group of) some number of sets,
maybe but not certainly one.

>(They
> are a special case in that the sumti happen to
> have a single
> referent to start with, so quantification is
> not very
> interesting, but that's not a violation of the
> general rule.)

Well, only {lo'i broda} is guaranteed a single
referent (unless you mean the group — which I
doubt you do). Does this also mean that {PA lo'i
broda} is always uninteresting? If not
meaningless?

But the point. If {pa lo selcmi be lo broda} is
like {pa lo'i broda}, either a set with a single
member or a single broda, then in this case
(only? — well, maybe for {gunma} too), the count
is not by the satisfiers but by their content.
If {pa lo'i broda} is, like {lo selcmi be lo
broda} a set of unspecified size, then it breaks
the pattern of the gadri of giving a structure of
the same sort with a defined number of members --
or that number of members standing alone.
>
> > Actually, I don't think there can be a good
> > reason for the identification, so I don't
> really
> > expect you to provide one. What I have been
> > presenting is (now five) reasons not to
> accept
> > the identification, to see if you can knock
> any
> > of them down.
>
> Could you make a succint list of the remaining
> reasons? I think I lost truck, sorry.

the two sides have different numbers of
referents; even if they have the same number
there is no necessity that they be the same
referents; they count by different units; there
partitives are different.

> > Essentially the same objections apply to this
> > latest definition as well: the first is PA
> brodas
> > (collectively), the second is some
> collections of
> > PA brodas — maybe but not necessarily only
> one
> > — and that one may or may not be the one
> picked
> > out {loi broda}.
>
> "x1 is the set of x2" gives a function: for a
> given
> x2 there is one and only one x1 that satisfies,
> so
> {lo'i} as a contraction of {lo selcmi be lo} is
> well
> defined.

Not if "is a set of" is {selcmi} as presently
defined. If you want a new definition, then
aannounce it beforehand. Incidentally, you don't
need the complex, what you want is just {lu'i lo
broda} — without any problems. It works
slightly better with {gunma}, which gives the
whole list.

> > You are welcome to use {selcmi} in that way
> --
> > once you advertise it. In that case, x2 is
> > presumably {loi broda}, not {lo} (or, of
> course,
> > {lo} in your ideal sense if you are point
> > shifting again.
>
> Point shifting? It's plural {lo}, as always.
>
Well, always since when: it is not in your
proposed definitions, for example. But I meant
whether you were using {lo} for collective rather
than distributive gfoups.