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BPFK Section: Inexact Numbers

posts: 2388


wrote:

>
> pc:
> > 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.
>
> Yes. I take every unquantified sumti as a
> plural constant,
> i.e. a constant with one or more referents.

Well, we've been over this before. If you are
going to make reference sometimes a relation
rather than a function, it becomes one all of the
time. That is, variables become plural, too. I
suppose that it does happen that as a matter of
fact variables are always assigned on a single
referent but that can't be built into the system
(and, indeed, would result in no variable be
usable to generalize on one of the plural terms).

The "constant" continues to worry me — what do
you mean by that expression. It cannot be
negation transparency of course, because that
doesn't work in one direction or the other. I
suppose it just means that the expression refers
to the same thing(s) wherever it occurs (yada
yada) as opposed to a variable which can refer to
different thing in various occurrences. Ao it is
not very surprising after all,since this was
always assumed (descriptions stick).

>
> From my part, you are welcome to offer an
> alternative system.
>
> The system I propose consists of lo/le/la and
> non-fractional
> quantifiers. That's all we need.
>
> Sets, masses, typicals and fractional
> quantifiers are bells
> and whistles as far as I'm concerned, added for
> back compatibility
> with CLL but really not a relevant part of the
> system. I think they
> have been added in a fairly systematic way
> given those constrains.
> I can certainly imagine more elegant functions
> for them, but they
> wouldn't agree with CLL. If you suggest
> something else and there
> is support for the idea, I'll be happy to go
> along with it.
>
Well, I did offer a version of my own a while
back (with fractionals as far as I can remember)
and with collective {loi lei lai}. You objected
that some of the things that I had for
descriptors you had for quantifier expressions
(and I think I had my quantifier expressions
wrong from my point of view, too) but otherwise
did not comment on the project as a whole. I
think it was internally consistent, however, once
the quantifiers are corrected to read, for
example, {(su'o) da broda} = Ex:FxAy:Fyy
among x (I assumed plural quantifiers, to be sure
-- I could redo it in terms of groups, which
would be formally identical, though a bit
wordier). It also seemed to agree with CLL pretty
much — except for universally accepted changes,
like allowing unlabelled {lo} to be something
other than all the brodas or whatever.
I haven't implemented the notion that collective
predication is alone basic, but it should run
smoothly, with individual and distributive
predication being definable (real definitions).
Failing that, I think the problem of indication
type of predication is the single most complex
one — that is, finding a sensible method within
the context of the language: we could solve the
problem by just putting a word for C or D at each
place, but that gets to be way too long.
I like the idea of not having fractional
quantifiers at all but using (I suppose you
intend) longer expressions involving {se'i} and
the like.