WikiDiscuss

WikiDiscuss


BPFK Section: Inexact Numbers

posts: 2388


wrote:

>
> pc:
> > OK. So you allow at least some members of
> the
> > outer domain into the range of variables.
> That
> > works, too. But it would be a good idea
> towarn
> > people of it, since it is not the presumed
> > situation.
>
> I would have said strict restriction to the
> inner
> domain was the exceptional case, so that's the
> one that would need warning when context is not
> enough. (The warning would consist of a {poi
> zasti}
> or similar.)

Well, of course, strict restriction to the inner
domain is just what "To be is to be the value of
a variable" means, despite the obvious reasonable
extention to the outer domain; "a exists" is
defined as "Ex x = a." Whether that is the usual
case with natural languages is highly
problematic. In the best cases the evidence is
mixed and subject to both possible
interpretations — implicit context shifting or
outer domains.

> > > We are obviously working under different
> > > definitions.
> >
> > That is a useful hypothesis. What is your
> > definition — or at least a characterization
> that
> > covers these cases?
>
> I gave it many times already: Every
> unquantified sumti
> is a plural constant. Outer quantifiers on a
> sumti
> quantify over the referents of the constant:
> PA sumti = PA da poi ke'a me sumti.
>
> If you absolutely require plural variables and
> quantifiers in order to have plural constants,
> then
> introduce {da'oi}, {de'oi}, {di'oi} as plural
> variables, and {su'oi} as the plural
> existential
> quantifier (that one should be enough), and we
> can
> define the singular variables and quantifiers
> in
> terms of them.

If we can define singular quantifiers in terms of
plural (as we can), shouldn't the plural
quantifiers be given the basic forms and the
others the more remote ones. Generally, it would
seem that variables function better as plural
than as singular, especially given that {lo} and
the like are instances of them (and are not, we
hope, sets or groups). The "constant" part
remains a problem, of course.

> > But back to the original point, whether {lo'i
> > broda} has the same referent as {lo selcmi be
> lo
> > broda}, consider
> > {pa lo'i broda} refers to a set containing
> > exactly one broda, a member of {lo'i broda}
> in
> > fact, or to that one broda itself.
>
> I know that's how you want to define it, and
> that's
> what I don't like. I want the meaning of {PA
> sumti}
> to depend only on the referents of sumti,
> not on
> its form.

And how does this not? The referent of {lo'i
broda} is a set of broda and what is among it is
either some broda or some set of broda (just what
{me} means with sets is somewhat obscure, since
it is "defined" for other types of entities. The
referent(s) of {lo selcmi be lo broda} is (a
group of) several sets of broda, what is among
them (or it) is (a group of)several sets of broda
-- size indefinite.

> > {pa lo selcmi be lo bbroda} refers to one set
> of
> > broda, which set may be of any size.
> I don't think quantifiers quite refer, but I
> think
> we basically agree on the meaning of that one.

Odd, I thought I was copying your usage, but let
us agree that that is just loose usage and we
know what we mean here (though if the going gets
rouggh we may have to go back ans spell it out a
bit more).

> I want
> {pa lo'i broda} to have this meaning too.

But that would be most strange and the result of
depending on the expression in the {lo} case. Or
at least so it appears to me. Perhaps this is
one of those cases of not clearly marked (or not
carefully observed) differences in what we are
talking about. I think I am talking about
current Lojban (your usage possibly excepted),
are you talking about your ideal system? (If so
it seems to me monstrously inefficient, but that
is another discussion).

> > Similarly,
> > {lo'i pa broda} is a set containing exactly
> one
> > broda,
>
> No problem with that.
>
> > {lo pa selcmi be lo broda} is a single set of
> > broda, which set may be of any size.
>
> No problem with that.
>

Why isn't this a serious objection to your claim
of the identity of the two encircling phrases?
Does merely specifying how many satisfiers of the
predicate are involved completely change the
nature of the referring expression? Why?