WikiDiscuss

WikiDiscuss


BPFK Section: Inexact Numbers

posts: 2388


wrote:

>
> pc:
> > 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."
>
> For me, {abu zasti} and {su'o da zo'u da du
> abu}
> are quite different.

Of course, since you allow at least parts of the
outer domain in the range. No problems in the
long run. Part of the prejudice against this is
an old philosophical claim that usually comes out
as "Existence is not a predicate," to which the
stock reply is "'Exists' sure is." The
Lesniewskian approach (parts of which lie behind
much of the plural logic and/or group theory) is
that every well formed sumti is "in the domain"
("has a referent", I suppose this means). this
has the advantage of doing away with intensional
contexts but the disadvantage of having to ask
all the time about whether something is real or
not. We could collapse {da poi zasti} sdown to a
single simple form — and probably should if this
approach become general. Lojban has rejected
this idea several times however.

> > 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.
>
> If the singular ones are the ones used more
> frequently,
> then they should get the short forms. In any
> case, this
> question is not one of logical consistency but
> one of
> convenience.

True;I am just thinking like a system constructor
here.

> > 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.
>
> What other things, besides constants, can
> instantiate
> variables in logic?

Descriptions, which at least in logic are not
constants (in the sense I think you mean by
that).

> > > 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.
>
> Well, that's the point. In my definitions it is
> no
> more obscure than any other broda, {lo'i [PA]
> broda}
> is just {lo selcmi be lo [PA] broda}. It is
> not
> a special case.


But I thought the issue was about {PA lo'i broda}
and {PA lo broda}; we seem to agree on the inner
quantifiers — though I think that counts against
your identification.

> > 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?
>
> I am talking about the proposed definitions,
> yes.

Well, the definition set where this is proposed
is so defective from the get-go that I have never
seen any reason to take it seriously. However,
this proposal can be separated from its context
and be proposed for a more adequate base. In that
case, it seems to me t0o give the results that
you find objectionable, {pa lo selcmi be lo
broda} is a set of some of broda of some size,
{pa lo'i broda} is a one-memberd set of broda or
a single broda (depending on what that base is).

> > (If so
> > it seems to me monstrously inefficient, but
> that
> > is another discussion).
>
> And to me it seems wonderfully efficient. How
> do we
> test efficiency? With examples?

Well, I suppose we look to see how often we need
the various expressions and which one fits best
with this ditribution. To be sure, a consistent
pattern running though the whole gadri set
(ignoring the typicals and the like) would count
for something as well.

>
> > > > 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?
>
> Why should it be? {lo'i broda} = {lo brode}
> does
> not of course entail {broda} = {brode}.

I don't get the point of this. Yes, a set of
brodas is typically not itself a broda, but no
one suggested they were; the question was about
the whole phrases.

> > Does merely specifying how many satisfiers of
> the
> > predicate are involved completely change the
> > nature of the referring expression? Why?
>
> By definition:
>
> {lo'i PA broda} = {lo selcmi be lo PA broda}.
>
That is, of course, your definition. Since its
appropriateness is ultimately the point at issue,
citing it as an explanation is mere question begging.