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Jordan:
> On Sun, Nov 10, 2002 at 01:19:58PM -0000, And Rosta wrote:
> [...]
> > (Had they been importing, they would have meant "There are at
> > least y broda, and x of them per y broda are brode".) The
> > rationale for this is to make DeMorgan work more elegantly
> > Cardinals (other than no) are importing. {su'o, pa, re} are
> > cardinals. {so'e, ro, me'i ro} are fractionals. {no} neutralizes
> > the cardinal/fractional distinction (and is by deduction
> > nonimporting)
>
> I object to calling "ro" a fractional.
This seems to be a major point of disagreement, but I don't know
what your reasons are.
If I try to think of how else you might understand "ro", what I
come up with is the idea that in {ro broda} (but not ro da, when
da is unrestricted), ro is a cardinal number whose value is
equal to the cardinality of the quantified set. This is what
ro as a so-called inner quantifier means. So for a set of
cardinality 0, ro broda is synonymous with no broda, which
gives you just the meaning you want.
If that's the sort of idea you're operating with, I think I
could agree with it, except that I don't see how to get it
to mesh with unrestricted ro da. OTOH we can't get away
from an asymmetry:
either
ro1 lo ro1 broda
ro1? da poi broda
ro2 da
or
ro2 lo ro1 broda
ro2 da poi broda
ro2 da
where ro1 is cardinal ro and ro2 is fractional ro.
> I don't think it is anything
> like a fraction---it certainly isn't the same as 100/100 or 1/1
Of course it isn't. As I explained, fractional quantifiers are not
fractions.
> > I think this gives the scheme Jordan, Jorge et al want: A-E-I+O+
> >
> > A- = ro (nonimp because fractional)
> > E- = no
> > I+ = su'o (imp because cardinal)
> > O+ = su'o+na (but NOT me'iro)
>
> Yeah---I'm not sure what that me'iro stuff is about. Not all is
> su'o+naku or naku+ro. Maybe xorxes can explain that
>
> > (In what I have said here, I am contradicting what I said yesterday,
> > because I had been making the mistake of thinking of su'o as a
> > fractional (i.e. as "some of" rather than as "one or more of")
> > (Partly this is because I don't really think of cardinals as
> > quantifiers.))
>
> Can't they be thought of as a bunch of existential quantifiers?
> ci da ==
> ExEy(y != x & Ez(z != y & z != x & ....)
>
> Maybe there's a better way though?
I prefer to think of cardinals as primitives that function as
the cardinalities of sets. But I don't claim that's the only
way to handle them.
> > Let me move on to a bit that we might not agree on:
> [...]
> > Define two cmavo:
> >
> > fi'au = non-importing PER (< fi'u)
> > fu'oi = importing PER (blend of fi'au + su'o)
> >
> > these have a grammar similar to fi'u and pi (e.g. {fi'au so'e},
> > {fu'oi so'e}, {fi'au ro}, {fu'oi ro}
> >
> > When functioning as fractional quantifiers, bare ro & so'e are
> > technically ambiguous between fi'au and fu'oi. The ambiguity
> > should not matter to usage, because there is no good reason
> > to want to make a claim where it does matter
>
> First, as I said above, I don't consider {ro} to be a fractional
> quantifier. There's certainly nothing in the way of us getting
> importing {ro} when we need it without defining new cmavo (which
> no one will *ever* use)
But the main points of irresolution seem to concern areas that
have no actual bearing on usage, so if defining new cmavo allows
a resolution it is to be welcomed.
> or any cmavo hijacking (which is quite
> mabla): {rosu'o}. (Btw, does anyone know what the naku rules for
> {rosu'o} would be?)
This misses the point, which was that the point of disagreement
concerns not sayability but whether fractional quantifiers mean
"There are at least y broda and x of them are brode" or
"Either there are at least y broda and x of them are brode or
there are not at least y broda".
> Anyway, I've not been dealing with the import of so'o, so'e, etc,
> and I still think they are off topic. so'o needs a bit of other
> foo before we debate a minor issue like import---we don't have rules
> about naku boundaries for them, etc. So my suggestion is that the
> consideration you're giving to consider 'fractional quantifiers'
> as a general class is a red herring
If we can agree that ro is not a fractional, then indeed we can
file away my remarks until we at some future date consider
fractionals. (so'o seems pretty clearly a cardinal, btw)
However, I currently don't see how we can get away from fractional
ro altogether, though I can see how either of the two schemes
I outlined above make sense:
either
ro1 lo ro1 broda
ro1? da poi broda
ro2 da
or
ro2 lo ro1 broda
ro2 da poi broda
ro2 da
where ro1 is cardinal ro and ro2 is fractional ro.
--And.