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On Sun, Nov 10, 2002 at 08:10:38PM -0000, And Rosta wrote:
> 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.
My idea of "ro" is that it is similar to a for loop in a programming
language. Basically it takes two arguments: a variable, and a
propositional function, and then evaluates the propositional function
to make a proposition using each iteration of the variable. If it
is asserted, it asserts each of these individual propositions.
To me there's nothing fractional about the way it operates: it
simply is an iterative operator. If your suggesting that that means
that an "inner quantifier" of {ro} has to be sorta a different sense
of the word, then I agree with you...
Then again, maybe I am misunderstanding what you mean by "fractional"
and "cardinal" quantifiers.
> 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.
For me when the range is restricted, all we are doing is changing
how many things the quantifier is going to cause the variable to
iterate over.
I agree with you that for a set of cardinality zero, the truth of
{ro broda cu brode} == {no broda cu brode} (both are true). The
latter simply says {naku su'o broda cu brode}---"it is false that
there exists a broda such that brode"---which is true because there
are no broda.
--
Jordan DeLong - fracture@hidden.email
lu zo'o loi censa bakni cu terzba le zaltapla poi xagrai li'u
sei la mark. tuen. cusku
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