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Jordan:
> 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..
I don't agree with me, though. And I think the point is decisive.
See below.
> Then again, maybe I am misunderstanding what you mean by "fractional"
> and "cardinal" quantifiers
"Fractional" = like so'e, like x-per-y.
"Cardinal" = like su'o, pa, re, ci...
But anyway, we have identified several different meanings that have
to do with "ro" or "all".
1a. "There is at least 1 broda and 1 per 1 of them is brode".
1b. "Either there is at least 1 broda and 1 per 1 of them is brode
or there is not at least 1 broda".
The idea behind these is that you say what proportion either of
everything or of the whole of the set of broda is brode.
2. "n broda are brode, where n is the cardinality of lo'i broda"
This is compatible with "inner ro".
3. Iterative operator: for however many x (that are broda) there
are, x is brode. This is basically an extension of your story
about cardinals as interated existentials.
We can see 2 & 3 as the same thing, I think. For unrestricted
quantification it would just mean "For however many x (things) there
are, x is brode. If there were 90 things in the universe, then
ro would = 90.
The analysis of ro as a cardinal is already licensed by "inner
ro" that perforce must be a cardinal. We can take this as a
decisive argument in favour of jordanian ro: only jordanian ro
is consistent with inner ro.
In the light of this, I'll accept that ro expresses a cardinal
number.
The understanding of ro that John and xod and I had had is
better done in terms of 'fractional' quantifiers. The means
for expressing fractionals is better left to another thread,
as you said.
To summarize the entire discussion so far:
"all of" is certainly importing even if only by irresistible
implicature.
But "ro" does not mean "all of"; it expresses a cardinal number,
the number of broda that there are. If there are 0 broda, then
ro = 0. Hence it is nonimporting.
The model of quantification favoured by John and xod is valid,
but ro is not the lexical means for implementing it. (I haven't
grouped pc in with John and xod, because I never understood
his reasons for his position -- he seemed to give no reason
but "that's how it is in proper logic".)
So, John and xod. Are you going to acquiesce??????????
Everybody else has already voted jordo.
--And.