[lojban] Re: A (rather long) discussion of {all}

[John E Clifford <lojban-out@lojban.org>]

Interesting.  I haven't thought about what to do with numerical quantifiers yet -- they don't
arise for the present problem, which is just singular vs. plural.  II am not sure how to make the
distinction simply in a language other than spelling it out in separate clauses as you do below. 
I don't suppose that something like distributive and collective but more detailed would apply
(most of the interesting cases would be more to the collective side apparently).  We have noted
occasionally through the years that "collective" covers a number of different states of affairs:
those you mentioned as well as three people carrying an object from a to b with each carrying it
part of the way or with two actually lifting and one supervising, or with each pair carrying ti
aprt of the way and so on.  Your suggestion -- which gets harder to implement the more we get into
relation (rather than predicates) -- goes eome way into making that explicit, whwereas now we do
not enquire into the details of collective predications.  As I work out the details of the
relation case, I will look at what possibilities arise for these finer distinctions.  Thanks.

--- Jorge Llamb�as <jjllambias@gmail.com> wrote:

> On 7/17/06, John E Clifford <clifford-j@sbcglobal.net> wrote:
> > Pluralist:
> [...]
> >  Pa is d-true for I and A iff for every d in R(a) I(P)(1)(d) = 1
> >  Pa is c-true for I and A iff R(a) numbers n and I(P)(n)(R(a)) = 1
> [...]
> > F is true for I and A iff
> > F = Pa and Pa is d-true for I and A or Pa is c-true for I and A.
> [...]
> 
> This way of interpreting things immediately raises the question of
> why limit ourselves to the two extremes, d-true and c-true, which
> I will re-lablel as 1-true and n-true. We could define:
> 
> Pa is 2-true for I and A iff for any X that numbers 2 in R(a) I(P)(2)(X) = 1
> Pa is 3-true for I and A iff for any X that numbers 3 in R(a) I(P)(3)(X) = 1
> ...
> Pa is n-true for I and A iff for any X that numbers n in R(a) I(P)(n)(X) = 1
> 
> And then:
> 
> F is true for I and A iff
> for some n, F = Pa and Pa is n-true for I and A
> ...
> 
> For example, we would say that "the students know one another" is true
> because it is 2-true, (where "a" is "the students" and "P" is "know
> one another").
> 
> But even doing that, we would still be leaving things out, because I want
> "the three boys carried the three chairs to the garden" to be true even when
> it is not n-true for any n, for example because two boys carried one chair and
> one boy carried two chairs.
> 
> mu'o mi'e xorxes
> 
> 
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