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

["Jorge Llambías" <lojban-out@lojban.org>]

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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