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

["Jorge Llambías" <jjllambias@gmail.com>]

On 7/13/06, John E Clifford <clifford-j@sbcglobal.net> wrote:

> A is an assignment iff A is a function from variables to concepts
> A(c/x) is an assignment just like A except that it assigns the concept c to variable x instead of
> A(x).

(I assume assignment A and relation A are different things, it might
be a good idea to use different letters.)

Question: Given an assignment A, is the assignment A(c/x) also given,
or are they independent functions?

> If a is a term, R(a) = I(a) if a is a name, R(a) = A(a) if a is a variable,  R(a) is a concept c
> such that F is true for A(c/x), if a = txF

So R is a function from terms to concepts. Is it called something?
We don't know what "F is true" means at this point, not sure if this
could lead to circularity.

> Where P is a predicate and a a term, Pa is d-true for I and A iff  for every individual i included
> in R(a) and for every concept c s.t. I(c) = i, I(P)(c) = 1

That would be "every individual i included in I(R(a))", I think.

> A Pluralist model
...
> C is a relation between concepts and items in D, such that for every d in D, there is at least
> once c such that c is related by C only to d (C/d)

What's (C/d) ?

The restriction for every d doesn't seem to have an equivalent in the
singularist model.

> And interpretation I is a function which assigns
...
> To A the function from pairs of concepts into {0,1} such that I(A)(R(a)R(b)) = 1 iff
> for every thing d such that R(a)Cd holds, R(b)Cd holds

Couldn't A be defined more generaly for any c1,c2 like for the singularist
model, instead of just for R(a)R(b)?

mu'o mi'e xorxes