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

[John E Clifford <clifford-j@sbcglobal.net>]

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

> 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.)

Yeah; this thing went through at least three versions so somethings didn't get caught up from one
version to the next.  Will fix.  thanks.

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

Yes, that is, given A and c and x,  A(c/x) is defined.

> > 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?

Well, the usual expressions is "reference" but that doesn't seem appropriate here.

> We don't know what "F is true" means at this point, not sure if this
> could lead to circularity.

These definitions are all collapsed forms of recursive definitions (I was trying to keep this as
uncomplicated as possible -- but when you simplify one place it always makes a probelm sowhere
else).  So txF is a term of a degree higher than F is a formula and truth for F is defined then
before R for txF is defined.
   
> > 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.

Yes, R(a) is just a concept, not a set.  Deeper thanks, as that was a real problem, not just an
infelicity.
 
> > 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) ?

A specific c such that cCd.
 
> The restriction for every d doesn't seem to have an equivalent in the
> singularist model.

I'm not sure it is needed (I'm not sure it is needed here, come to that, but it was a quick
solution to a problem I saw -- there may be others).  It would require something like that there
be a concept for set, which is less plausible somehow.  the point where this comes up may need
some reworking, which is why this kite is up.

 
> > 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)?

Yes, but it was stuck in here looking toward a definition of truth.