Re: [lojban] xorlo and masses

[Martin Bays <mbays@sdf.org>]

* Thursday, 2011-08-18 at 23:28 -0300 - Jorge Llambías <jjllambias@gmail.com>:

> On Thu, Aug 18, 2011 at 9:25 PM, Martin Bays <mbays@sdf.org> wrote:
> > * Wednesday, 2011-08-17 at 08:04 -0700 - John E Clifford <kali9putra@yahoo.com>:
> >
> > From this and your other mails, I am understanding that want to base
> > Lojban on Lesniewskian mereology.
> >
> > I'm hazy on exactly what this would mean, but allow me to guess.
> >
> > Our universe consists of Wholes, and is partially ordered by the "part
> > of" relation. All the things we would usually consider as individuals in
> > our universe are Wholes. In addition, we have mereological sums, i.e.
> > supremums with respect to the "parthood" partial order, of arbitrary
> > sets of Wholes.
> >
> > The interpretation of an ordinary sumti is a Whole; selbri are
> > interpreted as relations on our universe of Wholes.
> >
> > Presumably {me} is interpreted as the parthood relation.
> >
> > A unary predicate P is 'distributive' iff
> >    \forall x,y. ( ( x Part y /\ P(y) ) --> P(x) ).
> >
> > To handle quantification, I suppose it is necessary to assume that every
> > whole is the sum of atoms - quantification is then over those atoms.
> 
> You can still have quantification without assuming that every whole is
> the sum of atoms. You just used quantification over wholes to define
> 'distributive'.
> 
> >> In my xorlo, terms and quantifiers all assume plurality,
> >> with singularity as a limit case.
> > - does this mean that you want {ro da} to be a plural quantifier rather
> > than the singular quantifier (i.e. quantifying over atoms) it would be
> > in the above account? Does this mean you don't want to assume we're
> > working in an atomic Boolean algebra? If not, how to deal with {re da}?
> 
> I think you can still define "re da" in the usual way. The only thing
> is that without atoms "re da broda" will always be false for any
> distributive broda. So most predicates would not be *fully*
> distributive. But I think you can define a more useful "relative
> distributivity". Something like:
> 
> A predicate P is 'distributive with respect to Q' iff
>  \forall x,y. ( ( Q(x) /\ x Part y /\ P(y) ) --> P(x) ).
> 
> Would that work?

Do you mean that we could then talk not about global atoms but about
"P-atoms", by which I mean the x which are minimal such that P(x)? And
so have {re P cu broda} mean that two of the P-atoms broda?

That seems plausible...

Martin

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