Re: [lojban] xorlo and masses

[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?

mu'o mi'e xorxes

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