* Wednesday, 2011-08-17 at 08:04 -0700 - John E Clifford <kali9putra@yahoo.com>:
> If by plural predication (which seems an odd term, but no worse than usual in
> Logjam
(not my invention!)
> ) you mean that terms may have multiple referents (that reference is a
> relation, not a function)
Yes, and correspondingly that unary predicates are interpreted as
elements of the power set of the power set of the universe, rather than
just of the power set of the universe.
> and quantified variables may have several simultaneous instantiations,
> then xorlo has (finally, a couple of years ago) plural predication.
> This is a change from the long history of Logjam, where we had
> (officially, but we behaved as though it wasn't there) singular
> predication with C-sets doing the work of pluralities.
What's a C-set?
> Now, it turns out that the logic of plural reference (a better term,
> if we are talking about the same thing) is exactly the same as that
> for L-sets (which were around all the time but we never had the
> insight to use them), so some few of us too highly indoctrinated
> logicians tend to continue to use the L-set language or something
> equivalent to it, even when we know we are just talking about
> things.So, the answer is (i), but some still talk as though the answer
> is (iii), not that it makes any difference in practice.
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.
(So now our universe is really just the power set of the set of atoms,
with parthood being inclusion... but I'll continue with the mereological
terminology anyway)
Now if I understand you correctly, you want there to be no other form of
collectivisation.
So I suppose we would have to have {se gunma} == {me}?
{zilgri} could correspond to the sup operation.
This all seems quite reasonable. Is my summary accurate?
One thing which doesn't fit: you say
> 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}?
Martin
> ----- Original Message ---- From: Martin Bays <mbays@sdf.org> To:
> lojban@googlegroups.com Sent: Wed, August 17, 2011 6:46:34 AM Subject:
> Re: [lojban] xorlo and masses
>
> * Tuesday, 2011-08-16 at 09:11 -0700 - John E Clifford
> <kali9putra@yahoo.com>:
>
> > [snip useful analysis]
> >
> > Now, can we get back to the issue, whatever it was? Or has it been
> > resolved by careful sorting out?
>
> My original question, which I'm afraid did develop into a tangled mess
> of confusion though I had specifically hoped it wouldn't, was in short
> whether (i) post-xorlo Lojban has plural predication, or (ii) whether
> it just emulates plural predication by using groups-as-individuals, or
> (iii) both. I wasn't expecting (iii) to be the answer, but it seems it
> is.
>
> So yes, basically resolved - my thanks for your involvement in which
> - modulo details of precisely how plural predication works, and how it
> interacts with groups-as-individuals.
>
> Martin
>
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