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Date: Sun, 16 Oct 2011 13:11:46 -0400
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
Subject: Re: [lojban] {zo'e} as close-scope existentially quantified plural variable
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* Sunday, 2011-10-16 at 01:05 -0400 - Martin Bays <mbays@sdf.org>:

> * Sunday, 2011-10-16 at 02:56 +0100 - And Rosta <and.rosta@gmail.com>:
>=20
> > but you'd still be wanting a way of unambiguously showing that
> > something isn't a kind. There aren't any ready-made candidates for
> > that, but afaik the lVi gadri are essentially undefined, little used,
> > and little needed, so you might argue that use for them.
>=20
> That's actually not a bad idea. So {loi cinfo} would be some plurality
> of actual lions, working like xor{lo} but not allowed to get a kind.
> Given the plural reference, this isn't even all that far from the
> historical meaning of lVi.
>=20
> So then I'd understand {lo} as being simply ambiguous between {loi},
> {lo'e} and {loi ka}; xorxes would complain that that's almost but not
> quite accurate, because sometimes the {loi ka} version blocks the
> others; meanwhile, I would be amazed by his ability to dynamically
> switch kinds in and out of his domains to make quantified statements
> make sense - but from a distance, happy in my constantish kindless
> universe.
>=20
> Sounds good.

Some further thoughts on that:

(i) with this definition, {loi} is very close to Chierchia's version of
the iota operator, which is his explanation of "the": when applied to
a predicate in a domain, it gives the maximal plurality in the domain
which satisfies the predicate if there is a unique such (as there is
with a distributive predicate like a noun). For this to coexist with
normal quantification, the domain should be some glorked subdomain of
the full domain.

So maybe {loi} should actually be defined like that. {loi cinfo} means
precisely the same thing as "the lions". With non-distributive
predicates, the obvious thing would be for it to get *some* maximal
plurality satisfying the predicate (or, which comes to the same thing,
to required that the subdomain be glorked such that there is a unique
maximal plurality satisfying the predicate)

(Terminology: Here I'm assuming, as always, after Chierchia after Link,
that our domain is an atomic boolean algebra which is upwards complete
as a lattice (i.e. has arbitrary joins), and that a subdomains is a
sub-upwards-complete-boolean-algebra; in other words, a subdomain
consists of a subset of the set of atoms of the domain, along with the
joins of all subsets of that subset. 'Plurality' is the least icky
terminology I've found to refer to an element of such a domain; it can
be but doesn't have to be an atom. Chierchia and others use 'sum'.)

(ii) Even without this subtle modification of {loi}, I was wrong to
suggest that {lo} is (essentially) ambiguous just between {loi}, {lo'e}
and {loi ka} - because the existential resolution of kinds doesn't agree
with {loi}, as the quantifier should get tightest scope. Rather,
a fourth item should be added to the list: {pi za'u} (if {pi za'u} is
our plural existential quantifier, which I think it reasonably could be
(even though it only really makes good intuitive sense when the domain
is downwards-closed), such that {pi za'u broda cu brode} means "for some
plurality X such that broda(X), brode(X)") - where this has to be
substituted in for the {lo} after all exportation to the prenex.

e.g. {lo cinfo cu zvati ro mi purdi}
    -> {ro da poi purdi zi'e pe mi zo'u pi za'u cinfo cu zvati da}
    =3D=3D FA x:(purdi(x)/\mine(x)) EX X:cinfo(X). zvati(X,x)
	(using capital letters for plural variables)
(in this case {pi za'u} could be replaced by
the singular existential {su'o} with no change in meaning, but that
isn't always true)

Maybe it should be {pi za'u loi broda} instead, which is closer to the
'C' approach I was trying for existential cases of unfilled variables;
I'm not sure.

Martin

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