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Re: [lojban] {zo'e} as close-scope existentially quantified plural variable
Martin Bays, On 16/10/2011 18:11:
* 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>:
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.
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.
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.
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.
Why some glorked subdomain, rather than just the full domain?
So maybe {loi} should actually be defined like that. {loi cinfo} means
precisely the same thing as "the lions".
I think "the lions" would mean {lei cinfo}, actually, but that's a point about English, and doesn't contradict your underlying point.
(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}
== 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.
This is too complicated for me to grasp at first reading, and unfortunately I can't afford the time necessary to grasp it.
--And.
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