* Monday, 2011-10-17 at 01:40 +0100 - And Rosta <and.rosta@gmail.com>:
> 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.
>
> Have you thought about rules for default outer quantifiers and scope
> interactions with negation, and so forth?
xorlo's seem good: no default outer quantifier; any outer quantifier
has domain the referent-set of the description. As for scope - the
description gives a Skolem function, which probably gets bound outside
all quantifiers. Probably the Skolem function is actually just
a constant unless the loi expression contains an unbound variable.
Examples with these rules, where GL stands for 'glorked' and acts
syntactically like a quantifier:
{ro broda loi brode cu brodi} ->
GL X:brode(_). FA x:broda(_). brodi(x,X)
{ro da loi brode be da cu brodi} ->
GL F:brode(_,\1). FA x:broda(_). brodi(x,F(x))
{broda su'o ka loi brode cu brodi ce'u} ->
GL X:brode. EX x:(ka[brodi(X,\1)](_)). broda(zo'e,x)
> > 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?
Having it with the full domain would essentially replicate the
functionality of {pi ro broda}.
> > 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.
Just making a veridiciality distinction? Or specificity too?
> > (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.
In short: kind predication sometimes resolves to some kind of plural
existential quantification with innermost scope (I think xorxes agrees
on that, modulo the terminology 'resolves'); I was forgetting this.
Martin
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