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Subject: Re: [lojban] {zo'e} as close-scope existentially quantified plural variable
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On Sun, Sep 25, 2011 at 12:30 PM, Martin Bays <mbays@sdf.org> wrote:
>
> Would you even agree that, in the case that we have a predication
> P(k1,k2) about kinds k1, k2

(which is already in your Nirvana form)

> which correspond to properties Q1(X), Q2(X),
> and if the predication resolves existentially in all variables, then it
> resolves as in the subject line of this thread, i.e. to
> =A0 =A0EX (X1,X2). (C(X1,X2) /\ P(X1,X2))
> where C is a context-glorked relation which depends on any quantifiers
> (including ones over worlds) which the current predication is in the
> scope of, and which is such that C(X1,X2) implies Q1(X1)/\Q2(X2)?
>
> (X, X1, X2 all plural mundane variables, i.e. not allowed to take kinds,
> but not restricted to atoms)

That would seem to be the definition of "resolves existentially",
right? If you can find a new model in which what you expressed in
terms of kinds can be reexpressed in terms of an existential
quantification over the manifestations of the kinds, then we say that
the predication about kinds in the original model "resolves
existentially" in the new model.

>> Where we seem to desagree is in thinking that this "resolution" is
>> somehow a necessary step in the interpretation of the original
>> predication. You seem to be saying that a domain of discourse that
>> includes a kind but not its instances is somehow defective.
>
> Yes, I think so. "lions are in my garden" and "one or more lions are in
> my garden" are equivalent - one is true iff the other is. Our formalism
> should reflect that. So a model in which it holds of the kind Lion that
> =A0 =A0in(Lion, my garden)
> it should also hold that
> =A0 =A0EX l. (lion(l) /\ in(l, my garden))
> , and vice-versa.

No, because you don't have lion instances in the first model, so the
second one doesn't hold in that model. You have a different model for
each of the sentences that are truth value equivalent.


>> (But at the same time you have
>> no objection to domains that include an individual but not its stages,
>> although there are analogous types of predications about individuals
>> that can be resolved as existential quantification over stages.
>
> I think they resolve as existential quantification over worlds; does this
> agree with what you mean by 'stage'?

No, that's the interpretation that corresponds to the one with kinds.
In the stages model, time is not an index over worlds, but it is only
a dimension of one world (like space). In the one world, instead of a
single individual that shows up again and again in many of the worlds
indexed by t, we have a lot of stages, one for each time of the same
world. So instead of quantifying over worlds, you quantify over
stages. The analogy is that in the case of kinds, you have many worlds
(each of which indexed not just by t, but by a spatial location as
well) and a single in dividual that shows up again and again in many
of the worlds indexed by space-time. If instead you have a single
world with many places, then you have a different manifestation of the
kind at every place, instead of the kind showing up here and there.

(That's an oversimplification, because kinds don't just show up in
spatiotemporally indexed worlds, but in all sorts of other worlds too.
But the space to time analogy is useful.)

> "John is sometimes wise" holds at every time iff "John is wise" holds at
> some time.

Rather "John sat there" is true if, in the one world that extends
throughout time just as it extends throughout space, there is a stage
of John j such that sits(j, there) holds.

> Since there's no new object like a kind involved, there's no need for
> any new axioms which acceptable models must satisfy.

The object analogous to the kind is none other than John himself. The
stages of John, dispersed along the time dimension, are analogous to
the manifestations of the kind, dispersed througout space.

> If we made "sometimes wise" into a single predicate "sometimes-wise",
> then we would want to make it an axiom that it agrees with "sometimes
> wise"; that's vaguely analogous to the case of kinds. Is that the kind
> of thing you mean?

Kind of. I'm comparing a predicate that may apply to some of the
time-stages of John but not necessarily to all, with a predicate that
may apply to some of the space-manifestations of a kind, but not
necessarily to all.

mu'o mi'e xorxes

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