* Saturday, 2011-09-24 at 13:18 -0300 - Jorge Llambías <jjllambias@gmail.com>:
> > In xorxes' system, however, things aren't really as simple as this talk
> > of constancy might make them seem. According to my current understanding
> > of xorxes' system: the constant given by {lo} is often a kind,
>
> Yes.
>
> > and kind
> > predication often resolves as existential quantification.
>
> Meaning that you can reexpress some predications about kinds that
> don't involve existential quantification as a predication about
> instances of the kind that do involve existential quantification. Yes,
> I agree you can do that (for a certain type of predication).
Great!
Would you even agree that, in the case that we have a predication
P(k1,k2) about kinds k1, k2 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
EX (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)
(Here I've made C a relation rather than a set, which is a subtle
difference but I think an improvement)
(I'm also here inverting my original suggestion with respect to kinds
- originally this was meant to be how zo'e first resolves, with kinds
allowed as witnesses of the existential; here it would first resolve as
a kind, and then (sometimes) to an existential which doesn't allow
kinds. Again, I think this is an improvement.)
> 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
in(Lion, my garden)
it should also hold that
EX l. (lion(l) /\ in(l, my garden))
, and vice-versa.
(Here, lion(Lion) is not intended to hold).
If one holds but not the other, something's screwy. We should not accept
such a model, any more than we'd accept one where it doesn't hold of our
among relation 'me' that FA x. x me x.
> (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'?
"John is sometimes wise" holds at every time iff "John is wise" holds at
some time.
Since there's no new object like a kind involved, there's no need for
any new axioms which acceptable models must satisfy.
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?
> )
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