* Monday, 2011-09-26 at 19:31 -0300 - Jorge Llambías <jjllambias@gmail.com>: > 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) Yes > > 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) > > 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. I meant to ask whether you agree that this is the right form for that existential quantification, when it does resolve to one. > >> 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. > > 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 forgetting about the formalism for a second, surely you'd agree that "lions are in my garden" is logically equivalent to "one or more lions are in my garden" in every reasonable sense? In particular, that you can deduce each from the other? It's part of the basic underlying theory of english semantics, if you like. If we have models where this equivalence fails, like the one you mention which has Lion but no lion instances, then our models are failing to model this basic underlying theory. It's in that sense that I'd consider them deficient. > [snip stages explanation] > > 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. OK, thanks, I see the analogy now. So in response to your original remark > >> (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. : yes, were we to have a setup like the one you sketch above, then just as with kinds, a model in which "John sat there" is true had better have an actual John-stage which actually sits there. The only reason that I wasn't raising this objection was because I wasn't assuming a setup with stages. Unless you really think it's necessary, I'd prefer to avoid getting into the details of handling space and time for now. But briefly: I'm currently thinking we should handle neither with the stage approach, and rather both with the worlds approach (so a "world" would actually be a co-ordinate (possible world, time, space)). An argument for another day, perhaps! Martin
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