According to quantifier variance (QV), there are many families of quantifiers, including the ordinary English family that quantifies over such things as dogs, chairs, holes and shadows, the abstemious ontologist's family that quantifies only over elementary particles, the organicist family that quantifies over elementary particles and living things, and so on. None of these is in any way primary or more fundamental than the others.
The main motivation of QV is to protect apparently reasonable people (whether ordinary or ontologist) against making lots of false statements. While the abstemious ontologist says "There are no chairs anywhere", she doesn't actually disagree with the ordinary person who says "There are five chairs in the room", as they use different quantifiers.
Here is an interesting alternative. Keep the QV story's claim that the ordinary person's "There are" and the ontologist's "There are" mean something different. But deny that they are both quantifiers. Only the ontologist is quantifying. The ordinary person is doing something else.
What about the plurality of ontologists? Are they all quantifying, or is only one camp quantifying? I suspect that most of ontologists are quantifying. And most are saying things that are false. So, unlike QV, I am only interested in saving the ordinary person from making lots of false statements. Ontologists doing ontology do so at their own risk.
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Hmmm, but what do you take quantification to be?
A question I have: It may turn out that ordinary English "quantification" can be defined via restriction of ontology-quantification, but if the English sentences are not quantification at all how could that be? Yet it seems wrong to rule that out a priori, no?
Ironically, this may be a mere terminological dispute. :) I'd take it that if ordinary English "quantified" statements have a semantics that is similar to, and do much the same thing inferentially, as ontology-quantificational statements, then it should count as quantification. And I definitely think that if we can define ordinary English statements via ontology-quantifier restriction then that's a pretty good sign it's quantification too.
Are you simply building things into your notion of quantification, so that I (or Hirsch) have a more "formal, skeleton-like" understanding of what counts as a quantifier, and you have a more "metaphysical, fleshed-out" understanding of what counts as a quantifier?
(Interestingly, I feel like something related happens with Meinongians and Quineans.)
I guess what I'm getting at is this: If you are building all of that into what counts as a quantifier, then aren't you sort of begging the question?
Is saying "the only [real] quantifier is the pruss-quantifier--everything else is a mere schmantifier (though certainly they look very very similar to quantifiers)" really any different from saying "certain hirsch-quantifiers are fundamental," which is precisely what the quantifier variantist denies?
To be fair though, maybe you don't mean for it to be a mere terminological dispute. The way for this to *not* be a mere terminological dispute would be for you to argue that, actually, ordinary language has a very different semantics from what we might have thought and have been doing. Conceptually possible -- empirically very unlikely though, no?
P.S. I'm no believer in quantifier variance. I just imagine this might be a question they might have.
Well, I am inclined to think that a real quantifier must quantify over fundamental entities.
The semantics for a real quantifier are different from those for the ordinary one.
For instance, the truth conditions for an ordinary English "There exists a round table" in a metalanguage that only has perfectly natural terms are something like: there are simples arranged roundly and tablewise. This is very different from the kind of semantics we give for the fundamental quantifiers.
Well, I am inclined to think that a real quantifier must quantify over fundamental entities.
The semantics for a real quantifier are different from those for the ordinary one.
For instance, the truth conditions for an ordinary English "There exists a round table" in a metalanguage that only has perfectly natural terms are something like: there are simples arranged roundly and tablewise. This is very different from the kind of semantics we give for the fundamental quantifiers.
Last comment. Interesting interpretive point: I actually take the quantifier variance project to be a sort of argument for the futility of the sort of metaphysics done in the last fifty years. In other words, I think quantifier variance is supposed to save *metaphysicians* from speaking falsehood -- so as to undermine metaphysics. (I don't think it's primarily to save *ordinary English speakers* from falsehood.)
I think QV is a way of cashing out the idea that metaphysicians who appear to disagree are actually "saying the same thing" and, although both sides say things that are true, at the same time their apparent "disagreements" are futile.
The problem with QV it seems to me is that Hirsch cashes out "saying the same thing" as "having the same content," and he has an overly-coarse-grained "set of possible worlds" notion of content.
Aside from the fact that this seems an implausible explication of "saying the same thing" and of content (for all the reasons we all know), I fear that the very notion of content that he uses to undermine metaphysics is *self*-undermining and gets *him* into trouble. For he needs a way to define the expanded quantifiers in terms of the more restricted ones, and apparently sometimes can only do so using hyperintensional notions, e.g., impossible counterfactuals (and I agree that he would need such things if he were to have any hope of doing so -- though I'm not sure even that is enough). But then it seems unclear why the metaphysicians are unable to help themselves to these notions and give a more fine-grained notion of content that makes their disputes turn out legitimate.
That said, I think there is something to the idea that a lot of metaphysical disputes involve both sides "saying the same thing" in some sense, and are sort of pointless. But I think it'll have to be a bit more sophisticated than this. It'll have to be possible for two sides to be "saying the same thing" even when certain hyperintensional contexts discriminate between the contents of their assertions. In fact, whether both sides count as "saying the same thing" may even be context-sensitive. I'm not sure yet.
Moreover, I'm not anti-metaphysical at all. In fact, I think there is plenty of metaphysics that is substantive and is not futile at all, and I'm more interested in isolating that from the rest rather than undoing metaphysics. [As it happens, ancient, medieval, and early modern philosophers seem to me to do the substantive sort of metaphysics more frequently, as well as a lot of contemporary Aristotelian-minded thinkers.:)]
Thanks. Let me see if I've got this.
You can of course choose to reserve the name "quantifier" only for pieces of language that involve a domain fundamental entities. But when the QVer says that there are many equally good quantifiers, he simply means that there are many equally true pieces of language that "syntactically" or "on the surface" appear to contradict each other, and that are made up of equally good "quantifiers" that involve quantifier-like inference rules and whose semantics can be modeled via Tarski-type definitions of the sort we know from linguistics, etc. In particular, this happens in apparent disputes between metaphysicians. (You can put pressure on how well-defined all of this is, but the reply that one can recognize quantifier-like behavior when one sees it seems fair to me.)
At least, I *think* that's what they mean!
Whereas you would seem to have a different understanding of how to individuate pieces of language? (In particular, what counts as a quantifier.) E.g., according to you, pieces of language are individuated relative to a semantics where the meta-language only includes perfectly natural terms.
Interesting! Though I still wonder whether you're really disagreeing with the QVer here at least in the case of ontology vs ordinary English, this makes it that metaphysicians are actually disagreeing, even if they are not disagreeing with the ordinary folk.
Take the fundamental existential quantifier (F) and the ordinary "existential quantifier" (E). It is, I think, false that they can each be modeled via Tarski-type definitions.
It all depends on the choice of metalanguage.
Suppose we want to give Tarski-style semantics for "Ex(G(x))" and "Fx(G(x))".
Case 1: We are giving these definitions in a language that has E, e.g., ordinary English. In this case, the Tarski-type definitions specialized to the example are:
(1.1) There exists(E) an x that satisfies G.
(1.2) There exists(E) an x that is fundamental and satisfies G.
These are, indeed, similar semantics. But similarity of definition that uses non-fundamental terms in the metalanguage need not mark genuine similarity of phenomena. If we want to look at similarity of definition as a mark of genuine similarity, we should give the definition in a language whose terms are fundamental, a structural language to put it in Siderese.
Case 2: We are giving these definitions in a language that has F, e.g., Ontologese. In this case the definitions will be something like:
(2.1) There exist(F-plural) xs that are arranged Gwise.
(2.2) There exists(F) an x that satisfies G.
It is clear now that these two definitions are very different. In fact, it is only the second that looks like the familiar Tarski-type definition of existential quantification. The first uses plural quantification (it may actually be even more complicated than (2.1) if we want to take into account the fact that the domain of E includes lacks and the like) and the second uses singular quantification. But logically plural and singular quantification are different. And being arranged Gwise is different from satisfying G.
Case 3: In each case, we give the Tarskian definition using a metalanguage that either has both "quantifiers" or using two metalanguages, a different one for each. In any case, we get these definitions:
(3.1) There exists(E) an x that satisfies G.
(3.2) There exists(F) an x that satisfies G.
Now, these two DO look exactly parallel.
But I assume we agree that saying that a quantifier is something that has the syntactic and inferential rules of a quantifier is inadequate to defining a quantifier. One can stipulate things that aren't quantifiers at all but that have the same syntax and logic as a quantifier does. ( See: http://alexanderpruss.blogspot.com/2013/12/introducing-doppelgangers.html ) One needs to supplement this with a Tarski-like semantics. OK, but if one gets to use the same alleged quantifier in the semantics, that supplementation does nothing for: trivially, we can always do that: "ZxG(x) iff there Zs an x that satisfies G".
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