Okay, I can at least start with this . . .
Concerning Finn & Bueno: as I said, a wonderful paper, full of insight. I’m particularly grateful for the four-part counterclaim to quantifier variance around which they structure the paper, because you can then use those four issues as a kind of checklist for any defense of QV. That will be part of another post I’ll write, but for now I want to consider a different question.
Finn & Bueno write that Ǝ “invariably has the function of ranging over the domain and signaling that some, rather than none, of its members satisfy the relevant formula. Yet the quantifier-variance theorist requires Ǝ to have multiple meanings. . . . This raises the issue of how the meaning of a quantifier can differ, and what the other meanings could be. And it is this issue that we tackle, arguing that one cannot make sense of variation in quantificational apparatus in the way the the quantifier-variance theorist demands.”
I think there’s a subtle but crucial equivocation going on here, around the term “meaning”. Consider this from the Sider paper referenced above: Sider also wants to know what these “candidate meanings” could be, but he lays out the question differently. “Understand a ‛candidate meaning’ henceforth as an assignment of meaning to each sentence of the quantificational language in question, where the assigned meanings are assumed to determine, at the least, truth conditions. ‛Candidate meanings’ here are located in the first instance at the level of the sentence; subsentential expressions (
like quantifiers)[my itals] can be thought of as having meaning insofar as they contribute to the meanings of the sentences that contain them.”
If Sider means “can be thought of as having meaning
only insofar as they contribute to the meanings of the sentences” (which I believe he does), then we have an important distinction. It would be possible, on this view, for the meanings of
sentences containing quantifiers to vary according to one’s chosen L, while the quantifiers
themselves do not vary. They still get used only one way, the way Finn & Bueno think they must. We would thus fulfill the requirement that Ǝ always has to mean what it ought to mean in well-formed logical expressions. But there’s still room for “quantifier variance” if the meaning resides not at the level of the quantifier but, as Sider suggests, at the level of the sentence.
An example might be helpful. I say “numbers exist”; you say “numbers do not exist”. Each of us would have to use Ǝ to formulate our position in Logicalese. What I’m arguing is that we’re each going to use Ǝ
the same way, as we state our respective contradictory positions. The difference in our statements is not at the subsentential, quantifier level. We have no quarrel about "variation in quantificational apparatus." We differ on
what exists, not on the use of the quantifier.
Is this still
quantifier variance? I say yes, in spirit if not in name. It sharpens the question of multiple ontologies rather than dismissing it. Granted, I’m also suggesting that the term “quantifier variance” is perhaps poorly chosen, since it does seem to imply that it’s the meaning of the quantifier per se, rather than any sentence formed using it, that can change. But the reason why someone would want to posit QV is unaffected. The question never was “Can we find multiple meanings for Ǝ (or ‛&’ or ‛→’ or any of the other operators)?” Rather, what Hirsch is interested in is the question, “Can sentences about existence (which logicians express using Ǝ) change their meanings based on what criteria the speaker is using for existence? Can people talk past each other because their sentences, as a result, mean different things? If so, is there one privileged or distinguished way we ought to write these sentences in order to capture something true about the structure of the world?” If we accept ontological pluralism, then the last question (usually) gets a “no,” but all those many ontologies will still be expressed with well-behaved, consistent operators, satisfying Finn & Bueno. (And yes, I agree with them and with Sider that logical pluralism is untenable as an argument for QV.)
This analysis overlaps with another problem I want to raise about the entire debate, concerning whether ‛Ǝ’ is uniquely troublesome in that it’s used to refer to both a quantifier
and a predicate. But I’ll save it and invite comment on this question of equivocation on “meaning”. To summarize: Is it the quantifier whose meaning changes, or the sentences in which the (unchanged) quantifier occurs? And if the latter, is it still QV?