• J
    “Quantifier variance” is a term generally credited to Eli Hirsch, who in turn claimed inspiration from Hilary Putnam. It’s a version of ontological pluralism which poses questions about whether terms like “exists”, “there are”, “object”, and “Ǝx” necessarily have privileged meanings or designations.

    Here’s a good description from Hale and Wright (2009):

    Quantifier-Variance is the doctrine that there are alternative, equally legitimate meanings one can attach to the quantifiers – so that in one perfectly good meaning of ‛there exists’, I may say something true when I assert ‛there exists something which is a compound of this pencil and your left ear’, and in another, you may say something true when you assert ‛there is nothing which is composed of that pencil and my left ear’. And on one view – perhaps not the only possible one – the general significance of this variation in quantifier meanings lies in its deflationary impact on ostensibly head-on disagreements about what kind of objects the world contains: [it may be] a matter of their protagonists choosing to use their quantifiers (and other associated vocabulary, such as ‛object’) to mean different things – so that in a sense they simply go past each other. — Bob Hale and Crispin Wright

    So this is a way to clarify or dissolve problems in mereology and, perhaps even more basically, to help resolve ancient quarrels between nominalists and Platonists about abstracta. Do numbers exist? It depends on how you restrict/define your quantifiers, and there is no correct or privileged way to do this, says the proponent of quantifier variance. This is the “deflationary impact” that Hale and Wright talk about: It reduces ontology to something much less than it appears. As Matti Eklund puts it here: “Both Hirsch and Putnam take their ontological pluralism to entail that ontological questions are shallow. Hirsch says for instance that the proponent of quantifier variance ‛will address a typical question of ontology either by shrugging it off with Carnapian tolerance for many different answers, or by insisting with Austinian glee that the answer is laughably trivial.’” In other words, there are either many, equally good ontologies that will allow the scientist and/or philosopher to accomplish what she wants to accomplish, or else the whole question is verbal, and silly -- “it depends what you mean,” and you can mean whatever is consistent, or at least acceptable to your fellow language-users.

    This is a super-rough sketch, but I hope good enough to pose the meta-problem I want to raise. To set it up, let me bring in Theodore Sider, not a fan of slapdash quantifier variance. He says, in "Ontological Realism": “Every serious theory of the world that anyone has ever considered employs a quantificational apparatus, from physics to mathematics to the social sciences to folk theorists. Quantification is as indispensable as it gets.” No one, Sider says, can avoid “choosing fundamental notions with which to describe the world.” If your fundamental notion is that “reality” and “the world” and “fundamental” are non-objective, that is still a fundamental notion. However, you could claim to “accept the idea of structure as applied to logic but deny that there is distinguished quantificational structure in particular.” Sider calls this “in essence, quantifier variance,” and he doesn’t think it works.

    Can I accept logical structure (aka the rules of logic or rationality or inferential validity) while leaving empty – or at least unspecified – the “existence stuff” we want to plug into our ontology? Here’s another way of asking the question: Does logical structure entail ontological commitments about things like grounding, “simples,” existence, Ǝx, and other tools of the trade? Is there any way that such commitments can be rescued from the charge that they’re either pragmatic or merely verbal? And yet a third, very simple way to pose the question: Can quantifiers really “mean different things,” as long as inferential rules and other logical apparatus are respected?

    I think this question, in whatever version, is a hard one. Just to give a taste of the kind of complexity involved: Borrowing an example from Sider, let’s say I am a non-native English speaker who has recently learned the language. I mistakenly believe that the word for “number” is “fish”. You and I have a conversation in which we discover we’re both nominalists. You say, correctly from our shared point of view, “numbers do not exist”. I agree with you, saying “fish do not exist”. Sider claims, I think rightly, that this is not a “verbal dispute” in the classic sense of two people talking past each other because they use words differently. You and I both mean the same thing – we are each thinking the same thing about numbers – but I have made a verbal mistake. Presumably, genuine disagreements between languages can’t be analyzed and resolved in this way. And what about disagreements about quantifiers? (This is me now, not Sider.) If I say “mereological composites exist” and you say “there is no such thing as a mereological composite”, which kind of dispute is going on? Are we disagreeing about concepts, while using the same words? Or are we holding the concept of “existence” steady, while (someone is) making a mistake in terminology? How could we know which of us is making the mistake?!

    I don’t know nearly enough about quantifier variance to have solid positions on any of this. I know just enough to realize that the question is of critical importance for ontology. So I’d welcome any responses, especially from philosophers who have been wrestling with this for a while. Can we have quantifiers without “distinguished metaphysical status”?
  • Banno
    Interesting. But

    Quantifier Variance Dissolved

    (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance is not an ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent.

    In your example, it is difficult to see how folk could come to agree that they are both nominalists in such circumstances...

    That is, I think the fourth objection is the most telling.
  • J
    Thanks, Banno. The paper looks right on target. Sider also has a lot of arguments against quantifier variance. I'll read it carefully and reply. But just looking at objections i - iv, I agree that (iv) raises issues but perhaps should be phrased, "QV appears not to be compatible with charitable translation, and thus requires a defense of its internal consistency." Soften it, in other words. And I think (i) is largely where the debate between Hirschians and Siderians takes place. Sider says the quantifiers have to be unrestricted. But let me read and cogitate . . .
  • Banno
    Cheers. And thanks for the thread - far and away the most interesting in a few weeks.

    I'm thinking that in order to interpret charitably, the domain must be held constant - we presume that we share the same beliefs. I don't understand how we could have a conversation if we were each talking about a different domain.

    But that might be contentious, and needs work. And it has profound implications - relativism and antirealism are waiting in the wings...
  • J
    Agree about the profound implications. It's all part of the same discussion we visited back with Davidson et al.

    Thanks for appreciating the thread!
  • Banno
    What did you make of the article after a read?

    For those who don't see the point of the topic, consider

    In contemporary metaontological discussions, quantifier variance is the view according to which there is no unique best language to de- scribe the world. Two equivalent descriptions of the world may differ for a variety of pragmatic purposes, but none is privileged as providing the correct account of reality.Finn and Bueno
  • J
    Funny, I was just sitting down to start a reply. I thought the article was brilliant, in about a dozen ways. Enormously helpful in clarifying the issues, especially when read side by side with the Sider paper. I also think there are a couple of points they missed which I want to try to articulate. I'm a slow (re)reader and even slower writer. I'll be back with something in a day or two, hopefully.
  • J
    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?
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