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date: 30 June 2022

On Quantification and Ontology

Abstract and Keywords

In this article, I discuss the Quinean view on ontological questions (they concernwhat there is) and compare it to various alternatives. Special attention is paid to what really is at stake between the Quinean and her opponents, for example Meinongians who focus on existence predicates, apart from issues of labeling. I then turn to compare different versions of the Quinean view. One can accept that ontological questions concern what there is while differing in many ways over the nature of ontological questions. In recent years, theorists of many different stripes, including for example both friends of the doctrine of quantifier variance such as Eli Hirsch and ontological realists such as Ted Sider, have held that there are different possible existential quantifier meanings, and this has been central to how they view ontology. I discuss what it means to say that there are different possible existential quantifier meanings.

Keywords: ontology, quantification, Quine, quantifier variance, ontological realism, Meinongianism

1. Introduction

Quine famously starts off his “On What There Is” (1948) by saying,

A curious thing about the ontological problem is its simplicity. It can be put in three Anglo-Saxon monosyllables: “What is there?” It can be answered, moreover, in a word—“Everything”—and everyone will accept this answer as true.

(He goes on to note that there can, of course, be disagreement about cases.) The way Quine here presents this, he makes it sound as if he is saying something self-evident. But as Quine is well aware, and as he in effect goes on to discuss, there are other possible conceptions of the “ontological problem.” Just to mention one obvious alternative: one can think that there is a distinction between what there is and what exists and hold that the ontological problem instead concerns what exists.

The view Quine himself subscribes to—that the ontological problem concerns what there is—is one standardly described as a view on which ontological questions are quantificational. It is the expressions that philosophers tend to regiment using the existential quantifier—“there are,” “some,”… —that express what the ontological problem is about.1 When Quine and those who follow him hold that the ontological problem concerns what there is, they can do so either because they think that there really is no distinction between what there is and what exists, or because they think that there is such a distinction but only questions about what there is are properly ontological. In practice, they have always tended to take the former route. It is not immediately clear what it means to say that there “is no distinction.” Merely to say that necessarily, something is F if and only if it is G isnot obviously to say that there is no distinction between asking whether something is F and asking whether something is G. It is tempting to say that there is no distinction only if it is analytic that whatever is also exists and vice versa. But an implicit appeal to analyticity is in tension with Quine’s skepticism about the notion. However, while there may be real problems here I will not further problematize this issue.

The Quinean view is the dominant one on what, following Quine, I keep calling the ontological problem. But there are alternatives to the Quinean view, and there are also important distinctions to draw between different versions of the Quinean view. Some possible views in the vicinity are (a) the “neo-Meinongian” view that it may that there are things that don’t exist, and the ontological problem concerns what exists and not what there is (for views in this vicinity, see e.g. Parsons, 1980; Chisholm, 1973; Priest, 2005; Routley, 1980, 1982; and McGinn, 2000)—but it must be kept in mind that there are important differences between these theorists);2 (b) the view that the ontological problem is best construed as concerning what is real or what is fundamental (for various views roughly along these lines, see e.g. Fine, 2001; Heil, 2003; Cameron. 2008); (c) the view sometimes discussed—see Lewis’s (1990) discussion of Routley’s views—to the effect that there is both ontologically innocent and ontologically loaded quantification, and the ontological problem concerns what there is in the ontologically loaded sense of “there is”; and (d) the view of theorists like Ted Sider (e.g., 2009b, 2011) to the effect that ontology does not plainly concern what there is but instead what “there is” in the sense of the existential quantifier of a properly “joint-carving” or “natural” language—Ontologese as I will call it, following established practice. What Sider relies on is the notion of naturalness brought in by David Lewis (1983, 1984). Note that while the suggestion as it has developed has employed the potentially controversial notion of naturalness, the underlying idea can be stated in more general terms: ontology does not concern what there is in the ordinary sense of “there is” but in the sense of a technical notion of what “there is.” There are other views to consider as well, and we bring them up in due course.3

Views (a) and (b) are, on the face of it, alternatives to the Quinean view, while views (c) and (d) can, on the face of it, seem like versions of the Quinean view, since these views are views on which ontological questions are quantificational. But there are complications. Views (c) and (d) can be suspected, whether in the end justly or not, as being mere notational variants of views (a) and (b). One can see the ontologically neutral quantifier described in (c) as a quantifier that is restricted to what exists or is real or fundamental, and one can likewise see Sider’s joint-carving quantifier as a quantifier that is thus restricted.4

In my presentation of Quine’s view, and of views (a) through (d) just mentioned, I have spoken of what the ontological problem is and of what ontology concerns. I will continue to speak this way. But there are distinctions to keep in mind. One question is what ontology as actually practiced is concerned with. The “ontological problem” is then the problem ontologists actually try to solve. A different question is what ontology ought to be concerned with. One can think that the questions have different answers. For example, one can think that Quineans are right about actual ontology—ontology as actually practiced is concerned with what there is—while thinking that the issue that Quineans are concerned with is trivial and insignificant, and the theoretically significant problem in the vicinity, the one ontologists ought to be concerned with, is about what is fundamental. I will discuss the issue of what ontology ought to be concerned with. (Even if the Quinean view arguably is the dominant view on the ontological problem; that does not mean that the Quinean answer has to be the right answer to the question of what ontology is concerned with. Ontologists may have a mistaken conception of what they do. The way they go about things might suggest that they really are concerned with what is fundamental, even though that is not how they describe what they are concerned with.)5

2. Evaluating the Quinean view

To the extent that the Quinean—somehow—relies on questions about what there is and about what exists amounting to the same thing, it seems that the natural way to evaluate her view is by considering whether they actually amount to the same, or whether there can be, or are, things that don’t exist. And the natural way to investigate this issue is to ask questions like the following: Might, say, “there is a famous detective who doesn’t exist, viz. Sherlock Holmes” be true? Or does the truth of negative existentials, statements of the form “___ does not exist” require the possibility of there being some things that don’t exist? One can then argue over whether some such sentences really strike us as true, and about whether it is what they semantically express that is true. However, there is a different approach to the issue of whether questions about what there is and questions about what exist ought to be taken to amount to the same thing. Robert Stalnaker (2012, 120) says, critically discussing “neutralism” (the view that the quantifier is “ontologically neutral” and instead ontological questions are about what exist):

The neutralist responds [to Quine] that the evidence about the use of the word “exist” in natural language is not clearly on the Quinean’s side, but we should not tie the issue to a question about the meaning of the word “exist” in natural language… A proper interpretation of the issue, I think, takes us back to the Carnapian roots of Quine’s views about ontology. For Carnap (and here I think Quine would agree), if you accept a framework that involves the full apparatus of standard first-order quantification and thereby commit yourself to the intelligibility of questions about the extent of the domain, about which predicates of one’s language are correctly predicates of which members of the domain, and about questions of identity and distinctness of what is picked out by various specifications of members of the domain, then that is all there is to ontological commitment to the domain. Further ontological distinctions are illegitimate metaphysics. One may allow for various kinds of distinctions between members of the domain, including very general and abstract distinctions between categories of objects, but they require an explanation not required for an explanation of the concept of existence.6

One way to express the Quinean view that there is no distinction between what there is and what there exists is to say that existence predicate works in such a way that, trivially, ∀xExists(x).7 Call an existence predicate that works this way trivial. Then Stalnaker’s point can be put as follows. On any reasonable view there are good questions about which quantified sentences are true and about identity and distinctness among what is quantified over. But even if it really is true that English draws a distinction between what there is and what exists—and so English contains a nontrivial existence predicate—the question remains: is a nontrivial existence predicate really part of the ideology we should accept?8 Methodologically, Stalnaker’s point seems right: it is more important to consider what distinctions we ought and ought not to draw than it is to consider what distinctions ordinary thought happens to draw.

Note that just as a Quinean can say, taking a cue from Stalnaker, that even if natural language does draw a distinction between what there is and what exists, there is no actual need or justification for a nontrivial existence predicate, someone opposing the Quinean view can in principle adopt a corresponding strategy. For example, a neo-Meinongian might say that even if natural language does not draw a distinction between what there is and what exists, there is still a theoretical need for such a distinction.

Some remarks on the viability of the approach that Stalnaker suggests are in order. Stalnaker can and should of course himself acknowledge that there are potentially important metaphysical distinctions between different things they take to be: between the actual and possible, or between the abstract and the concrete, or between the mind-independent and the mind-dependent, between the fundamental and the nonfundamental, and so on. Now suppose some would-be opponent of Stalnaker’s line says that the distinction between what exists and doesn’t exist is the distinction between the actual and the possible, or between the abstract and the concrete, or between the mind-dependent and the mind-independent, and so forth—that is, suppose she draws the distinction using ideology that Stalnaker is in a position to adopt. (Contrast: she takes the distinction to be primitive, or explains it only in terms Stalnaker would reject.) What then to say? The friend of Stalnaker’s line then cannot reasonably object to the distinction as such. What she can say, and may be tempted to say, is that while the distinction is an important metaphysical one, it isn’t a properly ontological one. But what does the use of the label “ontological” do here? If two theorists agree on what is quantified over, and on what the metaphysically important distinctions are between the kinds of things quantified over, what are these further issues concerning whether the quantification is “neutral” or “ontologically committing,” or concerning whether a particular distinction is properly ontological, and best seen as a distinction between things that exist and things that don’t exist? There is an emptiness charge here: the dispute over whether a given distinction is ontological, or concerns existence, may seem like a dispute over how to use the labels “ontology” and “existence.” However, even if such an emptiness charge can be made to stick, that doesn’t mean that the whole dispute is empty. Occasionally in the literature arguments are presented given which existentially quantificational questions are perfectly trivial to settle in the affirmative. I will refer to these arguments as easy arguments. A quick example: Is there such a thing as Sherlock Holmes? Well, Sherlock Holmes is admired by many. So there is something admired by many, namely Sherlock Holmes. So there is such a thing as Sherlock Holmes. Generally, the strategy is to find, for any given name “a,” an intuitively true sentence “a is F,” and note that the truth of this sentence entails that there is such a thing as a. If one can find such a sentence for Sherlock Holmes, one can similarly find such sentences for Vulcan, Zeus, and so on. I won’t here try to evaluate easy arguments but only talk about what sort of thing they show if sound. An opponent of the Quinean view on metaontology can take the lesson of easy arguments to be the following: There surely are significant ontological questions. For example, the theist’s and the atheist’s dispute over God is not trivial. But by an easy argument, it is trivial that there is such a thing as God. So the significant ontological question cannot be that of whether there is such a thing. It must concern something else: for example, it may concern whether God exists. If, say, the neo-Meinongian relies on easy arguments, she may disagree with the Quinean about what there are, and this is a real disagreement even if the aforementioned emptiness charge really does stick. (Although someone who is a Quinean about ontology can in principle say that easy arguments show that ontology is easy and leave it at that. Compare here, e.g., Thomasson 2007, 2008.)

In fact, the relevance of easy arguments to the viability of the Quinean conception of ontology is evidenced already in Quine’s “On What There Is” (1948): Quine starts off the article by discussing at some length the puzzle of “Plato’s beard.” The easy argument at issue there concerns the fact that in order for it to be true that so-and-so doesn’t exist, there must still be a thing such as so-and-so, for from “__ doesn’t exist,” “there is something such that it doesn’t exist” follows. Quine attempts to respond to it by appealing to Russell’s theory of definite descriptions and offering a way to construe names as definite descriptions.

3. Varieties of Quineanism

Even assuming that, somehow or other, the Quineans are right that ontological questions are quantificational, there are many further distinctions to be drawn. There are different ways to be a Quinean. Some of the relevant distinctions are as follows.

First, it might be that there are different modes of being and, relatedly, that “there is” is polysemous, being associated with different meanings, corresponding to the different modes of being. There are numbers and there are tables, but are there numbers in a different way than the way in which there are tables? (Note that the metaphysical issue here, whether there are modes of being, is importantly different from the semantic issue of whether the quantifier is polysemous. Compare a simpler case: “jade” is not polysemous, but it is true of two different kinds of things.) Analogously, “there is” could fail to be polysemous even if there are modes of being. The general kind of view sketched is associated with thinkers as disparate as Ryle (1945) and Heidegger (1927), and it has been revived, in a new guise, in work by Kris McDaniel (2009, 2010) and Jason Turner (2010). Later I return to the views of McDaniel and Turner.

Second, it might be that “there is” is polysemous in a different way: only some types of uses are relevant to the ontological question. One possibility is that “there is” sometimes expresses objectual quantification and sometimes expresses substitutional quantification, and the ontological question is expressed by uses of “there is” that express objectual quantification.9 Another possibility would be the view that quantification is sometimes ontologically loaded and sometimes ontologically neutral.

Third, there are questions concerning first- versus higher-order quantification. One question is whether there is genuine higher-order quantification alongside first-order quantification. A second question is whether, if there is higher-order quantification, higher-order quantification too is ontologically committing.

Fourth, the quantifier, even if not polysemous, might be semantically indeterminate as between several different meanings. One possibility is that it is indeterminate as between an ontologically relevant meaning and another one. A different possibility is that the different meanings it is indeterminate between are equally ontologically relevant. Hilary Putnam (2004, 37) has in many writings stressed the supposed indeterminacy of the quantifier, and the indeterminacy he has in mind is of the latter kind. For example, he says

to ask whether mereological sums really exist would be stupid. It is, in my view, a matter of convention whether we say mereological sums exist or not…. How can the question whether something exists be a matter of convention? The answer, I suggest, is this: what logicians call “the existential quantifier,” the symbol “(∃x),” and its ordinary language counterparts, the expressions “there are,” “there exist” and “there exists a,” “some,” etc., do not have a single absolutely precise use but a whole family of uses.

Jessica Wilson (2011) takes the actually used existential quantifier to be semantically indeterminate, and suggests that metaphysical inquiry be understood to partly issue in precisification of the quantifier.10

Fifth, regardless of whether the quantifier is actually semantically indeterminate, it can be, and has been, held that there are different possible existential quantifier meanings, different possible meanings for an existential quantifier to have, and that this is relevant to how to conceive of ontology. Eli Hirsch has highlighted this concern, but he has made clear that part of the inspiration comes from Putnam’s work11. Hirsch has used the label quantifier variance for the thesis. Even if “there are Fs” is true, given the actual sense of “there are,” there could be an alternative meaning for “there are” to have, such that “there are no Fs” is true given that meaning of “there are”—and there is nothing that metaphysically privileges the actual meaning of “there are” or any of the other quantifier meanings. For example, Hirsch (2011, 68, 139) says “the world can be correctly described using a variety of concepts of ‘the existence of something’,” and “different concepts of an ‘object’ might be employed in different conceptual schemes, schemes that are all adequate for describing the world.” An integral part of this doctrine as presented is that no concept of existence is metaphysically privileged (Hirsch 2002, 62f). Being in the relevant sense a Quinean, Hirsch happily goes back and forth between speaking of different existential quantifiers and different concepts of existence.

A view that has been much discussed lately, in part as a reaction to the views of Putnam and Hirsch, is that there are alternative quantifier meanings but one such meaning is metaphysically privileged. Thus Sider (2009b) says,

I think that there is indeed a single best quantifier meaning, a single inferentially adequate candidate meaning that (so far as the quantifiers are concerned) carves at the joints. That is: I accept ontological realism.

Sider’s terminology has caught on, and “ontological realism” is standardly used for the thesis that there is, among possible quantifier meanings, a metaphysically privileged one and ontology ought to be concerned with the quantifier with that meaning.12

Both the friend of the doctrine of quantifier variance and the ontological realist agree that there are different possible existential quantifier meanings. I refer to this joint assumption as the multitude assumption (MA). Ontological realism, as characterized, is not strictly committed to that idea: an ontological realist could hold that there is a unique quantifier meaning and it carves at the joints. But those who subscribe to ontological realism, for example Sider himself, in fact tend to hold that the ordinary existential quantifier does not carve at the joints.

It is important to stress what MA, as intended, comes to. There are some well-known and relatively straightforward theses in the vicinity, but they are not the theses that are at issue in the debate. One thesis is that natural language contains both objectual and substitutional quantifiers. Whatever the fate of this thesis, it is orthogonal to present concerns. MA, properly understood, is a claim about objectual quantifiers. A second thesis is one that is like Frege’s views on predication and higher-order quantification. Frege believed in unrestricted quantification over objects and in separate unrestricted quantification over the worldly correlates of predicates, “concepts.” Whatever the fate of this view, it’s not what we are dealing with here. We are concerned with first-order quantification. A third thesis is that languages are sorted, and different quantifiers range over different sorts of objects even if the sorts are of the same type. But again, this does not seem to be what is at issue. MA is the view that there are different first-order, objectual, unrestricted quantifiers. Once this is clarified, MA should seem far from obvious.

One way to highlight the fact that it is not clear what exactly MA says is to point out that there is a dilemma in the vicinity. If all that is meant is that the nonsemantically individuated string “there is,” or the symbol “∃,” can have different meanings, then what is meant is trivial. If what is meant is that it can have different meanings while still meaning what it actually means, then what is meant is something absurd. How can this dilemma be avoided? Something Hirsch (2011, 71) gestures toward is that for an expression to have an unrestricted quantifier meaning it is necessary that it obey the standard introduction and elimination rules for the existential quantifier. Sider, too, refers to inferential adequacy as a necessary condition in his characterization of ontological realism. He explains inferential adequacy as follows: “Call a candidate meaning ‘inferentially adequate’ if the core inference rules of quantification theory come out truth-preserving under the truth conditions it determines. For example, inferentially adequate candidate meanings that count ‘John is a philosopher’ as true must also count ‘Something is a philosopher’ as true” (Sider, 2009a, 393). Later I return to the issue of how best to understand MA.

Also, someone who holds that the existential quantifier is semantically indeterminate is arguably committed to MA: the linking principle would be that the different precisifications of the quantifier can be seen as corresponding to different possible existential quantifier meanings. I problematize what MA means, but, at least prima facie, it is easier to defend MA if one thinks that the different possible quantifier meanings are exactly the precisifications of the actual quantifier. One can then say that the possible quantifier meanings qualify as being such precisely by virtue of being precisifications of the actual quantifier meaning.

As mentioned previously, Kris McDaniel and Jason Turner have revived the idea there are different modes of being. More precisely, the McDaniel-Turner view is that in Ontologese, there are different quantifiers expressing the different modes of being. Where Fs and Gs have different modes of being, there are two quantifiers in Ontologese, ∃1 and ∃2, such that “∃1xF(x)” but not “~∃1xG(x)” is true, and “∃2xG(x)” but not “~∃2xF(x)” is true. These quantifiers expressing the different modes of being are, it is suggested, more natural than a more general quantifier would be.

Earlier I presented a list of would-be alternatives to Quinean views on the ontological problem, while allowing that some views that I presented as alternatives may be best regarded as possibly unorthodox versions of the Quinean view. Taking the essence of a Quinean view to be that the ontological problem is to be stated using an existential quantifier, there are many different views that should count as Quinean. Van Inwagen (1998, 2009) presents a kind of orthodox Quineanism. He describes and briefly defends a number of Quinean theses, some of which are that being is the same as existence, that “being is univocal,” and that the “single sense of being or existence” is adequately captured by the existential quantifier of formal logic. Van Inwagen’s two latter theses rule out that the existential quantifier is semantically indeterminate or polysemous. Nothing van Inwagen says immediately rules out a view like Sider’s, but the discussion suggests that van Inwagen rejects MA, for the argument against that he gives against the quantifier being indeterminate seems also to rule out there being different possible quantifier meanings. One might say that van Inwagen is a monistic Quinean, while someone who holds in one way or other that there are different existential quantifier meanings—whether because she believes in modes of being, or she believes the quantifier is in some way polysemous or indeterminate, or she believes in MA—is a pluralistic Quinean.

Many of the questions that can be asked given Quineanism can be asked also given neo-Meinongianism and other alternatives to Quineanism. Let me focus on neo-Meinongianism. Instead of asking about polysemy of the quantifier, one can ask about polysemy of “exists.” Just as it can be held that the quantifier is semantically indeterminate, it can be held that the meaning of “exists” is indeterminate. Just as there are, according to MA, different possible quantifier meanings, it can be maintained that there are different possible nontrivial concepts of existence. And, analogous to Sider’s view, there is the possible view that while there are different nontrivial concepts of existence, one of these concepts is privileged. However, not all ideas can be easily transposed to the new setting. As noted previously, the idea that there are different existential quantifier meanings has been explicated by appeal to a condition of inferential adequacy—a criteron for being an existential quantifier meaning is being governed by the standard inference rules. This idea cannot be straightforwardly applied to explicate what is meant by talk of different concepts of existence, for it is unclear what would be the distinctive inferential role of a (nontrivial) concept of existence.

4. Ontologically different languages

Related to MA is the claim that there are what I will call ontologically different languages, where two languages are ontologically different if they employ different unrestricted quantifiers such that (a) for some predicate F, “∃xFx” comes out true in one and untrue in the other, while (b) this is due solely to the differences in meaning between their quantifiers and the predicate means the same in the two languages. Call the claim that there can be ontologically different languages OD. One way that one can accept MA but reject OD is if one operates with a certain holistic picture of language and believes that two languages can have quantifiers with different meanings only if there also are other general differences in what the expressions of the languages mean.

Ontological realists tend to commit to OD. While they don’t see themselves as asking the question whether there are Fs in the ordinary sense of “there are Fs,” they still take themselves to be concerned with Fs: what they ask is whether “there are” Fs in the Ontologese sense of “there are.” Sider (2011) defends the view that there only are subatomic particles and sets but with the important twist that the quantifier used for stating this is the one expressed not by the ordinary quantifier but the one expressed by the Ontologese quantifier. This allows him to give speeches like the following: “While it may be absurd to deny that there’s any sense in which—for example—there is a hole in a perforated sock, it’s not absurd to deny that ‘in a metaphysical sense’ there exist holes” (Sider, 2011, 172). The picture Sider presents is that the ordinary sentence “there are holes” is true but “there areOntologese holes” is false, where “hole” means the same thing in the two sentences. This picture requires OD. If there aren’t ontologically different languages, Sider cannot truly say, speaking English, that in the sense of the “there are” of Ontologese, there are only subatomic particles and sets. What he can say is that in the sense of the “there are” of Ontologese, there are no “holes,” “tables,” and “people.” But he cannot help himself to the assumptions, letting him get rid of the quotation marks around these predicates (cf. Cameron, 2010a, 256).

There are good questions regarding the relation between the Sider-style ontological realist on the one hand and on the other hand someone who rejects Quineanism in favor of an alternative view according to which ontology is concerned with what exists, or with what there fundamentally is, or with what is real. On the face if it, the former is a good Quinean and the latter is not. However, one may also think that the differences between saying that ontology is concerned with what is fundamental and saying that it is concerned with what falls under a quantifier ranging only over the fundamental are only superficial. One difference is that the Sider-style ontological realist commits herself to MA, the claim that there are different possible quantifier meanings, and the opponent of Quineanism need not commit herself on that issue.

Here is an argument against OD.13 Consider all possible atomic sentences and their truth-values. Whenever we compare two supposed unrestricted existential quantifiers, differing extensionally, we can ask how they relate to all possible atomic sentences. If one of the quantifiers, “∃1,” is such that “∃1xF(x)” is true and the other, “∃2,” is such that “~∃2xF(x)” is true then we can consider all possible atomic sentences “Φ(ξ)” where “Φ“ expresses what “F” expresses. Are there any true such sentences? Then “∃1” is (for all that this case shows) a genuine unrestricted existential quantifier; but “∃2” is not. If, by contrast, all such sentences are false, then “∃1” is not a genuine unrestricted quantifier, but for all this case shows, “∃2” may be.

The reason that this is better seen as an argument against OD than as an argument against MA is that someone who defends only MA and not OD might for example respond by saying that a given quantifier might not be able to meaningfully interact with all names and predicates—this is the “holism” mentioned previously.

The argument itself is straightforward. But what objections can be raised against it? One natural objection is that the reasoning presupposes that if satisfaction of an inferential adequacy condition is necessary for being an unrestricted quantifier, then what is necessary is satisfaction of the classical inference rules—but there are no good reasons for thinking that these rules cannot allow for exceptions. It is not even a given that the ordinary quantifier satisfies these rules. Let me stress a few things in response. First, what is needed for the argument aren’t the standard rules in full generality; for example, it suffices for the argument that a necessary condition for “∃“ being a quantifier is that where “F(ξ)” is atomic, “∃xF(x)” is true if “F(a)” is, where ‘a’ is any name filling the argument place of “F(ξ).” Second, even if some further restrictions can be motivated, for example by appeal to the supposed fact that “a=a” is true even if a does not exist, the sorts of specific cases that are relevant for present purposes—recall Sider on holes—involve ordinary contexts and are arguably quite different from these special cases. Third, considerably weakening the inferential adequacy condition conflicts with taking inferential adequacy to be an important necessary condition on something’s being a quantifier. Fourth, as we will see later, taking the inference rules to be the standard ones is what most naturally fits a natural version of Quineanism.

A more interesting objection, to my mind, says that the argument against MA takes for granted that it is a given what predicates and names are, and hence what the possible atomic sentences are—but that this cannot be taken for granted given what is currently at issue.14

What does it take for something to be a name?15 Sophisticated inferential criteria crucially appeal to an expression’s interacting with existential quantifiers in the right way. But in a dialectical context where it is a live possibility that there are, in some sense, different existential quantifiers, one cannot then presuppose as given a unique notion of a name. A simple semantic criterion saying that something is a name if and only if there is something to which it refers has the same upshot, for obvious reasons. Such a semantic criterion is arguably too simple. An empty name is a name but doesn’t refer. And it can be argued that some expressions of other categories also refer. But more sophisticated versions of a semantic criterion of namehood present the same problem. Suppose there is a special reference relation, call it name-reference, such that only names can stand in that relation to their worldly correlates. Then a semantic criterion can appeal to that relation. As for empty names, it can be said that names are characterized not by name-referring but by their aiming to name-refer, where an expression aims to name-refer iff: it is only if the expression name-refers that atomic sentences of which it is part are true. This more believable semantic criterion introduces the same problem as the simple criterion did. Consider a true sentence “F(a)” which appears to falsify “∃2”‘s claim to be a quantifier, due to the fact that “~∃2xF(x)” is non-true. And suppose we speak the language of which “∃2” is part. If in that language we correctly describe “F(a)” as ‘true’, then it seems we should not in that language speak of “a” as “aiming to refer”: for the sentence is “true” even if “there is” nothing to which “a” refers. So “a” then does not count as a name. So we still have the kind of pluralism that we get with the simple semantic criterion for being a name.

A simple syntactic criterion, according to which something is a name already if it occupies the right syntactic position, would perhaps be a criterion given which it can be presupposed what the names are even when OD is treated as a live possibility. But this criterion overgenerates in a way that seems unacceptable (Turner, 2010, 15).16

Here, then, is a recipe for defending the spirit of OD. One can argue, in the manner indicated, that any otherwise defensible criterion for being a name is such that it cannot be presupposed that there is a unique notion of name unless it is also presupposed that there is a unique existential quantifier meaning. In this way, one can stand firm against the argument I presented. But it all gets very messy. What we have are really collections of notions—quantifier, name,…—such that there are different languages with, in some sense, different counterparts of these notions; and within each language there are certain close relations between the notions in that language’s collection. Something is a quantifiern, for various n, if it interacts with namesn and predicatesn in the right way. This general characterization of the situation can sound more helpful than it is: using the label “namen” for the different notions of a name gives the impression that these different notions are species of the same genus. But it would need to be made out that it is so: calling the different notions “notions of a name” does not make it so. One may easily be skeptical of the suggestion that emerges on behalf of OD. We have come a long way from any simple and relatively intuitive idea of a multitude of quantifiers. An inferential adequacy criterion might have seemed helpful and illuminating when it appealed to the familiar notion of a name, but we have come a long way away from that.17

5. Looking at Quine’s texts

Throughout I have discussed the “Quinean” view on ontological questions, but I have not related much to Quine. One reason for this is that there is much in Quine’s own views that was peculiar to Quine; only some of what Quine said has been stressed also by later theorists. (For example, Quine strictly emphasized regimentations of natural language in ways his followers have not often done. Properly taking Quine’s stance on this into consideration would introduce many complications.)

But there is a general theoretical issue, relating to what has come up in the discussion of the argument against MA, that is useful to illustrate by considering some passages from Quine—although my focus will still not be on what exactly Quine himself thought. Consider the following passage from Quine (1970), a passage that primarily concerns some supposed disanalogies between first- and second-order quantification:

Consider first some ordinary quantifications: ‘(∃x) (x walks)’, ‘(x) (x walks)’, ‘(∃x) (x is prime)’. The open sentence after the quantifier shows ‘x’ in a position where a name could stand; a name of a walker, for instance, or of a prime number. The quantifications do not mean that names walk or are prime; what are said to walk or to be prime are things that could be named by names in those positions. To put the predicate letter ‘F’ in a quantifier, then, is to treat predicate positions suddenly as name positions, and hence to treat predicates as names of entities of some sort. The quantifier ‘(∃F)’ or ‘(F)’ says not that some or all predicates are thus and so, but that some or all entities of the sort named by predicates are thus and so.

Quine’s overall point here is that predicates don’t name things, and because of this there is a disanalogy between first-order and second-order quantification, making second-order quantification unintelligible.

Regardless of whether Quine’s claim regarding second-order quantification is correct, there is an underlying point about the structure of the argument that is worth stressing in its own right and that I want to focus on here. The underlying idea is it is because how names work that quantification into name position works the way it does, and one can only legitimately suppose that the quantification in “(∃F) Socrates Fs” works that way if one assumes predicates are relevantly like names. Generally, a view suggested by Quine’s remarks is if a name “a” is such that there are true sentences of the form “F(a),” that marks a certain kind of achievement on the part of “a”; and when first-order quantification expresses ontological commitment that is because such quantification generalizes over names, and names function in the way sketched.

Call what has just been sketched nominal Quineanism, due to its focus on names. I think nominal Quineanism should be a natural and attractive view for anyone who favors a Quinean view on ontology. It is moreover a view with proper Quine credentials, in light of the passage from Quine (1970). However, there are important passages elsewhere in Quine suggesting that nominal Quineanism was not Quine’s own view. Consider Quine (1968, 209):,

A place where we see a more trivial side of ontological relativity is in the case of a finite universe of named objects. Here there is no occasion for quantification, except as an inessential abbreviation; for we can expand quantifications into finite conjunctions and alternations. Variables thus disappear, and with them the question of a universe of values of variables. And the very distinction between names and other signs lapses in turn, since the mark of a name is its admissibility in positions of variables. Ontology thus is emphatically meaningless for a finite theory of named objects, considered in and of itself.

For the friend of nominal Quineanism, it would be natural to say that even if variables disappear from the theory itself, the mere fact that the theory contains name-predicate sentences means that the theory is committed to some objects, for in order for the theory to be true, the name must refer to something. Judging by this passage Quine, by contrast, appears to hold that what makes something a name is that it interacts with quantifiers in the right way, and that in the absence of quantifiers there is no sense to be made of the suggestion that some expression really is a name.

One question for any Quinean concerns which stand to take on this issue, and how to answer this question ties in with some earlier themes. First, earlier, when discussing MA, I noted that friends of the view tend to appeal to a condition of inferential adequacy when talking about what makes something a genuine quantifier meaning—and by inferential adequacy is meant satisfaction of the standard inference rules for the quantifier. Nominal Quineanism provides a justification for this stance. If one starts with the view that names function a particular way and the quantifier generalizes into name position, then one assigns the quantifier a role that it best plays if it obeys the standard inference rules. Second, note that the difficulties concerning the criterion for being a name, discussed previously, problematize nominal Quineanism. Nominal Quineanism presupposes that names are identifiable independently of how the quantifier works. If the only workable criterion for something to be a name is something like the semantic criterion, or an inferential criterion appealing to how names interact with quantifiers, then this assumption is false.


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(1) For material concerning how quantification in natural language actually works, see, for example, Westerståhl and Peters (2006) and Szabolcsi (2010). In the main text I talk of “some” and “there is” pretty much interchangeably. This does in principle substantively affect some issues that come up. It can be held that “some things don’t exist” is more plausible than “there are things that don’t exist.” But while this is potentially relevant to the issues at hand, it does not affect any of the points I am concerned to make here.

(2) For the Meinongian inspiration, see Meinong (1904).

(3) One interesting alternative that I do not pause on here is Jody Azzouni’s view (e.g. 2010a, 2010b), according to which no expression of natural language strictly expresses that which the ontological problem concerns, but we sometimes use “there is” and sometimes use “exists” to express this.

(4) Ross Cameron sometimes speaks of ontology as concerned with what is fundamental (see Cameron 2008), and sometimes he speaks of it as concerned with what exists in the sense of a fundamental quantifier (see Cameron 2010a, 2010b), apparently taking these descriptions to be equivalent. There is no indication that he changed his view between 2008 and 2010.

(5) Compare Cameron (2010b), 250.

(6) Stalnaker’s talk of members of a domain may rub the neutralist the wrong way. A neutralist may wish to protest that to understand the quantifier as ranging over a domain may seem to be to understand it nonneutrally. But I don’t think Stalnaker’s domain talk need be understood that way, and at any rate Stalnaker’s underlying point is independent of this fact about how it is stated.

(7) There are arguably problems, related to the problems discussed earlier regarding how to understand the “no distinction” idea, concerning how best to understand the “trivially.” Is it sufficient that “∀xExists(x)” is necessarily true for it to be trivially true? If not, what more is needed? That it be analytic? But I here pass over these problems, important though they may be.

(8) The point Stalnaker makes is rather similar to a point David Lewis (1990) makes in discussing the views of Richard Routley. Routley distinguishes between so-called existentially neutral and existentially loaded quantification, reserving “exists” for loaded quantification. His view is then that no philosophically controversial entities exist. He is a “noneist.” But he thinks that the existentially neutral quantifier ranges over them all. Lewis’s reaction is that it is Routley’s “neutral” quantifier that corresponds to “our” quantifier (the quantifier of those that do things in the orthodox, broadly Quinean way). And he says that when Routley introduces a separate, “loaded” quantifier, he “sees a distinction that is not really there” (p. 30).

(9) Quantification is standardly understood as objectual: the values of the variables are conceived of as objects, and a quantified sentence “∃xF(x)” is true if there is an object that the predicate F is true of. Substitutional quantification is thought of differently: one simply considers which expressions can take the place of the variable and whether sentences that result from substituting these expressions for the variable are true.

(10) The possibility of semantic indeterminacy also looms large in Chalmers (2009). Sider (2003) presents a prominent argument against the possibility that the quantifier might be semantically indeterminate. The argument has been extensively discussed. See Korman (2010) for discussion and overview of the relevant literature.

(11) See the essays collected in Hirsch (2011).

(12) As noted in the main text, Sider (2003) argues that the existential quantifier cannot be semantically indeterminate. In other works (e.g., 2009b, 2011), Sider takes there to be different possible quantifier meanings. Liebesman and Eklund (2007) make a case that Sider’s argument against indeterminacy in the quantifier generalizes so as to—if good—also rule out there being different possible quantifier meanings. Sider (2009a) is a reply to Liebesman and Eklund.

(13) The argument I go on to give is in the spirit of arguments given in Hawthorne (2006) and Eklund (2007, 2009). While there are some differences, it would just be tedious to get into them. Most of the discussion of the argument will concern a particular objection that can be raised against it, and the discussion of the objection is entirely novel.

(14) Another objection still is that because of cardinality worries one cannot really speak of all possible predicates. Such worries deserve being taken seriously, but there are different ways to get around them. Maybe it suffices to say this for now: even if one cannot speak of all possible predicates, in full generality, one can still use this sort of test to whittle down the range of possible quantifier meanings too much for comfort for proponents of MA. So long as one can find atomic sentences against which to, so to speak, test some purported existential quantifiers, one can see whether a purported quantifier interacts with these atomic sentences in the right way.

(15) Many of the considerations that follow in the next couple of paragraphs in effect come from Turner (2010), 15f.

(16) As Turner notes, the example he uses is similar to one used in Williamson (2003), 441–443.

(17) Sider’s own favored reply (2007, 218f, and 2011, 191f) to the problems in the vicinity of what I have brought up is to say that one quantifier interacts with “names1” and “predicates1” and another interacts with “names2” and “predicates2.” (Sider discussses quantifier variance in the relevant passages, but the problems discussed equally concern his ontological realism.) That seems immediately to conflict with his seeming commitment to OD, on the assumption—seemingly made in Sider’s discussion—that nothing is both a predicate1 and predicate2.