1.1 The Problem of Nonexistents

Are there things that do not exist? At first, this question seems easy to answer: of course not. How could something be without existing? Aren’t the ideas of being something and being an existing thing the same? On the other hand, it seems that we can produce examples of things that don’t exist. Santa Claus doesn’t exist, thankfully, but sadly neither does Spider-Man. But Santa Claus and Spider-Man are not identical, and though they have some features in common, they also differ: although both typically wear costumes with a lot of red, Santa Claus does a deeper dive into the private information of people than social media companies, while Spider-Man knows that with great power, there must also come great responsibility. So, there are at least two things – Santa Claus and Spider-Man – that do not exist. These two examples seemingly form the tip of a large nonexistent iceberg containing innumerable creatures of myth and fable. For example, no Greek God exists, and neither do any of the Roman Gods, but aren’t the Roman Gods the same Gods just with different names? No Norse Gods exist either, but the Norse Gods are not the same nonexistent Gods as the Greek Gods.

The case that I’ve stated for nonexistent objects seems reasonably straightforward: We can distinguish nonexistent objects from one another, which means that we can count nonexistent objects; we can count nonexistent objects only if there are nonexistent objects; therefore, there are nonexistent objects. In short, nonexistent objects are available to be quantified over. Among contemporary philosophers, the view that there are nonexistent objects is called “Meinongianism,” named after Alexius Meinong, about whom more will be said later in this section.

There is a second, related argument that stems from answering affirmatively a fundamental question that will be raised again and again through the history of philosophy: does “thinking of” denote a two-place relation between a thinker and what that thinker is thinking of? If “thinking of” does denote such a two-place relation, then whatever is thought of must be something, even if it does not exist. I can think of Spider-Man – maybe I do this too often – and so Spider-Man is something I stand in a relation to. But Spider-Man is something I stand in a relation to only if Spider-Man is something. So, Spider-Man is something. (As we’ll see in Section 1.2.3, the argument is often attributed to Meinong, but it is only one element in his case for nonexistent objects.)

Let’s take a step back. “Whether there are things that don’t exist” is akin to other metaphysical questions such as the following:

• Q1: Are there things that are not concrete?

• Q2: Are there things that are not particulars?

• Q3: Are there things that are not present?

• Q4: Are there things that are not actual?

Does assimilating the big question to these questions presuppose that the big question is conceptually open in the way that – perhaps to varying degrees – these questions here are conceptually open? Platonists and nominalists debate Q1, and it seems that few nominalists think that a negative answer to Q1 is mandated by our concepts.Footnote ⁹ Similar remarks apply to Q2. With respect to Q3 and Q4, we do find some philosophers arguing that negative answers are conceptually mandated: certain presentists or actualists think that it is conceptually necessary that everything is present or actual.Footnote ¹⁰ With respect to Q3, one putative reason for claiming that a negative answer is conceptually mandated is that the verb “are” appearing in Q3 is present-tensed but there is no “untensed” conjugation of this verb that could be used to state a meaningful version of Q3 that could be nontrivially affirmatively answered. With respect to Q4, one putative reason for claiming that a negative answer is conceptually mandated is that “actual” is redundant: To say that a proposition is actually true is just to say that a proposition is true, and to say that there is an actual entity that is a certain way is just to say that there is an entity that is that way.

Similarly, perhaps nonexistent objects are conceptually impossible. Suppose that existence reduces to quantification: To say that dogs exist, for example, is just to say that there are dogs, and to say that I exist is just to say that something is identical with me. If existence reduces to quantification in this way, then the claim that there are nonexistent objects just is the claim that there are things such that there are no such things. And that claim is logically incoherent! It seems then that nonexistent objects are conceptually possible only if existence is not reducible to quantification.

In contemporary metaphysics, the dominant view is still that existence reduces to quantification. But in the history of philosophy, this view is decidedly in the minority. For example, in Novotný’s (Reference Novotný2013) masterful study of late scholastic views about beings of reason, Novotný (Reference Novotný2013: 29) notes that for the scholastics, existence and being are not the same: “exists” is a first-order predicate not reducible to the quantifier, and it denotes a nontrivial property that some but not all items enjoy. The question of whether there are things that don’t exist is by their lights conceptually open, and given this, it is unsurprising to find a range of opinions on this question expressed.

Perhaps a quick dip into some of the history of the problem of nonexistents will be helpful.

1.2 Some Dead People on Nonexistent Objects

I will not pretend that this section is comprehensive. Instead, I will discuss how the problem of nonexistents was addressed by a select few historical figures at certain points in their philosophical journeys. Still, a scattershot survey of this sort can be useful even if all that it does prevents contemporary philosophers from thinking that the problem of nonexistence has its origins in the early part of the twentieth century.

One reason why the problem of nonexistents was so thorny in the history of philosophy is that for many philosophers, the idea of being is itself not particularly straightforward. Aristotle said that “being is said in many ways,” and although what exactly he meant by this is contested, it seems that the way in which a substance is “said to be” is not the same as the ways in which members of other ontological categories are “said to be.”Footnote ¹¹ Does Aristotle’s claim imply that “being” is semantically ambiguous? Or does it imply that there are modes of being? Are both of these implied?Footnote ¹² (Ontological pluralism will be discussed more in Section 2.7.)

Regardless, according to Aristotle, even nonexistent objects can, in some way, be said to be – and in fact, there must be a way in which they can be said to be, since we can say true things about them. (Just as one might wonder whether “thought of” is a two-place relation between a thinker and a thing, one might wonder whether “about” is a two-place relation between a truth and a thing.) Even nonbeing itself can in some way be said to be!Footnote ¹³

What is it to exist? We might provisionally reserve the word “exist” for things that can truthfully be said to be in the way that we can truthfully be said to be. On this usage, we exist, plants exist, but nonbeing does not exist. However, according to a strict Aristotelian, given this usage, properties, relations, events, and so on do not exist either. A broader proposal is that something exists if and only if it belongs to one of the Aristotelian categories.Footnote ¹⁴ On this proposal, you exist, and so do your properties, but none of nonbeing, blindness in an eye, or centaurs exist. Given this proposal, we could safely attribute the claim that there are nonexistent objects to those historical figures who follow Aristotle’s doctrine of the categories so understood. One such figure is Suarez, to whom we now turn.

1.3 A Contemporary Application of Meinongianism

One of the most prominent Meinongians, although he prefers the label “noneist,” also embraces nonexistent objects partly because they are theoretically useful. Priest (Reference Priest2005) argues that nonexistent objects provide the resources for a proper theory of intentional sentential operators. Here is some of the background to this idea. David Lewis (Reference Lewis1986) argued for an ontology of possible worlds because such an ontology is theoretically fruitful. Part of its theoretical fruitfulness is that modal operators – a small subset of intentional operators – can be understood as quantifiers over possible worlds, which in turn clarifies their logical properties. Lewis thought that these non-actual worlds all existed; Priest disagrees here, claiming that no non-actual world exists even though there are many such worlds. And in way, Priest goes further by claiming that there are nonexistent impossible worlds as well. This richer framework of worlds allows for a richer set of reductive analyses not possible in Lewis’s system.

Consider belief. I believe many things, such as that 7 + 5 = 12, that the sky is blue, and that the authoritarian threat to democracy needs to be addressed head on. Some of my beliefs are what I believe is merely contingently true, while others are necessarily true. Focus on beliefs about matters that are contingent. Here is a natural, but not mandatory, model of belief: When one believes, one locates oneself in a sphere of possible worlds that are consistent with what one believes.Footnote ³¹ A toy illustration of this model: early in life, I am a blank slate – I have had no experience, and so I do not exclude any possible worlds as ones that I am not located at. I acquire some experience – I see that the sky is blue. Now I place myself in a sphere of possible worlds at which the sky is blue. As I acquire further beliefs about contingent matters, this sphere shrinks. To be maximally opinionated about contingent matters is to locate oneself in exactly one possible world. To be omniscient with respect to contingent truths is to know exactly what world one is in. This model mode suggests a reduction of the intentional operator of belief to a universal quantifier over possible worlds: to believe that P is for P is to be true at all of the worlds in the sphere in which I locate myself.

This model does fairly well with contingent beliefs, although there is at least one hiccup: on this model, if I believe that P, I believe all that is entailed by P. Suppose I believe that P, and that Q is entailed by P. Since I believe P, P is true at all of the worlds in the sphere in which I locate myself. Since P entails Q, Q is also true at all of the worlds in the sphere in which I locate myself. But then, given this model, I believe Q as well. That’s surprising, but worse is to come: since every necessary truth is entailed by any proposition, it follows that from the fact that I believe P, which is a contingent truth, I thereby believe all the necessary truths. This doesn’t seem plausible. So, it looks as though, even if modal operators like “necessarily” reduce to (or at least can be modeled by) quantification over possible worlds, other intentional operators resist such a treatment.

Enter impossible worlds. Suppose that P is contingent, that P entails Q, and that I have no opinion about Q. Although there is no possible world at which P and not-Q are both true, there are nonetheless worlds in which P and not-Q are both true. And since I have no opinion about P, I locate myself in a sphere of worlds that includes some P and Q worlds and some P and not-Q worlds. Belief can be understood in terms of universal quantification, provided that the domain includes impossible worlds.

An impossible world seems like a paradigmatic example of a thing that cannot, and so does not, exist. There are treatments of impossible worlds on which these things do exist. But if the best theory of impossible worlds is a theory on which they are nonexistent, and if impossible worlds are theoretically useful, we have a pragmatic reason to traffic in them, much like the pragmatic reason Lewis offered for trafficking in possible worlds.Footnote ³²

In general, the putative theoretical usefulness of nonexistent objects is a challenge for foes of nonexistent objects. They need to show that either the jobs nonexistent objects are called to do are not needed to be done or that the jobs can be done by existent objects instead.

1.4 Zalta’s Object Theory

Suppose that there are nonexistent objects. This supposition leaves it open what they are like. According to many friends of the nonexistent, expressions such as “the round square” and “the golden mountain” denote nonexistent objects; let’s assume they do. So, is the round square round? (And square?) Is the golden mountain a mountain? There seems some pressure to answer “yes,” for if the round square weren’t round, and the golden mountain weren’t a mountain, why would we call them that? The characterization postulate is the claim that whenever a predicate appears as part of a definite description that denotes something, that predicate is true of the object. The characterization postulate implies that the golden mountain is a mountain.

But it seems that the characterization postulate has counterexamples. Consider the description “the existent round square.” Suppose that this denotes an object. It must be round and square, but also exist! Perhaps “the existent round square” doesn’t denote – but then why believe that “the round square” does? So, it seems that either some denoting phrases do not denote or the characterization principle must be replaced with something less permissive.

But perhaps there is a third option. One of Meinong’s students, Ernst Mally (Reference Mally1912), argued that we need to distinguish two ways in which a predicate might be true of an object – or, better put perhaps, two ways in which a property might be had by an object: the property might be exemplified by the object or it might be encoded by the object. The golden mountain is a mountain – but it only encodes the property of being a mountain, unlike Mount Everest, which exemplifies this property.

More recently, Mally’s idea has been defended by Ed Zalta (Reference Zalta2006), and incorporated in his object theory.Footnote ³³ Zalta’s object theory doesn’t distinguish between quantification and existence, but does hold that some concrete things could have existed without being concrete. I suspect that Zalta’s theory is merely terminologically different from a theory in which the contingently nonconcrete are nonexistent objects. But let’s explore the theory first. Here are its relevant components.

First, everything exists necessarily, although many of what necessarily exists is only contingently concrete. Socrates is a necessary existent who is contingently concrete. Included in what necessarily exists are abstract objects, which are also necessary nonconcrete.Footnote ³⁴ Hence, the distinction between concrete objects and abstract objects is not an exhaustive distinction, since a merely possibly concrete object is not an abstract object.

Second, there are two fundamentally different modes of predication or ways in which an object can “have” a property.Footnote ³⁵ Sherlock Holmes exists and is a detective, but he does not exemplify being a detective, unlike one of my neighbors who is a concrete detective for the local police force. Rather, Sherlock Holmes, who is an abstract rather than concrete object, encodes being a detective. It seems to be part of Zalta’s (Reference Zalta2006: 663) theory of objects that such abstract objects encode all and only those properties that are inherent in our conceptions of them.

Third, as a matter of necessity, the only objects that encode properties are abstract objects.Footnote ³⁶ Things that are or could be concrete never encode but always exemplify properties.

The first two parts of the system are independently motivated. The first part is motivated by virtue of being a consequence of the simplest version of quantified modal logic.Footnote ³⁷ The second part is motivated by traditional concerns about putative nonexistent objects, such as creatures of fiction and myth. But why accept the third component?

Plausibly, the nature of a nonexistent object is exhausted by the properties that they encode; these properties constitute its essence in the strict sense. The essence of a thing in this strict sense is not simply the collection of features it exemplifies as a matter of necessity. (As Fine (Reference Fine1994) argued, it is not part of my essence that I am a member of my singleton set, although I am a member of it as a matter of necessity.) It is of the essence of the golden mountain that it encodes being a mountain. Here is a hypothesis: In general, an object encodes a property if and only if it is a part of its essence. However, this hypothesis is incompatible with Zalta’s third component.

There are three options. First, scrap the idea of an essence in the strict sense. Second, take the notion of an essence in the strict sense as an additional primitive, over and above the primitives of encoding and exemplifying. (Accordingly, essentially having a property would be a third way of having a property.) Third, give a reductive account of essence in terms of other aspects of the theory.

Zalta (Reference Zalta2006: 678, 691) pursues the third option and provides a disjunctive theory of essence: What it is for a property to be essential to an object depends on whether the object is an abstract object or a possibly concrete object. A feature F is essential to an abstract object just in case, necessarily, it encodes F. For possibly concrete objects, Zalta (Reference Zalta2006: 679) distinguishes between weak and strong essential features. A feature F is weakly essential to a possibly concrete object just in case, necessarily, if it is concrete, it exemplifies F. A feature F is strongly essential to a possibly concrete object just in case F is weakly essential to it but it is not the case that it necessarily exemplifies F. Being a member of his singleton set is not strongly essential to Socrates, for although it is weakly essential to him, Socrates belongs to that set necessarily. Recall that Socrates necessarily exists but is only contingently concrete. In every world, Socrates is a member of his singleton set, even those worlds in which he is nonconcrete. Similarly, Socrates is weakly essentially not identical with Kit Fine, but he also is necessarily not Kit Fine, and hence Socrates is not strongly essentially not identical with Kit Fine.

Although it looks initially promising, the theory is subject to counterexamples. Wildman (Reference Wildman and Jago2016: 186) considers being human and that the Eiffel tower is essentially a tower. This is a property that is strongly essential to Socrates (given Zalta’s definitions), but is intuitively not essential to Socrates. Wildman (Reference Wildman and Jago2016: 186–190) considers a series of ways of modifying Zalta’s theory in light of even more counterexamples, but Wildman (216: 188) notes that the final theory he arrives at is “a terribly complicated definition, which manages to avoid counterexamples only via the accumulation of gerrymandered, ad hoc restrictions.” Since I share Wildman’s judgment here, I will refrain from tediously documenting the epicycles.

As already noted, Zalta denies that possibly concrete objects encode properties. On the theory considered here, possibly concrete objects encode properties as well as exemplify them. Moreover, we accept Zalta’s account of essences for abstract objects for all objects: A property F is essential to an object just in case it encodes that property. Like Zalta, we accept that if an object encodes a property, it encodes that property in every world in which it exists. We add an additional axiom to the theory: If x encodes F, then in any world in which x is concrete, x exemplifies F. This axiom governs both possibly concrete objects and abstract objects, although the latter only trivially. Given that nothing can exemplify inconsistent properties, the axiom implies that possibly concrete objects never encode inconsistent properties. (Nothing said prohibits abstract objects, such as the round square, from encoding inconsistent properties, that is, properties that cannot be jointly exemplified.)

It is part of our conception of what Sherlock Holmes is that he is a detective. Object theory makes sense of this by having Sherlock Holmes encode that property. But it is not part of our conception of Sherlock Holmes that he is a member of his singleton set. He fails to encode that property. (But Sherlock Holmes does exemplify this property, and does so as a matter of necessity!) But we make similar remarks about Socrates. It is part of our conception of what Socrates is that he is a human being, but not that he is a member of his singleton set. A uniform way of making sense of these remarks is that Socrates encodes humanity but not being a member of the singleton of Socrates.

Although I have just mentioned our conceptions of objects, I am not suggesting that which objects encode which properties is a consequence of what concepts we happen to have . This is not consonant with the background metaphysics in which there is a domain of abstracta whose existence and essence is independent of us. Rather, in the case of abstracta, because there are so many of them – roughly, for any set of encodable properties, there is an abstract object that encodes all and only those properties – our conceptions are bound to latch on to something. With respect to abstracta, our conceptions are excellent guides to essences: Because there are so many of them, our conceptions of an object are virtually guaranteed to match an object so conceived. With respect to actually concrete things, perhaps not. We have no a priori guarantee that a given conception perfectly tracks the essence of a concrete thing. But we know this. We know that it is much harder to discern the essence of Socrates than the essence of Sherlock Holmes.

The theory is remarkably simple, and as far as I can see free of counterexamples. One possible concern is whether Zalta’s (Reference Zalta2006) original theory correctly identified the essence of abstract objects; if it did not, the theory proposed here is in trouble too, since it delivers the same verdicts for abstract objects as Zalta’s theory. So, consider Sherlock Holmes. One might think that Sherlock Holmes essentially depends on Arthur Conan Doyle. How do we capture this dependence if Sherlock Holmes encodes being a detective but doesn’t encode any way of being related to Arthur Conan Doyle? It is not clear we need to. In Zalta’s original theory, there is an entity that encodes all and only the properties Sherlock Holmes is depicted as having in the stories. But there is also an entity that encodes all these properties plus further properties that account for its being related to Arthur Conan Doyle. (Perhaps among these properties are being first thought of by Arthur Conan Doyle, or first written about by Arthur Conan Doyle, and so on.) The former entity is not essentially related to Arthur Conan Doyle, but the latter is. We can let our intuitions about essences assist us in deciding which entity is the referent of “Sherlock Holmes.”

In what respect is this theory of essence that I have proposed reductive? If Fine says that a property is essential to x, the theory we are considering translates this as saying that x encodes the property. Rather than provide a reductive account of the phenomena, one might worry that the theory in question merely relabels it. I am not unduly concerned: What matters is that we have two ways of having a property instead of three. Whether to call the second way of having a property “encoding” or “inclusion in the essence of a thing” is of little importance.

Let us turn now to three objections to nonexistents.

1.5 Denials of Nonexistents

We’ve seen several reasons for accepting nonexistent objects in our metaphysics. We’ll now look at several reasons against so-doing.

2.1 Introduction

Metaphysicians by and large are earnest and serious. They conceptualize the task of metaphysics as the discovering of substantive truths about reality by way of philosophical investigation. Although a metaphysician might theorize about thought and language, or other ways of representing, they do so only in the service of theorizing about what that thought and language represents.Footnote ⁴³ The metaphysician is interested in words like “freedom,” “existence,” “parthood,” or our concepts of freedom, existence, or parthood, only insofar as examining them will shed light on freedom, existence, and parthood. We can imagine a project of trying to describe what our ordinary conceptions of freedom, existence, or parthood are, and such a project would be of value; Strawson (Reference Strawson1964) calls this sort of project “descriptive metaphysics.” But most metaphysicians do not construe what they are doing as merely descriptive metaphysics, which if done well produces merely a body of definitional or conceptual truths, rather than substantive truths about reality. This conception of the aims of metaphysics stretches at least as far back as Kant, who held that metaphysics as a science is possible only if it contains foundational synthetic a priori truths.Footnote ⁴⁴

This is especially true of ontologists. Perhaps most of metaphysics can be reconceptualized as descriptive metaphysics without a loss of its sense of importance. But can ontology be reconceptualized as descriptive ontology without loss?

Consider the special composition question: “under which conditions do some things compose a further thing?”Footnote ⁴⁵ Putative answers include universalism, which is the view any things that have no parts in common compose a whole, nihilism, which is the view that many things never compose a further thing, stuck togetherism, which is the view that many things compose a thing when those things are sufficiently stuck together, and organicism, which is the view that many things compose a thing when the activity of those things constitutes a life.Footnote ⁴⁶ For our purposes, having these four answers on the table suffices.

The debate between these four is an ontological debate, and judging by the quantity of attention it has received, it seems to be a substantive debate as well. But maybe this appearance is misleading. In what follows, we will first examine some metaontological positions that hold that this debate is not substantive. The first position, inspired by recent work by Eli Hirsch, is that the debate about composition is a merely verbal debate. The second position, also inspired by Eli Hirsch, is more subtle, but suffice it for now to say that it doesn’t require the claim that the debates are merely verbal in the sense delineated by the first position. After examining these views and some responses to them, we will consider the metaontological position of Amie Thomasson, according to which the debate about composition is “easily answered.” And in Section 2.7, we will discuss the status of ontological pluralism and how it relates to these debates.

2.2 Hirsch and Quantifier Variantism

Imagine possible communities of human beings much like us except they take the answer to the special composition question to be obvious. Suppose the members of each of these communities speak languages that look and sound much like English – whether they speak English or the same language as each other will be explored more later in this section. One community thinks that universalism is obviously true, another thinks that nihilism is true, and so on. For them, the answer to the special composition question is as obvious as it is that bachelors are unmarried and that 7 + 5 = 12. From our perspective, such a community is clearly possible even if we doubt it could be actual. For what would ground this consensus? Are the community members in a cult or obstinately dogmatic? Set the question about the ground of consensus aside for a moment – we will return to it.

Suppose members of one community come into contact with another. Suppose, for example, that members of the community that thinks that nihilism is obvious (henceforth: “the nihilist community”) make contact with members of the community that thinks that universalism is obvious (henceforth: “the universalist community.”). Initially, they are pleased at how much they agree on – they have the same mathematics, for example. But they are stunned when they learn the vast apparent differences between them with respect to composition – stunned enough that they wonder whether they are in fact speaking different languages rather than speaking the same language but disagreeing about obvious truths. After all, it is not very charitable to interpret your conversational partner as though he or she were making an obvious mistake if there are alternative interpretations of what he or she means available. And so members of these communities begin to look for alternative interpretations.

Pretend that you belong to the universalist community. When you say that there is something made of the xs, the members of the nihilist community seemingly say that there are only the xs. But you notice that whenever members of the nihilist community make a sentence that sounds like it uses a quantifier, what they say is necessarily equivalent to a sentence that does use a restricted quantifier whose domain contains only things without parts. And now you have a way of charitably interpreting your nihilist friends. They have an expression that functions like a quantifier, but it is semantically primitive (in the sense mentioned in the previous section). It’s ok if you can’t grasp its meaning in the way that people who grow up in that community can – it’s enough that you now understand the truth conditions of sentences in which that expression appears. In this respect, your situation is better than the situation of Lewis with respect to the Meinongian: you can understand what is in effect the nihilist’s “inner quantifier” because you can produce sentences necessarily equivalent to sentences in which it appears, whereas Lewis (allegedly) could not do that with respect to the Meinongian’s inner quantifier.

Now pretend that you belong to the nihilist community, and that you are trying to understand the universalist community. They seem like crazy Meinongians to you – by your lights, they seem to be quantifying over what there isn’t. But you recall from Lewis (Reference Lewis1990) that there is a way to simulate quantification by placing prefixing an operator in front of a quantifier. When the Meinongian says something that sounds like “Most supervillains are more interesting than the heroes that are their archenemies,” you understand them as saying something that is equivalent to “according to the fiction that there are fictional characters, most supervillains are more interesting than the heroes that are their archenemies.” Perhaps that is what people in the universalist community are doing: they are doing something like simulating quantification. After much communication with them, your hypothesis bears fruit. There is a fiction – an absurd fiction, of course – that composition occurs whenever there are some things. And corresponding to this fiction is an operator, “according to the fiction of universal composition.”Footnote ⁴⁷ What you discover is this: Whenever the universalist uses a sentence that seemingly contains a quantifier, it is always necessarily equivalent to a sentence in your language that contains this operator followed by a genuine quantifier. For example, when the universalist says something that sounds like “there are tables,” what they say is necessarily equivalent to the claim that you express by saying, “According to the fiction of universal composition, there are tables.”

Now let’s take a step back. Each community has a way of interpreting the other community so that the other community expresses reasonably believed truths rather than obvious falsehoods. Given this fact, it seems that members of either community have no reason to think that they genuinely disagree with the members of the other community, at least not about matters of ontology. There might be a disagreement about which language is a more convenient language to speak, though this disagreement might be pressing only once members of different communities have romantic entanglements with each other that result in children who must be raised and decisions about how to raise them.

Moreover, now each community can consider a hypothesis for why the other community finds what they say to be obviously true.Footnote ⁴⁸ An expression is semantically primitive if and only if there is no complex expression within the language in which it appears that is equivalent in meaning to the original expression. But an expression can be semantically primitive and still yield conceptual truths. (For example, that red is a color.) The simplest conceptual truths stateable using semantically primitive expressions tend to be obviously true. Each community has an expression that functions like an existential quantifier in that the expression licenses the characteristic inference rules that govern that quantifier, namely existential instantiation and existential generalization, and similarly each community has an expression that functions like a universal quantifier. Moreover, each community’s quantification-like expression yields a conceptual truth. When someone in the universalist community says something that sounds like “composition always occurs,” what they express is a conceptual truth, and when someone in the nihilist community says something that sounds like “composition never occurs,” what they say expresses a conceptual truth – and these conceptual truths are compatible with each other. (This is why there is no genuine ontological disagreement over whether composition occurs between the two communities.) These conceptual truths are expressed by easy-to-understand (if you belong to the relevant community) sentences, and so are easy to know as well – and this is why there is so much widespread agreement among members of a given community. For each community, there is something that sounds like the special composition question, and its answer is trivial and obvious. Given this, it seems that each of these languages is as good for describing reality as any of the others.

But what does this have to do with us? We don’t belong to any of these communities, and the answer to when composition occurs is not obvious. And whatever that answer is, it doesn’t seem to be a conceptual truth. But think now about how members of any of those communities will try to interpret us! Some of us believe in universalism; some of us believe in nihilism; some of us believe in organicism; and some of us believe in sufficiently stuck-togetherism. Each of these positions corresponds to a possible language in which sentences that sound like expressions of these positions express conceptual truths.Footnote ⁴⁹ From their perspective, a plausible hypothesis is that it is unsettled or indeterminate which language we are using. And because it is unsettled, there is no fact of the matter about which of these positions is true – and no fact of the matter about which of these positions is a conceptual truth.

On the hypothesis that it is indeterminate which of these languages we speak, there is no substantive question about when composition occurs. Here is an analogy to consider. Consider the word “rich.” How much money must someone have in order to be rich? It’s indeterminate how much: There is no precise monetary amount necessary and sufficient for being rich because we never settled what that amount is.Footnote ⁵⁰ But we could have settled this, and there are other languages that are exactly like English except that in them “bald” corresponds to a precise cutoff point; the languages differ from each other in where this cutoff point is drawn. In each of these languages, having fewer than some n number of hairs is necessary and sufficient for “bald” to apply, and in each of these languages, this is a conceptual truth. So, although it is indeterminate in our language which n corresponds to being bald, it is still a conceptual truth that there is some n such that having fewer than n hairs is necessary and sufficient for being bald. Similarly, although it is indeterminate which language we speak, it is determinate that on each language the answer to what sounds like the special composition question is a conceptual truth, whatever that answer might be.

Members of these other communities have a good reason to accept this hypothesis about us. Do we? Here is one reason for us to be cautious. Consider a language L that is a lot like English and that contains a sentence S that expresses a conceptual truth in L. Suppose that what S expresses in L is necessarily equivalent to what is expressed by a sentence E in English. It doesn’t follow from this that E expresses a conceptual truth, or that the question of whether E is true is non-substantive. Imagine a community much like ours except that children are taught at an early age that the word “water” just means “substance consisting of H₂O molecules.” In this language, the sentence “water is the substance consisting of H₂O molecules” expresses a conceptual truth, and the truth that it expresses is necessarily equivalent to the truth that we express when we say that water is the substance consisting of H₂O molecules. What we express is not a conceptual truth, but rather a synthetic empirical claim, albeit one that is necessarily true. It is a substantive claim because facts about the chemical makeup of water are not built into the semantics of “water” in English.Footnote ⁵¹ And it might be that in a similar way facts about the metaphysical constitution of reality are not built in the meaning of quantifier expressions – and so statements about what there is are substantive claims rather than assertions of conceptual truths.

If principles about when composition occurs, or other apparently basic ontological truths, are not baked into the semantics of quantifier expressions, what is? A plausible answer is the inferential principle governing those expressions.Footnote ⁵² So, for example, it is part of the meaning “something” that it follows from the claim that Charlie is a dog that something is a dog, and it is part of the meaning “everything” that this inference is valid: if everything is finite, and Kris is among what there is, then Kris is finite. Is this it? That is, is merely obeying the characteristic inferential rules governing “something” necessary and sufficient for an expression to have the same meaning as our word “something”? If so, then our actual meaning for this expression is importantly different from the other putative alternative meanings for it; perhaps the differences are significant enough that we should not think of them as genuine alternative meanings. A related question is whether obeying these characteristic inference rules is necessary and sufficient for an expression to have the same meaning as “something” in our language. If it is, then these alleged alternative meanings for “something” do not exist, and quantifier variance is not possible!Footnote ⁵³

In what follows, I will assume that the answer to this related question is “no,” and so quantifier variance is not immediately ruled out. Given this answer, there is a further interesting question about why the quantifier-like expressions can be used to express conceptual truths about, speaking very loosely, what there is, while our expression cannot be so used. Can we imagine different languages that contain quantifier-like expressions such that speakers of those languages associate with those expressions concepts that are analogous to our concept of a domain of quantification, but for which it is not conceptually true what is included in this conception of a domain of quantification? That is, can we envision an alternative language to English in which the sentence in that language that sounds like “whenever there are some xs, there is a y composed of those xs” expresses a truth that is a substantive rather than conceptual truth, and similarly for the other alternative languages we are considering?

Thus far, I have focused on the contrast between conceptual truths and nonconceptual truths, and have labeled the latter “substantive.” The idea was to explore the thought that not much is really at stake in putative ontological debates if the answers to the corresponding ontological questions are always either conceptually true or conceptually false or conceptually indeterminate. And, as already noted, this way of considering the question of substantivity was driven by the Kantian idea that, in general, metaphysics aims to discover nonconceptual truths, and is thus bankrupt as an enterprise if it cannot succeed in this aim. But perhaps there is a different way of demarcating the substantive from the nonsubstantive that doesn’t closely track the distinction between conceptual and nonconceptual truths. Perhaps the mere fact that there are possible alternative languages of the sort that we have envisioned in which sentences that sound like “composition always occurs” or “composition never occurs” express truths is sufficient to make the debate over composition nonsubstantive – even if in those languages the sentences express truths that are not conceptual truths. Let’s explore this furthermore.

The semantic value of an expression is whatever object directly partially grounds the truth conditions of sentences in which that expression occurs. Plausibly, any entity can be the semantic value of a name; I am the semantic value of the name “Kris.” And, plausibly, the semantic values of predicates are properties. What about quantifiers? A natural answer, which I will assume in what follows, is that the semantic values of quantifiers are higher-order relations, that is, relations that relate properties.Footnote ⁵⁴ Consider the sentence “some dogs are red.” On the natural answer, the semantic value of “some” is a relation that relates the property of being a dog and the property of being red if and only if at least one dog is red.

The binary relation that is the semantic value of “some” is conditionally reflexive in this sense: If property F bears this relation to property G, property F bears this relation itself. (This is because the fact that some F is F follows from the fact that some F is G.) It is also symmetric. (This is because the fact that some G is F follows from the fact that some F is G.) But it is not transitive. (It does not follow that some F is H from the fact that F is G and some G is H.) In general, binary relations are exemplified by two things (or one thing twice over), and for any binary relation, there is a set of ordered pairs such that the first element of a pair bears that relation to the second element of that pair; such a set is the extension of that relation. Here is a hypothesis: The semantic values of the words that sound “something” in these alternative languages we are considering also have higher-order binary relations that are conditionally reflexive and symmetric but otherwise differ with respect to their extensions. Given this hypothesis, the alternative languages contain expressions that are quantifier expressions, and I will call these possible semantic values “alternative quantifier values.”

In virtue of what is something the semantic value of an expression? This is a metasemantic question, and one of direct relevance to metaontology. An initial first answer is facts about how that expression is used. Among other things, expressions are used to assert propositions that speakers take to be true. For any expression in a given language, there is a set of sentences that speakers of that language are disposed to sincerely assert. An interpretation of a set of sentences is an assignment of semantic values to the expressions appearing in that sentence. An interpretation of a set of sentences is charitable to the extent that the sentences in that set are true given that interpretation. Our initial first answer says that an expression E has semantic value S in virtue of the fact that the most charitable interpretation of the set of sentences that contain E that speakers are disposed to assert is one which E is assigned the semantic value S.Footnote ⁵⁵

This initial first answer needs revising, and we will come that to soon enough, but for now observe that this metasemantic theory doesn’t appeal to a distinction between conceptual and nonconceptual truths – all sentences in a set to be interpreted count equally when it comes to charity, as construed above. We could have a more complicated theory in which there is stratification: some sentences, perhaps those speakers that of the community regard as conceptual truths, count for more than others when determining how charitable an interpretation of them is.Footnote ⁵⁶ But we won’t develop this more complicated theory here, since our current goal is to see whether there is a way of making the debate over composition nonsubstantive without appealing to the idea of conceptual truth. We will, however, consider a second way of stratifying sentences that appeal to the average level of confidence speakers have when asserting sentences. In general, on average, speakers are disposed to very confidently assert “the sun will rise tomorrow” and “2 + 3 = 5,” and are disposed to fairly confidently assert “composition sometimes occurs.”

Recall that speakers of these alternative languages are very confident in their seemingly ontological assertions – unlike speakers of our languages! And so on the second way of measuring the charity of interpretation, we heavily favor an assignment of a quantifier value to a quantifier expression that makes those confident assertions come out true. These assertions are confidently made, but this does not make them conceptual truths; we confidently assert “the sun will rise tomorrow,” but this sentence does not express a conceptual truth.

To sum up where we are so far, there are possibly alternative languages that contain quantifier expressions that sound and function like our expression “some,” and that have different semantic values than the value of “some,” and these different semantic values have a different extension than extension of the semantic value of “some.” In one of these languages, a sentence that sounds like “composition always occurs” expresses a truth; in another language, a sentence that sounds like “composition never occurs” expresses a truth. On the other hand, it is not clear whether when we say, “composition always occurs,” what we say is true, or false, or indeterminate. We have not yet captured the idea though that the question of when composition occurs is nonsubstantive. But we just need one extra ingredient to do so: the claim that, from a metaphysical perspective, each of these alternative quantifier values is as a good as each other and as good as the semantic value of our quantifier, and so there is no metaphysical respect in which one of these languages does a better job than any of the others when it comes to describing reality.

Is this extra ingredient true?

2.3 Sider on “Structure”

The distinction between properties that carve nature closer to the joints and those that do not is well-entrenched contemporary metaphysics, largely due to the work of David Lewis (Reference Lewis1983, Reference Lewis1984, Reference Lewis1986). The distinction between properties that account for genuine and objective similarities between things is intuitive: dogs have something importantly in common with each other by virtue of being dogs, while dogs and cats do not have something importantly in common with each other by virtue of not being violins. But Lewis argued that this intuitive distinction does real philosophical work: Among other things, it is useful for characterizing supervenience, what makes a generalization a law of nature, what distinguishes intrinsic and extrinsic properties, and what makes a word refer to something. When a distinction is both intuitive and theoretically useful in a variety of contexts, it is reasonable to look for additional contexts in which it can be employed. This is what Sider (Reference Sider, Chalmers, Manley and Wasserman2009, Reference Sider2011) does: Sider argues that we can “go beyond the predicate”: not only do some predicates correspond to nature’s joints, perhaps in virtue of referring to properties that carve at the joints, but so too do some quantifiers, and perhaps so too do other expressions, such as sentential operators and connectors.

That some quantifiers correspond more to joints than others is somewhat intuitive. Consider the difference between “some dog is red” and “exactly seven dogs or exactly 13 dogs or between 935 and 2036 dogs are red.” Isn’t the quantifier contained in the second sentence more gerrymandered or gruesome than the one in the first sentence? It wears its disjunctiveness on its face. Furthermore, consider that one reason for thinking that a predicate corresponds to a highly natural property is that this predicate (or one coreferential with it) appears in highly a successful theory. Similarly, though, Sider (Reference Sider2011: 188) argues that the existential quantifier appears in highly successful theories in physics, mathematics, logic, and so on. So insofar as appearing in successful theories is a good guide to corresponding to naturalness, there is a good case that the existential quantifier corresponds to a natural joint. Given that there are both intuitive and theoretical considerations that favor it, Sider’s modest extension of Lewis’s conception of naturalness is accordingly reasonable. Sider calls the view that the existential quantifier corresponds to a quantificational joint “ontological realism.”

A possible response is that Sider’s argument supports the claim that the existential quantifier appearing in physical theories and the existential quantifier appearing in mathematical theories correspond to quantificational joints. But does Sider’s argument support the claim that these quantifiers are strictly the same? Maybe there are two quantificational joints.Footnote ⁵⁷ Perhaps it does when supplemented with a claim about simplicity: the hypothesis that there is one, rather than two, quantificational joints is a simpler hypothesis, and that it provides a reason to believe it over its alternatives.

Sider (Reference Sider, Chalmers, Manley and Wasserman2009) endorses a view that has come to be called “reference magnetism.” According to reference magnetism, one of the factors that determines whether an expression refers to (or has as its semantic value) a given entity is how natural that entity is both in absolute terms and relative to other candidate referents of the expression. The more natural a thing is, the more referential pull it possesses. A sufficient degree of naturalness can trump use so that the correct interpretation of what we say is one in which we say many falsehoods. Both the naturalness of candidate referents and the charitableness of an interpretation come in degrees, and no one knows how much naturalness it takes to trump a certain amount of charitableness. Broadly speaking, then, even given that there is a perfectly natural quantificational joint, there are two possibilities: It is sufficiently natural to trump charitableness and so it is the referent of the ordinary English expression “something,” or it is not. In the former case, ontological disputes conducted in English are not merely verbal in Hirsch’s sense; in the latter case, they might be, but if they are, there is a fallback option: Conduct the debates in an artificial language in which quantificational expressions are stipulated to refer to the quantificational joints. Sider calls this language “Ontologese.” According to Sider, debates about “what there is” in Ontologese are substantive debates.

Ontologese contains expressions that function analogously to how quantifiers function. In a moment, I will want to ask some questions in (rather than about) Ontologese, so let me introduce a convention: When an English expression is followed by an “*,” that expression’s semantic value is that perfectly natural entity that is the closest candidate among all other perfectly natural entities for being the semantic value of the English expression. (If there is a tie for closeness here, let us stipulate that the English expression followed by the “*” fails to have a semantic value rather than ambiguously has more than one.) So, for example, “there is*” expresses the analogue of existential quantification of in Ontologese.

Sider (Reference Sider2011) doesn’t believe that there is* very much. His preferred ontology* is one in which there are* the fundamental entities that will be posited by our best physics, and perhaps in addition to those entities there are* sets, but not much else. I say this neither to praise nor to criticize this ontology*, but rather because it raises an interesting question about Sider’s ontology (rather than his ontology*): Is it an ontology that contains nonexistent objects?

The answer to this question might depend on whether “there is” and “there is*” have the same semantic value. Let’s assume that they do not, and that charity has trumped naturalness when it comes to determining the semantic value of “there is.” Given this claim, although “there are tables” is true, “there are* tables” is not true. Recall that, in Section 1, in the context of discussing Aristotelian meta-ontologies, I considered the proposal that to exist is to belong to one of the Aristotelian categories. On my view, what would distinguish the Aristotelian categories from other ways of carving up the world into classes of entities is that the Aristotelian categories would correspond to genuine ways of being – where a way of being is a quantificational joint.Footnote ⁵⁸ A prima facie reasonable generalization of this idea is that for x to exist is to have a way of being in this sense, that is, for there to be a possible quantifier whose semantic value is a quantificational joint and that quantifies over x. Here is why this generalization is reasonable: if being something – that is, being quantified over – is different from existing, then it seems that what matters when assessing whether a theory’s ontology is costly is what the theory says exists. Similarly, though, if being something is different from being something*, then what matters when assessing whether a theory’s ontology is costly is what the theory says about what there is*. Either there are two things relevant to the costliness of an ontology or what exists just is what there is*.

Given this reasonable generalization, and given that “there are tables” is true, “there are* tables” is not true, it follows that tables do not exist, even though there are tables. This consequence is a bit weird, and we will discuss in a moment about how to avoid it. But note also that, like the Meinongian views discussed in Section 1, the position that we are discussing distinguishes both an “inner” and “outer” quantifier, because whenever “there are* Fs” is true, “there are Fs” is true, but the converse is not always the case. On the Meinongian theories, the inner quantifier corresponds to that which exists.

In light of this discussion, perhaps we should reconsider the generalized idea that to exist is to have a way of being. “Exist,” like “there is,” is an expression of ordinary English. If charity trumps naturalness with respect to the latter, it is hard to see why it would not with respect to the former. An interpretation of “tables exist” that makes it false doesn’t seem very charitable. If “exists” does not carve at the joints, then perhaps what exists and what is costly in ontology come apart. This is what Ross Cameron (Reference Cameron2010) suggests: We are ontologically committed to what our best theories say exists* rather than what they say exists.

These remarks suggest that it is not necessary for an entity to exist that it has a way of being. Maybe it is not sufficient either! Recall that Meinong’s official view seems to be one in which both the inner quantifier and the outer quantifier correspond to quantificational joints.Footnote ⁵⁹ But then it follows from the generalized idea that if Meinong’s official view is true, then absolutely everything exists – even the nonexistent round square!

It seems then that the generalized idea should be scrapped, despite its initial plausibility. Scrapping it, however, then leaves open a question that we would like answered, namely, what is existence?

Let’s return to the discussion of ontological realism. One worry is that it generates hard questions about naturalness that might seem to be pseudo questions.Footnote ⁶⁰ There is the existential quantifier and the universal quantifier. It is hard to see why one of them would be more natural than the other. But if they are equally natural, and both correspond to a quantificational joint, then it seems that there is kind of metaphysical redundancy: Why does the world have two joints here when every theoretical purpose served by positing just one of them? Perhaps redundancy is preferable to arbitrariness, but probably better not to have to choose.Footnote ⁶¹ That said, the same sort of problem already faced Lewis’s original theory of naturalness. For example, every nonsymmetric relation has a converse. Some nonsymmetric relations might be highly natural. But if so, is the converse relation equally natural? For example, perhaps is earlier than is a highly natural relation; but if so, what should be said about its converse is later than?

Perhaps there are no perfectly natural nonsymmetric relations, and more generally, whenever there is apparently redundant perfectly natural properties or relations, none of the properties or relations are perfectly natural. This is an interesting hypothesis, but if true, it is hard to see how to defend it.Footnote ⁶² Moreover, the natural extension of this hypothesis is that whenever there are some features that are inter-definable with each other, then none of these features are perfectly natural. This natural extension implies that ontological realism is false.Footnote ⁶³ However, this fallback position would not be refuted: that there is a most natural meaning for the existential quantifier, even if it is not a perfectly natural meaning. Call this position ontological near realism.Footnote ⁶⁴

Ontological near realism might suffice to respond to Hirsch’s challenge, provided that this most natural meaning is natural enough to trump charity to enough extent that it ends up being what is meant when ontological disputes are conducted. And even if it is not natural enough, one could still conduct disputes in the language of Near Ontologese.

Moreover, there is something like an inductive reason to take ontological near realism seriously. Let’s consider our track record when it comes to discovering perfectly natural properties or relations. What actually is our success rate? We have learned that properties that we might have thought were good candidates for being perfectly natural properties or relations are not really: colors, shapes, simultaneity, among others, are not perfectly natural. We hypothesize that some of the properties currently postulated by what we regard as fundamental physics are perfectly natural properties – but I don’t think we know this. It seems like it is really hard work to discover the perfectly natural properties and relations exemplified by concrete objects. Why think that we are doing better with respect to the perfectly natural properties and relations in logic? Even though, as Husserl and Frege persuasively argued, logic is not the study of how to reason properly, logic, including quantificational logic, was developed to be a tool to aid us in improving our reasoning. How lucky we are to hit on a perfectly natural quantificational feature so early on!Footnote ⁶⁵

2.4 Amie Thomasson and Easy Ontology

Consider two arguments, unimaginably labeled “A1” and “A2.”

So, the number of shoes in the room is the same as the number of feet in the room.

So, there are numbers.

Here are some initial comments about these arguments. A1 is not formally valid, although it seems that the conclusion in some sense follows from its premise. Determining in what sense though is the primary task of this section. There are many contexts in which the premise of this argument would be taken as obviously true, but in each of these contexts, the truth expressed would be an empirical rather than a priori truth. A2, on the other hand, is formally valid. And there are many contexts in which its premise would be taken as obviously true, though in this case, the truth is a priori. However, some philosophers are notoriously skeptical about whether there are numbers. They seem to think it is not obvious whether the conclusions of these arguments are true. What’s going on?

Let’s focus for now on A1, and let’s imagine some philosophers who think that, although it is a hard question whether there are numbers, there are in fact numbers. What is the sense in which the conclusion of A1 follows from its premise? Plausibly, on their view, the sense is this: It is an argument with a suppressed premise that when made explicit yields a formally valid argument. That suppressed premise is this: Some things and some other things can be put in a one-to-one correspondence if and only if the number of the first things is identical with the number of the second things.

What is the epistemic status of this biconditional? Here we find division in their ranks. Some of these philosophers think that this biconditional is known by way of a special faculty of rational insight that can peer into the realm of abstract objects. This view does sound a bit akin to mysticism, especially since it is difficult to see what physical correlates to the faculty could realize it – unlike our various empirical perceptual faculties, for which there are well-developed scientific theories of how they work. Accordingly, these philosophers might be somewhat confident of the deliverances of this alleged faculty, but worries about whether this faculty actually exists prevent them from being too confident.

A second group of philosophers think that this biconditional is supported by its inclusion in a well-supported theory, such as the theory that there are numbers. What makes this theory well-supported is that it explains that data it is meant to explain in a fruitful, simple, and coherent way.Footnote ⁶⁶ Do fruitfulness, simplicity, and coherence track truth? Not obviously invariably, especially when these theoretical virtues are appealed to metaphysical rather than empirical contexts. Are these philosophers making a leap of faith that they are? Or does the fact that theories that have these virtues are easier for us to formulate, believe, and apply itself provide a pragmatic reason to believe them?Footnote ⁶⁷ These are hard questions. Whatever their answers might be, the difficulty of these questions suggests that the biconditional that is the implicit premise of A1 should be endorsed only tentatively.

All these philosophers agree that the question of whether this biconditional is true is a hard question. However, if it is a hard question whether this biconditional is true, it is also a hard question whether the conclusion of A2 is true.Footnote ⁶⁸ And since A2 is a formally valid argument, this means that it is also a hard question whether the premise of A2 is true. But it seemed that there were plenty of contexts in which this premise is obviously true! How can a question be hard if there are contexts in which it is easily answered?

Maybe this question should lead us to rethink something. Amie Thomasson (Reference Thomasson2015) has argued that what we should rethink is the claim that it is a hard question whether the biconditional implicitly in play in A1 is true. On the contrary, this is an easy question: It is obviously true, because it is an obvious conceptual truth. Consider a second example illustrating this idea. It’s obvious, to me anyways, that I have as many toes as I have fingers. And it is an obvious conceptual truth that I have as many toes as I have fingers if and only if the number of my toes is the same as the number of my fingers. (This conceptual truth is an instance of the more general conceptual truth mentioned earlier.) It follows from these two claims via an obviously valid inference that the number of my toes is the same as the number of my fingers. And it follows from this via an obviously valid argument that there are numbers. How then could the question of whether there are numbers be a hard question for me to answer? How obtuse would I have to be to not know the answer given all of this?

Maybe the question that I am trying to ask – the question that I think is a hard question – isn’t really the question of whether there are numbers. Maybe it is the question of whether numbers are real; or maybe it’s the question of whether a metaphysically fundamental quantifier would quantify over numbers.Footnote ⁶⁹ But, as we will discuss later in this section, Thomasson thinks that these questions are pseudo-questions: There is no additional question of this sort to even ask, so there is no hard question in the neighborhood of the easily answered question.

Let’s consider another ontological debate that, according to Thomasson, is easily settled: the debate over whether there are ordinary objects such as chairs and tables. As Thomasson notes (Reference Thomasson2007: 155–170; Reference Thomasson2015: 129–130), compositional nihilists try to “save the appearances” by describing the conditions under which assertions that an ordinary object exists is well-founded even if strictly false; for example, the claim expressed by “a table exists” is well-founded if and only if there are some impartite entities arranged in a table-like configuration.Footnote ⁷⁰ But, according to Thomasson, it is a trivial conceptual truth that whenever there are some impartite entities arranged in a table-like configuration, there is a table. And so the well-foundedness conditions for assertations about tables presented by the nihilist are really truth conditions for assertions about tables. On her view, nihilism is accordingly trivially (and obviously) false.

Let’s pause for a moment. What does “some impartite entities are arranged in a table-like configuration” mean? And can this meaning be explained without assuming that there are tables? For example, “some impartite entities are arranged in a table-like configuration if and only if their collective shape is the shape of a paradigmatic table” presupposes that there are paradigmatic tables. Eliminativism is in serious trouble if the only accounts of the well-foundedness of ordinary table judgments presuppose the existence of tables! But in a similar way, it will be harder to show that it is trivially true that nihilism is false if the conceptual truths appealed to explicitly presuppose the existence of composite objects. Consider two different claims.

If the only way to secure the conceptual truth of C1 is to unpack “table-like configuration” so that to be in a table-like configuration means, among other things, that composition has occurred, then the fact that C1 so understood is a conceptual truth doesn’t show that it is trivial or obvious that nihilism is false. Similarly, if C2 is a conceptual truth, but C1 is not, we do not have an easy argument against nihilism, since it is compatible with nihilism that C2 is a conceptual truth. So, it seems that both eliminativism and Thomasson’s view require definitions of expression like “table-like configuration” that do not explicitly assume that there are tables, or even that there are composite objects. Eliminativism is arguably refuted if such definitions are impossible; Thomasson’s view would not be refuted, but would be unmotivated, at least as it applies to the debate over nihilism.

In general, for any kind of thing, Ks, such that it is a putatively easy question whether there are Ks, two conditions must be met. First, there must be a noncircular way to state claims of the form: if there is a K-favorable circumstance, then there is a K.Footnote ⁷¹ Second, it must be obvious that there are K-favorable circumstances. (If it is an empirical claim that there are K-favorable circumstances, then it is an obviously true empirical claim.) Much attention has been focused on whether the first condition can be met; you got a taste of this debate in the previous paragraphs.Footnote ⁷² But note that, although the most ambitious version of Thomasson’s position is one which all ontological debates are easily settled, this is not a version that Thomasson herself is committed to. Moreover, even if it turns out that there is no general way to show that all ontological questions are easily settled, a piecemeal version of Thomasson’s view on which this ontological question (e.g., are there numbers?) is easily settled, and that ontological question (e.g., are there composite objects?) is easily settled, and this one, and so on, is still an interesting view that would challenge many metaontological approaches to these specific questions.

This is good to keep in mind, because there do seem to be some hard ontological questions even given the conceptual truth of a relevant conditional claim – they are hard because it is not obvious whether the antecedent is satisfied. For example, consider the hard ontological question about whether there is a God. Consider now two claims that are plausibly conceptual truths.

G1 is perhaps more clearly a conceptual truth than G2, though one might worry that there is no way to explicitly unpack what it is to be holy without including the consequent of G1 is in the definition. But suppose that there is – still, it is not at all obvious that anything is holy! It doesn’t seem that the question of whether something is holy is much easier to answer than the question of whether there is a God. Attend now to G2. I think that no explicit definition of the antecedent will spit out the consequent. But G2 might be a conceptual truth nonetheless, though the argument for why it has this status is a little indirect: It is part of the conception of God that God is all-loving, and so if there is a God, then, necessarily, God loves everyone. But it also seems that the only way in which the antecedent of G2 could be true is if there is a God; on no other metaphysics does this seem guaranteed.Footnote ⁷³ However, it is also not at all obvious that the antecedent of G2 is true, and it seems that the reason to think that G2 is a conceptual truth is also a reason to think we have no more evidence for the antecedent than we do for the consequent.

Consider next the following:

T strikes me as just as much of a conceptual truth as Thomasson’s examples. (This claim is consistent with none of them being conceptual truths.) So, is the question of whether there are times easy? Surprisingly not – but that’s because although it might have seemed obvious that there are things that are simultaneous, whether this is the case is a thorny question in both physics and the philosophy thereof. Given standard interpretations of the special and general theories of relativity, there is no such relation as the relation of simultaneity. A Thomassonian ontologist of the nineteenth century might have thought that the question of whether there are times is trivially settled, but she would have been mistaken. We thought there were simultaneous happenings, but we learned otherwise. No two things are ever simultaneous full stops; at best, they stand in a three-place relation of relative simultaneity, assuming that such reference frames are even well defined. (They might not be.)

Can’t this sort of thing happen elsewhere? What if we just have the wrong theory of the world? For example, our conception of an event seems to be a conception of a happening in time. So, this seems like a conceptual truth: Something is an event only if it occurs in time. But if there are no times, then it follows that there are no events either.Footnote ⁷⁴

Let’s consider the following:

I’m inclined to think that S is true, and considerations from relativity do not render its antecedent vacuous. But I see no case for thinking that S is a conceptual truth! Rather, it is a substantive claim that is the core of what is at issue between relationalists and substantivalists about spatiotemporal connections. Moreover, whether S is true won’t be settled by appeal to physics alone – metaphysical considerations such as appeals to explanatory power, simplicity, and other theoretical virtues will play an important role as well.Footnote ⁷⁵ Whether S is true is a hard ontological question.

How damaging is the hardness of the question of whether S is true to the thesis that ontology is easy? Whether S is true will not be settled purely by a priori speculation – physics will play a large role here. But the extent to which considerations of physics, or of empirical science more generally, are relevant to answering ontological questions corresponds to a difference in degree rather than kind. Consider the special composition question. I don’t think it’s obvious that empirical scientific considerations are wholly irrelevant to answering this question, and here are two different strands of reasoning that suggest their relevance. First, it is initially plausible that composition occurs when some the putative parts stand in some sort of bonding relation. But physics, chemistry, and other empirical sciences can offer better accounts of what sort of bonding relations there are than would be given by an analysis of our inchoate concepts of bonding. Second, it is prima facie plausible that if there are natural (as opposed to non-gerrymandered/gruesome) properties at different levels of nature (e.g., the chemical level, the biological level, etc.), then there must be composite objects that “occupy” those different levels and that instantiate those natural properties. Empirical scientific considerations are relevant to assessing whether there are natural properties at these different levels. Given that empirical scientific considerations are relevant, but not by themselves decisive, to the positive case for composite objects, they might also be relevant to the negative case as well.

We’ve discussed whether the ontology of numbers is easy.Footnote ⁷⁶ Is the ontology of other mathematical domains as easy? Let’s consider the question of whether there are sets. If the ontology of sets is easy, then there is a conditional that is conceptually true, whose antecedent is obvious, and whose consequence is a claim about the existence of some set or sets. What is this conditional? This might have seemed like a conceptual truth at the turn of the twentieth century: Whenever there are some entities and some predicates, there is a set of all and only those entities that satisfy the predicate. But this alleged conceptual truth generates the paradoxical set of all nonself-membered entities, as Russell (Reference Russell and van Heijenoort1967) pointed out.Footnote ⁷⁷ What about this: Whenever there are things that do not have members, there is a set that contains all and only those things? This is a plausible claim but is it a conceptual truth? This claim implies that there can’t be more individuals than any set could contain, which is also plausible, but it’s not clearly a conceptual truth. Perhaps the axioms of set theory are collectively conceptual truths – but which version of set theory? There are many, apparently competing, set theories. If the axioms of one, and not more than one, of these theories are true, which of these are true seems to be a substantive question about sets rather than a trivial question answerable by attending to our concept of a set.

However, maybe the assumption that these different set theories are in competition is not true. Consider the idea that the criterion for existence in mathematics is logical consistency.Footnote ⁷⁸ This idea fits nicely with the idea that mathematical ontology is easy. So, consider a principle that explicitly weds them.

Perhaps Conex is a conceptual truth. If Conex is a conceptual truth, then perhaps each of these apparently competing set theories are also conceptual truths, but are not in competition because the same concept of set is not used by each of these theories.Footnote ⁷⁹ Let’s explore this furthermore.

Suppose that Conex is a conceptual truth. Consider a particular set theory, say ZFC set theory. It might not be a straightforward question whether ZFC is logically consistent, but the question of whether a given theory is logically consistent is always a conceptual question regardless of whether the theory is a theory of set theory or physics or …. So, if ZFC is logically consistent, it is a conceptual truth that ZFC is logically consistent. I assume that, in general, when it is a conceptual truth that if P, then Q, and it is a conceptual truth that P, then it is a conceptual truth that Q. So, given that it is a conceptual truth that ZFC is logically consistent, and that Conex is a conceptual truth, it is also a conceptual truth that there are entities that obey the axioms of ZFC.

Consider next a set theory S that seemingly competes with ZFC, but which is also logically consistent. There is an equally good argument for the conclusion that it is a conceptual truth that there are entities that obey the axioms of S. Might the entities that obey the axioms of ZFC be the same as those that obey S? To answer this question, we need to say a bit more about what it would be for two different set theories to compete. First, the two theories must be about the same relation, which in this case would be the putatively unique relation denoted by the predicate “is a member of.” Second, there must be entities such that the two theories imply logically inconsistent claims about how those entities are related by that relation. (There might be an overlap among these entities, but it is sufficient for one plurality of things to be collectively nonidentical with another plurality when something is among one of the pluralities but not among the other.) On the set theoretic pluralism we are considering (on behalf of the proponent of easy ontology), one of these two claims must be false.

2.5 Restating the Hard Ontological Question?

Ontological realism – the claim that there are quantificational joints in reality – was introduced partly as bulwark against Hirsch’s quantifier variantism.Footnote ⁸⁰ The idea was that even if it turned out that the ontological questions asked in ordinary language are trivially answered, there is still an interesting and nontrivially answerable ontological question that can be asked in Ontologese, which is (allegedly) a possible language in which all expressions correspond to metaphysical joints, including quantificational expressions.Footnote ⁸¹ In response to Thomasson’s easy ontological approach, Sider (Reference Sider2011: 195–197) makes two claims: first, Thomasson’s project of easy ontology is possibly threatened if ontological realism is true, and second, it is a substantive question whether ontological realism is true, rather than easy an question in Thomasson’s sense.

Here is a summary of Sider’s rationale for the first claim. A conceptual truth is a truth that is both definitional and true. Whether an interpretation of a language is charitable is a function of whether that interpretation maximizes the truth value of sentences in that language that speakers of it are disposed to sincerely assert in appropriate conditions; but some sentences are such that it is more important to determining how charitable an interpretation is: A sentence is definitional when interpreting it as false makes an interpretation far less charitable than making other sentences false. However, the extent to which an interpretation is charitable is not the only factor that determines whether the interpretation is true: It also matters how natural the entities referred to by expressions give that interpretation. These scales can pull in different directions, and so it is in principle possible that the correct interpretation of a language is one which some definitional claims are nonetheless false. Sider suggests that conditionals like “If there are as many shoes are as there are feet, then the number of shoes is the same as the number of feet” are definitional. But in order for them to also be conceptually true, there can’t be a quantificational joint such that (1) there is an interpretation of “there are” that assigns to “there are” that quantification joint, and on that interpretation, this conditional expresses something false, and (2) the naturalness of that interpretation is strong enough to trump charity, and so even though these conditionals (and others like it) are definitional, the correct interpretation of them is one in which they are false. If there is such a quantificational joint, then these conditionals are false despite their status as definitional; let us call a quantificational joint that meets these two conditions a “doom joint.” Ontology is easy only if there is no doom joint.

It’s tempting to think that these three claims stand or fall together: the claim that ontology is easy, the claim that it is not a hard question whether there is a doom joint, and the claim that there is no hard analogue in Ontologese of an easy ontological question. Ontology is easy if and only if ontological questions can be settled wholly by empirical enquiry and conceptual analysis; if ontology is easy, then there is no doom joint. So, if ontological questions can be settled wholly by empirical inquiry and conceptual analysis, then there is no doom joint. But what is the status of that conditional? It seems to be a conceptual truth. And what is the status of the antecedent? If it is true, it also seems to be a conceptual truth that it is true. So, if we assume that ontology is easy, it seems that it follows that it is a conceptual truth that there is no doom joint. Is it a conceptual truth that there is no doom joint? If there is a quantificational joint, it’s hard to see how it could be a conceptual truth that there is no doom joint. However, it is a conceptual truth that if there are no quantificational joints at all, then there is no doom joint. So, if it is a conceptual truth that there are no quantificational joints at all, it is also a conceptual truth that there is no doom joint.

It seems then that the best way to defend the project of easy ontology is to argue against the possibility of quantificational joints on conceptual grounds rather via some more abstruse metaphysical rationalization. Unsurprisingly, then, this is what Thomasson (Reference Thomasson2015: 300–317) does. She argues that there are a variety of functions expressions can have, and that there isn’t a good reason to think that the semantic function of a quantifier is to carve the world at a quantificational joint. Instead, she suggests that quantificational expressions are formal expressions, where part of what it is to be a formal expression is that the question of whether that expression carves at the joints does not arise. In this respect, formal expressions would be akin to punctuations such as parentheses; it doesn’t even make sense to ask whether “{” and “}” carve closer to the joints than “[” and “].” Perhaps “syncategorematic” would have been a better word choice than “formal” here, since the former expression was primarily used to refer to a class of expressions that do not correspond to entities, unlike, for example, names and predicates, whereas the latter expression has been used in a multiplicity of ways.

That said, it is not clear to me whether Thomasson thinks that words like “something” are syncategorematic. And there is a good reason to think that they are not. The standard semantics for quantifiers is one in which they are assigned semantic values, specifically, higher-order properties or relations.Footnote ⁸² Just as the easy ontologist refrains from criticizing the ontological commitments of mathematics on philosophical grounds external to mathematical practice, she should refrain from criticizing the ontological commitments of semantics on philosophical grounds external to linguistic practice.Footnote ⁸³ Given this, the assumption that the quantifiers correspond to higher-order properties or relations is dialectally safe. But it is properties and relations that, in general, appear on the naturalness scale. Given that “something” corresponds to a property or relation, how can it not be an initially open question – one that is not settled by our concepts – where on this scale it is? Given that “something” corresponds to a property or relation, how can it not be an initially open question whether there are other property or relations that are possible semantic values for expressions that a function like “something” does in other languages? And how can it not be an initially open question whether one of these possible semantic values is either a perfectly natural property or relation, or at least more natural than any of the relevant alternatives to it?

Thomasson claims that it is not part of the semantic function of a quantifier that it carves nature at its joints. This might be true. But even if it is not part of its semantic function to do this, it might nonetheless do it! It is not part of the function of a hammer that it makes a good paper weight, and yet a given hammer can make a good paper weight. I doubt that it is part of the semantic function of a predicate qua predicate that it carves nature at the joints, yet many of them nonetheless do. And those that do not carve nature at the joints are not defective in the sense that they fail to fulfill their semantic function. Predicates have many semantic functions. One of them is to complement a noun phrase in order to produce a complete declarative sentence that is capable of being true or false. A predicate that failed to do this might be defective qua predicate, just as a name that fails to refer to anything might be defective qua name. But predicates like “blue,” “grue,” “in New Jersey,” and so on are not defective qua predicates even though what they correspond to are not very natural properties. It seems then that some predicates carve nature at the joints better than others, presumably by virtue of denoting properties that are more natural than others, even though it is not part of the general semantic function of predicates to carve at the joints. Why isn’t the same then true of quantifiers?

2.6 Further Potentially Hard Questions

Suppose Thomasson is correct, and that many ontological questions are easy. Does any hard metaphysical question in the ballpark of the easy ontological question remain? For example, suppose that both the ontology of numbers and of physical objects is easy. Still, mightn’t we wonder if numbers are grounded in physical objects, or vice versa? And isn’t that question a hard question?

Consider the following biconditional: Something is perforated if and only if there is a hole in it. This biconditional is as obviously true as the other biconditionals of this sort that we have discussed; if these others are conceptual truths, this one is as well. Conversely, if the others are not conceptual truths, neither is this one. Instead, what is a conceptual truth is this conditional: If there are holes, then something is perforated if and only if there is a hole in it.Footnote ⁸⁴ Accordingly, the question of whether there are holes is as easily affirmatively answered as the question of whether there are numbers or composite objects. Suppose then that there are holes. But holes and the physical things that host them – for example, bagels and donuts – are not metaphysically on a par, even if there is an easy argument for both.Footnote ⁸⁵ The presence of a hole is explained by the existence of a perforated object; the direction of explanation in this biconditional is clear.

Others, however, are not. Many philosophers think that wholes are grounded in their parts. But consider this: Human beings are bilaterally symmetric. Something is bilaterally symmetric if and only if it has a left side and a right side. This biconditional also feels like as much of a conceptual truth as any of the others. So, human beings have left and right sides. A similar argument suggests that human beings have top and bottom halves as well. Left sides and bottom halves are parts. Now, I can see the case for the claim that the particles that make me up are metaphysically prior to myself. It’s less clear though that my left half is metaphysically prior to me; these kinds of parts are sometimes called “arbitrary undetached parts,” and I think part of why this label is apt is that these parts are not as fundamental as the wholes they are parts of. Either way, though, I think there are no obvious or easy metaphysical truths about grounding: Whether my left half is prior to or posterior to (or equal in priority with) me requires serious and systematic thinking.

Is the project of easy ontology threatened by the existence of hard metaphysical questions about grounding?Footnote ⁸⁶ If the epistemology and methodology of questions about grounding must be the same as the epistemology and methodology of questions about ontology, then questions about grounding would be “easy” if and only if questions about ontology were. And if the former questions were hard, the latter would be as well. But we don’t know that the epistemology and methodology of these questions must be the same. So, although it would be interesting to learn that there are still hard metaphysical questions even given the easiness of ontology, the former fact would not clearly be threatening to the latter.Footnote ⁸⁷

There are similar questions about ontological categories. For example, Flocke and Ritchie (Reference Flocke and Ritchie2022) persuasively argue that even if there are easy arguments for the existence of a certain kind of entity, there can still be a hard metaphysical question about what the nature and structure of things of that kind, including the question of what ontological category they belong, are. For example, they note that Thomasson offers an easy ontological argument for events. But there are different theories about events. On one theory, events are individuated by the causal relations they stand in. On another theory, events are structured entities that consist of objects, properties or relations, and times. It seems that both theories can’t be true. So, it seems that there is a hard metaphysical question about the nature and structure of events.

Perhaps though, if ontology is easy, these theories about events are not actually in competition. Perhaps there are entities that are individuated by their causal relations, and there are other entities that correspond to structures of objects, properties or relations, and times. (Though recall the earlier discussion about whether there are times.) Neither the former nor the latter are definitively the events. Instead, our conception of what events are is compatible with either being events. Rather than a hard metaphysical question about what events really are, we face soft questions about which richer conception of events is most useful to employ for a given purpose. In other words, the question is not what events are, but which conception of events we ought to use.Footnote ⁸⁸ For example, perhaps the conception of events as individuated causally is more useful in the context of scientific explanation, while the conception of events as consisting of objects, properties or relations, and times is more useful in the context of assigning values to consequences or blameworthiness to agents. Given easy ontology, pluralism about events seems as plausible as pluralism about sets.

Maybe there are many ways to be a set. Maybe there are many ways to be an event. Are there also many ways to be period? That’s the topic of the next section!

2.7 Ontological Pluralism

Ontological pluralism is the view that there is more than one way to be. The rough slogan that all versions of ontological pluralism assert is that in addition to different kinds of beings, there are also different modes of being. Different versions of ontological pluralism spell out this slogan more in different yet (hopefully) more precise ways.Footnote ⁸⁹ Here I focus on a version of ontological pluralism that is also reasonably called “quantifier pluralism.”Footnote ⁹⁰ On this version of ontological pluralism, modes of being correspond to possible meanings for existential quantifiers. But we have a choice point here: Perhaps any possible meaning for an existential quantifier is a mode of being, or perhaps only those possible meanings that are sufficiently metaphysically natural (in the sense of “natural” invoked by Lewis and Sider) are modes of being.Footnote ⁹¹ In McDaniel (2017: 37), I opted for the latter, and here I will presuppose a version of ontological pluralism that is true if and only if there is more than one relatively fundamental meaning for an existential quantifier, where an existential quantifier meaning is relatively fundamental if and only if no other quantifier meaning is more fundamental than it. For the sake of brevity, in what follows I will use “ontological pluralism” to designate this version of ontological pluralism unless context demands that I note that it is one version of ontological pluralism out of many.

By my lights, there is no case for ontological pluralism that is independent of considerations in first-order metaphysics and ontology. Accordingly, I will not focus on the reasons for accepting or rejecting ontological pluralism here.Footnote ⁹² Instead, I will focus on how ontological pluralism interacts with the other metaontological theses discussed here. Ontological pluralism occupies an interesting position in the dialectical space in which the views discussed earlier have been placed. Thomasson’s easy ontology is a form of ontological monism incompatible ontological pluralism; her rejection of quantificational joints rules out ontological pluralism just as much as ontological realism. Sider’s ontological realism is also incompatible with ontological pluralism – though Sider permits that there might be many possible meanings for the existential quantifier, only one of them is relatively fundamental. (And by Sider’s lights, that relatively fundamental meaning is itself perfectly natural.)

This leaves Hirsch’s ontological deflationism. In McDaniel (2017: 37), I claimed that on this understanding of ontological pluralism, Hirsch’s ontological deflationalism is a version of ontological pluralism. The reasoning was straightforward, though perhaps simplistic as well. Ontological deflationalism implies that there is more than possible one meaning for the existential quantifier, and at least two of these meanings are such that they are metaphysically on a par and at least as natural as any other possible meanings for the existential quantifier. But so understood then ontological deflationalism implies there is more than one relatively fundamental quantifier meaning – and hence implies ontological pluralism.

I anticipated that some would find this upshot surprising, since ontological deflationalism is supposed to be a deflationary view – it’s in the name after all – while ontological pluralism seems to be a paradigmatically inflationary view. For what it is worth, in personal conversation, it seems that few have been convinced. A recent paper by Arturo Javier-Castellanos (Reference Javier-Castellanos2019) offers a general diagnosis of where things (allegedly) have gone wrong. Let’s examine this diagnosis.

The ontological realist, ontological deflationalist, and ontological pluralist are each happy to talk of an ideal language for doing metaphysics. Javier-Castellanos (Reference Javier-Castellanos2019: 278) says that “a language is metaphysically better … than another to the extent that it allows for a more metaphysically perspicuous description of reality … [and] a language is ideal … if there is no better language”; he also notes that a similar characterization can be given for expressions: Some expressions carve nature at the joints more than others, and a fundamental expression is one for which no expression is more natural than it. Javier-Castellanos (Reference Javier-Castellanos2019: 278–279) claims that I (along with Sider (Reference Sider2011: 8) and Turner (Reference Turner2010: 421)) claim that a language is ideal if and only if every primitive expression in that language is a fundamental expression; Javier-Castellanos calls this “the simple analysis,” and argues that ontological deflationalism is a version of ontological pluralism only if the simple analysis is true.

Javier-Castellanos (Reference Javier-Castellanos2019: 283) asks us to consider three languages that differ only in their primitive quantifiers: a nihilist language, a universalist language, and a common sense language. Let us assume that what the quantifier variantist will grant each of these is an ideal language. There is also a language – a pluralist language – that contains all three quantifiers. Given the simple analysis, this pluralist language is also ideal. Accordingly, if this version of quantifier variantism is true, a corresponding version of ontological pluralism is also true. Javier-Castellanos notes that one can’t simply revise the simple analysis to say that a language is ideal if and only if an expression is a primitive expression of that language if and only if it is perfectly natural – since doing so yields that none of the nihilist, universalist, or common sense languages are ideal, contrary to this version of quantifier variantism.

Javier-Castellanos (Reference Javier-Castellanos2019: section IV) suggests that we need to rethink the relation between the idealness of a language and the naturalness of its primitive expressions. The simple analysis is an atomistic account of ideality, one that explains it in terms of the naturalness of its (discrete) primitive expressions. Javier-Castellanos suggests instead that the ideality of a language is explanatorily primary; an expression is perfectly natural if and only if it is a primitive of some ideal language or other (p. 285).

Given this holistic account of perfect naturalness, Javier-Castellanos (Reference Javier-Castellanos2019: 286) proposes new accounts of ontological pluralism and quantifier variantism. Here’s the basic idea, although I’ll modify a few of the small details. A quantified language is a language that contains at least one primitive existential quantifier expression. Ontological pluralism is the view that every ideal language is a quantified language that has multiple primitive existential quantifiers in it. To return to the toy example used two paragraphs ago, our quantifier variantist denies this claim: The nihilist language, for example, is an ideal language even though it contains only one existential quantifier expression. So, on this clever reconceptualization of these views, quantifier variantism does not imply ontological pluralism, and some versions of quantifier variantism are inconsistent with ontological pluralism. Javier-Castellanos (Reference Javier-Castellanos2019: 288) notes that some versions of quantifier variantism are also versions of ontological pluralism, but this is a weaker claim than the claim that all versions of quantifier variantism are versions of ontological pluralism.

Before considering criticisms of this proposal, let’s see how, given this holistic account, other interesting metaontological views could be reformulated. There seems to be a straightforward way to formulate ontological realism: Ontological realism is the view that every ideal language is a quantified language, and every ideal quantified language contains the same existential quantifier expression. Since the “easy ontology” metaontological view is supposed to be inconsistent with ontological realism, perhaps this metaontological view should be formulated so as to imply that not every ideal language is a quantified language; if there are no quantificational joints in reality, then the absence of an existential quantifier should not automatically make the language less than ideal. Finally, ontological nihilism could be formulated as the position that no quantified language is an ideal language.Footnote ⁹³

I don’t have strong feelings about this, but I do wonder about whether the formulation of ontological pluralism is apt. Let’s consider two alternative formulations: one weaker than Javier-Castellanos’s, and one stronger. The weaker one first: Instead of formulating ontological pluralism as the view that every ideal language is a quantified language that has multiple primitive existential quantifiers in it, formulate it as the weaker view that some ideal language is a quantified language that has multiple primitive existential quantifiers in it. On this weaker formulation, quantifier variantism might still imply ontological pluralism, provided that whenever there are some ideal languages that contain distinct existential quantifier expressions, there is also an ideal language that contains at least two of those distinct existential quantifier expressions. I do not know whether this proviso is true, however.Footnote ⁹⁴

Now let’s consider a stronger formulation of ontological pluralism: Every ideal language is a quantified language that has multiple primitive existential quantifiers in it, and it is the same primitive existential quantifiers in each ideal language. This stronger formulation of ontological pluralism is inconsistent with Javier-Castellanos’s formulation of quantifier variantism, and plays up the “inflationary” metaphysical aspect of the view. In fact, this formulation of ontological pluralism runs parallel to the formulation of ontological realism I offered in a pleasing way: Both ontological pluralism and ontological realism agree that every ideal language is a quantified language and that the quantifier expressions in each ideal language are the same, but they disagree about the number of existential quantifier expressions in them. This is a neat result.

As I said, I don’t have strong feelings about any of this, largely because I regard the task of properly classifying a view as belonging to a larger family of views to be not unimportant but certainly secondary to the task of figuring out which view is true. If there are relatively natural classes of views, then how to classify a view might be a substantive question; I’m not sure that there is, however.Footnote ⁹⁵ That said, it can be a substantive and important question whether the presuppositions of a classificatory system are correct – and so let’s turn to the question about whether holism about ideal languages is true.

Let me state at the outset that if the sole reason for preferring holism over atomism is that we can better classify metaontological views given holism than atomism, then we have at best a very weak reason for accepting holism. It would be better if, for example, holism solved a genuine puzzle. Javier-Castellanos argues that it does (Reference Javier-Castellanos2019: 291–292) – it provides a solution to the problem of redundant natural expressions not available to the atomist. Recall the puzzle: We have many collections of expressions where it seems that at least one member of the collection is highly natural – perhaps perfectly natural – but where it also seems like there is massive metaphysical redundancy if each of them enjoys the same degree of naturalness. Some examples are the existential and the universal quantifier; the various mereological expressions such as parthood, proper parthood, overlap, and so on; after than and before than; the truth functional connectives; and so on. Let’s focus on the latter, since that is what Javier-Castellanos focuses on. But as he notes, there is a schema for a variety of views that he could be developed.

So, consider two pairs of connectives: the first of which consists of disjunction and negation, and the second of which consists of conjunction and negation. Each pair is sufficient to define all of the other truth-functional connectives, so the triplet consisting of disjunction, negation, and conjunction contains a redundant connective. Should we thereby say that none of these is a natural expression? Javier-Castellanos (Reference Javier-Castellanos2019: 291–292) suggests that we allow that each of them is a natural expression, but soothe our intuitions against redundancy in the following way: There is an ideal language that contains the first pair, a different ideal language that contains the second pair, but no ideal language that contains the triplet. If there were a third ideal language of that sort, then there would be genuine metaphysical redundancy.

What can be said against holism? It seems that given holism, there is no deep explanation of why certain languages are not ideal – languages whose lack of ideality seems best explained by the omission of certain expressions. Suppose that among the fundamental expressions are normative expressions.Footnote ⁹⁶ Suppose that the remaining fundamental expressions are logical (including quantificational) expressions and those that come from physics. A language that contained only the latter would be incomplete even though it would be sufficient to characterize physical reality fully. And the reason why such a language would not be ideal would be that it was incomplete – it is missing other perfectly natural expressions. Holism is ill-equipped to make sense of that idea, since holism implies that betterness of language is prior to naturalness of expressions. Relatedly, there are other ways in which languages can fail to be ideal: In addition to missing natural expressions, they can contain primitive yet nonnatural expressions. There is a hard question about which way of falling short is worse – but in both cases, it seems that the explanation for why a language is less than ideal is the presence or absence of expressions. This fact seems to be reflected in intuitive sorting judgments. For example, we know that any language that has “grue” as a primitive predicate is not an ideal language; its presence suffices for their nonideality.