6 — God Over All: Divine Aseity and the Challenge of Platonism

6

Making Ontological Commitments (1)

Neutralists and neo-Meinongians reject the customary view that first-order logical quantifiers are devices of ontological commitment. The view that first-order quantifiers are ontologically neutral is defended. It is shown that there are no good arguments that first-order logical quantification is ontologically committing and that an analysis of ordinary language reveals that the informal quantificational expressions which are abbreviated by formal quantifiers are in fact not ontologically committing. Moreover, it is shown that decided disadvantages ensue if we take first- order quantifiers to be devices of ontological commitment. Intentional statements, tensed statements, modal statements, and mereological statements provide examples of discourse which make it implausible to treat first-order quantifiers as devices of ontological commitment. The theist is perfectly rational to reject the criterion of ontological commitment underlying the Indispensability Argument for Platonism.

At the heart of the Indispensability Argument for Platonism about mathematical objects, propositions, possible worlds, and the like lies a criterion of ontological commitment, emanating from the late W. V. O. Quine, which comes to expression in the first premiss of that argument:

I. If a simple sentence (i.e., a sentence of the form ‘a is F’) is literally true, then the objects that its singular terms denote exist. Likewise, if an existential sentence is literally true, then there exist objects of the relevant kinds; e.g., if ‘There is an F’ is true, then there exist some Fs.

According to this criterion, singular terms and existential quantifiers are devices of ontological commitment. It is worth noting that such a criterion is not a criterion of existence, telling us what exists. Rather, the criterion is intended to disclose to us the existential commitments of our discourse. It tells us what we must believe exists if we regard certain statements as true. The criterion says, in effect, ‘You believe that such-and-such is true? Then you must also believe that the objects referred to by your singular terms and the objects that you say there are actually exist. You’re committed to the existence of such entities, so long as you maintain that what you said is true.’ If we feel uncomfortable about the ontological commitments of our discourse, we can always avoid such commitments by denying that what we said is true. But we would have to swallow hard before denying, say, that ‘2 > 1’ in order to avoid commitment to the reality of numbers.

Now I suspect that the non-philosopher would regard this neo-Quinean criterion of ontological commitment, not only as a piece of linguistic imperialism, but also as a preposterous attempt to read the nature of reality off human language. Why should we think that human language so closely mirrors reality as to allow us to

do (p.97) metaphysics by means of linguistic analysis? Is it not absurd to think that, while the truth of the statement ‘Three men entered the tavern’ involves no ontological commitment to numbers, the truth of the statement ‘The number of men who entered the tavern is three’ does?

Why Accept the Realist’s Criterion of Ontological Commitment?

I share fully the layman’s scepticism about the realist’s criterion of ontological commitment. This scepticism ought to motivate us to ask what good reason or argument there is that such a criterion is true. Amazingly, it turns out that virtually no arguments are offered by realists for the truth of their criterion. For example, Peter van Inwagen is a prominent contemporary metaphysician who champions what he calls ‘Quine’s theses on ontological commitment’.1 So what are these Quinean theses and why ought we to accept them? In a more recent piece, van

Inwagen spells out exactly what he understands by ‘Quine’s theses on ontological commitment’ and explains their role in resolving ontological disputes:

The parties to such a dispute should examine, or be willing in principle to examine, the ontological implications

of everything they want to affirm. And this examination should consist in various attempts to render the things they want to affirm into the quantifier-variable idiom (in sufficient depth that all the inferences they want to make from the things they want to affirm are logically valid). The ‘ontological implications’ of the things they affirm will be precisely the class of closed sentences starting with an existential-quantifier phrase (whose scope is the remainder of the sentence) that are logical consequences of the renderings into the quantifier-variable idiom of those things they want to affirm. Parties to the dispute who are unwilling to accept some ontological implication of a rendering of some thesis they have affirmed into the quantifier-variable idiom must find some other way of rendering that thesis

into the quantifier-variable idiom (must find a paraphrase) that they are willing to accept and which does not have the unwanted implication.2

(p.98) So the basic idea is that you must first put what you believe into the form of statements of first-order quantified logic. Then you are ontologically committed by any existentially quantified sentences which are implied by what you believe. If you want to resist those commitments, you are obligated to come up with a paraphrase of your original belief that does not have such implications.

Van Inwagen characterizes Quine’s meta-ontological theses as a set of rules or a strategy for settling ontological disputes. Now this is remarkable. Rules or strategies may be useful or effective, but they are not the sort of statements that are true or false. Van Inwagen’s characterization implies that Quine’s theses are neither true nor false, any more than are rules for the arbitration of labour disputes.

So why should we embrace Quine’s meta-ontological method for settling ontological disputes? Van Inwagen answers that it is the ‘most profitable strategy to follow to get people to make their ontological commitments clear’.3 So the suggestion is that we should adopt the method because of its profitability. Van Inwagen illustrates the

profitability of Quine’s method by appeal to its utility in the ontological dispute over holes. Do holes really exist? Or are some things just holey? In order to avoid quantifying over holes, van Inwagen says, the materialist has to put forward paraphrases of key sentences that are ‘bizarre’. ‘Certain untoward consequences of a strict nominalistic materialism thus become evident only when one adopts Quine’s strategy for clarifying ontological disputes—and it is unlikely that they would otherwise have been noticed.’4 The general lesson to be drawn from this, he says, is that

‘If Quine’s “rules” for conducting ontological disputes are not followed, then…it is almost certain that (p.99) many untoward consequences of the disputed positions will be obscured by imprecision and wishful thinking.’5

I am far from impressed with this attempt to motivate adoption of Quine’s strategy for resolving ontological disputes. Even if Quine’s strategy did yield clear answers to ontological disputes, there is no reason to think that those answers are true, since no reason has been given to think that it is true that the ontological commitments of a discourse are disclosed by the criterion in question. Moreover, ironically, the alleged untoward consequences of anti-realism mentioned by van Inwagen are themselves precisely the result of adopting Quine’s procedure! If one denies that existential quantification is ontologically committing, one will not be troubled by quantifying over holes and other dubious entities, nor will one be forced to offer bizarre paraphrases of one’s original statements. The person who rejects Quine’s meta-ontological rules will thus not be saddled with the untoward consequences that trouble van Inwagen. The exposure of such consequences thus provides no reason at all for adoption of Quine’s

procedure. Indeed, Quine’s procedure, I think, has the decided drawback that it could force us to embrace all sorts of spurious reifications like, for example, holes. In that sense, Quine’s procedure is not at all a profitable strategy to follow to get people to make their ontological commitments clear.

In any case, Quine’s meta-ontological procedure does not, in fact, succeed in making the ontological commitments of a discourse clear. Consider van Inwagen’s own example of a quantified sentence which supposedly commits the person who asserts it to the existence of properties:

(S) Spiders share some of the anatomical features of insects.

Applying Quine’s method, van Inwagen says that if we examine the meaning of this sentence, we find that what it says is this: ‘There are anatomical features that insects have and spiders also have’, or in the idiom of quantification, ‘It is true of at least one thing that it is such that it is an anatomical feature and insects have it and spiders also have it.’6 Now, if there are anatomical features that insects have and that spiders also have, then it follows that there are

anatomical (p.100) features that insects have. And if there are anatomical features that insects have, then there are anatomical features—period. An anatomical feature seems to be a property. So, van Inwagen concludes, it follows that properties exist.

But is that really what (S) says? (S) appears to be a universally quantified statement about spiders. But in contrast to existentially quantified statements, such a universally quantified statement makes, on the customary criterion of ontological commitment, no existential commitments, since logically it is a conditional of the form For any x, if x is a spider, then x has some of the anatomical features of insects.7 So (S) carries no ontological commitments.

This faux pas on van Inwagen’s part raises the very interesting and important question of exactly how to put a sentence acceptably into the idiom of quantification. Van Inwagen himself points out that there is no such thing as the unique translation of some sentence into what he calls ‘the quantifier-variable idiom’, for two reasons: (i) the quantifier-variable idiom is present in different degrees in various translations of the original sentence, and (ii) there

are alternative, creative ways of translating the original sentence into the quantifier-variable idiom.8

With respect to (i), van Inwagen gives the example of rendering the sentence ‘Every planet is at any time at some distance from every star’ into the quantifier-variable idiom of increasing complexity in four successive steps, beginning with the simple ‘For any x, if x is a planet, x is at any time at some distance from every star’ and finishing with the very complex ‘For any x (x is a planet → For any y (y is a star → For any t (t is a time → There is

some z (z is a distance & x is at t separated from y by z))))’. How much of the original sentence is put into the quantifier-variable idiom, says van Inwagen, will depend on the purposes of the person who is doing the translation.

This fact raises the question why the anti-realist should not be content to render (S) in the quantifier-variable idiom as simply ‘For any x, if x is a spider, then x shares some of the anatomical features of insects’, which is ontologically non-committing. Even if we suppose (p.101) that some individual thing a is a spider, so that we may infer

that a shares some of the anatomical features of insects, we are not committed to the existence of features by the truth of that conclusion. We might simply refrain from quantifying over features.

Van Inwagen himself confronts a similar situation with regard to quantifying over distances in the example about stars. Since he admits that he cannot give a coherent account of such an object as a distance, and the original sentence is intelligible without such objects, van Inwagen says that he is inclined to reject the final translation, which quantifies existentially over distances. So why not just stop short of quantifying over such entities in order to avoid dubious ontological commitments?

Van Inwagen’s answer, as we have seen, is that our translating into the quantifier-variable idiom must proceed ‘in sufficient depth that all the inferences we want to make from the things we want to affirm are logically valid’. So if we want to draw certain inferences but do not like the entity to be quantified over, we must come up with a paraphrase which avoids quantifying over the dubious entity. So, in the stars example, van Inwagen invents an ingenious paraphrase that avoids mentioning distances but preserves the inferences he wants to make.

Here is where the philosophical creativity alluded to in reason (ii) comes into play, for there is no one right way to paraphrase the relevant sentence. Different paraphrases will leave us with different ontological commitments, and which one we choose to adopt will depend, van Inwagen admits, on personal philosophical and even aesthetic preferences. That undermines the objectivity of one’s ontological commitments.

Quine recognized that the application of his criterion of ontological commitment to ordinary language would bring with it all sorts of fantastic and unwanted ontological commitments. So he limited its legitimate application only to an unknown, official, artificial language involving the appropriate logical paraphrases of the statements of our best scientific theories. Van Inwagen is more radical than Quine in that he sanctions the unrestricted use of Quine’s criterion even with regard to ordinary language statements in the quantifier-variable idiom and so is prepared to accept the ontological commitments which the lack of acceptable anti-realist paraphrases brings with it.9

(p.102) But then van Inwagen faces a twofold challenge: first, since he wants to avoid the most bizarre commitments of ordinary language, he needs to provide a general, universally applicable way of paraphrasing ordinary sentences which carry unwanted ontological commitments that eliminates those commitments. Second, he needs to show that anti-realist paraphrases cannot similarly be found for ordinary sentences involving commitment to abstract objects like properties. But van Inwagen admits that he can do neither. With respect to the first task, he says that he would like to be able to show that it is always possible to provide a paraphrase of sentences about various unwanted objects, but ‘to do that, I think, it would be necessary to discover a general, universally applicable

way of paraphrasing ordinary sentences of the kind we are interested in’, which he admits he cannot do.10 With

respect to the second task, he says, ‘I cannot hope to provide an adequate defense of this position, for an adequate

defense of this position would have to take the form of an examination of all possible candidates for nominalistically acceptable paraphrases of such sentences, and I cannot hope to do that.… My statement “We can’t get away with [nominalism]” must be regarded as a promissory note.’11 But a mere promissory note is plainly inadequate as a defeater of anti-realism.

In light of its lack of objectivity, we might justifiably look at the whole Quinean procedure with a marked scepticism. We still seem to be left with a good deal of ‘imprecision and wishful thinking’ about (p.103)ontological disputes. Seeing the dubious entities, like distances, to which the procedure is leading, one might simply decline to make the relevant inferences from the things that one wants to affirm, since so doing would involve dubious reification. Or one might question why ontological commitment should hang so crucially on the availability of a paraphrase, especially given the lack of objectivity of the commitments of the paraphrases and the dubiousness of

some of those commitments.12 Indeed, the relativity of one’s ontological commitments, on van Inwagen’s view,

seems subversive of his meta-ontological method. For if ontological commitment means that one is committed to those entities which must exist if the sentences of a certain class are to be true, then it follows that we have no ontological commitments, since, given the creativity of paraphrase, none of the postulated entities must exist.

Even more fundamentally, however, one might simply reject the view that existential quantifiers and singular terms are devices of ontological commitment. That is not to say that we have no means in English of indicating our ontological commitments. Rather, it is to say that the use of existential quantification and singular terms in sentences we take to be literally true does not inevitably commit us to the existence of the things we refer to or say there are.

So let us look more closely at each of the devices taken by proponents of the Indispensability Argument to be ontologically committing.

Existential Quantification and Ontological Commitment

Consider first the allegedly ontologically committing nature of existential quantification. Quine claimed that his criterion was ‘scarcely contestable’ because the formal logical quantifier (∃x) is explained by the words ‘there is an object x such that’.13 Notwithstanding, many (p.104) anti-realists dispute the claim that the existential (or particular) quantifier is ontologically committing to whatever x stands for. Prominent among these are neo-Meinongians and neutralists (Figure 1).

Neo-Meinongianism and Neutralism

Richard Routley (who later changed his name to Sylvan) was a maverick Australian philosopher who helped to revive the views of the late nineteenth-century Austrian philosopher Alexius Meinong. Meinong became famous— or perhaps ‘infamous’ would be the better word—for his theory of objects, according to which there are not only existing objects, but also non-existent objects. Meinong’s most radical contention was that non-existent objects, like existing objects, have properties. Pegasus, for example, has the property of being a winged horse, and the round

square has the properties of being round and of being square. Meinong’s most famous statement was his aphorism: ‘There are objects of which it is true that there are no such objects.’14 Now, obviously, if Meinong took the existential quantifier to be a device of ontological commitment, his statement would be flatly self-contradictory, as

many unsympathetic interpreters have taken it to be. But Meinong took the existential quantifier to be ontologically neutral in its commitments. Given an ontologically neutral interpretation of the existential quantifier, it is unobjectionable to assert that there are things that do not exist. In this neutral sense, it seems obvious that there are things that do not exist—unicorns, centaurs, Zeus, for example—and the Quinean claim that everything exists seems, by contrast, bizarre.

Routley is willing to affirm that traditional quantificational logic is, as he puts it, ‘existentially loaded’.15 So, in order to signal the difference in his interpretation of the quantifier, Routley proposed calling (p.105) the neutral quantifier the particular quantifier, symbolized as ‘P’, to be read ‘for some…’, in contrast to the existentially loaded existential quantifier ∃. So the statement ‘Some things do not exist’ would be symbolized (Px) (¬Ex), where ‘E’

stands for the predicate ‘exists’.

Tufts University philosopher Jody Azzouni, though no neo-Meinongian, agrees with Routley’s ontologically neutral logic and is the most prolific proponent of neutralism today.16 The main difference is that, whereas Routley substitutes the neutral particular quantifier for the existentially loaded existential quantifier, Azzouni denies that the existential quantifier is existentially loaded and so sees no need of a substitute. Azzouni thinks that the reason Quine just took it as obvious that the existential quantifier is ontologically committing is because Quine thought that the ordinary language idiom ‘there is/are’ carries ontological commitment and that this idiom is straightforwardly

represented by the existential quantifier. Azzouni sharply challenges the claim that the ordinary language expressions codified by the existential quantifier inevitably imply the mind- and language-independent existence of the items quantified over. On Azzouni’s view, no idiom—even ‘exists’—in ordinary language is ontologically committing.17 As evidence of the ontologically non-committing nature of ‘there is/are’ phrases in the vernacular, Azzouni adduces various examples of what he calls ‘ontically irrelevant’ uses:18

(1) No mouse—not Mickey Mouse, not Minnie Mouse—has ever been depicted in movies as a plumber, although there are several that have been depicted as pirates.

(2) There is a certain position in society that I deserve, but because of certain unscrupulous people, I’ve failed to procure it.

(3) There is a certain imaginary woman that Jane and Heather dream about regularly.

(4) There are many ways of getting around this.

(5) There are as many goddesses as gods in Greek mythology.

Moreover, there is evidence of a similar sort that ‘exist’ is also ontically neutral in the vernacular:

(p.106) (6) Strategies for circumventing anger exist.

(7) Although waltzes designed to last more than ten hours exist, people rarely dance unexpurgated versions of them.

Azzouni believes that the ordinary speaker would be quite surprised to learn that his use of ‘there is/are’ with respect to fictional characters, dream figures, ways of going about something, and so on, oblige him to acknowledge the reality of such things or to offer paraphrases to avoid such ‘there is/are’ statements. Ordinary language speakers sense no obligation to offer paraphrases of such sentences if challenged concerning their ontological commitments;

rather, they just clarify that such statements were not to be taken in an ontologically committing way.19 ‘Ordinary

speakers find the philosopher’s charge of ontic commitment in many cases as silly because ontic commitment (and ontology) seems irrelevant.’20

Azzouni agrees that we often do use ‘there is/are’—and even more frequently ‘exist’—in ontically relevant ways to assert our belief in the mind- and language-independent reality of some thing.21 But the linguistic phrases themselves are not ontologically committing simply in virtue of their meaning. The linguistic meaning of ‘exists’ does not change with its ontically relevant or irrelevant uses. The locutions are neutral in and of themselves, and

different users on different occasions may use the same ‘there is/are…’ phrases with different ontological commitments in mind. The way ordinary language speakers indicate or deny ontological commitment is by such devices as tone of voice, addition of words like ‘really’, or contrastive use of ‘exist’ with ‘there is/are.’ In Azzouni’s view, then, there just are no idioms in the vernacular which, by virtue of their meanings alone, are ontologically committing. Ontological commitment is thus a varying, person-relative matter.

Prospects of Neutralism

So one way the theist who wants to defeat the Platonist’s Indispensability Argument can do so is by advocating a neutral view of (p.107) quantificational logic. Not only do I find such a view to be tenable—which is all the theist need contend in order to undercut the Indispensability Argument—but I am persuaded that it is correct.

There are two ways in which existential quantification has been thought to be ontologically committing: first, through the semantic theory of logical quantification and, second, through the linguistic meaning of the quantifiers. Let us look at each in turn.

Semantics for Quantificational Logic

Objectual Semantics

According to so-called objectual semantics for quantificational logic, the variables (like x, y, and z) which lie within the scope of our quantifiers range over a specified domain of objects to pick out various objects in the domain. In order for a universally quantified statement to be true, that statement must be true no matter which object in the domain is plugged in for the variable. In order for an existentially quantified statement to be true, at least one of the objects in the domain, when plugged in for the variable, yields a true statement. Now some theorists, including Quine, have maintained that such objectual semantics for sentences we take to be true commits us ontologically to all or at least some of the objects in the domain.

This claim is misconceived. There is no reason to limit one’s domain of quantification to existing objects or to think that it must include existing objects. We are at liberty to quantify over anything we choose, whether it exists or not. For example, a historian may quantify over past US Presidents, asserting truly that some of them were born outside the United States. It would be a metaphysical extravagance to think that merely quantifying over past US Presidents commits one to a tenseless theory of time, according to which temporal becoming is illusory and past, present, and future entities are ontologically on a par. Or again, we may quantify over courses of action which we are contemplating, assessing which of them would likely lead to disaster. In this case, the courses of action which are not chosen as a result of such deliberation never do exist. Or again, we may quantify over hobbits in Tolkien’s novels, asking how many of them are said to live underground, without committing ourselves to the existence of hobbits. And in everyday matters, we quantify over things like holes, Fridays, problems, needs, and so on,

without (p.108) thinking that we are thereby committing ourselves to the reality of such things.

As Azzouni points out, whether one is ontologically committed to objects said to be in the domain depends entirely on whether the quantifiers in the second-order language (or metalanguage) used to establish the domain are themselves devices of ontological commitment.22 Without that presupposition, talk of objects’ being in a domain no more commits us to anything real than do the ground-level assertions. If I choose to quantify over Fridays in 2014, I am no more committed to the existence of Fridays by such a decision than I am by my assertion ‘There are five Fridays in October’.

Substitutional Semantics

Azzouni reminds us that there is another semantics for quantificational discourse which is admitted on all sides not to be ontologically committing to objects in a domain, namely, so-called substitutional quantification. On a substitutional understanding of quantification, one does not take the variables within the scope of the quantifier to range over a domain of objects; rather, we take the variables as dummy letters which may be replaced by linguistic expressions in order to form sentences. A universally quantified statement is true just in case the substitution of any term for the variable in the sentence following the quantifier yields a true sentence. An existentially quantified statement is true just in case the substitution of at least one term for the variable in the sentence following the quantifier yields a true sentence. So, for example, ‘All cats are mammals’ is true just in case any singular term plugged into ‘If x is a cat, then x is a mammal’ is true; and ‘Some cats are black’ is true just in case at least one singular term, when plugged into ‘x is a cat and x is black’, yields a true sentence. Since one is simply substituting words for the variables, no objects in a domain even come into view.

Early proponents of substitutional semantics, like Ruth Barcan Marcus, therefore considered it superior to what they took to be the ontologically inflationary objectual semantics championed by Quine.23 Quine himself recognized how alien to ordinary language (p.109) objectual semantics is, when construed as carrying ontological commitments, and he also conceded that substitutional semantics would avoid such ontological commitments.24 Quine’s main objection to substitutional quantification was that many things in the world over which we want to quantify do not have singular terms, like names, denoting them. But for the theist that presents no problem. The theist will insist that God is able to name any object that exists. ‘He determines the number of the stars and calls them each by name’ (Ps. 147: 4). I am reminded of Wilfrid Sellars’s appeal to ‘the language of omniscience’, in which every object has a

name.25 The truth conditions for substitutional quantification may be successfully stated relative to the language of omniscience, even if many, or most, objects have not yet received names in English.26

Some philosophers have sought to avoid ontological commitment to abstract objects by construing the semantics for abstract discourse substitutionally, rather than objectually.27 But Azzouni’s point is more modest. The lesson to be learned from substitutional quantification, he thinks, is that a semantics for quantificational discourse need not involve ontological commitment to objects.28 Apart from a stipulation that the quantifiers of one’s meta-level language are ontologically committing, even the objectual semantics for ground-level quantificational discourse is just neutral.29

(p.110) The fundamental point is that there is no reason to treat the quantifiers of the metalanguage setting up the domain as ontologically committing, unless it is so stipulated. The debate on ground-level quantifiers thus replays itself on the meta-level, and the neutralist sees no reason to take the metalanguage quantifiers, any more than the ground-level language quantifiers, as carrying ontological commitments. Azzouni summarizes:

The lesson should be clear: Objectual quantifiers have ‘objects’ to range over only relative to a body of claims in a metalanguage that itself gains access to these ‘objects,’ if at all, via what its own quantifiers range over. And

if those (metalanguage) quantifiers do not carry ontological commitment, then neither do the objectual quantifiers

that the metalanguage quantifiers help provide objectual semantics for. A slogan: One can’t read ontological commitments from semantic conditions unless one has already smuggled into those semantic conditions the ontology one would like to read off.30

Only if the Quinean were able to show that the informal quantifiers of ordinary language which are codified by the formal quantifiers of objectual semantics are ontologically committing could he justifiably insist that formal quantifiers are ontologically committing. That forms a segue to the second way in which it has been claimed that quantification is a device of ontological commitment.

Linguistic Meaning of Quantificational Expressions

A neo-Quinean like van Inwagen makes no appeal to objectual semantics to justify taking the existential quantifier to be a means of ontological commitment. Rather, he proceeds simply on the basis of the linguistic meaning of quantificational expressions in ordinary language which the formal quantifier abbreviates.

Saul Kripke, whose pioneering work in modal semantics made him one of the twentieth century’s brightest philosophical luminaries, insists that the objectual (or, as he calls it, referential) quantifier (p.111) derives its meaning entirely from ordinary language quantificational expressions:

We did not learn quantification theory as our mother tongue. Somehow or other the weird notation ‘(∃x)’ was

explained to us, by teachers or books, either by such examples as ‘“(∃x) Rabbit (x)” means “there is an x which is a rabbit”’, or by a formal definition of satisfaction, couched in English.… And the quantifiers will be said to range over a non-empty domain D, where the technical term ‘non-empty’ is explained by saying that D is non-empty

iff there is an element in D, or the equivalent. If the interpretation of the English ‘there are’ is completely in doubt, the interpretation of the formal referential quantifier, which depends on such explanations, must be in doubt also; perhaps the explanation the teacher used when he taught it to us was couched in a substitutional language, and we spoke such a language when we learned his interpretation!…Nonsense: we speak English, and the whole

interpretation of the referential quantifier was defined by reference to ‘there are’ in its standard employments.31

Kripke thinks the assertion ‘There are rabbits’ undoubtedly commits us to the existence of rabbits; but he himself acknowledges that there are English uses of ‘there is/are’ which are not ontologically relevant, as in ‘There is a good chance’ or ‘There are three feet in a yard’. Kripke’s disagreement is merely with ‘anyone who doubts or denies that English has any resources for making genuinely existential assertions’32—a position to which no neutralist ascribes.

Kripke and the neutralist concur on the overriding point: if the existential quantifier is defined in terms of the ordinary English ‘there is/are’, then if the latter is not ontologically committing, neither is the former. Van Inwagen agrees that it is so defined: ‘The meaning of the quantifiers is given by the phrases of English…that they abbreviate. The existential quantifier therefore expresses the sense of “there is” in ordinary English.’33The problem for van

Inwagen is that such a sense does not seem to be ontologically committing. Consider Thomas Hofweber’s list of some of the things we ordinarily say there are:

• something that we have in common

• infinitely many primes

(p.112) • something that we both believe

• the common illusion that one is smarter than one’s average colleague

• a way you smile

• a lack of compassion in the world

• the way the world is

• several ways the world might have been

• a faster way to get to Berkeley from Stanford than going through San Jose

• the hope that this dissertation will shed some light on ontology

• the chance that it might not

• a reason why it might not34

It would be fantastic to think that there are real objects answering to these descriptions. There is no evidence that the ordinary language speaker labours under the delusion that there are.

Van Inwagen does not directly engage neutralism, which denies that ordinary language quantificational expressions are ontologically committing. All van Inwagen really offers for thinking that quantificational expressions are ontologically committing is the synonymy in ordinary language of ‘there is/are’ and ‘there exist(s)’. Synonymy is really beside the point, however, for the neutralist denies that either expression is ontologically committing in ordinary language. It is worth emphasizing, in view of van Inwagen’s insistence that ‘existence’ is not only synonymous with ‘being’, but univocal as well,35 that the non-committing character of ‘there is/are’ and ‘there

exists’ in ordinary language is not, according to neutralism, due to any equivocation of such expressions, as though there were one meaning which is ontologically committing and another which is not. Rather, on Azzouni’s view, these expressions in the vernacular just do not force ontological commitments in virtue of their meaning.

Robert Adams thinks that the English word ‘exists’ is univocal in its various uses but observes that it is metaphysically lightweight in ordinary language. He writes,

(p.113) I believe that the meaning of ‘exist’ and of (informal) quantifiers is metaphysically light in natural languages. I think we speak sincerely and literally, but without meaning to commit ourselves on deep metaphysical issues, when we say, as we do, that there are rocks as well as roosters, shapes and sizes, numbers and theorems, molecules composed of several atoms, amoebas and other living cells that split in two, cities and states, laws and agreements, properties and relations, words that are spoken and written, books that exist in both printed and electronic forms—and so on. I suppose that few if any of us would say that all of those objects are fundamental

metaphysically.36

I think that Adams’s observation about the lightweight nature of existence predications and informal quantifiers in ordinary language is obviously correct. We commonly say that there are, for example, shades of grey, differences in height, angles from which something can be seen, principles, hostilities, prospects for success, primes between 2 and 12, hours before dawn, dangerous excesses, drawbacks to the plan, and so on, without imagining that there are mind- independent objects of these sorts.37

In Adams’s view, what is asserted to exist in a metaphysically light sense is a matter of linguistic conventions and one’s personal interests. It is in this light sense, I think, that a lightweight Platonist like John Burgess affirms the existence of abstract objects, as well as most other things.38 Adams’s claim that the sense of ‘exists’ in ordinary

language is very lightweight accords well with Azzouni’s claim that existential quantification and ‘exists’ are not ontologically committing in the vernacular.

Disadvantages of Existentially Loaded Quantifiers

Intentional Statements

Furthermore, there are decided disadvantages to taking formal and informal quantificational expressions to be ontologically committing. First, we should be logically hamstrung when it comes to dealing with (p.114)intentional statements. Routley is especially emphatic about there being true intentional statements in which things that do not exist are referred to or quantified over, for example:

1. Ponce de Leon was searching for the Fountain of Youth.
2. Some people don’t believe in any of Meinong’s non-existent objects.
3. An actual person sometimes wants something that doesn’t exist.
4. A cyclone, code-named Thales, is expected to form in the Coral Sea.
5. Some mathematicians mistakenly think that every consistent item exists.

Since intentionality results in intensional, as opposed to extensional, contexts, he observes: ‘The overwhelming part of everyday, and also of extraordinary, of scientific and of technical discourse is intensional.’39 Statements of this sort are universally regarded as true. But they are not generally regarded as genuine statements about things that do not exist because intensional contexts are ‘opaque’, that is to say, one cannot quantify into such contexts or refer to the objects which are the denotations of the singular terms appearing in those contexts.

But why not? This exemption is simply the unpleasant consequence of adopting the customary criterion of ontological commitment, if that criterion is to be at all plausible. Exempting intensional frameworks might well be seen as an ad hoc adjustment aimed at saving an otherwise implausible criterion. On a neutral logic, quantifying into intensional contexts is not ontologically committing and so need not result in ontological extravagances. So from (1) above, one may validly infer

1. 6. There is something that Ponce de Leon was searching for,

meaning merely that the explorer was not aimlessly rambling about, but had an object in mind, for which he was looking. This is not to say that in certain situations the assertion of a statement like (6) does not convey and would not be taken to convey the speaker’s conviction about the real existence of something. It is merely to insist that quantificational phrases are not, in virtue of their meaning, ontologically committing.

(p.115) Van Inwagen exploits the situational relativity of neutral quantificational phrases to try to make the neo- Meinongian position look silly:

One day my friend Wyman told me that there was a passage on page 253 of volume IV of Meinong’s Collected Works in which Meinong admitted that his theory of objects was inconsistent. Four hours later, after considerable fruitless searching, I stamped into Wyman’s study and informed him with some heat that there was no such passage. ‘Ah,’ said Wyman, ‘you’re wrong. There is such a passage. After all, you were looking for it: there is something you were looking for. I think I can explain your error; although there is such a passage, it doesn’t exist. Your error lay in your failure to appreciate this distinction.’ I was indignant.

My refusal to recognize a distinction between existence and being is simply my indignation, recollected in tranquility and generalized.40

In this admittedly funny story, Wyman, presumably an adherent of neutral logic, is prepared to quantify into an intensional context without ontological commitment: after all, van Inwagen was not just browsing through Meinong; there was something he was intent on finding. By contrast, van Inwagen, a meta-ontological Quinean, knows that, given his own criterion of ontological commitment, quantifying into such a context would lead to an ontological falsehood, so van Inwagen exempts intensional contexts from the quantifier’s reach.

But with what justification? The implication of the joke is that neutral logic would lead us into egregious misunderstandings. But that is surely not the case. Any neutralist would recognize that Wyman’s original assertion would be taken to imply that upon turning to page 253 of volume IV, one might read Meinong’s confession, and that van Inwagen’s indignant protest that there is no such passage was intended to convey the opposite. Everyone knows that ‘there is’ is often used in ordinary language to express the existence of real world objects—but, according to the neutralist, not always and (p.116) automatically. There are contextual clues and rhetorical devices by means of which we can make our intentions clear. Ironically, in his discussion of neo-Meinongianism, van Inwagen himself uses italics to signal an ontologically relevant use of ‘there is’: ‘There is no nonexistent poison in the paranoid’s

drink. There is no such thing as his uncle’s malice.’41 Thus, by double italicizing Wyman’s statement ‘there is such a

passage, but it doesn’t exist’, van Inwagen fosters the desired appearance of contradiction. As his closing remark indicates, van Inwagen misinterprets the neo-Meinongian’s advocacy of neutral logic as the attempt to draw a distinction between being and existence.42 But neo-Meinongians like Routley regard ‘being’ and ‘existence’ as synonymous but lightweight and, therefore, not ontologically committing.

Van Inwagen is assuming his own meta-ontological criterion of ontological commitment when he issues the following challenge to the neo-Meinongian: ‘If you think there are things that do not exist, give me an example of one. The right response to your example will be either, “That does too exist,” or “There is no such thing as that”.’43 Here the two prongs of the ‘right response’ make it evident that van Inwagen is assuming that ‘there is’

carries ontological commitment, so that the second prong, ‘There is no such thing as that’, means to deny that the thing in question does exist. So if I, in response to his challenge, say, ‘the hole in my shirt’, a retort by van Inwagen, ‘That does, too, exist’, seems ontologically extravagant; while the retort, ‘There is no such thing as that’, means only that the hole in my shirt does not exist in a metaphysically heavy sense, which is precisely what I already affirmed! On a neutral logic, I can quantify over holes in my shirt without ontological commitment to holes as existing things. To return to the subject of intensional contexts, given a neutral logic, I can quantify into an intensional context like ‘Peter contemplated the two holes in my shirt’ by asserting ‘There are two holes in my shirt which Peter contemplated’ without ontological commitment to holes, whereas an existentially loaded logic will be hobbled in its permitted (p.117) inferences by the presupposition of the neo-Quinean criterion of ontological commitment.

Tensed Statements

A second respect in which existentially loaded quantification is markedly disadvantageous concerns tensed statements about no longer existent or not yet existent individuals. Routley is a presentist, who denies that the past and future are on an ontological par with the present. I have elsewhere argued at length in favour of such a tensed view of time and consider it a natural concomitant of theism.44 Even if some partisans of tensed time deny that future contingent statements are true or false, nonetheless, very few have the temerity to deny that past-tense

statements about individuals who do not presently exist are true.45 For example, it seems indisputably true that ‘There have been forty-four US presidents’. The non-existence of most of them is no impediment to our quantifying over past US presidents. To infer from the truth of such statements that time is, in fact, tenseless and that past and future individuals are on an ontological par with present individuals would be to draw a breathtaking metaphysical inference on the basis of the slim reed of the neo-Quinean criterion of ontological commitment.

It is noteworthy that in debates over presentism, tenseless time theorists tend simply to presuppose without argument that quantification is ontologically committing, and so our ability to quantify over past/future individuals in true sentences is taken to commit us to their existence.46 Thus, Theodore Sider muses, ‘Since ordinary talk

and (p.118) thought are full of quantification over non-present objects, presentists are in a familiar predicament: in their unreflective moments they apparently commit themselves to far more than their ontological scruples allow.’47 In fact, the only person in a predicament here is the presentist who also accepts the neo-Quinean criterion

of ontological commitment. It never seems to occur to tenseless time theorists that our ability to quantify over purely past/future individuals in true sentences might be a good reason to reject the criterion of ontological commitment which they unquestioningly presuppose. Sider himself thinks that the presentist should adopt a sort of fictionalism: sacrifice the truth of past- and future-tense statements in favour of their quasi-truth or verisimilitude. There is no reason the presentist should accept such a fool’s bargain, for it is far more obvious that, for example, the statement ‘Some medieval theologians wrote in Latin’ is true than that the neo-Quinean criterion of ontological commitment is true. Sider notwithstanding, we do speak as if presentism is true, but we do not speak as if quantification is a device of ontological commitment. That is why we quantify freely over merely past objects without thinking that such objects therefore exist.

The tensed time theorist can hardly be blamed if he elects to deny the neo-Quinean criterion of ontological commitment rather than surrender his view of time. Of course, if we had strong independent grounds for preferring a tenseless view of time, then Routley’s argument would be void. But we have, in my view, no such grounds.48

The case of tensed truths serves as just another illustration of Routley’s first point about logic’s inability to handle intensional contexts when the quantifiers are taken to be existentially loaded. From ‘Aristotle was born at Stagira’, for example, we cannot infer that ‘Someone was born at Stagira’, since that would involve quantification over a non- existent. The advantage of neutral logic is that it allows us to quantify into such intensional contexts without the need for elaborate paraphrase or committing ourselves to the existence of the things quantified over.

(p.119) Modal Statements

A third and related respect in which existentially loaded quantification threatens to lead to metaphysically outrageous conclusions concerns modal discourse. Oxford logician Timothy Williamson has argued on purely logical grounds for the radical thesis that everything that exists exists necessarily.49 Williamson calls this view

necessitism. Contingentism is just the denial of this view, namely, the view that some things exist contingently.

In order to accommodate the apparent fact that many concrete objects do not exist necessarily, Williamson maintains that such objects could have been, and, indeed, once were or will be, abstract objects (or, at least, non-concrete objects).50 So, for example, I, as a necessary being, could have been and once was a non-concrete object. I existed prior to my conception—not, of course, as a concrete, spatiotemporal object, but as a non-concrete object which later became concrete. What sort of object was I? I was once a merely possible person, an impersonal thing which

could be and did become a concrete person, and in worlds in which I never exist as a person, I remain a merely possible person.51 So on Williamson’s view, I am not essentially a person.

Most people (including professional metaphysicians!) find necessitism to be an outrageously implausible thesis which we should, if at all possible, avoid. It is therefore noteworthy that Williamson’s arguments for necessitism depend crucially on taking the quantifiers of first-order logic to be devices of ontological commitment. For example, he compares favourably arguments for necessitism with Lewis and Sider’s arguments against presentism based upon quantification over past realities:

(p.120) David Lewis challenges presentists to analyse in their terms sentences such as ‘There have been infinitely many kings named John’ (compare ‘There are infinitely many possible stars’), in order to cast doubt on the truth of presentism. Ted Sider challenges sceptics who claim that the dispute between presentism and eternalism is merely verbal to analyse in presentist terms sentences of the form ‘Half the objects from all of time that are Ks are Ls’

(compare ‘There are at least as many possible planets as possible stars’).52

These lame arguments for a tenseless theory of time, depending as they do on the assumption that existential quantification is ontologically committing, ought, in my opinion, to cast more doubt on the neo-Quinean criterion of ontological commitment than on presentism.

As the parenthetical comparisons in the quotation suggest, Williamson considers the non-paraphrasability of certain quantified modal truths like ‘There are uncountably many possible stars’ to indicate ontological commitments on the part of the person who asserts them. The same assumption underlies his boast that necessitists (unlike contingentists) can straightforwardly use quantification over possible worlds.53

Williamson makes no attempt at all to justify the assumption that first-order quantification is existentially loaded. He merely explains:

By definition, ontology concerns what there is. Claims of the form ‘There is a G’ are naturally paraphrased by first- order sentences of the form ∃x Gx. The quantification in ‘There is a G’ is not into predicate position, even if ‘G’ is replaced by ‘property’, ‘relation’, or ‘concept’. Ontology is part of metaphysics. The content of the ontological commitment is true if there is a G and false otherwise. Its truth value depends on how the mostly non-linguistic world is, as characterized in first-order terms.54

The problem is that sentences of the form ‘There is a G’ or even ‘G exists’ have a very light sense in ordinary English, and so some justification is needed for taking the formal quantifiers that abbreviate them as involving metaphysically heavy commitments.

(p.121) Williamson’s deductive formulations of his arguments for necessitism make it especially clear that he takes first-order quantifiers to carry ontological commitments,55 for the arguments will typically involve some premiss in which it is asserted that (∃x) (x = y), leading to a necessitist conclusion like

NNE.□((∀x)(□(∃x)(x=y))).

That is to say, necessarily, for any x, necessarily there is an object to which x is identical. But on a neutral logic, (NNE) is itself innocuous. Of course, necessarily, everything is necessarily identical to something, namely, itself; but that does not imply that that thing exists. So, for example, Allah is identical to Allah, but Allah is not identical to Zeus, whether or not either one exists.

Necessitism illustrates the sort of metaphysical debacle which the neo-Quinean criterion of ontological commitment helps to generate.56 Williamson declares, ‘what we want is not a weak modal logic, neutral on the relevant metaphysical questions. Rather, we want a strong modal logic that answers those metaphysical questions.’57 I should think that precisely the opposite is true. We want a modal logic that is neutral as to ontological commitments.

Williamson complains in another context that ‘Metaphysics based on weak logic wastes its time taking crank theories seriously.’58 To the contrary, basing metaphysics on an existentially loaded, metaphysically strong modal logic helps to generate a theory like necessitism, which is about as cranky as they get.

Mereological Statements

Finally, a fourth area where the disadvantages of existentially loaded quantification become evident is mereology, or the study of parts and wholes. Contemporary debates in mereology have focused upon the (p.122) so-called special composition question, namely, what conditions have to be met in order for a plurality to compose an object.59 The predominant answer to that question among contemporary metaphysicians is mereological universalism. This view

assumes a principle of unrestricted mereological composition (UMC), according to which any plurality whatsoever composes an object:

UMC. Necessarily, whenever there are some things, then there is a fusion of those things.

So Lewis, on the basis of (UMC), holds that there is such a thing as a trout-turkey, a fusion, for example, of the front half of a particular trout and the back half of a particular turkey.60 Given (UMC), there are even objects like the sum of me and √2. ‘Though the view presents a wildly counterintuitive description of reality,’ Ross Inman observes, ‘there are surprisingly powerful arguments in its favor, which partly explains its widespread appeal among many contemporary metaphysicians.’61 That appeal is so strong that Hud Hudson can write, ‘the view becoming (if not already) the orthodoxy among those writing in mereological metaphysics is that composition is absolutely unrestricted; any plurality whatever has a mereological sum or fusion’.62

Does (UMC) force us to include such wildly counter-intuitive objects as trout-turkeys in our ontological inventory? No; it is only the conjunction of (UMC) with the neo-Quinean criterion of ontological commitment that would foist such commitments upon us. Hence, some theorists have sought to soften the impact of (UMC) by denying that it involves ontological commitment to any object in addition to the plurality of objects summed together. Lewis gives the following assurance:

To be sure, if we accept mereology, we are committed to the existence of all manner of mereological fusions. But given a prior commitment to cats, say, a commitment to cat-fusions is not a furthercommitment. (p.123) The fusion is nothing over and above the cats that compose it. It just is them. They just are it.… In general, if you are already committed to some things, you incur no further commitment when you affirm the existence of their fusion. The new commitment is redundant, given the old one.63

Lewis’s back-pedalling is eloquent testimony to the implausibility of so bloated an ontology as that apparently sanctioned by (UMC). The difficulty for Lewis is that he accepts the neo-Quinean criterion of ontological commitment, so that his meta-ontology commits him, in spite of himself, to the existence of objects over and above the plurality of objects composing the fusion.64 He says, ‘Only if you speak with your quantifiers wide open must

you affirm the trout-turkey’s existence. If, like most of us all the time and all of us most of the time, you quantify subject to restrictions, then you can leave it out. You can declare that there just does not exist any such thing— except, of course, among the things you’re ignoring.’65 But, Lewis concedes, ‘Once you’ve said “there is” your game is up.’66

Hardier advocates of (UMC) do not shrink from admitting the additional objects into their ontology. Thus, an obviously discomfited Lynne Rudder Baker writes,

So, are sums objects or not?…Since I have endorsed universalism, I must (hold my nose and) say that sums are objects. However, the unpalatability of commitment to arbitrary sums is mitigated by the fact that the ontological

difference that sums make is negligible: the only ontological effect of holding that sums are objects is to increase the number of existing objects.67

We can, however, avoid the noxious smell of mereological universalism simply by abandoning the neo-Quinean criterion of ontological commitment. Given neutral quantifiers, we can talk freely about (p.124)mereological sums without ontological commitment. Existentially loaded quantification is a positive impediment to mereology and, hence, to metaphysics, an assumption which the discipline would be well without.

Concluding Remarks

The foregoing considerations are sufficient, in my opinion, to warrant rejection of the neo-Quinean view of formal and informal quantifiers. But that conclusion may remain moot. What is important for our purposes, rather, is that these considerations, coupled with the want of any arguments for the truth of the neo-Quinean meta-ontological rules, certainly suffice to show that the neo-Quinean criterion of ontological commitment is far from incumbent upon us and that therefore the theist may plausibly reject it. Alex Orenstein wisely reminds us that ‘There are fashions in philosophical explications’, one of which is today taking metaphysically heavy existence assertions to be

expressed by the first-order existential quantifier.68 It is perfectly reasonable to buck the fashion trend in this regard.

So doing opens the door for affirming truths like ‘There is a prime number between 2 and 4’ without commitment to the existence of mathematical objects.

Notes:

Peter van Inwagen, ‘God and Other Uncreated Things’, in Kevin Timpe (ed.), Metaphysics and God (London: Routledge, 2009), 19.
Peter van Inwagen, ‘Being, Existence, and Ontological Commitment’, in David Chalmers et al. (eds), Metametaphysics: New Essays on the Foundations of Ontology (Oxford: Clarendon, 2009), 506. These theses are not really expressive of Quine’s original criterion of ontological commitment. I shall on occasion mark the difference by calling what passes today as Quine’s criterion of ontological commitment the neo-Quinean criterion.
Peter van Inwagen, ‘Meta-ontology’, in Ontology, Identity, and Modality (Cambridge: CUP, 2001), 28; similarly, van Inwagen, ‘Being, Existence, and Ontological Commitment’, 506; Peter van Inwagen, ‘Quantification and Fictional Discourse’, in Anthony Everett and Thomas Hofweber (eds), Empty Names, Fiction, and the Puzzles of Non-Existence (Stanford, CA: Center for the Study of Language and Information, 2000), 236, where he calls the Lewises’ paper on holes ‘a paradigm of the application of Quine’s strategy’. The paper in question is David Lewis and Stephanie Lewis, ‘Holes’, Australasian Journal of Philosophy, 48/2 (1970): 206–12.
Van Inwagen, ‘Meta-ontology’, 31.
Ibid.
Peter van Inwagen, ‘A Theory of Properties’, in Dean Zimmerman (ed.), Oxford Studies in Metaphysics, i (Oxford: Clarendon, 2004), 113–15.
Interestingly, in the version of the argument in his Metaphysics, 3rd edn (Boulder, CO: Westview, 2009), 299–300, van Inwagen himself takes a similar sentence to be a universally quantified statement.
Van Inwagen, ‘Meta-ontology’, 23–4. The quantifier is either the universal or the existential quantifier, and the variable is the x which can take on various values.
To see how his neo-Quineanism leads him to the bold, if nuanced, affirmation e.g. that fictional characters exist, see van Inwagen, ‘Quantification and Fictional Discourse’, 235–47. According to van Inwagen, competing ontologies of fiction should be evaluated by (i) seeing how well they explain our reactions to the whole range of sentences we use to talk about fiction and (ii) our ability to integrate these explanations with (a) an acceptable philosophy of the quantifier and (b) an acceptable general ontology (247). When judged by such criteria, it seems to me very plausible that the implication of our discourse about fictional characters that ‘There are fictional characters’ is no more ontologically committing than a sentence like ‘There’s at least one thing that you overlooked: his lack of compassion’, i.e. not committing at all.
Peter van Inwagen, Material Beings (Ithaca, NY: Cornell University Press, 1990), 108. See further Achille C. Varzi, ‘Words and Objects’, in Andrea Bottani et al. (eds), Individuals, Essence, and Identity (Dordrecht: Kluwer Academic Publishers, 2002), 49–75. Without challenging the Quinean Criterion of Ontological Commitment, Varzi attacks its usefulness in disclosing the ontological commitments of ordinary language speakers. For there is no objective procedure for determining the correct logical form of a sentence, and many paraphrases are simply ingenious attempts to avoid reference. If the paraphrase avoids some of the ontological commitments of the original sentence, how shall we decide which statement to take as true? Varzi charges that van Inwagen’s linguistic revisionism involves ‘a plain misconstrual’ of the statements of ordinary language speakers (65).
Van Inwagen, ‘Theory of Properties’, 118–19.
Van Inwagen’s paraphrase for distances e.g. quantifies over numbers, so that the original statement, which made no mention whatsoever of numbers, winds up committing us to the reality of not just stars and planets, but an infinity of numbers! Is ontology really that easy?
W. V. O. Quine, Philosophy of Logic, 2nd edn (Cambridge, MA: Harvard University Press, 1986), 89.
Alexius Meinong, ‘The Theory of Objects’ (‘Über Gegenstandstheorie’, 1904), tr. Isaac Levi et al., in Roderick M. Chisholm (ed.), Realism and the Background of Phenomenology (Atascadero, CA: Ridgeview, 1960), 83. In German: ‘Es gibt Gegenstände, von denen gilt, daß es die gleichen Gegenstände nicht gibt.’ See discussion in J. N. Findlay, Meinong’s Theory of Objects and Values, 2nd edn (Oxford: Clarendon, 1963), 44–50.
Richard Routley, Exploring Meinong’s Jungle and Beyond: An Investigation of Noneism and the Theory of Items (Canberra: Australian National University Research School of Social Sciences, 1979), 56.
I am grateful to Jody Azzouni for extensive personal discussion of neutralism.
Jody Azzouni, ‘Ontological Commitment in the Vernacular’, Noûs 41/2 (2007): 220 n. 4.
Jody Azzouni, ‘Ontology and the Word “Exist”: Uneasy Relations’, Philosophia Mathematica, 18/1 (2010): 77–84.
Azzouni, ‘Ontological Commitment in the Vernacular’, 224 n. 38.
Azzouni, ‘Ontology and the Word “Exist”’, 78–9.
Ibid., 89. Azzouni thinks that mind- and language-independence is, in fact, the criterion of existence which ordinary language speakers have collectively adopted, though the criterion cannot be established by conceptual analysis or philosophical argument.
Jody Azzouni, Deflating Existential Consequence: A Case for Nominalism (Oxford: OUP, 2004), 54.
Ruth Barcan Marcus, ‘Quantification and Ontology’, Noûs, 6/3 (1972): 245. This article includes some wonderful illustrations of the ontologically inflationary character of objectual semantics if it is taken to be ontologically committing.
W. V. O. Quine, The Roots of Reference (LaSalle, IL: Open Court, 1973), 89, 135–6. Quine sought to avoid such unwanted commitments by restricting his criterion of ontological commitment to an artificial language somehow purged of the offending expressions.
Wilfrid Sellars, ‘Realism and the New Way of Words’, Philosophy and Phenomenological Research, 8/4 (1948): 604–5.
See discussion in Michael J. Loux, ‘Ontology’, in C. F. Delaney (ed.), The Synoptic Vision: Essays on the Philosophy of Wilfrid Sellars (Notre Dame, IN: University of Notre Dame Press, 1977), 66–7; cf. Loux, ‘Rules, Roles, and Ontological Commitment: An Examination of Sellars’ Analysis of Abstract Reference’, in Joseph C. Pitt (ed.), The Philosophy of Wilfrid Sellars: Queries and Extensions (Dordrecht: D. Reidel, 1978), 247.
Dale Gottlieb, Ontological Economy: Substitutional Quantification and Mathematics (Oxford: OUP, 1980).
Azzouni, Deflating Existential Consequence, 57. Note the difference between Azzouni’s view and Dale Jacquette’s neo- Meinongian view that the domain is expanded to comprise both existent and non-existent objects. Jacquette, ‘Meditations on Meinong’s Golden Mountain’, in Nicholas Griffin and Dale Jacquette (eds), Russell vs. Meinong: The Legacy of ‘On Denoting’ (London: Routledge, 2009), 195–6).
Azzouni himself takes meta-level claims about domains, quantifiers, and the like to be merely metaphorical, not literal: Azzouni, ‘Ontological Commitment in the Vernacular’, 222 n. 18; similarly, Jody Azzouni, ‘A New Characterization of Scientific Theories’, Synthèse, 191/13 (2014): 2993–3008. Azzouni’s appeal to a metaphorical metalanguage is an emphasis associated with figuralist or pretence theoretical views of abstract discourse, to be discussed in Chapters 9 and 10.
Azzouni, Deflating Existential Consequence, 55.
Saul Kripke, ‘Is there a Problem about Substitutional Quantification?’, in Gareth Evans and John McDowell (eds), Truth and Meaning: Essays in Semantics (Oxford: Clarendon, 1976), 379.

(32) Ibid., 380.

Van Inwagen, ‘Quantification and Fictional Discourse’, 239.
Thomas Hofweber, ‘Ontology and Objectivity’ (Ph.D. dissertation, Stanford University, 1999), 1–2.
See e.g. van Inwagen, ‘Being, Existence, and Ontological Commitment’, 482–92.
Robert Adams, ‘The Metaphysical Lightness of Being’, paper presented to the Philosophy Department colloquium at the University of Notre Dame, 7 Apr. 2011.
See Gerald Vision, ‘Reference and the Ghost of Parmenides’, in Rudolf Haller (ed.), Non-Existence and Predication (Amsterdam: Rodopi, 1986), 297–326.
Recall Ch. 1, ‘Terminological Clarifications: Platonism’.
Routley, Exploring Meinong’s Jungle, 8. He presents his theory of objects as the key to intentionality.
Peter van Inwagen, Ontology, Identity, and Modality: Essays in Metaphysics (Cambridge: CUP, 2001), 16. As the name ‘Wyman’ reveals, what we have here represented is the caricature of Meinongianism given by Quine in his influential essay ‘On What There Is’, Review of Metaphysics, 2 (1948): 21–38, not genuine Meinongianism. See comments by Graham Priest, Towards Non-Being: The Logic and Metaphysics of Intentionality (Oxford: Clarendon, 2005), 108.
Van Inwagen, Ontology, Identity, and Modality, 16; cf. Van Inwagen, ‘Fiction and Metaphysics’, Philosophy and Literature 7/1 (1983): 68.
See also van Inwagen, ‘Theory of Properties’, 129; Van Inwagen, ‘Being, Existence, and Ontological Commitment’, 480.
Van Inwagen, Ontology, Identity, and Modality, 16; similarly, van Inwagen, ‘Theory of Properties’, 129; Van Inwagen, ‘Being, Existence, and Ontological Commitment’, 481.
See my The Tensed Theory of Time: A Critical Examination (Dordrecht: Kluwer Academic Publishers, 2000) and my The Tenseless Theory of Time: A Critical Examination (Dordrecht: Kluwer Academic Publishers, 2000).
Ulrich Meyer is right: ‘Caesar did cross the Rubicon; that’s what started the civil war. Any philosophical view that forces us to deny claims like [that] is for that reason unacceptable’: ‘The Presentist’s Dilemma’, Philosophical Studies, 122/3 (2005): 223.
See, e.g. David Lewis, ‘Tensed Quantifiers’, Oxford Studies in Metaphysics, i (2004): 3–14. Notoriously, Lewis also presented a similar quantificational justification for belief in modal realism on the grounds that there are ways the world might have been. Not only is such a metaphysical commitment to the reality of other worlds extravagant, but by the same token, there are also, then, impossible worlds, ways the world could not have been—Margery Bedford Naylor, ‘A Note on David Lewis’s Realism about Possible Worlds’, Analysis, 46/1 (1986): 28–9; Takashi Yagisawa, ‘Beyond Possible Worlds’, Philosophical Studies, 53/2 (1988): 175–204—which reduces modal realism to absurdity.
Theodore Sider, ‘Presentism and Ontological Commitment’, Journal of Philosophy, 96/7 (1999): 325.
See further Trenton Merricks, Truth and Ontology (Oxford: Clarendon Press, 2007), who challenges the argument that past- and future-tense truths require the tenseless existence of truthmakers of such statements.
Timothy Williamson, Modal Logic as Metaphysics (Oxford: OUP, 2013).
Williamson recoils from calling objects which are contingently non-concrete ‘abstract’ because they do not fit in with paradigmatic abstract objects like mathematical objects (ibid., 7). But abstract objects come in a bewildering variety, and by the definition of ‘abstract’ as ‘causally impotent’, such non-concrete objects qualify as abstract objects. So it is not unfair, I think, to say that on Williamson’s view, I could have been and, indeed, once was, an abstract object.
Williamson rejects the predicative reading of ‘possible person’, according to which a possible person is a kind of person, in favour of the attributive reading, according to which a possible person is something that could have been a person (ibid., 10–12). Cf. Williamson’s correction of A. N. Prior for referring to a merely possible person as ‘someone’ rather than ‘something’ (ibid., 68).
Ibid., 368; cf. 150. The references are to David Lewis, ‘Tensed Quantifiers’, Oxford Studies in Metaphysics, i (2004): 3–14; Theodore Sider, ‘Quantifiers and Temporal Ontology’, Mind, 115/457 (2006): 75–97.
Williamson, Modal Logic as Metaphysics, 376.

(54) Ibid., 261. (55) Ibid., 288–96.

See Takashi Yagisawa, ‘Critical notice of Modal Logic as Metaphysics, by Timothy Williamson,’ Notre Dame Philosophical Reviews (15 Oct. 2013), <http://ndpr.nd.edu.sci-hub.bz/news/43612-modal-logic-as-metaphysics>.
Williamson, Modal Logic as Metaphysics, 429. Boldly asserting that ‘Logic has no metaphysically neutral core’, Williamson affirms that ‘on the standard objectual interpretation of the first-level quantifiers, the semantics cannot “serve as a neutral device for exploring alternative views about possible objects”’ (146).

(58) Ibid., 226.

For what follows, I am indebted to Ross Inman, ‘On Christian Theism and Unrestricted Composition’, paper presented at the annual meeting of the Evangelical Philosophical Society, Milwaukee, WI, Nov. 2012.
David Lewis, Parts of Classes, with an Appendix by John P. Burgess, A. P. Hazen, and David Lewis (Oxford: Basil Blackwell, 1991), 80.
Inman, ‘Christian Theism and Unrestricted Composition’.
Hud Hudson, ‘Confining Composition’, Journal of Philosophy, 10312 (2006): 633.
Lewis, Parts of Classes, 81–2.
Phillip Bricker rightly protests Lewis’s claim to ‘ontological innocence’, commenting, ‘If I am ontologically committed to A and to B, then I am thereby ontologically committed to [the mereological sum] A+B. For that reason I don't need to list A+B as a separate item in my ontology. But it is a separate item in this sense: it is not identical to any of the other items in my ontology. It really (literally, altogether) exists.’ Phillip Bricker, personal correspondence, cited by Lynne Rudder Baker, The Metaphysics of Everyday Life: An Essay in Practical Realism (Cambridge: CUP, 2007), 192.
Lewis, Parts of Classes, 80.

(66) Ibid., 81.

Baker, Metaphysics of Everyday Life, 193. She says this only after futilely trying to differentiate sums from genuine objects.
Alex Orenstein, ‘Is Existence What Existential Quantification Expresses?’, in Robert B. Barrett and Roger F. Gibson (eds), Perspectives on Quine (Oxford: Basil Blackwell, 1990), 266. Orenstein follows neutralists in introducing an existence predicate instead in order to express existential claims.

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