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.

Here the truth of ‘a is F’ is said to require the existence of some object which is the referent of the singular term ‘a’.

What is at stake here is one’s theory of reference. Must singular terms refer to something in order for a sentence featuring them to be true, and does successful reference imply that there is something in the world which is the referent (or denotation) of the relevant term? Proponents of the Indispensability Argument answer ‘Yes’ to both of these questions.

Free Logic, Neutralism, and Neo-Meinongianism

In contrast to neo-Quineans, so-called ‘free’ logicians and neutralists challenge the claim that the use of singular terms in sentences we take to be true is ontologically committing. One might also think that this claim is repudiated by neo-Meinongians. For example, Routley holds that the sense of ‘refer’ in ordinary English is ontologically neutral, (p.126) although the word has become existentially loaded in philosophical usage:

The word ‘refer’ is used in everyday English (see OED), in the relevant sense, to indicate merely the subject or topic of discourse, or subject-matter, or even more loosely what such discourse touched upon or what was drawn attention to or mentioned. Any subject of discourse can count as referred to, including nonentities of diverse kinds; in this sense there is not commitment to existence. Superimposed on this non-theoretical usage we have a philosophers’

usage which embodies theoretical assumptions about language, according to which the reference of a subject expression is some existing item (or extensionally characterised entity) in the actual world.1

Because the word ‘refer’ has become so loaded with existence assumptions among philosophers, Routley thinks that we have little choice but to reserve the word ‘refer’ for the relation between a singular term and an existing entity.

So he concedes that a singular term ‘a’ has reference only in the case that the object a exists. Nevertheless, even if a does not exist, ‘a’ can still be ‘about’ or ‘signify’ or ‘designate’ a. Reference can be defined in terms of

aboutness: to say that ‘a’ refers to b is to say that ‘a’ is about b, and b exists. ‘Then “refers to” is existentially loaded and can do the classical work of “hooking language onto the world”…’2 But we can still use ‘a’ irreferentially as the proper subject of a true sentence.

Appearances notwithstanding, however, Routley, along with other neo-Meinongians, remains, in a sense, deeply committed to referentialism with respect to singular terms. For he construes reference as a relation between words and objects. Indeed, neo-Meinongianism is a kind of hyper-referentialism, in that it takes there to be objects correlated with every singular term, whether occurring in a true sentence or not. Meinong held that there are non- existent objects correlated with singular terms like ‘the golden mountain’ and even with contradictory terms like ‘the

round square’.3 Routley concedes (p.127) that for Meinong, every term designates an object, but Routley insists that on Meinong’s view, not every such object exists.4 Granted; but Routley is able to deny that such terms successfully

refer to their correlative objects only by taking reference to be existentially loaded. Inasmuch as there are, indeed, such correlative objects, no singular terms are truly vacuous or empty, even if they are, in Routley’s peculiar, existentially loaded sense, irreferential. Neo-Meinongianism accepts wholeheartedly the assumption that successful reference is a relation in which words stand to certain objects, and even goes so far as to say that no singular terms fail to stand in such a relation.

The conviction that there are objects standing in relation to singular terms sets neo-Meinongianism apart from neutralism, which denies that successfully referring terms require correlative objects. When we assert ‘2 is an even prime number’, the anti-realist neutralist and neo-Meinongian agree that we have spoken truly, despite the fact that 2 does not exist. But whereas the neutralist holds that my having successfully said something about 2 does not require that there is any object answering to the term ‘2’, the neo-Meinongian holds that there is, indeed, such an object, though it does not exist.

Free logic is more of a mixed bag. Developed only since the 1950s, free logic accepts that the quantifiers of first- order logic are ontologically committing, but it denies that singular terms are devices of ontological commitment. As John Nolt explains, free logic can be semantically characterized as a formal logic whose quantifiers are interpreted objectually with respect to a specified domain D—which is usually taken to be the class of existing objects—but whose singular terms may either refer to objects outside of D or fail to refer at all.5 Free logic employs an existence predicate ‘E’ in order to distinguish terms that refer to members of D from those that do not. For any singular term t, ‘t exists’ is true if and only if t refers to a member of D. (p.128)Empty or vacuous singular terms are simply terms that fail to refer to a member of D.

As Nolt indicates, singular terms which do not refer to an existing object may be regarded either as irreferential (not referring to anything at all) or as referring to something not in the domain D. In order to allow reference to something outside D, one can provide a dual domain semantics, as Nolt explains:

In a single-domain semantics the domain typically represents the class of the existing things, and empty singular terms have no referents.…In a dual-domain semantics…singular terms may refer to objects outside the quantificational domain. These outlying objects are collected into a second or outer domain, in contrast to which the usual quantificational domain is described as inner. The inner domain typically represents the class of existing things; the outer, correlatively, includes nonexistents. Thus on a dual-domain semantics all singular terms refer, but not all refer to existing things; the term ‘empty’ is therefore not equivalent to ‘non-referring’ or ‘non-denoting’, as it is in single domains semantics.6

Dual domain semantics sounds very much like neo-Meinongianism, unless one adopts a pretence theoretical approach to the outer domain and its members, whereas single domain semantics is akin to neutralism with respect to singular terms.

Advocates of so-called positive (as opposed to negative or neutral) free logic maintain that certain sentences can be truly asserted even though they contain singular terms that do not refer to any existing objects. But because free logic, unlike neutral logic, takes the first-order quantifiers to be ontologically committing to existing objects, free logic must impose restrictions on the rules of inference known as Existential Generalization (EG) and Universal Instantiation (UI), so that they hold only for things to which the existence predicate applies. So, for example, from the truth of ‘Sherlock Holmes is the most famous detective of English fiction’, we cannot infer that ∃x (x = the

most famous detective of English fiction). By the same token, from the arithmetic truth that 3 < 5 we cannot infer that ∃x (x < 5). By contrast, the neutralist welcomes such inferences, since on neutral logic, in contrast to free logic, the quantifier ∃ is not a device of ontological commitment.

(p.129) Singular Terms and Ontological Commitment

So how shall we assess the neo-Quinean’s claim that the use of singular terms in sentences we take to be true commits us to the existence of the things referred to? Azzouni points out that the majority tradition, which opposes the minority neo-Meinongian tradition, remains deeply conflicted about how to understand vacuous singular terms. Azzouni identifies four powerful, conflicting intuitions that serve to divide the majority tradition:

1. 1. Aboutness. When we talk or think about something, we often do so in a singular way.

2. 2. Normality. Thoughts and statements about non-existents have the same form and structure as ordinary statements about existents.

3. 3. Truth. Thoughts and statements about non-existents have specific truth values.

4. 4. Nonexistence. There are no objects serving as referents of vacuous singular terms. Azzouni’s neutralism aspires to satisfy all these intuitions.

Azzouni denies the crucial assumption underlying both neo-Meinongian and neo-Quinean views that statements involving singular terms ‘are true and false on the basis of the properties had by objects referred to by the singular terms appearing in those statements’.7 He distinguishes between referenceR (or aboutnessR), which is a relation between a term and an object, and referenceE (or aboutnessE), which is not a relation, but a characterization that

applies to empty singular terms in a discourse.8 This distinction allows Azzouni to maintain that the use of singular terms is ontologically neutral: ‘the ordinary words “about” and “refer” are neutral between uses of them that indicate genuine relations between language and thought and the world, and pseudo-relations: terms that have the appearance of relations but aren’t’.9 Azzouni differentiates his view from those of the (p.130) neo-Quinean and the neo- Meinongian, who are united in construing reference and aboutness as in every case a relation to an object, whether existent or nonexistent. For Azzouni, referenceE and aboutnessE are object-directed, in the sense of being intentional, but they are not relations to an object of any sort.10 So, for example, the singular term ‘2’ does not, in Azzouni’s

view, referR to anything, for there is no object to which this term stands in a relation; but ‘2’ is aboutE the number 2, in that one’s thoughts are 2-directed. Azzouni is even willing to say, using the ontologically neutral quantifier, that

there is something to which we referE and aboutE which we speak.11 But by such an ontologically irrelevant assertion, he means to indicate merely the object-directedness of our thought and discourse. Azzouni thus offers a nuanced account of reference, according to which not all singular terms in true statements need have real-world referents.

It seems to me that Azzouni is on the right track here. As Routley observed, it is a datum of ordinary language that we frequently assert true statements which contain singular terms which do not denote existing objects. Consider the following examples:

• The weather in Atlanta will be hot today.

• Sherrie’s disappointment with her husband was deep and unassuageable.

• The price of the tickets is ten dollars.

• Wednesday falls between Tuesday and Thursday.

• His sincerity was touching.

• James couldn’t pay his mortgage.

• The view of the Jezreel Valley from atop Mt Carmel was breath-taking.

• Your constant complaining is futile.

• Spassky’s forfeiture ended the match.

• He did it for my sake and the children’s.

It would be fantastic to think that all of the singular terms featured in these plausibly true sentences have objects in the world corresponding to them.

(p.131) Examples like these are legion. In fact, I suspect that singular terms which refer to real-world objects may actually be the exception rather than the rule in ordinary language. Consider the following paragraph quoted by the British philosopher Michael Dummett from a London daily:

Margaret Thatcher yesterday gave her starkest warning yet about the dangers of global warming caused by air pollution. But she did not announce any new policy to combat climate change and sea level rises, apart from a qualified commitment that Britain would stabilize its emissions of carbon dioxide—the most important ‘greenhouse’

gas altering the climate—by the year 2005. Britain would only fulfil that commitment if other, unspecified nations promised similar restraint.

Nothing unusual about such discourse—but, as Dummett observes, ‘Save for “Margaret Thatcher,” “air” and “sea,” there is not a noun or noun phrase in this paragraph incontrovertibly standing for or applying to a concrete object…’12 A lightweight Platonist, Dummett is unfazed about postulating objects as referents for such terms; but those who have a more robust sense of reality will be very hesitant about augmenting the world’s population so profligately.13

It is noteworthy that several of Dummett’s examples have to do with socially constructed realities like policies, commitments, and nations. On the influential analysis of Berkeley philosopher John Searle, socially constructed realities involve our assigning some function or status to a mind-independent object, according to the schema X counts as Y in C, where C is some social context.14 For example, in our social context, a certain object counts as a screwdriver. Given human intentionality and civilization, it should come as no surprise that our discourse is pervaded by talk of such socially constructed objects. But, arguably, the only existing objects in such cases are the mind-independent Xs, which are seen as Ys.

Money, for example, arguably does not exist, except in a metaphysically light sense. At most, what exist are things like pieces of (p.132) metal or paper, which in a certain social context count as money. If some South Pacific islanders decide to use cowrie shells as currency, the shells count as money in their society. If a disease were to wipe out the population of the island, the shells would still exist without any intrinsic change, but there would no longer be any money. The shells are not identical to the money, since they have different properties (for example, the shells antedated the money). But neither are there monetary objects distinct from the shells, since the shells are rightly taken to be money. It is better to say with Searle that socially constructed reality involves human beings’ imposing functions on objects. Once this is done, social or institutional facts can contain symbolic elements which transcend the objects.

Consider, for example, a touchdown’s being worth six points. Searle comments, ‘The expression “six points” does not refer to some language-independent objects in the way that the expressions “the man,” “the ball,” “the line,”…refer to language-independent objects. Points are not “out there” in the way that…men, balls, and lines are out there.’15 Once the appropriate conventions are in place, we can refer successfully to the touchdown scored at the

end of the first quarter, even though objectively there is no such thing. There can thus be objective facts about social reality without the existence of the object referred to. Searle is therefore inclined to speak of social (or institutional) facts rather than objects.

So how does God see things? Searle notes, ‘God could not see screwdrivers, cars, bathtubs, etc., because intrinsically speaking there are no such things. Rather, God would see us treating certain objects as screwdrivers, cars, bathtubs, etc.’16 The implication of socially constructed reality is that our discourse is pervaded by singular terms which do not refer to existents.

The Nature of Reference

How is it that we are able to assert truly sentences with empty singular terms? In order to get at this question, we first need to address the question, do vacuous singular terms refer? And in order to answer (p.133) that question, we need to ask what it is to refer, or what is the nature of reference? This question is largely neglected by contemporary theorists. Almost all contemporary theories of reference are actually theories about how to fix reference, rather than theories about the nature of reference itself.17 The unspoken assumption behind most contemporary theories of reference is the presupposition that reference is a word–world relation, so that terms which refer must have real-

world objects as their denotations. The very title of Quine’s influential book Word and Object betrays this assumption.18 Back in 1969, John Searle could assert that it is a ‘generally accepted axiom’ concerning reference and referring expressions that whatever is referred to must exist.19Searle regarded this axiom as a tautology, since it

says only that one cannot refer to a thing if there is no such thing to be referred to. Searle just took it for granted that reference is or involves a word–world relation.

This underlying assumption remains widespread. In a standard philosophical encyclopedia, Timothy Williamson calls reference ‘the central relation between language or thought and the world’.20 (p.134)Williamson is right about the importance of reference; but the assumption that reference is a relation begs the question against certain theories

of reference. In distinguishing referenceR, which is, indeed, a word–world relation, from referenceE, which is a non- relational sort of reference, Azzouni challenges this widespread assumption.

It seems to me, however, that Azzouni’s evolving views on reference have not yet come to the most satisfactory form. For his referenceR is simply what most theorists take reference to be, and his referenceE remains unexplicated and mysterious. We are left wondering what it is and how it works.

It therefore behoves us to look more deeply into the nature of reference. It is an experiential datum that referring is a speech act carried out by an intentional agent.21 Words in and of themselves engage in no such activity. Lifeless and inert, words are just ink marks on paper or sounds heard by a percipient. Absent an agent, shapes or noises do not refer to anything at all. If, for example, an earthquake were to send several pebbles rolling down a hillside which randomly came to rest in the configuration JOHN LOVES SUSIE, the names—if we would even call them names— would not refer to anybody.22 As Searle argues, ‘Since sentences…are, considered in one way, just objects in the world like any other objects, their capacity to represent is not intrinsic but is derived from the Intentionality of the mind.’23 (p.135) An interpreting agent uses his words as a means of referring to something.24 Referring is thus an intentional activity of persons, and words are mere instruments.

It is the great merit of the Swedish philosopher Arvid Båve’s new deflationary theory of reference that he takes truly seriously the fact, given lip service everywhere, that it is persons who refer to things by means of their words, so that words at best refer only in a derivative sense, if at all.25 As obvious as this point is, theorists of reference remain

strangely oblivious to the fact. Reference continues to be very widely construed as a relation obtaining between words and objects in the world. This is the case with all of the deflationary theories of reference critically surveyed by Båve—whether disquotational (S. Leeds, H. Field, P. Horwich), propositional (P. Horwich), or anaphoric (R. Brandom). The neglect of persons in favour of words is also the crucial shortcoming of Azzouni’s theory. Although Båve does not do so, he might have indicted all of the foregoing theories (p.136) simply for their neglecting to construe reference primarily in terms of the speech acts of persons. Båve’s significant contribution to our understanding reference is that he furnishes a central schema formulated in terms of the referring activity of persons. Båve provides the following schema for reference:

(R) a refers to b if and only if a says something (which is) about b,

where ‘a’ always stands for a speaker. Though formulated in terms of persons rather than words, this account is truly deflationary because it does not attempt to tell us anything about the nature of reference itself. It leaves it entirely open whether reference is a relation (as Gottlob Frege and Alexius Meinong assumed) or whether it is an intentional property of a mind (as held by Franz Brentano and Edmund Husserl).

Taking reference to be a relation between a speaker and some object does make (R) ontologically committing to either existing or non-existing objects which are the referents of which one speaks. But no such commitment is involved for someone who, like Azzouni, stands in the tradition of Brentano and Husserl in thinking of reference as an intentional activity of agents which may or may not be correlated with real-world objects.26 J. N. Findlay indicts Meinong primarily for his failure to appreciate his mentor Brentano’s insight into the nature of reference:

Meinong assumes throughout his treatment that an object is in some sense a logical prius of a conscious reference or intention: for there to be a conscious reference or intention there must in some wide sense be something which that reference or intention is ‘of’.… Since this is (p.137) obviously not true in an ordinary sense in the case

of some conscious intentions, there must, Meinong thinks, be a subtle sense or senses in which there are objects of such conscious intentions.… What should be seen is that this whole line of argumentation is wrong:…what our usage shows is that ‘thinking’ and its cognates are not relational expressions like ‘above’, ‘before’, ‘killing’, ‘meeting’, &c., nor can they be said to express relations.… We cannot therefore validly take an object of thought out of its object-position in a statement and make it an independent subject of reference: from ‘X thinks of a Y as

being Z’ it does not follow that there is a Y which is being thought of by X, nor even that a thought-of Y really is Z.…

That intentionality is not a relation but ‘relation-like’ (relativliches) is, of course, an insight of Brentano’s: Meinong, who frequently surpassed his master, in this respect certainly lagged behind him. He could only conceive intentional references in terms of objects logically prior to them, on which they necessarily depended: hence, the many

absurdities of his theory of objects.27

As an illustration of a property that is merely relation-like, Findlay gives to-the-east-of-China.28 If China is really a constituent of this property, he says, then China must inhere, in all its solid immensity, in the Philippine Islands, which is absurd. Similarly, with respect to intentionality, if I think of X, my thinking-of-X is a mental relational property of which X is not a constituent. My state of mind has the relational property of being-directed-to-X, whether or not X exists. Of course, talk of properties here is just a useful façon de parler. We are simply engaged in the intentional activity of thinking-of-X or referring-to-X.

So on Båve’s account, if I assert ‘1 + 1 = 2,’ then I have said something about 2; it follows from (R) that I have thus referred to 2. But it does not follow that there is some such object, whether existent or non-existent, as the number 2. One has the option of avoiding the inference to ‘There is something to which I have referred’ by restricting, with the free logicians, Existential Generalization, or the option of granting the inference but rendering it harmless by denying, with neutralism, that the existential quantifier is ontologically committing. Hence, (p.138) Båve recognizes the neutrality of his theory for the debate between realists and anti-realists.

Given (R), we now ask, what does it mean to say that a says something ‘about’ b, as stipulated by (R)? Båve proposes to ‘analyse the expression “about”, and then explain “refer” in terms of it’.29 He offers the following schema as implicitly defining ‘about’:

1. That S(t) is about t,

   
   
   

   where S( ) is a sentence context with a blank slot for singular terms. Again, Båve’s account of aboutness is extraordinarily deflationary. It does not tell us what aboutness is, but simply provides a schema for determining what a that-clause containing a singular term (or, presumably, terms) is about. So, for example, that Ponce de Leon sought the Fountain of Youth is about Ponce de Leon and about the Fountain of Youth because the singular terms ‘Ponce de Leon’ and ‘the Fountain of Youth’ fill the blanks in the sentence context ‘ sought .’

   
   
   

   Now since (A) is so deflationary, I do not think we should take (A) as providing an analysis of aboutness or serving as an explanation of reference, as Båve claims. Indeed, taking (A) to explain (R) seems to get things exactly backwards. The reason why that S(t) is about t is because ‘t’ is used by some person to refer to t. On an account like Båve’s, so-called ‘speaker’s reference’—what the speaker has in mind—becomes paramount, for, given schema (R),

   the only genuine referring is that done by the speaker.30 Rather, schema (A) merely tells us when someone has said

   something about something, so as to meet the condition laid down by (R).

   
   
   

   (p.139) Båve recognizes that schema (A) is no more ontologically committing to objects than (R): ‘(A) itself is neutral on how to conceive of the position following “about” in the instances of (A), so that we could deny the validity of the inference to “There is something such that I have a certain belief about it”.’31 So if I assert, ‘Ponce de Leon sought the Fountain of Youth’, I have said something which is both true and about the Fountain of Youth (as well as about Ponce de Leon); but we are not entitled to infer with Meinong that there is a non-existent object called

   the Fountain of Youth which this sentence is about. I can, therefore, say things about non-existents like Pegasus, the accident that was prevented, holes, or numbers without committing myself to there being objects of which I am speaking. This accords with the nature of intentionality, since intentional states of mind are not always about real- world objects.32

   By construing, not just some, but all reference in terms of the referring activity of persons and understanding aboutness in terms of intentionality, we make an advance over Azzouni’s views to arrive at a more satisfactory neutralist account. This account is consistent with anti-realism because successful singular reference does not require that there be objects in the world which stand in some sort of relation to a speaker’s words. Of course, sometimes objects answering to the terms we use do exist. But in a surprisingly large number of cases, as our earlier illustrations showed, there are no such objects. That does not stop us from talking about them or referring to them, for these activities are, at least in such cases, purely intentional activities.

   
   
   

   (p.140) Disadvantages of Taking Singular Terms to be Ontologically Committing

   Not only does the use of singular terms in sentences we take to be true seem to be non-committing ontologically, but, just as there are disadvantages to taking first-order quantification to be existentially loaded, so there are disadvantages to taking reference in true sentences to carry existential implications.

   Karel Lambert, one of the pioneers of free logic, complains that, although modern logic in the late nineteenth century shed itself of various existence assumptions implicit in Aristotelian logic with respect to the use of general terms,33 modern logic remains infected with existence assumptions with respect to the use of singular terms, assumptions that should not characterize a purely formal discipline.34 For we have at the deepest level ‘a primordial intuition that logic is a tool of the philosopher and ideally should be neutral with respect to philosophical truth.… So if there are preconditions to logic that have the effect of settling what exists and what does not exist, they ought to be eliminated because they corrupt the ideal of logic as a philosophical tool.’35

   
   
   

   These existence assumptions regarding singular terms surface dramatically in the way in which standard modern logic handles identity (p.141) statements. For such statements cannot be true, according to standard logic, unless the referents of the singular terms employed in such statements exist. In other words, identity statements are ontologically committing for anyone who asserts them. But it seems bizarre to think that from a seemingly trivial truth of the form t = t, where t is some singular term, it follows that the thing denoted by tactually exists.

   Nevertheless, this is what standard logic requires. For from the truth of the predication ‘a is F’ it follows by Existential Generalization that ∃x (Fx), or that something is F. So if we let ‘F’ be the predicate ‘= a’, it follows from the identity statement a = a that ∃x (x = a), or that something is identical with a. The reader will recognize that this implication is troubling only if we take the quantifier to be existentially loaded. The neutral logician is unfazed by the inference that something is identical to a, since he does not take such a statement to carry a heavy metaphysical commitment. But for neo-Quineans and free logicians, with their existentially loaded quantifiers,

   ∃x (x = a) just is the symbolization of ‘a exists’.

   Lambert takes this ontological implication of mere identity statements to be absurd. For it would follow from the fact ‘Vulcan = Vulcan’ that there is some object identical with Vulcan, that is to say, that Vulcan exists. Standard logic avoids this untoward result by treating all identity statements with vacuous singular terms as false. So standard logic must regard a statement like ‘Vulcan = Vulcan’ as false, even though it appears to be a tautology which is necessarily true. Standard logic cannot therefore distinguish the truth value of identity statements like ‘Zeus = Zeus’ and ‘Zeus = Allah’. Yet, the first seems to be necessarily true and the second obviously false. Nor can standard logic affirm the truth of ‘Aristotle = Aristotle’ or ‘Lincoln = Lincoln’, since Aristotle and Lincoln no longer exist and so there are no things with which they can be identified. As I said before, it would be the height of ontological presumption to claim that the truth of such seemingly trivial statements implies a tenseless theory of time, according to which all persons throughout time are equally existent. Such an inference would only underscore the free logician’s claim that modern logic is still infected with inappropriate existence assumptions.

   
   
   

   

   As a result of its existence assumptions with respect to singular terms, standard logic becomes limited in its application to certain inferences and does not permit us to discriminate between inferences where the referentiality of the terms is crucial and those where it is (p.142) not.36 This violates the intuitive distinction between arguments whose validity does require existence assumptions and those which do not. For example, we are prohibited from inferring, ‘Lincoln was the Great Emancipator; Lincoln brooded; therefore, the Great Emancipator brooded’, an inference whose obvious validity should not be dependent on Lincoln’s existing. Standard logic also cannot be applied to a statement like ‘The object at position P on which no external forces are acting maintains a constant velocity’ because there is no such object. Moreover, one might think that the methods of logic should apply to reasoning involving singular terms which, for all we know, may or may not refer to existing objects, as was the case for astronomers who used ‘Vulcan’ for the suspected planet between Mercury and the Sun before knowing whether such a planet existed or not. Nolt observes that the obligation to confirm the existence of things before naming them

   is so irksome that ‘even mathematicians routinely flout it.… They get away with this, usually, only by being discreetly inexplicit about the underlying logic—which is, in consequence, not rigorously classical.’37 Advocates of positive (as opposed to negative or neutral) free logic maintain that certain sentences can be truly

   asserted even though they contain irreferential singular terms. This feature of positive free logic strikes me as well- motivated and eminently plausible. The truth of identity statements involving vacuous singular terms is of a piece with the evident truth of many sentences which feature vacuous singular terms.38 Free logic’s denial that the use of singular terms in sentences we take to be true is ontologically committing for their user is, I think, a step in the right direction. But because free logic takes the existential quantifier of first-order logic to carry existence commitments, it cannot avoid the Platonistic commitments of much abstract object talk, such as ‘There are prime numbers greater than 100’. Better to adopt a consistent neutralism, according to which (p.143) first-order quantifiers are also not ontologically committing. Such a neutral logic will not, technically speaking, be a free logic; but as Alex Orenstein

   asks: ‘Isn’t a logic which disassociates the quantifiers from existence a paradigm of a logic that is free of existence assumptions, indeed freer of existence assumptions than Lambert's variety?’39

   In sum, given a logic featuring existentially loaded quantifiers, the existence assumptions underlying the use of singular terms are going to force revisions in classical logic, like the restriction of Existential Generalization and Universal Instantiation, if plausible assignment of truth values to various sentences is to be preserved. We can avoid such major revisions by adopting a thoroughgoing neutral logic.

   
   
   

   Concluding Remarks

   In my opinion, the criterion of ontological commitment that comes to expression in premiss (I) of the Indispensability Argument is not only false, but, I should say, obviously false and wholly implausible. It is a meta- ontological thesis for which there is no good argument, and the linguistic evidence is overwhelmingly against it. Its assumption hinders logical reasoning. Most significantly for our purposes, it is outrageously inflationary ontologically, saddling us not only with innumerable abstract objects, but fantasies of almost every sort.

   
   
   

   But never mind; for the purposes of our study, our conclusion may be much more modest: simply that the criterion does not rationally impose itself upon us. One need not refute premiss (I) of the Indispensability Argument in order to defeat it; one need only undercut it by showing that it has not been proven. The theist is entirely rational to align himself with the many philosophers and logicians who rationally challenge this criterion.

   
   
   

   Notes:

   1. 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), 53. The OED is, of course, the Oxford English Dictionary.

      
      
      

   2. Routley, Exploring Meinong’s Jungle, 617.

      
      
      

   3. 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), 82.

      
      
      

   4. Routley, Exploring Meinong’s Jungle, 490.

      
      
      

   5. John Nolt, ‘Free Logic’, The Stanford Encyclopedia of Philosophy, 5 Apr. 2010, <http://plato.stanford.edu.sci- hub.bz/entries/logic-free>, §1.1. For a wonderfully limpid exposition of this semantical approach, see John Nolt, ‘Free Logics’, in Dale Jacquette (ed.), Handbook of the Philosophy of Science, v. Philosophy of Logic (Amsterdam: Elsevier, 2006), 1023–60.

      
      
      

   6. Nolt, ‘Free Logics’, 1025; cf. his ‘Free Logic’, §3.

      
      
      

   7. Jody Azzouni, Talking about Nothing: Numbers, Hallucinations, and Fictions (Oxford: OUP, 2010), 58. Azzouni continues: ‘or that fall within the range of one or another kind of quantifier appearing in those statements’.

      
      
      

   8. Ibid., 24. Azzouni actually uses blindingly tiny, lower case superscripts, for which I have substituted more visible upper case letters.

(9) Ibid., 44.

1. Cf. Jody Azzouni, ‘Singular Thoughts (Objects-Directed Thoughts)’, Proceedings of the Aristotelian Society Supplementary Volume, 85/1 (2011): 45–61, where he contrasts objects-directed thoughts with descriptive thoughts and equates ‘about’ with ‘in mind’.

   
   
   

2. Azzouni, Talking about Nothing, 45.

   
   
   

3. Michael Dummett, Frege: Philosophy of Mathematics (Cambridge, MA: Harvard University Press, 1991), 231.

   
   
   

4. Now, of course, neo-Quineans will claim that such sentences can be paraphrased in ways so as to avoid untoward ontological commitments. But then not only are these thinkers saddled with the two seemingly impossible tasks noted in the last chapter near the end of the section ‘Why Accept the Realist’s Criterion of Ontological Commitment?’, but they are also stuck with the implausible view that these sentences, at least, do commit us to such ontological grotesqueries.

   
   
   

5. John Searle, The Construction of Social Reality (New York: Free Press, 1995).

(15) Ibid., 68.

(16) Ibid., 12.

1. Symptomatic is Marga Reimer’s article ‘Reference’, in The Stanford Encyclopedia of Philosophy, 20 Jan. 2003,

   <http://plato.stanford.edu.sci-hub.bz/entries/reference>. She simply takes for granted that ‘Reference is a relation that obtains between expressions and what speakers use expressions to talk about.’ So ‘the central question’ concerning reference then becomes ‘How do words refer? What is the “mechanism” of reference?’ Oblivious to intentionality, she thinks that ‘certain types of words “hook onto” things in the world’, as though words had such an ability in themselves. She even says that proper names themselves ‘purport to refer’ to particular things, as if they were intentional agents.

   
   
   

2. See his remarks on vacuous names in W. V. O. Quine, Word and Object (Cambridge, MA: MIT Press, 1960), 177.

   
   
   

3. John R. Searle, Speech Acts: An Essay in the Philosophy of Language (Cambridge: CUP, 1969), 77. Ironically, Searle’s own construal of referring as a speech act strongly motivates a theory of reference that defeats the axiom, as we shall see. Significantly, Searle’s subsequent study of socially constructed reality seems to have convinced him that successful reference does not, in fact, require the existence of real-world objects as the referents of referential terms, for reference comes into play only after we have created certain mind-dependent ontological categories which make it possible to refer or fail to refer to e.g. the touchdown scored at the end of the fourth quarter, even though there is no language-independent object referred to by the relevant expression (Searle, Construction of Social Reality, 68, 76).

   
   
   

4. Timothy Williamson, ‘Reference’, in Donald Borchert (ed.), Encyclopedia of Philosophy, 2nd. edn (New York: Thomson- Gale, 2006). Joseph Margolis thinks that in the analytic tradition nearly everyone writing on the topic has assumed that reference is a relationship of some sort: ‘Reference as Relational: Pro and Contra’, in Rudolf Haller (ed.), Non-Existence and Predication (Amsterdam: Rodopi, 1986), 341. Diane Proudfoot and B. Jack Copeland observe that the thesis that reference is a relation, though deeply problematic, is entrenched in philosophy, psychology, linguistics, cognitive science, and artificial intelligence: ‘Wittgenstein’s Deflationary Account of Reference’, Language and Communication, 22/3 (2002): 331–2.

   
   
   

5. A fact emphasized by Searle, Speech Acts, 27; cf. Searle, Construction of Social Reality, 228. If Searle is correct that, in affirming that people have mental states which are intrinsically intentional, he has broken company with many, perhaps most, of the currently influential views in philosophy of mind—Searle, Intentionality: An Essay in the Philosophy of Mind (Cambridge: CUP, 1983), p. viii—then it is little wonder that contemporary theory of reference is in such turmoil! Look at the philosophical dead end reached by Alex Rosenberg, whose physicalism in philosophy of mind, coupled with his recognition that no physical object exhibits intentionality, lead him to deny that we ever think about anything, to claim that sentences are therefore meaningless, and to affirm that no sentence, including all the sentences in his own book, is true: Rosenberg, The Atheist’s Guide to Reality (New York: W. W. Norton, 2011), 43, 170–93, 235, 309.

   
   
   

6. Observing that it is ‘evident that it [object-directedness] is a property which no non-mental entity could possibly possess’, J.

   N. Findlay wryly remarks that, if stones refer to objects, then ‘they undoubtedly have, or are, minds’: Meinong’s Theory of Objects and Values, 2nd edn (Oxford: Clarendon, 1963), 6.

   
   
   

7. Searle, Intentionality, p. vii. ‘A sentence is a syntactical object on which representational capacities are imposed’ (pp. vii– viii). Language relates to reality in virtue of the fact that speakers so relate it in their performance of linguistic acts. ‘“How does language relate to reality?” is only a special case of “How does the mind relate to reality?”’ (197). Searle therefore regards philosophy of language as a branch of the philosophy of mind. That reference does not belong primarily to the category of language is evident from the fact that mental reference precedes linguistic reference: R. M. Sainsbury, Reference without Referents (Oxford: Clarendon, 2005), 216. We sometimes refer to something by merely gesturing or glancing, which underlines the fact that reference springs from intentionality, not language.

   
   
   

8. This is the answer to Horwich’s question, ‘How is it possible for those intrinsically inert ink marks (or some associated state of the brain) to reach out into the world and latch on to a definite portion of reality…?’ Horwich, Meaning (Oxford: Clarendon, 1998), 1. For a nice statement of the answer, see Alvin Plantinga, ‘Against Materialism’, Faith and Philosophy, 23/1 (2006): 3– 32, esp. 16–17; see also Dallas Willard, ‘Knowledge and Naturalism’, in William Lane Craig and J. P. Moreland (eds), Naturalism: A Critical Analysis (London: Routledge, 2000), 39–41. Searle points out that intentionality is more fundamental than language, since babies and even animals have intentional states. ‘Only someone in the grip of a philosophical theory would deny that small babies can literally be said to want milk and that dogs want to be let out or believe that their master is at the door’ (Searle, Intentionality, 5). Mental states are intrinsically (even if not always) intentional; intentionality cannot be reductively analysed, but is a ground floor property of the mind. By contrast, referring speech acts have a physical level of realization that is not intrinsically, but derivatively intentional (ibid., 27). According to Barry Loewer, it is today widely held that the semantic properties of natural language expressions are derived from the semantic properties of mental states: ‘A Guide to Naturalizing Semantics’, in Bob Hale and Crispin Wright (eds), A Companion to the Philosophy of Language (Oxford: Wiley-Blackwell, 1997), 108.

9. Arvid Båve, ‘A Deflationary Theory of Reference’, Synthèse, 169/1 (2009): 51–73. I am very grateful to Arvid Båve for extended discussion of Båve’s theory.

   
   
   

10. Brentano insisted upon the uniqueness of mental phenomena as object-directed or intentional. The object-directedness of mental reference does not imply that intentional objects exist in the external world. ‘All it means is that a mentally active subject is referring to them.’ Franz Brentano, ‘The Distinction between Mental and Physical Phenomena’, tr. D. B. Terrell from Psychologie vom empirischen Standpunckt (1894), vol. i, bk 2, ch. 1, repr. in Roderick M. Chisholm (ed.), Realism and the Background of Phenomenology (Atascadero, CA: Ridgeview, 1960), 50–1; Brentano, ‘Genuine and Fictitious Objects’, tr. D. B. Terrell from Psychologie vom empirischen Standpunckt, Supplementary Essay 9 (1911), repr. in Realism and the Background of Phenomenology, 71. For Husserl, by contrast, intentional objects are real-world objects about which one is thinking; but he denied that all intentional activity has intentional objects associated with it. Rejecting Meinongianism, Husserl held that, when no object exists, then the intentional activity exists without any object: Logical Investigations, 2 vols., tr. J. M. Findlay (New York: Humanities Press, 1970), ii. 595–6.

    
    
    

11. Findlay, Meinong’s Theory of Objects, 343–4.

    
    
    

12. Ibid., 40–1. See also Margolis, ‘Reference as Relational’, 327–57; R. Scott Smith, Naturalism and our Knowledge of Reality (Farnham: Ashgate, 2012), esp. ch. 2, where he interprets Fred Dretske, Michael Tye, and William Lycan as endorsing a view of intentionality which construes it as a property, not a relation.

    
    
    

13. Båve, ‘Deflationary Theory of Reference’, 63.

    
    
    

14. Saul Kripke, ‘Speaker’s Reference and Semantic Reference’, in Peter A. French et al. (eds), Contemporary Perspectives in the Philosophy of Language (Minneapolis: University of Minnesota Press, 1979), 6–27. Kripke recognized that words alone do not refer and so tried to explain the difference between what he took to be the semantic reference of the words and what the speaker meant to refer to by contrasting the speaker’s general intentions with his specific intentions. But Kripke neither provided an explication of this vaguely characterized difference nor showed its plausible application to actual practice. As Searle notes, Kripke’s distinction is not really about reference at all, since referring is something only speakers do, but is about the difference between the speaker’s meaning and the linguistic meaning of the relevant expressions. Searle, Expression and Meaning: Studies in the Theory of Speech Acts (Cambridge: CUP, 1979), 155; Searle, Speech Acts, ch. 4. But the linguistic meaning of the words is beside the point, so far as reference is concerned.

    
    
    

15. Båve, ‘Deflationary Theory of Reference’, 71. Or, with the neutralist, we could grant the inference but deny that it is ontologically committing.

    
    
    

16. Searle, Intentionality, 4. In Searle’s view, as in Husserl’s, not every intentional state has an intentional object. Every intentional state consists of an intentional content (which may or may not be propositional) in a psychological mode (such as fearing, desiring, believing, etc.) (Intentionality, 11–12). Since he takes intentional objects to be just real-world objects towards which one’s mental states are directed, it follows that in the case of intentional states which have no real-world objects, one has an intentional content without there being an intentional object. So e.g. when Johnny fears the bogeyman, Johnny has an intentional content associated with ‘bogeyman’ in a psychological mode of fearing. Searle’s view is in contrast with those who take intentional objects to be mere ‘notional objects’, i.e. what we think about, whether or not there are real-world objects correlated with such thoughts. The bogeyman is a notional object of Johnny’s thoughts. Peter Lamarque and Stein Haugom Olsen, Truth, Fiction, and Literature (Oxford: Clarendon, 1994), 183–4, see the idea of notional objects as continuous with Brentano’s understanding of intentional objects.

    
    
    

17. These include the assumptions that in the traditional ‘square of opposition’, A-statements like ‘All men are mortal’ imply I- statements like ‘Some man is mortal’, while E-statements like ‘No men are immortal’ imply O-statements like ‘Some man is not immortal’. Modern sentential logic strips Aristotelian logic of these existence assumptions by interpreting universally quantified statements to have the logical form of conditionals, e.g. ‘If something is a man, then it is mortal’, which carries no commitment to the existence of a man. Just as modern sentential logic aspires to be free of existence assumptions with respect to general terms, so free logic aspires to go one step further, to be free of existence assumptions when it comes to singular terms. According to Lambert, Free Logic: Selected Essays (Cambridge: CUP, 2003), 143–4, the central question posed by the free logician is why the assumption of existential import should be rejected for general terms but accepted for singular terms.

    
    
    

18. See Karel Lambert, ‘Existential Import Revisited’, Notre Dame Journal of Formal Logic, 4/4 (1963): 288–92; Lambert, ‘The Nature of Free Logic’, in Lambert (ed.), Philosophical Applications of Free Logic (Oxford: OUP, 1991), 3–12; Lambert, Free Logic, 17–24; so also Rolf Schock, Logics without Existence Assumptions (Stockholm: Almqvist & Wiksell, 1968), 7–15. Nolt observes that, because the domain of quantification cannot be empty, contemporary standard logic treats many existential claims as logical truths: ‘Free Logics’, 1025.

19. Karel Lambert, Meinong and the Principle of Independence (Cambridge: CUP, 1983), 98–9.

    
    
    

20. Lambert, Free Logic, 143–4.

    
    
    

21. Nolt, ‘Free Logics’, 1023.

    
    
    

22. E.g. Henry Leonard complains that the object languages of traditional logical systems cannot meaningfully contain such attributions as ‘t is fictitious’, since the truth of such an attribution requires that t exists, in which case, t is not fictitious after all. Thus, ‘t is fictitious’ is false if t does exist and false if t does not exist, in contradiction to ordinary English. Henry S. Leonard, ‘Essences, Attributes, and Predicates’, Proceedings and Addresses of the APA, 37 (1963–4): 29–30. To escape this dilemma, neo-Quineans sometimes resort boldly to affirming the existence of fictitious entities as abstract objects.

    
    
    

23. Alex Orenstein, ‘Is Existence What Existential Quantification Expresses?’, in Robert B. Barrett and Roger F. Gibson (eds), Perspectives on Quine (Oxford: Basil Blackwell, 1990), 265.