Fictionalism vs. Deflationism

Fictionalism vs. Deflationism Serious debates about the existence of entities of various sorts, including properties, numbers, propositions, possible worlds, and even institutional entities (such as corporations and marriages) have proliferated in post-Quinean metaphysics. The traditional debates raged between the heavy-duty realists on one side, who insisted that there are such objects (which serve as truth-makers for (the true parts of) the relevant discourse); and the eliminativists on the other side, who held that the terms in question fail to refer, and took the relevant range of discourse to be defective and in need of replacement. Between these extremes, fictionalism presented an attractive alternative. Broadly fictionalist approaches have been used in a number of different areas for a number of different purposes. Here I will focus squarely on fictionalism as it has figured in metaphysical debates about the existence of numbers, properties, propositions, possible worlds and the like—not on fictionalism as it has figured in the philosophy of science. As Mauricio Suarez (2010) makes clear, fictionalism in recent philosophy of science is “not primarily… a view In metaphysics or even ontology, but rather a view in methodology”—a view about the methodology of model-building according to which the imagination is indispensible in making representational modeling systems, and these models need not be treated as accurate or true to be useful, fertile representations for science. Nothing say below will bear on the acceptability of this form of fictionalism in philosophy of science, though I will occasionally mention what would follow for metaphysical versions of fictionalism about unobservable scientific posits. The goal of the fictionalist approach in metaphysics is to enable us to avoid being committed (with the heavy-duty realist) to saying that there really are such objects, while nonetheless (contrary to the eliminativist) taking the discourse in question to be perfectly acceptable (cf. Kalderon 2005, 3). The language in novels shouldn’t be taken as attempting to describe real people and activities, and its acceptability doesn’t depend on its truth. Instead, the language in novels is doing something else, such as engaging in a certain kind of pretense (within which it is appropriate to say some things and deny others). Similarly, according to the fictionalist, the discourse in question (whether it is the discourse of mathematics, possible worlds, or the courthouse) needn’t be taken to ontologically commit us to the disputed objects. We can preserve our ways of talking about properties or numbers, say, without having to accept properties or numbers into our ontology. Fictionalists are typically divided into two camps. Hermeneutic fictionalists interpret the relevant discourse as merely speaking fictionally or figuratively (Yablo 2001, 2005). Revolutionary fictionalists (Field 1980), by contrast, take themselves to be making a proposal: the restrained ontologist may choose to speak in a merely fictional or pretending way, regardless of whether the original discourse was doing so (Kalderon 2005, 5-7). I shall focus below on hermeneutic fictionalism, especially as developed by Stephen Yablo (2001, 2005), It is important to be clear, however, that what I shall have to say is about fictionalism as an approach (exemplified by some work of Yablo’s), not about Yablo’s views (taken to be exemplified by fictionalism). For Yablo has in fact tried out many views on the subject—from treating the statements as engaged in a kind of pretense or make-believe, to treating them as metaphorical or figurative, to his current appeal to the idea of non-catastrophic presupposition failure, as giving us reason for thinking that claims about the existence of numbers are less than fully ontologically committal. I will focus here only on the fictionalist strand of his work (2002, 2005), since what I am interested in is the viability of fictionalism as an approach, and its merits relative to deflationism. On changes in his view, see also his (2005, 110-111, first (unnumbered) note), and note 8 below. so henceforth when I speak simply of ‘fictionalism’, that is the view I shall have in mind. Hermeneutic fictionalists typically take the discourse of mathematics to be only making fictional or pretended assertions (claims that are supposed to be true only in the ‘fiction of mathematics’), or (in other versions) to be speaking somehow other than literally—i.e. figuratively or using simulation. On the hermeneutic fictionalist’s view, those who thought that mathematical discourse committed us to numbers were simply taking that discourse too seriously. More recently, interest has slowly been growing in a different alternative: the idea that some such ontological questions may be straightforwardly, even trivially answered, and so are not suitable subjects for serious ontological debate. Call this the deflationary meta-ontological approach. The idea is this: at least in many cases, what seem to be trivial entailments take us from uncontroversial truths to what seem to be true existence claims about disputed entities. Thus, as neo-Fregeans (Wright 1983, Hale & Wright 2001) have pointed out, from an uncontroversial sentence like ‘The cups and saucers are equinumerous’ we may infer ‘The number of cups is identical to the number of saucers’, from which we may infer ‘there is a number’—apparently settling the disputed question of the existence of numbers by way of this easy argument. Stephen Schiffer (1994, 1996, 2003) has argued that similar pleonastic ‘something from nothing’ transformations leave us with commitments to properties (as we move from: ‘Lassie is a dog’ to ‘Lassie has the property of being a dog’, to ‘There is a property’ (2003, 61)); to propositions (as we can move from: ‘Snow is white’, to ‘the proposition that snow is white is true’ to ‘there is a proposition’); to events (as we move from ‘Jane was born on a Tuesday’ to ‘Jane’s birth was on a Tuesday’ to ‘There is an event’ (2003, 63)), and other disputed entities. Amie Thomasson has argued that easy arguments also take us from a sentence even eliminativists don’t dispute: ‘There are particles arranged tablewise’, to the transformed sentence: ‘There is a tablewise arrangement of particles’ to the ontological sentence: ‘there is a table’, thus landing even would-be eliminativists with commitment to ordinary objects (2007a, 162-168). These three deflationary views are not exactly the same: the neo-Fregean employs Hume’s principle as a biconditional, and argues that the singular terms in the transformed claims are referring on grounds of their appearing in true identity statements. Schiffer’s something from nothing inferences, by contrast, are only one-way entailments that need not involve an identity statement. The easy arguments Thomasson endorses include both of these, but are not limited to cases in which we can start from an uncontroversial truth—she allows that we may easily answer existence questions even in cases in which no such undisputed claim is available, as long as we have mastery of the application conditions for the noun employed in stating the existence question and can determine (empirically or logically) whether those conditions are fulfilled. But for purposes of this paper we can put those differences aside, as the three views have this much in common: in each case, the deflationist argues that an undisputed claim in which there is no mention of an entity of type J (nor any use of the concept J or any concept supposed to be co-referential with J) may be combined with a conceptual truth that functions as what Schiffer calls a ‘transformation rule’ to give us a transformed claim that seems redundant with respect to the undisputed clam. Yet the transformed claim also seems to entail a straightforward answer to the disputed ontological question. Thus all three are meta-ontologically deflationary in the sense that they make many classic ontological disputes easy to resolve—too easy to be suitable subjects for serious metaphysical debate. So for example, we can move from: Undisputed claim: I ate two bagels Transformation rule: If P ate N bagels, the number of bagels P ate is N Transformed claim: The number of bagels I ate is two Ontological claim: There is a number (namely two). Or from: Undisputed claim: This bag is red Transformation rule: If N is Q then N has the property of Q-ness Transformed claim: This bag has the property of redness Ontological claim: There is a property (namely of redness) But while the deflationist thinks that ontological questions may be answered via these trivial transformations, the view is not a form of linguistic or ontological reductionism. The meta-ontological deflationist is not committed to the ontological claims being translatable into a more basic idiom (which holds our ‘true’ ontological commitments)—indeed most meta-ontological deflationists (Schiffer, Thomasson) treat the entailments as being one-way entailments from the undisputed claim to an ontological claim that makes use of new terms. On Thomasson’s view, for example, while competent speakers are entitled to make the inference from ‘there are particles arranged tablewise’ to ‘there is a table’, the reverse does not hold as a conceptual entailment, as it is conceivable that, e.g. plenum matter suitably arranged could constitute a table instead. The deflationist is not committed to the idea that all talk about the disputed entities can be translated into talk about more basic entities; but only that from undisputed claims (not mentioning the disputed entities or employing the relevant concepts) we may make inferences that entitle us to refer to the new entities and to conclude that there are such things. Nor is the deflationist’s view that numbers, properties or other disputed entities can be ‘ontologically reduced to’ or are ‘nothing over and above’ the entities referred to in the undisputed claim. On the contrary, the deflationist acknowledges that new singular terms are introduced that seem guaranteed to refer to a new kind of entity—not identifiable with any of those referred to in the undisputed claim. So while the meta-ontological approach is deflationary in the sense of rendering disputes about the existence of these entities pointless, the first-order metaphysical view that results (about numbers, properties, etc.) is not deflationary. Instead, the result of this deflationary metaontological approach is typically a first-order simple realism about the disputed entities. The outcome of the easy arguments is that we should accept that there are the numbers, properties, etc. in the only sense these terms have—a sense in part constituted by the transformation rules that introduce the terms to our discourse. Not all deflationists are clear about this. Schiffer, for example, often speaks as if the entities to which we acquire commitment in this way have a special deflated or ‘pleonastic’ ontological status, distinguishing them from ordinary things like trees and tables. In my view this is a mistake: the right thing to say is simply that in each case there are Ps in the only sense ‘P’ has. But this simple realist view may still be distinguished from traditional Platonism: for while the deflationary metaontologist verbally agrees with the Platonist that there are such entities, the deflationary metaontologist denies that this is a ‘deep’ and ‘explanatory’ ontological posit. The objects are not ‘posited’ to ‘explain’ what makes our claims true. Instead, the existence of the entities in question is a trivial consequence of the truth of other sentences one accepts. While still a minority view, the deflationary metaontological approach has been receiving increasing discussion and winning some new converts. In addition to those who have directly defended easy arguments for various entities, several prominent metaphysicians suggest that we should simply accept that easy arguments like these answer standard existence questions asked in English, and that as a result the real work of ontology must move on to other territory, e.g. asking not ‘what exists’ but rather ‘what grounds what?’ (Schaffer 2009) or ‘what is there really?’ (Cameron 2010) or ‘what is constitutive of reality?’ (Fine 2009). I do not mean to endorse that shift, but merely point to even these serious metaphysicians as converts to the idea that standard existence questions asked in English may be easily answered. The view has a number of attractions. The first attraction is its ability to lay to rest seemingly endless debates about the existence of entities of various sorts. But there are other attractions as well. Chief among them is the ability to demystify our knowledge of numbers and other abstracta. As Hale and Wright put it, the view is motivated by its ability to “tackle directly the question how propositional thought about such objects is possible and how it can be knowledgeable” (2009, 178). For given the trivial transformations we can see how speakers may acquire knowledge of these things by knowing the uncontroversial truths and mastering the rules of use for the terms that entitle them to make inferences from those uncontroversial truths to the existence of numbers and the like. We can thus avoid the epistemic problems the traditional Platonist faces in saying how we can ‘come into contact with’ and thereby come to acquire knowledge of abstracta. The view also has been promoted as enabling us to accept that there are the relevant entities without the ontological difficulties incurred by Platonists who treat them as explanatory posits (though full discussion of these ontological issues would have to take place elsewhere; see also Thomasson 2007a, 2009b). Finally, the view is motivated by its ability to give an apt reading of our discourse—by treating the transformations that seem redundant in ordinary English as genuinely trivial. In many ways, fictionalism and deflationism are similar views. Both are equally opposed to both traditional Platonism and to traditional eliminativism about disputed entities. Both bring to ontological debates a ‘no worries’ attitude that suggests that we can preserve the discourse in question without saddling ourselves with a heavy-duty ontology (such as Platonism in mathematics). And they tend to appeal to the same sort of philosopher: someone who suspects the heavy-duty realist of taking the discourse in question too seriously, and suspects the eliminativist of overreacting by rejecting a perfectly functional range of discourse. And both may claim to avoid the ontological and epistemic problems of traditional Platonism while preserving the discourse. But despite all they have in common, fictionalism and deflationism are rivals. The views are clearly in conflict, for deflationist asserts that there are entities of the disputed kind, while the fictionalist does not (either denying this or remaining neutral). Not only do the views conflict: the fictionalist line is wielded in making one of the most frequent attacks on the deflationist’s ‘easy’ arguments in favor of entities of various kinds. For while the inferences that (according to the easy ontologist) take us from undisputed claims to controversial ontological conclusions seem to be clearly acceptable in ordinary English, the fictionalist’s response is to deny that the ontological claims we apparently get as outputs from transformation rules are to be understood as serious assertions about the disputed topic at all—and so to deny that they really provide answers to ontological questions. More precisely, this is the response of the hermeneutic fictionalist. The revolutionary fictionalist would say that they needn’t be so understood. Another response—the dual quantifier approach—denies that what they are asserting is genuinely existential in import (Hofweber 2005a, 2005b, 2007). I discuss this response elsewhere. As Yablo writes “the a priori approach to existence questions is undermined by doubts about literality” (2000, 23). So, does the fictionalist approach undermine the a priori approach to existence questions? Do the motivations that the fictionalist marshals for his view over Platonism also give reason for preferring it to the deflationist alternative? Most importantly: supposing you were inclined to look for an alternative to traditional Platonism and eliminativism: which of these rival views should we choose? I will only be comparing the two approaches where they both seem to have a plausible account. That is, there may be some existence questions that do not appear answerable by easy arguments. For example, (barring verificationism) existence questions about the theoretic entities of physics, for example, do not seem susceptible of being answered via trivial entailments from uncontroversial truths. For purposes of this paper I will leave to the side questions about what view to adopt on such issues. Those are the questions I will discuss below. I will begin by discussing the motives for adopting a fictionalist position. Then I will examine the argument that fictionalists wield against the deflationary metaontological approach. I will argue, however, that the argument does not give any grounds for rejecting deflationism but merely begs the question against it. Moreover, I shall argue, close attention to this argument reveals an important problem for fictionalism, and a crucial disanalogy between the disputed discourse (about numbers, about properties) and overtly fictional or make-believe discourse. Finally, I will argue that motivations for fictionalism are served as well or better by deflationism. All in all, then, I will argue that deflationism may provide the preferable approach for those who suspect that heavy-duty realists are just taking things too seriously. Motives for Fictionalism Early versions of fictionalism were motivated primarily by the desire to avoid the perceived ontological excesses of heavy-duty realist views, such as traditional Platonism about numbers or properties. The advantages early fictionalists sought were ontological: not having to ‘posit’ the disputed objects to make sense of the discourse. But deflationists have argued extensively that the kind of simple realism one gets from the deflationary approach to ontology incurs no such ontological disadvantages. Thomasson (2007a) argues that those who accept the truth of the undisputed claim do not truly offer a more parsimonious ontology by denying the truth of the ontological claim, and responds to other ontological objections to deflationism, for example that it involves us in some sort of ‘magic’ (2009b). Neo-Fregeans have also shown why the anxious metaphysician’s demands that there be some ‘guarantee’ that there ‘really are’ the needed entities to refer to are illegitimate (Hale/Wright 2009). If these arguments are correct, then the deflationary realist, like the fictionalist, avoids the ontological problems of heavy-duty realism: where ontological issues are concerned the two views are on a par. Since these ontological issues have been discussed extensively elsewhere, I will leave further discussion of them to the side here. The fictionalist might also claim epistemic advantages over the Platonist: for while the Platonist is left with the puzzle of how we could come to know these causally disconnected posits, the fictionalist may explain our knowledge of mathematical truths in terms of our knowledge of non-mathematical truths combined with use of the relevant generative principles of games of make-believe. But again, the fictionalist view isn’t motivated over deflationism in this way; the deflationist view was introduced precisely to account for how we can come to know mathematical truths by way of trivial inferences (available to any who have mastered the rules of use for our terms) from uncontroversial, non-mathematical truths. In any case, the most recent and well-developed version of fictionalism takes a different and more interesting approach. On Yablo’s view, the most telling reasons to accept his version of fictionalism are not to do with avoiding epistemic problems or an unwanted ontology, but rather with the ability of fictionalism to ‘give the most plausible account of the practice’—that is, of the discourse surrounding our talk of numbers, properties, or other questioned entities: “At one time the rationale for fictionalism was obvious. We had, or thought we had, good philosophical arguments to show that X's did not exist, or could not be known about if they did. X's were obnoxious, so we had to find an interpretation of our talk that did not leave us committed to them. That form of argument is dead and gone, it seems to me. It requires very strong premises about the sort of entity that can be known about, or that can plausibly exist; and these premises can always be exposed to ridicule by proposing the numbers themselves as paradigm-case counterexamples. But there is another possible rationale for fictionalism. Just maybe, it gives the most plausible account of the practice. It is not that X's are intolerable, but that when we examine X-language in a calm and unprejudiced way, it turns out to have a whole lot in common with language that is fictional on its face.” (Yablo 2001, 87) I propose that we take Yablo at his word: that the ontological arguments in favor of fictionalism are ‘dead and gone’, and that the action lies in assessing which view gives the best account of the discourse. I will argue, however, that although fictionalism may have been well-motivated against Platonist competitors in this way, it cannot be so motivated against deflationism: for deflationism gives a better account of the discourse. 2. The Fictionalist’s Case against Deflationism Yablo argues for his variety of fictionalism by emphasizing analogies between overtly fictional or make-believe discourse and the discourse about numbers, about properties, about propostions or other disputed entities. He also emphasizes the ability of his view to account for some otherwise puzzling features of our discourse about numbers. I will return to the latter point below; for now, let us begin by examining what Yablo thinks discourse about numbers has in common with overtly fictional or make-believe discourse, and why he thinks this forms the basis for an argument against deflationism. Yablo (2001, 2005) makes use of Kendall Walton’s (1990) work on ‘prop oriented’ make-believe in making his case that talk of numbers has much in common with overt make-believe talk. He expresses the view regarding mathematical objects as follows: [Numbers (as they figure in applied mathematics)] are part of a realm that we play along with because the pretense affords a desirable—sometimes irreplaceable—mode of access to certain real-world conditions, viz. the conditions that make a pretense like that appropriate in the relevant game. (2005, 98) The transformation rules that apparently leave us saying that numbers, properties, possible worlds, and the like exist, Yablo suggests, are analogous to what Walton calls generative principles in games of make-believe, which (in conjunction with props) yield only pretend or simulated assertions. So, for example, as Walton develops the view, children playing a game of make-believe may adopt the generative principle that stumps are to count as bears (i.e., that we are to pretend that any stump is a bear) (Walton 1990, 40). The stumps are the ‘props’ in this game, and (combined with the generative principle) may generate make-believe truths, such as that there are five bears in the back yard. Speaking within the game, a player only pretends when she says ‘look out, there are five bears!’, and does not commit herself to there really being five bears. Nonetheless, she does commit herself to the ‘real content’ of the claim—that is, roughly, what information it communicates about the props (that there are five stumps). Likewise, on Walton’s view, if we say ‘A woman named ‘Anna’ died on the train tracks’ in the context of discussing Anna Karenina, we do not commit ourselves to there really being a woman so-named who died on the tracks. Instead, we only commit ourselves to the real content of the claim: that the relevant book says so, using the novel as a prop in our game of make-believe, in which we employ the generative principle that what the book says counts as true in the make-believe game authorized by the fiction. So similarly, on Yablo’s view, the transformation rules cited by neo-Fregeans are best understood simply as rules for generating make-believe truths within the ‘fiction’ of mathematics. (Similarly, transformation rules that apparently yield reference to properties, states, possible worlds, and the like are only principles for generating relevant truths in the property-fiction, possible-worlds-fiction, etc.). So, for example: The governing fiction [generative principle] of applied arithmetic says that whenever there are some E's, there is an entity their number that measures them cardinality-wise; if there are five E's, this further entity is 5 (Yablo 2001, 77). And so from the fact that there are five stumps in the backyard, we can (in conjunction with this principle) generate the claim that there is some number—five—of stumps. But this (like the claim about bears) should be taken merely as a truth-within the relevant make-believe—this time, the fiction of mathematics (Yablo 2001, 77). So those who say things like ‘the number of stumps is five’ do not commit themselves to there really being numbers. They do, however, commit themselves to the ‘real content’ of the claim: that there are five stumps (Yablo 2001, 77). The idea that those who utter claims in applied mathematics do commit themselves to something (the real content of the claim) is crucial to making Yablo’s view plausible. For it is that which enables him to preserve the idea that (although its literal content is figurative or pretending) our applied mathematical discourse is important, and enables us to state and commit ourselves to important truths about the world: those expressed in the real content, which is asserted. The fictionalist’s idea that the claims about disputed ontological entities shouldn’t be taken literally forms the basis for a worrying argument against the metaontological deflationary approach—in whatever form it takes. For while the deflationist wanted to say that easy arguments take us from uncontroversial truths to ontological claims that give us (positive) answers to disputed ontological questions, the fictionalist would block those arguments: for if the fictionalist is correct, then the apparent ontological claims we get out of the transformation rules lack the relevant force to give serious answers to ontological questions. They would instead be merely in the context of a pretense or make-believe, and would not even be intended to provide serious answers to disputed ontological questions. Thus the fictionalist accuses the deflationist of taking the disputed discourse too seriously by taking it to be making proper existence assertions when it is only simulating or pretending. If this criticism is correct, then it will give us reason to reject deflationism in favor of fictionalism. 3. A Problem for the Fictionalist’s Analogy But although Yablo motivates fictionalism by appealing to what he takes to be strong analogies between talk in applied mathematics and in works of fiction, an obvious disanalogy between mathematical and overtly fictional talk immediately suggests itself: that those making claims about numbers certainly don’t feel themselves to be engaging in mere pretend or make-believe talk. Yablo meets this objection by first trying to point to a great number of places in ordinary discourse where an element of pretense, metaphor, or figurative talk may be involved even if we do not explicitly think of ourselves as merely pretending. He also, in his later work, avoids this by saying that speakers may be engaged in simulation rather than make-believe, where: “Simulating is being in relevant respects as if one believed, while not believing except possibly per accidens” (2001, 90), and where simulating (unlike making believe) need not be an activity “easily brought to consciousness”. But even if we don’t feel that the shift to simulating badly undermines the analogy between mathematical and make-believe or figurative discourse, there is a more telling disanalogy that remains. For there is a disanalogy between the transformation rules involving number terms and the generative principles of an overt make-believe game. For it to make sense to say that we merely pretend that P, there must be a difference between what we are committed to in merely pretending that P, and what we would be committed to in really asserting that P: a speaker can merely pretend that P only if she is not committed to the truth of P. In the case of the pretense about bears, we can understand the distinction between what it is to assert that there really are five bears in the backyard, and what it is to merely pretend to assert it. For what it is for there to be a bear, for ‘bear’ to apply, is established by rules for applying the term in various situations, requiring, e.g., that there be a creature of a certain sort (perhaps the same sort as those ostended in a sample originally baptized as ‘bears’, or the like). We can leave the details to the side, because it’s pretty clear that however we understand the application conditions for ‘bear’, these are not met merely by the presence of a stump—there is something more (or rather, something else) that it would take for there to really be bears. So a speaker who pretensefully asserts (in the game of make-believe) that there are five bears, and really commits herself only to the real content: there being five stumps, undertakes very different commitments than one who seriously asserts the literal content: that there are five bears. Here it is clear that we can be committed to the truth of the real content (that there are five stumps) without being committed to the truth of the literal content (that there are five bears). Likewise, in the case of obvious works of fiction, we can see the contrast between what it is to merely pretend that a woman was killed on the tracks and asserting it: in the first case we are committed only to the real content: that the book says so, but that is a very different matter than the second case, in which we are committed to there actually being a woman who died. But it is not so easy to identify a similar contrast that enables us to say we are ‘merely pretending’ that there are numbers, properties, social objects, or other disputed entities, while committing ourselves only to the real content of the claims. I’ll begin with the easier case of institutional transformation rules, e.g., the rule that if two suitable people knowingly visit the Justice of the Peace, sincerely say the relevant vows and undertake the relevant paperwork, they come to be married (and so a marriage comes into existence). Should we say that this is merely a generative principle in a game of make-believe? Many have wanted to say something along these lines: that talk of corporations or marriages is a mere ‘manner of speaking’ or ‘legal fiction’, and Yablo uses talk of ‘marital status’ as an example of “figurative speech” (2001, 86). Even John Searle, who offers perhaps the best-developed philosophical account of institutional facts, speaks of: Our sense that there is an element of magic, a conjuring trick a sleight of hand in the creation of institutional facts out of brute facts… In our toughest metaphysical moods we want to ask… Is making certain noises in a ceremony really getting married?... Surely when you get down to brass tacks these are not real facts (1995, 45). Should we then hold that someone who says ‘We are married’ is just pretending to assert this (while all that is really asserted is the ‘real content’ of the claim: that certain vows and paperwork were undertaken)? No—all it takes to really be married just is to have undertaken the proper vows and paperwork in the proper context—to commit oneself to that ‘real content’ just is to commit oneself to the claim that we are married (and thus that there is a marriage). The only sensible contrast that can be drawn between what it is to merely pretend to assert that we are married, versus what it is to really assert it, is in terms of whether we are asserting or only pretending to assert that the vows and paperwork were undertaken. But then we can’t understand the claim “we are married” as really asserting that the vows and paperwork were undertaken (the real content), but not as really committing the utterer to the claim that they are married (the literal content). This brings to light an important disanalogy between the cases the fictionalist wants to identify as situations in which the speaker is merely pretending, making believe, or simulating, and paradigmatic cases of pretense or make-believe: in the case of works of fiction or children’s games of make-believe, there is a clear contrast to be drawn between committing oneself to the real content (the truth about the props) and committing oneself to the literal content: a difference between being committed to stumps versus bears, words on pages versus deaths on train tracks. That difference, however, is not obvious for the fictionalist about disputed ontological entities such as social entities, numbers, events and properties. Committing oneself to the vows and paperwork being undertaken does seem to commit one to being married. Similarly, to the extent that it sounds redundant in English to say “there are five stumps and the number of stumps is five”, being committed to the first claim does seem to commit one to the second, and so to there being a number; and being committed to ‘Snow is white’ does seem to commit one to accepting ‘The proposition that snow is white is true’. But then we cannot (as Yablo wants) take the latter claims, explicitly about numbers or propositions, to be merely pretending while the first is committing. Of course there are moves the fictionalist may make in response (I consider these below). Nonetheless, there certainly is not the clear and obvious contrast in these cases that there is in cases of overt make-believe and fiction between what speakers are committed to in asserting the real versus literal content. This seriously undermines the supposed analogy to genuinely fictional or make-believe discourse that was supposed to motivate modern fictionalism. It also makes evident an important and unnoticed challenge for the fictionalist approach, wherever it appears in metaphysics: we can claim to merely pretend, make-believe, or simulate that there are properties, possible worlds, or even fictional characters, while genuinely asserting only the ‘real content’ of the corresponding claims only if one can be committed to the real content without being committed to the literal content. So the fictionalist faces the challenge of saying how one may be committed to the real content without being committed to the literal content. I will return to discuss this challenge below. But first a clearer point can be made: the fictionalist’s criticism of deflationism does not hold up. Yablo claims that the deflationist’s easy arguments are “undermined by doubts” about whether the conclusions should be taken literally. But it is part and parcel of the deflationary meta-ontologist’s view that the uncontroversial claim that expresses the real content of the claim trivially or analytically entails the transformed claim (the literal content). The transformation rules are supposed to reflect rules of use that introduce the new terms to our vocabulary, just as legal definitions may introduce technical terms for (legal) marriage. According to the deflationist, these rules make the move from the uncontroversial claim to the transformed claim truly trivial. If that is the case, then a speaker who is committed to the uncontroversial claim (the real content) is thereby committed to the transformed claim (and to the ontological claim that follows from it)—even if she does not yet possess the new terms and concepts employed in the transformed claim. (Just as a speaker who says “Hey, John is an (eligible) unmarried man” is committed to John’s being a bachelor, even if she doesn’t possess the term ‘bachelor’). If, as the deflationist insists, these really do reflect rules of use for these terms (rules we master in being inducted into number talk), then no contrast can be drawn between what (according to the fictionalist) it takes for a speaker to be committed to the real content of number claims, and what it takes for the speaker to be committed to their literal content. Fine (2009, 4) similarly suggests that, if straightforward claims about the existence of numbers are ‘not strict and literal truths, then one is left with no idea either of what a strict and literal truth is, or of what the strict and literal content of these claims might be’. Cf. Hirsch (2002, 110). If that is the case, we can’t merely pretend that there are numbers while really committing ourselves only to the real content of number claims, any more than we can commit ourselves to vows and paperwork having been properly undertaken while merely pretending that we are married. Similarly, the idea that principles such as: ‘if an individual x is P, then there is some property P possessed by x’ merely generate make-believe truths (that it is true in the property-fiction that there is some property), (on the deflationist’s view) makes no more sense than the idea that the laws for marriage in the state of California only make it make-believedly the case that there are marriages, or even that the principle: ‘if there is a man and he is unmarried, then he is a bachelor’ just tells us when to make-believe that there are bachelors. In short, if (as the deflationist insists) these do reflect rules of use for the terms in question, then no sense can be made of the suggestion that the ontological claims we get as output from transformation rules are merely pretending—while we are committed only to the ‘real content’ expressed in the uncontroversial claim. For if the transformation rules reflect genuine rules of use for our terms (specifying sufficient conditions for the term ‘number’, ‘marriage’, or ‘property’ to apply) then nothing more is required for the ontological claim (the literal content) to really be true than for the uncontroversial claim (real content) to be true, and so in committing herself to the ‘real content’ of the claim a speaker also commits herself to the truth of the ontological claim—in the only sense it has—and cannot be merely pretending. Thus we can only entertain the possibility that the transformed claim is to be taken as merely pretending—a suggestion that was supposed to undermine the easy arguments—if we already presuppose that the deflationist’s view, grounded in the idea that such transformations are indeed trivial, is false. (The neo-Fregean insists that the undisputed claim and transformed claim have the same truth-conditions, while Schiffer holds that the later is a trivial, redundant consequence of the former, and Thomasson holds that the first analytically entails the second). The fictionalist’s criticism, in short, merely begs the question against the deflationist by assuming that there are no such valid trivial entailments. Thus the deflationist should not be at all moved by the fictionalist’s argument against them, and one of the most worrying lines against the easy ontological arguments of the deflationist is blocked—leaving the view intact. One might wonder whether Yablo’s more recent (2009) work on fail-safe presupposition failure fares any better. His line of argument there is based on the presupposition that the only thing to determine whether a term refers is its effects on the meaning and felt truth-value of a sentence (2009, 521). (The argument then works by showing how we can preserve the apparent assertive content and truth-value of, say, applied arithmetical sentences regardless of whether number terms refer.) This line of argument might worry the neo-Fregean, as their argument proceeds from the fact that singular terms for numbers figure in true identity statements to concluding that the terms refer—thus taking the appearance of the term in a certain kind of true statement as grounds for saying it refers. If we can take the assertive content of “the number of bagels=two” to be that there are two bagels, and take the truth of the latter (and other implications free of the presupposition that numbers exist) to account for the felt truth of the identity statement, then we may lose the justification for concluding that number terms refer on grounds of their appearing in an (apparently) true identity statement. But that argument is powerless against those forms of deflationism that do not rely on the idea that we are justified in concluding that there are numbers (properties, propositions…) because the terms figure in sentences (perhaps of a particular form, e.g. an identity statement) that seem to be true (or false). That is not Schiffer’s argument, nor is it Thomasson’s. On Thomasson’s (2007a) view, we have reason to think that the terms refer because we have reason to think that the application conditions for the term are fulfilled. In the cases at issue (for number terms, property terms and the like) the application conditions for the singular terms are guaranteed to be fulfilled given the truth of the uncontroversial claim. Thomasson and Schiffer make no use of the argument: since the singular terms appear in an apparently true claim (identity claim or whatever) the terms must refer. Instead, according to Thomasson, what determines whether a term refers is whether its application conditions are fulfilled. Moreover all three deflationary views would reject the idea that there is some presupposition of the transformed claim that might fail though the assertive content remains true. For on each of these views, the transformed claim is a trivial or analytic entailment of the uncontroversial claim. Thus there is simply no need for a ‘fail-safe’ mechanism; there are no ‘extra’ commitments in the latter two sentences that are not already implicit in the first, which might fail though the first is true. The fictionalist’s argument against deflationism also cannot be revived by suggesting that while the conclusion might not be merely pretending, it may involve ‘simulation’: if the transformation rules do reflect genuine rules of use for our terms, then the speaker cannot be merely simulating belief in numbers (where simulation is “being in relevant respects as if one believed, while not believing except possibly per accidens” (2001, 90; italics mine)). For if someone believes the undisputed claim that there are three cups on the table, it would be no accident that she believes that there is a number (of cups on the table), given that the latter would be a trivial consequence of the former. And if someone believes that Jane was born on a Tuesday, it would be no accident that she believes that there are events (e.g. of births). Thus it doesn’t help the fictionalist argue against the deflationist to suggest that the speaker is merely simulating (rather than pretending), even if we take simulation to be compatible with belief. The chief difference between the fictionalist and deflationist’s reading of the discourse used in ‘easy arguments’ lies in whether the transformation rules are taken to be generative principles in games of make-believe, or implicit definitions or introduction rules for the terms in question. So far, I have argued that the supposed analogy to generative principles in games of make-believe looks questionable on closer examination. The better analogy seems to be with institutional and legal terms, which are introduced by explicit definitions, and entitle us to make the relevant transformations trivially. But if that is the closer analogy to discourse about numbers, properties, and the like, then it seems thus far that the deflationist should be untroubled by the fictionalist’s criticisms, and is on the road to offering a better account of the discourse than the fictionalist has given. 4. How the Fictionalist Incurs a Debt But can’t the fictionalist deny that the inferences in question really are trivial, or reflect constitutive rules for the meanings of the terms in question, and thereby hold onto the idea that one may really assert the basic claim while only pretending to be committed to the ontological claim? Yes he may, but only at the cost of (1) abandoning the idea that this can provide any argument against deflationism, (as we have seen above) and (2) incurring a daunting argumentative debt. What debt does the fictionalist incur? Since he thinks that the ontological claims are merely pretending, it seems he must hold that there is something more it would take for the ontological claim to be literally true than for the undisputed claim to be true, or else we can’t make sense of the idea that one can be committed to the real content without being committed to the literal content. Interestingly, Yablo seems almost to notice this point at one stage, remarking that “’really’ is a device for shrugging off pretences…[but] I’m not sure what it would be to take ‘there is a city of Chicago’ more literally than I already do” (1998, 259). But he adds in the attached footnote “I have a slightly better idea of what it would be to commit myself to the literal content of ‘the number of As = the number of Bs’” (1998, 259 n.74). Unfortunately, he does not say what that idea is, and I don’t know what it could be, unless it’s the common idea (discussed below) that there really is some object. How can the fictionalist make good on this idea? What more could it be supposed to take for the literal content to be literally true, than merely for the real content to be true? There might be some who are tempted to think that more is required for there to really be numbers, properties, or even marriages and corporations, than can follow via trivial transformations from the truth of the undisputed statement: namely, that there really is some (new) object/entity/individual present. But as Thomasson has made evident (2007, 2009a), there is a problem with this use of generic terms like ‘object’. For the relevant general sense of ‘object’ in which it seems to make sense to say that there is a number there only if there is some object, involves using ‘object’ in a covering sense, under which we are licensed to make the inference from ‘there is an S’ (where S is any well-formed sortal term), to conclude that there is an object. As a result, we can’t deny that the original transformation succeeds on grounds of denying that there is an object; instead, we can first move from the undisputed claim to the specific ontological claim (there is a number), and then undertake another trivial transformation from the specific ontological claim to the generic ontological claim to reach the conclusion that there is an object; no further conditions are required to make that true than to make the undisputed claim and the specific ontological claim true. Another standard use of ‘object’ is as a sortal term, typically used to track medium sized unified and independently mobile lumps of stuff. It may well be that Yablo tacitly has something like this in mind, as he presents a great many forms of speech as involving ‘metaphor’ simply on grounds of their use of a term ‘thing’. So, for example, he takes as examples of non-literal speech such claims as “something tells me you’re right”, “there are some things better left unsaid”, “the last thing I want is to”, and so on (2000, 14). Such claims do not, intuitively, have anything non-literal about them, and it seems we can only see them as involving some kind of metaphor or make-believe if we think of the ‘thing’ here as involving some sortal use of the term that would appeal to a unified lumpish entity whispering ‘you are right!’ in your ear, and the like. But that seems to involve a misreading of the straightforward placeholder use of ‘thing’ here, not to reveal an unnoticed element of metaphoricality (in what the utterers would take to be perfectly straightforward speech). In any case, clearly anyone who thought that it took the presence of an ‘object’ in this sortal sense for there to be a number failed to grasp the number concept to begin with. Other ideas of what more it would take for the literal content to be true seem similarly inappropriate. If one held, e.g. that the literal truth of ‘there is a number (of bagels)’ would require there being something beyond the bagels that is causally efficacious (something to which one is not committed in just asserting the real content: there are two bagels), one would seem to have missed the point of our number concepts: there seems no reason to think that for there to be numbers there would have to be ‘things’ (apart from the bagels) that are causally efficacious. In fact, that would seem like quite an odd view of numbers to take: denying that there are numbers on grounds of denying that there’s anything causally efficacious is rather like denying there’s a frog here on grounds of denying that there’s anything that lights up. The requirement of causal efficacy might hold greater promise in some other cases: e.g. the fictionalist about the theoretical entities of physics might hold that what more it would take for the literal content of claims about the existence of theoretical entities to be true would be for the entities to make a causal difference (rather than talk of them merely proving useful to our calculations). David Armstrong (1989) of course places a causal efficacy requirement on the real existence of properties—though it is debatable whether this is revealing what it would take for there to really be properties (using our standard property talk) or rather proposing a new use of the term ‘property’ to better serve a theoretical purpose. Such suggestions in any case must be examined on a case-by-case basis. (For discussion of the requirement in the case of ordinary objects, see Thomasson 2007a, Chapter 1). 5. A Reply for the Fictionalist A different line of reply the fictionalist might try to make is as follows: the fictionalist might say that we can maintain that the conclusions of the ‘easy’ arguments are merely pretenseful or metaphorical without that requiring us to make any sense of what more it would take for the ontological claim to be literally true. For some terms may only have pretending or metaphorical uses, and so the fictionalist may hold that the disputed terms like ‘number’ and ‘property’ are always just metaphorically or pretensefully used. As a result, we can resist the pressure to say what more it would take for the relevant ontological claims to be literally true (as the terms may simply have no literal use) and avoid the daunting debt. Yablo acknowledges that “it hardly seems possible to use the words ‘number’ an ‘10’ more literally than I already do” (2000, 19). However, he suggests, we can make pretenseful use of a term even if there is no literal use with which we can contrast it: one may merely pretend that there is ‘gravid liquid’ even if this term has no literal use in English (the use may be guided by the idea of what ‘gravid’ is to mean in the book’s pretense: an ultra-heavy liquid ‘the tiniest drop of which weighs many tons”(2000, 20)). Similarly, we can say “She has a lot of smarts” even if there is no literal use of the noun form “smarts” in English, and say “He scared the bejeebers out of me” even though there is no literal use of ‘bejeebers’ enabling us to contrast what it would take for this to be literally true with what it takes for the relevant metaphorical claim to be apt—and so for the real content (that she is smart, that he scared me) to be true. But in the first case, one can say something about what more would be required for “there is gravid liquid in this test tube” to be literally true than for the corresponding real content to be true: clearly here, too, there is a difference between what one is committed to in asserting the real content of the claim (viz., that there are certain sentences on the page of the work of literature that serves as the ‘prop’ in the relevant game of make-believe) and what one would be committed to in asserting its literal content (that, at the least, requires commitment to the presence of a heavy liquid, not (just) to the presence of words in a work of literature). Even if we can’t say exactly what more is required, we can say that it would require that there be a liquid-filled test tube. Here there is mere pretense, but there is also the required difference between the real content one is committed to, and what one would be committed to in seriously asserting the literal content. What about if we say ‘she has a lot of smarts’? Here, Yablo, argues, even if the noun form ‘smarts’ has no literal meaning (but has its metaphorical meaning in the noun form informed by the literal meaning of the adjectival form ‘smart’), we can retain the metaphorical content even if we can’t say what it would take for it to be literally true that she has a lot of smarts (2000, 20). But in this case, as in the case of discourse about numbers and properties, there does not seem to be a difference between what one commits oneself to in asserting the real content (that she is very smart) and what Yablo would call the literal content (that she has a lot of smarts). Someone committed to saying that she is smart seems committed to saying that she has a lot of smarts—even if he doesn’t like to use the colloquialism. But nor does the latter use intuitively seem to be metaphorical, pretending, or anything other than literal. If I say ‘she has a lot of smarts’, I do not mean to be invoking a metaphor according to which she has little pink chips in her head called ‘smarts’: and lots of them, but rather simply using a different turn of phrase to say that she’s quite smart. Here it seems we lack the needed contrast, but we also lack a mere pretense. Or if you do think it is metaphorical in this way, then we can again say something about what more it you would commit yourself to in being committed to the literal content (that there are the pink chips) that you aren’t committed to in just asserting the real content. (Much the same analysis would go for the bejeebers case.) In each case again either the transformed claim seems not to be merely pretending or metaphorical, or we can make some sense of what more it would take for it to be literally true than for the real content to be true. So, I conclude, to maintain the view that the apparently ontological claims are merely pretenseful the fictionalist does retain the burden of holding that there is something more that it would take for claims about numbers, properties, and the like to be literally true—some additional conditions that are not guaranteed to be met even if the so-called ‘real content’ is true. But what? 6. The deflationary alternative I have argued that fictionalism doesn’t give us any reason for rejecting the deflationary approach, and that it also acquires an unpleasant argumentative debt. Still, some might be attracted to fictionalism on grounds that it can at least provide us with an alternative way of understanding what the so-called ‘transformation rules’ are doing, and how the disputed discourse can be acceptable without being committed to heavy-duty realism. The fictionalist does admittedly provide an alternative reading of the transformation rules that can save us from ontological commitments, but is it a preferable alternative? Why might one be attracted to fictionalism? One might be attracted to it on ontological grounds—as a way of avoiding commitment to the disputed objects. But as mentioned in section 1 above, while this may be an advantage over Platonism, it is not at all clear that deflationism, properly understood, has any such ontological difficulties—or that fictionalism can be motivated over deflationism on these grounds. One might be attracted to it on epistemic grounds—that the fictionalist avoids making our knowledge of numbers, properties, and the like mysterious, since it does not assert that there are these special abstract entities outside the causal realm that we must somehow get to know. Instead, the fictionalist may hold that we come to know arithmetical truths simply by knowing ordinary truths and mastering the relevant generative principles. But again (to the extent that it is a problem at all) the epistemic problem is a problem for Platonists, not deflationists. Indeed the whole neo-Fregean program in the philosophy of mathematics was designed with the goal in mind of demystifying our knowledge of mathematics by showing how we can acquire mathematical knowledge by way of undisputed non-mathematical claims and conceptual truths. The deflationist can account for our knowledge, say, of the truths of applied arithmetic as based on knowing ordinary truths and mastering the rules of use for the new terms in ways that licenses us to make the relevant transformations to acquire knowledge of mathematical truths. Yablo himself of course rejects these ontological and epistemic concerns even as grounds for endorsing fictionalism over Platonism; if anything they are even more clearly irrelevant to deciding between fictionalism and deflationism. If we put ontological and epistemic issues aside, fictionalism gives us a preferable alternative to deflationism only if the fictionalist can give us independent reasons for thinking that he gives a more plausible view of the discourse—giving us good reason for embracing his interpretation of the transformation rules over that given by the deflationist. But I have argued that closer attention to the contrasts between genuine fictional/pretenseful discourse and the case of the transformation rules used by easy ontologists to draw ontological conclusions suggests important disanalogies. These undermine the idea that fictionalism can be motivated over deflationism by its ability to give a better account of the discourse. Indeed, the disanalogies make the hermeneutic fictionalist appear to be offering a rather forced reading of what’s ‘really going on’ in number talk. It also leaves fictionalists in the unappealing position of having to require that something (what?) more be the case for there to really be those objects than is required for the real content to be true. The deflationary realist, of course, faces no such problem—for she does not say that statements about numbers, properties, or marriages are merely pretended, figurative, or simulated assertions. Instead, on the deflationist view, claims that there are prime numbers, or properties possessed by whales but lacked by sharks, or many marriages that won’t last, are literally true in the only sense these terms possess: a sense in part constituted by the transformation rules that introduce them to the language. The deflationist also has a number of advantages over the fictionalist in providing a good account of the discourse. To ordinary speakers, claims like “I ate two bagels and the number of bagels I ate is two” or “The shirt is red and the shirt has the property of redness” do sound redundant. The deflationist, unlike the fictionalist, may take them to be as redundant as they sound, and may take the apparent platitudes expressed in the transformation rules to be genuine platitudes reflecting rules of use for our terms. In ordinary English, the transformed claim does seem to be just a wordier way of restating the basic claim (or a way more suited to highlighting some parts of the information rather than others (Hofweber 2005a)), and so it’s a virtue to preserve the idea that these really are trivial entailments reflecting rules of use for the relevant English terms. Another advantage of the deflationist over the fictionalist is that the deflationist may take statements about numbers to be a priori and necessary. Yablo argues that he can account for the appearance of a priority and necessity of an arithmetical statement like ‘2+3=5’, by saying that the real content of claims of arithmetic (all that we care about) express logical truths, and so are necessary and a priori (2001, 90). But the deflationist can offer a more direct account of why arithmetical claims and even claims about the existence of, say, a prime number between 1 and 10, ‘strike us’ as a priori and necessary: because they are. For, on that view, claims about the existence of numbers (given the rules of use for the terms involved) are analytically entailed from basic claims that themselves are analytic. This captures the idea that numbers and the like exist necessarily. Their existence can be known a priori in that the truth of the ontological claim may be inferred by any competent users of the terms (who have mastered the relevant trivial inference) without the need for knowing any empirical truth (since one may begin the inference from an analytic claim). Thus on the deflationist view, unlike the fictionalist view, we can take these existence claims to be necessary and a priori at the level of literal content, not just at the level of real content. Yablo argues that fictionalism is preferable over Platonism given its ability to explain otherwise puzzling features of the discourse, and that may be so. But in each case, the deflationist can do as well as the fictionalist or better at explaining the relevant feature—so this line of argument provides no advantage for fictionalism over deflationism. Among these features is impatience: that is, the fact that mathematicians and others who use number talk are “strangely indifferent to the question of their existence” (2001, 89). This, Yablo argues, makes sense if that question is really irrelevant to the claims being made about the world (since all that is relevant is the real content of the claim). While that may be an adequate explanation of impatience, the deflationist can do just as well or better by explaining the impatience of mathematicians and other competent speakers as follows: Competent speakers are impatient at the question because the answer (Yes: there are numbers) is so patently obvious to anyone properly initiated into the practice of using our number terms. (Thus there is also a suspicion that those who think there is a real question at issue have gone astray somewhere—for one diagnosis of where, see Thomasson 2009a). One might worry that the deflationist is then committed to holding that eliminativists simply contradict themselves or are not competent speakers. Of course we need not treat them as semantically incompetent, as they use the terms perfectly well in non-philosophical contexts. Instead, we can give a Carnapian interpretation of what they are (perhaps unwittingly) up to in their philosophical pronouncements: but we can see them as implicitly suggesting a revision in our language. Beyond impatience, Yablo argues that the fictionalist can do better than the Platonist at explaining the apparent ‘insubstantiality’ of numbers; the fact that they lack a ‘hidden and substantial nature’, and that their identity relations are often indeterminate (2001, 89). Indeed the very idea that certain entities lack a hidden and substantial nature was introduced by Stephen Schiffer and Mark Johnston in defense of a deflationary view. While I agree that the natures of the entities in question are determined by the relevant rules of use, however, I would not want to treat the relevant entities as having some sort of distinctive second-class status. As mentioned above: I think the right response is to say that there are properties, numbers, etc. in the only sense these terms have—not in some reduced or second-class sense. For “this is what you would expect of something conjured up for representational purposes. Why should we have filled out the story further than needed?” (2001, 89). But again the deflationist can do as well or better: if we think of the transformation rules as object-language articulations of rules of use for the term being introduced, then it is easy to see how certain indeterminacies may result. Where the rules are open-ended, under-specified, and collectively determined, risks of indeterminacies and vagueness in the corresponding modal features enter in. Suppose, for example, that the rules of baseball say that if the batter arrives at the base first he is safe; if a fielder arrives first he is out. In that case, it is clearly left indeterminate what happens if there is a tie at first base. So similarly, if the introduction rules for a term are left gappy or open-ended, the existence and identity conditions for the corresponding entities may be correspondingly indeterminate. So, for example, are we entitled to infer that there is a property only if a predicate is truly applied—or also if it is falsely applied? (We can move from ‘Dobbin is a horse’ to ‘There is a property of horseness (that Dobbin has)’; can we also move from ‘Dobbin is not a unicorn’ to ‘There is a property of unicornness (that Dobbin lacks)’)? If our rules are not determinate, then there may be no determinate answer to the question of whether there is a property in such cases. If properties P and Q are everywhere co-instantiated across all possible worlds, does that show that the properties are identical? Again, if the rules of use (this time the co-application conditions) for our terms are indeterminate, there may be no answer to questions like these (see Thomasson 2009a). The other features Yablo mentions involve the fact that numbers, sets, properties and the like ‘come in handy as representational aids’, enabling us to say more about the ordinary concrete world. But we may retain Yablo’s insight that terms for numbers, properties, and other abstract entities are often introduced as representational aids to help share information about the concrete world—and yet still hold that the terms so introduced (given their rules of use) do refer. A good account of how the terms are introduced and what function they are introduced to perform is not in tension with the deflationist’s idea that the terms so introduced do, trivially, come to refer to entities not referred to in the basic claim, making the existence claims true in the only sense that the terms in question have. Yablo tells a nice story about how the relevant discourse might come to be introduced to serve functions (serving as a representational aid) rather different from the function of, say, names of people or of newly discovered biological species (which we might think of as introduced to track independently identified entities). This might help debunk a kind of naïve Platonism that thinks of number terms and property terms on analogy with terms for students or species. But it is in complete harmony with the deflationary project, which wants to begin by noting the different purposes different elements of discourse may serve, and the different rules of use our terms accordingly follow, while nonetheless allowing that the terms so introduced function perfectly well, and refer in the only sense these terms have. The deflationist, unlike the Platonist, is in a position to absorb and make use of a good functional analysis of the discourse, without incurring the disadvantage of being committed to the idea that there is something more that it would take for the literal content to be true. Thus the deflationist may absorb the advantages of a fictionalist view like Yablo’s while shedding its disadvantages. 7. Conclusion The classic attractions of fictionalism arose when it was developed as an (at the time perhaps the only plausible) alternative to heavy-duty realism on the one hand, and eliminativism on the other hand. While its original motivations were predominantly ontological and epistemic, more recently it has been motivated on grounds of its ability to offer a superior account of the discourse. And fictionalists have suggested that the can undermine the deflationist’s easy arguments by raising doubts about whether their conclusions were to be taken literally. I hope that this paper has made two things clear: One, that the fictionalist does not provide any argument that undermines the deflationist’s position. Two, that fictionalism cannot be motivated over its contemporary deflationary rivals on grounds of an ability to offer a superior account of the discourse. The analogies supposed to hold between genuine fictional and mathematical discourse are tenuous and easily undermined, and the deflationist seems better able to account for the features of the discourse. Thus the fan of fictionalism will have to return to more old-fashioned epistemic or ontological motivations. But again while fictionalism might seem an attractive way to avoid the epistemic problems of traditional Platonism, it can’t be motivated over deflationism on epistemic grounds. Those who are attracted to fictionalism over deflationism thus are left falling back on alleged ontological advantages of not having to ‘posit’ these ‘suspect’ entities, and at that stage the discussion returns to familiar territory (discussed, inter alia, in Thomasson 2009a). So it seems that although the rhetoric of fictionalism is often directed against the deflationist’s ‘easy arguments’, at the end of the day the fictionalist’s arguments are only persuasive if one implicitly has something like the Platonist view in mind as the opposition—or is keen to avoid ‘commitment’ to the ‘extra objects’ at all costs. If those ontological concerns are aptly put to the side where the deflationist’s simple realism is concerned (a position I haven’t argued for here, though deflationists have done so elsewhere), then it looks as if even that reason for preferring fictionalism evaporates. The deflationist metaontological picture, of course, faces objections of its own: most prominently the ‘bad company’ objection that questions whether we should blithely accept transformation rules, given that apparently parallel ones lead to problems or paradox; and worries about the notion of analytic entailment, or trivial or redundant transformations that is needed to ground the easy arguments. For reasons of space, I will not discuss those concerns here, though this has been done extensively elsewhere. On the bad company objection, see Schiffer (2003 Chapter 2), Hale and Wright (2000) and (2009, 191-2). On analytic entailments see Thomasson (2007a, Chapter 2). But assuming these difficulties can be avoided or overcome (and the ontological worries aptly kept at bay), it seems that although fictionalism was an attractive alternative to Platonism, on the contemporary stage, deflationism may provide a preferable view to fictionalism: able to preserve its advantages as well or better, while avoiding its difficulties. Indeed on reflection, perhaps a view like deflationism is what fictionalists should have been looking for all along as a persuasive and acceptable alternative to heavy-duty Platonism. And while heavyweight realists may be taking the disputed discourse too seriously, it may be that they, eliminativists, and fictionalists are all alike in taking the ontological debates too seriously, and thinking it would take something more for the ontological claim to be true than simply for the undisputed claim to be true. References: Armstrong, David M. (1989). Universals: An Opinionated Introduction. Boulder, CO: Westview Press. Austin, J. L. (1962). Sense and Sensibilia. Oxford: Clarendon Press. Boghossian, Paul (1996). “Analyticity Reconsidered”, Nous 30, no. 3: 360-391. Cameron, Ross (2010). “Quantification, Naturalness and Ontology”, in New Waves in Metaphysics, Allan Hazlett (ed.), New York: Palgrave-Macmillan, p8-26. Chalmers, David, Ryan Wasserman and David Manley, eds. (2009). Metametaphysics. Oxford: Oxford University Press. Dorr, Cian (2005). “What we disagree about when we disagree about Ontology”. In Mark Eli Kalderon, ed. Fictionalism in Metaphysics. Oxford: Clarendon. Eklund, Matti (2006a). ‘Neo-Fregean Ontology’. Philosophical Perspectives 20: 95-121. Eklund, Matti (2006b). “Metaontology”. Philosophy Compass 1/3: 317-334. Field, Hartry (1984). ‘Critical Notice of Wright’s Frege’s Conception of Numbers as Objects. Canadian Journal of Philosophy, 14: 637-62. Field, Hartry (1980). Science without Numbers. Princeton: Princeton University Press. Fine, Kit (2009). “The Question of Ontology”. In Chalmers, et al. Hale, Bob and Crispin Wright (2009). “The Metaontology of Abstraction”. In Chalmers et al. Hale, Bob and Crispin Wright (2001). The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics. Oxford: Clarendon. Hawley, Katherine (2007). ‘NeoFregeanism and Quantifier Variance’. Proceedings of the Aristotelian Society Supplementary volume LXXXI: 233-49. Hirsch, Eli (2002). “Against Revisionary Ontology,” Philosophical Topics 30: 103-27.. Hofweber, Thomas (2005a). “A Puzzle about Ontology”. Nous 39:2: 256-83. Hofweber, Thomas (2005b). “Number Determiners, Numbers, and Arithmetic” Philosophical Review vol. 114.2, pp. 179-225. Hofweber, Thomas (2007). “Innocent Statements and their Metaphysically Loaded Counterparts”. Philosophers’ Imprint Vol. 7, No.1: 1-33. Kalderon, Mark Eli (2005). Fictionalism in Metaphysics. Clarendon Press: Oxford. Schaffer, Jonathan (2009). “On what grounds what”. In Chalmers, et. al. Schiffer, Stephen (1994). “A Paradox of Meaning”. Nous 28: 279-324. Schiffer, Stephen (1996). “Language-Created Language-Independent Entities”. Philosophical Topics 24:1, 149-167. Schiffer, Stephen (2003). The Things we Mean. Oxford: Oxford University Press. Sider, Theodore (2006). “Quantifiers and Temporal Ontology”. Mind 115: 75-97. Sider, Theodore (2007). ‘NeoFregeanism and Quantifier Variance’. Proceedings of the Aristotelian Society Supplementary volume LXXXI: 201-32. Sider, Theodore (2009). “Ontological Realism” in Chalmers et al (2009). Strawson, P. F. and H. P. Grice (1956). “In Defense of a Dogma”. Philosophical Review 65, 2: 141-58. Suarez, Mauricio (2010), "Fictions, Inference, and Realism", in J. Woods (ed.), Fictions and Models: New Essays, Philosophia Verlag, Munich, pp. 225-245. Thomasson, Amie L. (2001). “Ontological Minimalism”, American Philosophical Quarterly, Volume 38, No. 4: 319-331. Thomasson, Amie L. (2007a). Ordinary Objects. New York: Oxford University Press. Thomasson, Amie L. (2007b). “Modal Normativism and the Methods of Metaphysics”, Philosophical Topics, 35/1&2: 135-160. Thomasson, Amie L. (2008). “Existence Questions”. Philosophical Studies. 141: 63-78. Thomasson, Amie L. (2009a). “Answerable and Unanswerable Questions” in Chalmers, et al. Thomasson, Amie L. (2009b). “The Easy Approach to Ontology”. Axiomathes 19 (1): 1-15. Walton, Kendall (1990). Mimesis as Make-Believe. Cambridge, Massachusetts: Harvard University Press. Wright, Crispin (1983). Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen University Press. Yablo, Stephen (1998). “Does Ontology rest on a Mistake?”. In Proceedings of the Aristotelian Society Supplementary Volume 72: 229-61. Yablo, Stephen (2000). “A Paradox of Existence”. In Anthony Everett and Thomas Hofweber, eds. Empty Names, Fiction, and the Puzzles of Non-Existence. Palo Alto: CSLI Publications: 275-312. Yablo, Stephen (2001). “Go Figure: A Path through Fictionalism”. Midwest Studies in Philosophy 25: 72-102. Yablo, Stephen (2005). “The Myth of the Seven”. In Mark Eli Kalderon, ed. Fictionalism in Metaphysics. Oxford: Oxford University Press. Yablo, Stephen (2009). “Must Existence Questions have Answers?” in Chalmers, et al. 38