Against Truth Jamin Asay Lingnan University jaminasay@ln.edu.hk Forthcoming in Erkenntnis Abstract I argue that there is no metaphysically substantive property of truth. Although many take this thesis to be central to deflationism about truth, it is sometimes left unclear what a metaphysically substantive property of truth is supposed to be. I offer a precise account by relying on the distinction between the property and concept of truth. Metaphysical substantivism is the view that the property of truth is a sparse (non-abundant) property, regardless of how one understands the nature of sparse properties (as universals, tropes, or natural classes). I then offer two new arguments against metaphysical substantivism that employ ideas involving recombination and truthmaking. First, I argue that there are no theoretically compelling reasons to posit the existence of a metaphysically substantive property of truth. Secondly, I argue that if we do posit the existence of such a property, then we end up with a view that is either contradictory or unmotivated. What we're left with is a metaphysically deflationary account of the property of truth that fully respects the metaphysical ambitions of truthmaker theory, and that is consistent with both the view that truth is a deflated, explanatorily impotent concept and the view that truth is an explanatorily powerful (though primitive) concept. 1. Introduction There is no metaphysically substantive property of truth. Although this thesis is frequently taken to be the central tenet of deflationary theories of truth, it is less common for theorists to be clear about just what a metaphysically substantive property of truth is supposed to be. The first goal of this paper is to give a precise account of what metaphysical substantivism 2 about truth is, and distinguish it from other substantivist theses about truth. Once my target has been identified, I shall offer two new arguments against such views that employ ideas involving recombination and truthmaking. What results is a deflationary account of the property of truth that may or may not be deflationary with respect to the concept of truth. Such a metaphysically deflationary account of truth is compatible with both deflationary and primitivist accounts of the concept of truth, and is fully compatible with the overall metaphysical ambitions of truthmaker theory. In what follows, I shall be relying on the distinction between the property of truth and the concept of truth.1 That there is, in general, a distinction between properties and concepts is familiar. Consider the case of water. On the one hand we have the property of being water, that property of fluids that are necessarily composed of H2O molecules. On the other hand we have our concept of water, according to which it's not (conceptually) necessary that water is H2O. For the purposes of this paper, I am officially neutral with respect to the nature of concepts; as for properties, I also take no stand, but argue that on any standard conception of metaphysically substantive properties, truth fails to qualify. By distinguishing between the property and concept of truth, we can identify two separate deflationary theses about truth. First, deflationism is often defined as the view that truth is not a property at all,2 or at least as the view that truth is not a "metaphysically substantive", "genuine", "heavyweight", or "robust" property of truth.3 Unfortunately, it's less common for any more to be said about what it is to be a metaphysically substantive property. One goal of this paper is to fill in that lacuna.4 The second deflationary thesis is that our concept of truth is explanatorily impotent.5 According to this thesis, our concept of truth serves merely an expressive function, not an explanatory one. That is to say, truth does not crucially figure into our accounts of other notions 1 Fortunately, drawing this distinction in the theory of truth is more and more common. Cf. Wright 2001, Alston 2002, Künne 2003: 2, Lynch 2006, Bar-On and Simmons 2007, and Damnjanovic 2010. See also Burgess and Burgess 2011. 2 E.g., Boghossian 1990: 161, Kirkham 1992: 307, Alston 1996: 41, Lynch 1998: 112, Merricks 2007: 187, and Young 2009: 564. 3 E.g., Horwich 1990: 38, Putnam 1991: 2, Wright 1992: 13, Blackburn 1998: 75, Engel 2002: 41, and Lynch 2006: 68. 4 See also Edwards (forthcoming), which considers and critiques a number of attempts to say what the distinction between substantive and deflationary properties is. Edwards, independently, ends up developing a conception of the distinction that closely matches my own. 5 E.g., Horwich 1990, chapter 3 and Williams 1999 and 2002. 3 (such as belief, assertion, or meaning), beyond its role as an expressive device. Truth is conceptually isolated, in the sense that we don't need it to explain any other concept, and we don't need other concepts (like correspondence or coherence) to explain it. Truth exists only to serve various expressive purposes. We can use 'true' to assert a claim that somebody made yesterday, even if we've forgotten what it was ("What she said is true"). Or we can use 'true' to express what would otherwise be an infinitely long disjunction or conjunction ("Something she said is true"; "Everything she said is true"). What we can't do, according to deflationists, is use truth to explain other notions in a way beyond using it as an expressive device. For example, although we can appeal to truth in explaining the nature of knowledge ("S knows that p only if 'p' is true"), here we just have an instance of truth being used as a device for expressing generalizations ("S knows that p only if p is 'wallabies wage war' and wallabies wage war, or p is 'penguins provide protein' and penguins provide protein, or ..."). What deflationists deny is that there's anything more to the explanatory utility of truth beyond the expressive conveniences it enables. As Michael Williams puts the point, "according to deflationists, there are no explanatory projects that require us to treat truth as a theoretical primitive" (2002: 148). Opposed to deflationism, then, are views such as Davidson's (1996) that take truth as a conceptual primitive; Davidson then uses that primitive concept of truth in order to offer a truth conditional account of the nature of meaning. My goal in this paper is to give a precise account of the thesis that truth is not a metaphysically substantive property, and then offer two new arguments in favor of it. The considerations that I raise do not, however, impinge on the truth of the second deflationary thesis. Given that the traditional theories of truth (e.g., correspondence, coherence, and pragmatic accounts) are usually placed in the "metaphysically substantive" camp, my arguments, if successful, transfer the debate in the theory of truth to that between whole hog deflationists about truth (i.e., those who subscribe to both deflationary theses) and conceptual primitivists about truth (e.g., Frege 1956 and Davidson 1996), who argue that truth is an explanatorily powerful concept, but not a metaphysically substantive property. 2. Metaphysical Substantivism About Truth The natural place to turn in order to get a handle on what a metaphysically substantive property of truth is supposed to be is the literature on the metaphysics of properties. 6 The philosophical discussion about properties involves the attempt to understand how it is possible 6 I follow Armstrong 1997 in my setup of the landscape. 4 that distinct objects can share the same feature-the "problem of the one over the many". Many philosophers accept that there is more to objects sharing a genuine feature than merely their falling under the same predicate. Green objects, for instance, resemble one another in a way that grue objects do not. As a result, we may distinguish between the sparse and abundant properties.7 The sparse properties are those that account for the genuine resemblances between objects. Abundant properties, by contrast, can be shared between objects without bestowing any resemblance upon them. There need not be any genuine feature held in common between all the objects within a 3.5 mile radius of the deepest point of the Atlantic Ocean, though there are genuine features held in common between all samples of gold. Different views regarding the metaphysics of properties offer different accounts of the nature of the sparse properties. Realists argue that objects share features in virtue of the existence of universals, objects that can fully exist multiply instantiated. When two objects share a genuine feature, they do so by instantiating the same universal. We may further subdivide realism about universals into extreme and moderate versions. Extreme realism is the Platonic view that universals exist transcendently, independently of their being instantiated. Moderate realism is the view that universals exist immanently, only when instantiated. The two forms of realism are united in arguing that the sparse properties all correspond to universals, whereas the merely abundant properties do not. Nominalists, by contrast, argue that there are no universals: reality is exhausted by the particular. Still, many nominalists also seek to distinguish the sparse from the abundant properties. Moderate nominalism is the view that the sparse properties correspond to sets of resembling tropes. Tropes are particularized property instances. If two objects share some genuine feature, that is due to their both possessing resembling tropes. Extreme nominalism rejects the existence of both universals and tropes, and maintains the sparse/abundant distinction by means of an appeal to naturalness. David Lewis (1983) presents a view that takes properties to be merely classes of objects. But some classes are more natural than others, where naturalness is taken to be a primitive notion that comes in degrees. The (more or less) sparse properties are identified with the (more or less) natural classes. I have now outlined four different standard accounts of what a sparse property is. My proposal is that we understand metaphysical substantivism about truth along those same lines. What it is for truth to be not just a property, but a metaphysically substantive property is for it to 7 Cf. the distinction between "Cambridge" properties and "non-Cambridge" properties (Shoemaker 1980). See Goodman 1954 for the canonical discussion of 'grue'. 5 belong on the sparse side of the sparse/abundant divide. 8 After all, it seems that truth is undeniably a property in the abundant sense.9 Lots of things are true-that snow is white, that grass is green, that two and two are four-just like lots of things are grue. What is distinctive about deflationists is that they don't see any genuine resemblances between all the truths. Substantive theorists of truth, though, claim that truths do genuinely share a common feature, and the traditional proposals attempt to give the correct analysis of it: truth as correspondence with the facts, coherence in an ideal system, useful belief, warranted assertibility, etc. We may now define metaphysical substantivism about truth as the disjunction of the following four theses: (S1) There is a transcendent universal truth. 10 (S2) There is an immanent universal truth. (S3) There is a resemblance class of truth tropes. (S4) There is a natural class of truths. 11 The goal of this paper is to argue against each of (S1) through (S4), and thereby defend metaphysical deflationism, the thesis that there is no metaphysically substantive property of truth, no matter how one understands the metaphysics of properties. Truth is at best a mere abundant property.12 8 Michael Lynch understands metaphysically substantive properties as those that determine a "minimally objective kind", such that all the members of the kind belong to the kind in virtue of having some shared property (in a nonprojectivist sort of way) (2006: 68). The possible shared properties Lynch has in mind (and that figure into his own account) seem to correspond roughly with the notion of a sparse property, and so his account of metaphysical substantivism coheres well with my own. 9 Perhaps a prosententialist (e.g., Grover, Camp, and Belnap 1975) might deny this. But many other deflationists accept it (e.g., Horwich 1990: 38-41). 10 Universals will henceforth be denoted by italicized words. 11 Perhaps there is a still weaker version of substantivism. For a nominalist who rejects even classes (e.g., Goodman 1956), the view might be that what it is for truth to be substantive is for the predicate 'is true' to figure crucially in explanations; my arguments below will also speak against this account. My thanks go to a referee for the suggestion. 12 Wright describes the disagreement between deflationists and substantivists by claiming that, for substantivists, "the character of the property [of truth] may not be transparent from the analysis of the concept" (2001: 753; cf. Lynch 2009: 116 and Damnjanovic 2010). How well this fits with my sparse/abundant distinction depends on how one understands the notion of transparency here. Wright's example involves water, and the familiar thought that the nature of the property is not immediately revealed by reflection upon the concept. The same is probably true of most sparse properties-our concepts of them won't automatically reveal their metaphysical essence. See Edwards (forthcoming) for criticism of this proposal. 6 Notice that we can distinguish between rejecting certain of these theses on grounds simply due to one's general views regarding the theory of properties, and rejecting them on grounds specifically to do with truth. One can, for example, reject all of them and still be a Platonic realist about universals. But if one is already committed on the problem of universals, that commitment will limit one's choices when it comes to the metaphysical status of truth. Moderate realists, for instance, will reject (S1) and (S3) simply in virtue of their view on properties. Whether they also reject (S2) will depend on their specific attitudes about truth. I shall be arguing against (S1) through (S4) without presupposing any particular solution to the problem of universals. Thinking directly about truth will lead us to reject each of these theses. 3. The Point and Purpose of Properties The first step to arguing against metaphysical substantivism involves appreciating the truthmaking role that properties play. Those who embrace the existence of universals or tropes do so not only because such things account for the resemblances between objects, but also because they are able to serve as truthmakers for contingent predicative truths. Truthmakers are the worldly items on which truth bearers depend for their truth.13 Suppose, for example, that Phil is six feet tall. Phil himself is not a truthmaker for the proposition14 that Phil is six feet tall, since the existence of Phil himself does not guarantee that the proposition is true. It is possible for Phil to exist and not be six feet tall. Something else is needed to account for the truth of the proposition.15 Someone who accepted universals (e.g., Armstrong 1997) would hold that what makes it true is a state of affairs-the compound object non-mereologically composed of both Phil and the six feet tall universal (supposing, as I shall, that there is such a universal). Someone who accepted tropes (e.g., Lowe 2007) would hold that what makes the proposition true is a particular six feet tall trope that uniquely belongs to Phil. Notice, then, the truthmaking powers that belong to tropes and universals. For any object x that instantiates some universal U, it will be true that x is U, and the state of affairs composed of x and U will make that claim true. For any object x that possesses a trope of type T, it will be true that x is T, and the trope will make that claim true. Now suppose that truth is a 13 See, e.g., Armstrong 2004. 14 I shall be employing propositions as my preferred truth bearer merely for the sake of simplicity. My arguments do not turn on any particular view as to the nature of truth bearers. (I have noted nonetheless the places where it may have some bearing on the argument; see notes 19 and 30.) I shall use '<p>' as shorthand for 'the proposition that p'. 15 Nearly all truthmaker theorists accept that truthmakers must at least metaphysically necessitate their truths (see Armstrong 2004 and Merricks 2007). But see Schaffer 2010 for dissent. 7 metaphysically substantive property in the manner of (S1), (S2), or (S3), such that there is a universal truth or collection of truth tropes. Any time a truth bearer is true, it will instantiate that universal, or possess a truth trope. Just as all green things instantiate green, or possess resembling green tropes, all true things instantiate truth, or possess resembling truth tropes. We may now notice how the substantivist about truth has abundant truthmaking resources for contingent predications. The proposition <Phil is six feet tall> is true, and true in virtue of either a six feet tall trope that belongs to Phil, or the state of affairs composed of Phil and the universal six feet tall. But in addition, the proposition itself either instantiates truth (thereby creating a new state of affairs), or possesses a truth trope. Those entities are also truthmakers for the proposition, as their existence guarantees the truth of the proposition. The realist now has two states of affairs that serve to make the proposition true, just as the moderate nominalist has two tropes available to serve as truthmakers. It is no objection to a view that it provides redundant truthmakers for truths. There is no one-one correspondence between truths and truthmakers. What is important to realize is how the two truthmakers available to the substantivist are distinct entities. For our purposes, we can think of distinct entities as just entities that are not identical. Fully distinct entities do not overlap at all in their composition; partially distinct entities do. Suppose, for example, that some particular a contingently instantiates the universal F. The state of affairs (a, F) composed of the two objects is a distinct existence from its components a and F because the whole is not identical to either of its individual parts. But though (a, F) is distinct from both a and F, it is not fully distinct from them, as it is composed by them. As a result, there is a "one-way" necessary connection between (a, F) on the one hand, and a and F on the other. The former cannot exist unless the latter do, but not vice versa. It's possible that a and F could both exist, but not (a, F). Such would be the case if a existed but wasn't F, though something else was. Hence, states of affairs are necessarily connected to their components: the existence of (a, F) depends upon the existence of its constituents, for (a, F) cannot exist unless a and F both do. Notice that this necessary connection is perfectly explicable, given the composition relations at work. Consider now the two truthmakers that the realist has available for <Phil is six feet tall>.16 One is a state of affairs composed of Phil and six feet tall. The other is a state of affairs composed of <Phil is six feet tall> and truth. These two objects are fully distinct entities. They 16 Exactly parallel remarks apply for the moderate nominalist. 8 don't (obviously) overlap at all in their composition: they share no parts.17 Because they are fully distinct, we should expect, at least absent some compelling considerations to the contrary, that there are no necessary connections between them. That is to say, because the two states of affairs are fully distinct, we should expect that one should be able to exist without the other. Normally, when we are confronted with two different objects that don't overlap at all, the default view would be that one could exist without the other. This is just the idea that distinct objects are able to freely recombine (see Armstrong 1989). Whether a given particular instantiates some universal is a separate matter from what other particulars are instantiating what other universals. To suppose otherwise is to impose greater "structure" on the world-things of type X can't exist unless different things of type Y also exist. Given that our two states of affairs-the one composed of Phil and six feet tall, and the one composed of <Phil is six feet tall> and truth-are distinct entities, the default, metaphysically parsimonious position is that one ought to be able to exist without the other. But this might seem highly implausible. How could Phil instantiate that universal and yet the proposition fail to instantiate truth? The view is that the proposition <Phil is six feet tall> cannot bind to truth unless Phil himself binds to six feet tall (and vice versa). These states of affairs appear to be necessarily connected despite being fully distinct existences. If there are necessary connections between the two states of affairs, then those connections ought to be traceable to other necessary connections obtaining between their components. Otherwise we will be forced to take the connection to be brute. Consider a familiar case of necessarily connected states of affairs: imagine a length of wire L that instantiates the two universals made of copper and electrically conductive. The state of affairs of L's being made of copper is necessarily connected to the state of affairs of L's being electrically conductive. What explains the necessary connection between the two states of affairs is the necessary connection that obtains between the two universals: conductivity necessarily accompanies copper.18 That sort of connection is not to be found in our case. The two universals-truth and six feet tall-do not depend upon each other for their existence; they're just separate, unique universals. They are instantiated by very different kinds of objects: very few, if any, true truth bearers are six feet tall! Furthermore, the connection we are looking for cannot be accounted for by finding a connection between these two universals, because we don't have one single object instantiating 17 Similarly, it is evident that the truth trope belonging to <Phil is six feet tall> is a distinct existence from the six feet tall trope belonging to Phil. The discussion that follows is framed in terms of states of affairs, but can be formulated just as well in terms of tropes. 18 See Armstrong 1983. 9 the two universals, as is the case with L. We are trying to account for a connection between a proposition and a certain universal on the one hand, and a person and a very different universal on the other. Our two states of affairs don't even share a common component, and so accounting for their mutual dependence on each other is all the more difficult.19 The usual channels for accounting for necessary connections between states of affairs are not open to the substantivist about truth. The only available option to the substantivist appears to be to just bite the bullet here and accept the necessary connection as brute, thereby forswearing the ability to give any account of the connection. While such a view is logically consistent, it does come at a severe theoretical cost. Accepting that there are necessary connections between distinct existences is tantamount to restricting the free recombination of distinct existences. When two universals are very different in their nature, they ought to be able to freely recombine, irrespective of what the other is doing. Other universals like green and red may well impose constraints on one another-objects that are green can't be red. But such failures of recombination are due to the intrinsic incompatibilities in the universals. The same cannot be said for truth and six feet tall: they don't even tend to instantiate the same kinds of objects. Furthermore, if truth exists, it places constraints of every other universal: a can't instantiate F, G, or H unless truth binds to, respectively, <a is F>, <a is G>, and <a is H>. If truth exists as a universal, it's mixed up in everyone else's business. By contrast, even if conductive and charged impose constraints on one another, they appear to be indifferent toward red and green, though these latter two may impose constraints on each other as well. If truth exists, it imposes constraints on every last universal. Accordingly, substantivists about truth take on indefinitely many restrictions on free recombination. Failures of free recombination worry some philosophers-Humeans and Lewisians, for example-more than others. But even those who are untroubled by the presence of some necessary connections between distinct existences do not advocate multiplying them beyond necessity, and so must recognize that the substantivist about truth takes on an extra explanatory burden that the deflationist does not. For every last truth, the substantivist posits the existence of two very different states of affairs (or tropes) that are composed of very different sorts of things, and holds that these two distinct states of affairs (or tropes) nevertheless necessitate the 19 For those who subscribe to "Russellian" propositions, the proposition <Phil is six feet tall> is composed of Phil and six feet tall, so there will be compositional overlap between (Phil, six feet tall) and (<Phil is six feet tall>, truth). But this still won't account for the needed connection. Even if <Phil is six feet tall> depends on Phil and six feet tall for its existence, we don't have an explanation for why it depends on them for its instantiating truth. For the proposition can exist even if false. 10 existence of each other. If a view posits the brute existence of necessary connections between distinct existences, it imposes greater structure on the world, and thereby incurs a theoretical cost. Such costs can indeed be justified. David Armstrong (1983), for example, posits the existence of necessary connections between distinct universals in order to give an adequate account of the laws of nature. So positing such necessary connections is not in and of itself fatal to a view. Still, positing brute necessary connections should not be done lightly, and should be done only to serve a greater theoretical good. The same can be said for positing entities (or a notion of naturalness) at all with respect to the metaphysics of properties. Universals, tropes, and natural properties are not posited without sufficient cause; one need not believe that for every predicate there is a corresponding universal or set of tropes, or that every property is natural. Not every property deserves to be sparse. So what reasons can justify these various metaphysical posits, such as universals, tropes, naturalness, states of affairs, and necessary connections between them? The answer is threefold. Here is David Lewis, describing Armstrong's moderate realism: "universals are sparse. There are the universals that there must be to ground the objective resemblances and the causal powers of things, and there is no reason to believe in any more" (1983: 345). Lewis here identifies two of the sources of justification for metaphysical positing in the theory of properties. We posit universals (or tropes or naturalness) when we need them to account for the genuine resemblances between objects. What separates the collection of green objects from the collection of grue objects is that the former all share a single universal (green), which cannot be said for the various grue objects. We also posit universals (or tropes or naturalness) when we need them to account for the causal properties of objects. The thought here is that objects have their causal powers in virtue of the properties they possess. The sparse properties are, in Armstrong's phrase, "the ontologically significant properties of objects, those in terms of which the world's work is done" (2004: 17). Being massive or charged or conductive are the sorts of properties that account for the causal order of the world; it is these properties, and not being three feet from the Washington Monument or being either in Alaska or Madagascar that figure into the causal laws of nature. A third reason for positing universals and tropes involves, as before, their use as truthmakers. Objects and their properties, whether understood in terms of universals or tropes, are needed to serve as the ontological grounds for the truths about the world. Hence, we can justify positing the existence of various states of affairs or tropes if they are needed to serve as truthmakers for truths. There are three sources of justification, then, for positing that a particular property belongs among the sparse properties. The sparse properties are those that account for the 11 genuine resemblances between objects, have causal powers, and are needed as truthmakers. We should posit such properties (and any necessary connections between them) only if doing so serves those needs. Our next question to consider is whether treating truth as a sparse property will fulfill any of these metaphysical purposes. First consider the topic of resemblance. Sparse properties are those that account for the genuine resemblances between objects. Objects resemble one another in virtue of instantiating the same universal, possessing resembling tropes, or belonging to the same natural class. Now, not all classes exhibit real resemblance-hence the distinction between the class of green objects and the class of grue objects. Our question is whether the truths are more like the green things or the grue things. Notice just how diverse the collection of truths is. It's true that snow is white, that echidnas live on Kangaroo Island, that hobbits don't exist, and that if I were to drop a piece of chalk it would fall to the floor. The class of truths is one remarkably heterogeneous collection. Indeed, each truth seems to be its own individual affair. The proposition that snow is white is true in virtue of snow's being white, the proposition that echidnas live on Kangaroo Island is true in virtue of echidnas' living on Kangaroo Island, and so on. The idea here is familiar to deflationists: the truth of <Snow is white> does not "consist in the same thing" as the truth of <Echidnas live on Kangaroo Island>. Sure, they "resemble" one another in that they are both true, but the resemblance stops there. They are both true, but for entirely separate reasons. The shared greenness of two things, by contrast, may well admit of a common explanation, due to a genuine property shared by both. The class of truths, it seems, is a great candidate for being a perfectly unnatural class, given its heterogeneity. If so, there is no need to promote truth to the status of a sparse property on the basis of shared resemblances between all truths, for there are none. It also seems unlikely that anyone would posit truth to serve any genuine causal role. We may posit mass and charge so that they may discharge their causal duties, but truth seems to be an altogether different beast. It is strange to think that truth would be the sort of thing that contributes to the causal order of the world studied by empirical science. By what mechanism would truth interact with the other universals in order to bring about various effects?20 Why does truth not figure into any physical laws or equations? Still, it may seem natural to make causal judgments involving truth, as in 'The truth of my beliefs caused me to ace my exam'. Deflationists have a metaphysically innocuous account of what is being said here, and it doesn't involve a causally active truth property.21 Suppose the 20 Cf. Levin 1984: 126, O'Leary-Hawthorne and Price 1996: 278, and McGinn 2000: 108. 21 See Horwich 1990 for an extended defense of the line I am adopting here (and Gupta 1993 for criticism). 12 exam has a single question: which U.S. president was succeeded by his own predecessor? Because I believe that Benjamin Harrison was succeeded by his own predecessor, that belief in part causes my hand to write the answer, which in turn causes the instructor to give me full credit. What is crucial is that I believe that Benjamin Harrison was succeeded by his own predecessor, and that Benjamin Harrison was indeed succeeded by his own predecessor. Nowhere are we forced to posit a causally active universal truth to account for my academic success. The appeal to truth in the initial causal judgment is nothing but another instance of the useful anaphoric and abbreviatory features of 'truth' and 'true'. Rather than saying that my belief that Benjamin Harrison was succeeded by his own predecessor when Benjamin Harrison was indeed succeeded by his own predecessor caused me to ace the exam, I can abbreviate and say that it's the truth of my belief that caused my success. 22 The generalizing feature of 'truth' becomes even more apparent in cases where I need to appeal to several of my true beliefs, rather than just one, in accounting for some particular practical success. Assuming the case is typical, even if we do appeal to truth in certain causal judgments, doing so only reveals the familiar expressive functions of 'truth'; such judgments do not push us into thinking that there is a universal truth beholden with causal powers.23 Finally we come to truthmaking: does promoting truth into a sparse property provide us with any needed truthmaking resources? As we saw above, positing a universal truth or set of truth tropes provides us with redundant truthmakers, not useful ones. Many truthmaker theorists rely on universals, states of affairs, and tropes in order to supply truthmakers; what they do not do is posit universals, states of affairs, and tropes specifically to do with truth. As before, the state of affairs of Phil's being six feet tall and Phil's six feet tall trope are perfectly adequate truthmakers for <Phil is six feet tall>. We do not need another state of affairs or trope involving truth to properly ground the truth of the proposition. Other kinds of propositions do not call for a sparse truth property, either. Existential propositions like <There are penguins> don't require 22 Moreover, one might argue that there is no genuine causality involving truth here, in that what's really doing the causal work is the fact that my answer matches the examiner's belief about the answer; the truth of my belief is beside the point in terms of what caused my exam score. My belief could have been false and yet yielded the same score, provided the examiner is similarly mistaken. (Thanks to a referee on this point.) 23 Nic Damnjanovic (2005) has argued that, given Jackson and Pettit's (1990) account of causal relevance, truth is a causally relevant property. But on this account, even clearly "logical" properties like identity turn out to be causally relevant. Indeed, nearly any property can turn out to be causally relevant in the appropriate sense. So the JacksonPettit account of causal relevance won't be useful in drawing the sparse/abundant property divide, and so deflationists may accept that truth is a causally relevant property in the Jackson-Pettit sense, a conclusion that Damnjanovic acknowledges (2005: 67). 13 truth tropes or states of affairs; they just require penguins. Negative existential propositions raise notorious truthmaker questions: what makes it true that there are no hobbits?24 Perhaps there are negative facts (Russell 1985), absences (Martin 1996), or one giant totality fact (Armstrong 2004) that makes it true, or perhaps it doesn't have any truthmaker at all (Lewis 2001). Regardless of who is correct here, no one thinks that what we need is a sparse property of truth to bind to the negative existential proposition.25 All told, the positive case for treating truth as a sparse property is weak. The class of truths is a great candidate for not exhibiting genuine resemblance, truth is not a causal property in any relevant sense, and truth is not needed as a property to serve any truthmaking function. Furthermore, the view incurs an extraordinary explanatory burden by imposing indefinitely many brute constraints on the free recombination of distinct existences. There are numerous theoretical costs to adopting metaphysical substantivism, and yet no clear benefits. Consequently, we have undermined the motivation for believing any of (S1) through (S4). There is no theoretical need for believing in metaphysical substantivism about truth, and so there is good reason for rejecting it. Now we may turn to a second line of argument against metaphysical substantivism. If there were such a thing as a universal truth or set of truth tropes, then it would provide an army of redundant truthmakers. That fact in and of itself is no objection to substantivism about truth; the real problem is that they would provide an army of fully distinct redundant truthmakers. If so, then the view runs straight into contradiction or an unmotivated metaphysics. 4. Taking Truth to Absurdity The second argument against metaphysical substantivism about truth takes the form of a dilemma. Suppose that any of (S1) through (S3) is true. 26 Then it is the case that for any true proposition <p>, there will be both its familiar truthmaker F and a redundant truthmaker for it 24 See Molnar 2000 for discussion of the truthmaking issues raised by negative existentials. 25 Though I cannot argue for the claim here, I am most sympathetic to the idea that negative existentials don't have truthmakers-that they are not true in virtue of some existing thing. Taking them to be made true by a sparse property of truth appears to be ad hoc: why should only negative existentials receive this special sort of treatment? But if we allow all truths to be made true by states of affairs composed by truth, then we trivialize the theory of truthmaking (and all its attendant ontological concerns, as I note below). 26 Admittedly, this second argument doesn't bear on (S4). 14 R.27 F and R are typically fully distinct;28 the important question is whether or not there are necessary connections between them. If there are no necessary connections between F and R, then R can exist even if F doesn't. R is a truthmaker for <p>, and so <p> can be true even if F does not exist. This, I argue below, is contradictory. If F and R are necessarily connected, then there must be some metaphysical justification for positing the existence of R and its (possibly brute) necessary connection to F. But there is no such justification, and so the view is unmotivated. Hence, metaphysical substantivism about truth is either contradictory or unmotivated. Let us dig into this argument with a concrete example. Take again our sample true proposition, <Phil is six feet tall>. The "familiar" truthmaker F here is either the realist's state of affairs composed of Phil and the universal six feet tall, or the moderate nominalist's six feet tall trope that belongs to Phil. The "redundant" truthmaker R here is either the state of affairs composed of the proposition <Phil is six feet tall> and the universal truth, or the truth trope belonging to <Phil is six feet tall>. F and R are fully distinct existences: they share no common parts.29 Either F and R can exist independently of each other, or there are necessary connections that obtain between them. Both ways lead to trouble. If F and R are not necessarily connected, then it's possible for R to exist and for F to fail to exist. Notice just what this possibility is. We have the proposition <Phil is six feet tall> instantiating truth, and so we have a true proposition. But this is also a possibility where Phil does not instantiate six feet tall. What we have, in other words, is a possible scenario in which Phil is not six feet tall, even though the proposition <Phil is six feet tall> is true. But that is impossible, since, necessarily, the proposition that Phil is six feet tall is true if and only if Phil is six feet tall.30 In effect, taking F and R not to be necessarily connected amounts to rejecting the necessary truth 27 I'm here supposing truthmaker maximalism, the claim that every truth has a truthmaker. Those who reject maximalism must also reject substantivism about truth, because substantivism entails maximalism. (If substantivism is true, there will be an R for every p.) 28 "Typically" because some truth bearers are about truth bearers, and hence there might be overlap in some cases between F and R. For example, suppose the proposition that there are propositions is true. F in this case can be any proposition, <There are propositions> included. R is the state of affairs composed by <There are propositions> and truth. So here we have a case of overlapping composition. 29 See again note 19 regarding Russellian propositions. 30 What isn't necessary is that the sentence 'Phil is six feet tall' is true if and only if Phil is six feet tall, for the sentence could have had a different meaning. The argument can easily be adjusted for sentences. The relevant absurdity would involve a possibility where the sentence, meaning what it actually does, binds to truth, although F doesn't exist. In this scenario, 'Phil is six feet tall' means that Phil is six feet tall, and is true, although Phil isn't six feet tall. 15 of a propositional T-sentence. Even substantivists accept the legitimacy of the propositional truth schema (i.e., necessarily, <p> is true if and only if p). If F and R are not necessarily connected-which, recall, I argue is the "default" view, given that they are fully distinct-then substantivism about truth reduces to absurdity. Suppose instead that F and R are necessarily connected, in spite of being fully distinct; their existence is tied up with one another, such that R cannot exist unless F also exists. I argued in the previous section that this view is surprising and suspect; there are no obvious independent grounds for taking F and R to be necessarily connected, and so to find them so connected is potentially ad hoc, and must involve positing a brute necessary connection between them. But, drawing on the findings from the previous section, we should posit entities like R, and their brute necessary connection to more familiar things like F, only when there are compelling metaphysical reasons for doing so, such as accounting for resemblance, causality, and truthmaking. R is not needed for any of those things, so positing its existence and its brute connection to F is unmotivated and ontologically gratuitous. Hence, if F and R are not necessarily connected, then contradiction results. If F and R are necessarily connected, then we have an unjustifiably ontologically expensive view. Metaphysical substantivism about truth is either contradictory or unmotivated. The substantivist road is a costly one, and offers no benefits to justify the expense. Notice also that this argument does not rely specifically on truth being a property rather than a relation. Suppose that truth is instead a two-place universal. (The correspondence theorist might have such a view in mind.) The proposition <Phil is six feet tall> stands in the truth relational universal to some correspondent, C. Here we have three things: the proposition, the relational universal truth, and the correspondent C. The proposition is true, and so the state of affairs composed of the three entities exists. There are two options for what C could be. It could just be the familiar truthmaker F (or something necessarily connected to it), in which case F itself is all we need to account for the truth of the proposition. The detour through the relational universal is unnecessary. Or C could be something fully distinct from and not necessarily connected to F. In that case, the state of affairs of the proposition's standing in the truth relation to C could exist even if F doesn't, for ex hypothesi they are not necessarily connected entities. In that case, the proposition will be true in spite of Phil's not being six feet tall. And so we reach the same conclusion as before: positing the relational universal truth leads either to contradiction or an unmotivated metaphysics. Metaphysical substantivism about truth is either contradictory or unmotivated. Even for those who embrace a serious metaphysics of properties and take truthmaker theory to heart, 16 there is no need to take truth itself to be a metaphysically serious property. Indeed, it seems that there would be absolutely no need for any property besides truth if we embraced substantivism about truth. If all we need is R to account for the truth of <Phil is six feet tall>, then we don't need Phil or the property of being six feet tall. The proposition and truth do all the necessary labor themselves. If truth were a distinct entity, we could use it to create a possible world in which all the propositions true in the actual world are true (by having each of those propositions instantiate truth), despite none of the familiar objects of the actual world existing in it. But that is absurd. Yet if truth can't do that labor by itself-if it needs help from things like Phil and six feet tall-then it's just a metaphysical deadbeat with nothing of its own to contribute. 5. Objections and Replies In arguing against metaphysical substantivism about truth, I have employed claims involving truthmaker theory. Substantivism runs into trouble because it bestows false truthmaking powers upon the property of truth itself. But isn't truthmaker theory itself a substantive theory of truth, or require one? And so haven't I argued against substantivism while at the same time presupposing it? Indeed, many have thought that truthmaker theory is a theory of the nature of truth.31 In fact, many believe that truthmaker theory is a modern incarnation of correspondence theory. Alex Oliver, for example, writes that truthmaker theory "is a sanitised version of a correspondence theory of truth" (1996: 69).32 The problem with this objection is that truthmaker theory is not a theory of truth at all. The thought that truths are made true by reality cannot reveal the nature of truth because it must already take for granted some antecedent notion of truth, and there is no reason why that notion cannot be deflationary. Suppose that all truths have truthmakers.33 Then for any truth bearer p, p is true just in case it has a truthmaker. But p has a truthmaker just in case there exists some object in virtue of which it is true. The notion of truthmaking needs to be analyzed in terms of 31 See, e.g., O'Leary-Hawthorne and Oppy 1997: 176 and Cameron 2008: 412. 32 See also Mulligan, Simons, and Smith 1984: 288-289, Fox 1987, Bigelow 1988: 122, Molnar 2000: 85, Read 2000: 67, Heathcote 2003, Armstrong 2004: 16, Mumford 2005, and Parsons 2009: 217. 33 This thesis-truthmaker maximalism-is highly contentious, even within the truthmaking industry. As noted above, negative existentials are candidate counterexamples. Because some truthmaker theorists think that some truths lack truthmakers, we can see that it cannot be any presupposition of truthmaker theory itself that it reveal the nature of truth, for according to non-maximalists there are truths whose truth cannot be formulated in terms of truthmakers. 17 truth, for it must account for the truth of truth bearers, and not their other features.34 We cannot, on pain of circularity, employ the truthmaking relation when defining the nature of truth.35 Truthmaker theory, then, relies on an antecedent notion of truth. It cannot itself be employed in saying what truth is, on pain of circularity. Hence, truthmaker theory itself is not a theory of truth, let alone a metaphysically substantive one. Truthmaker theory gives an account of what the ontological grounds for truths are; it can accomplish that task without also taking a stand on what truth itself is. Relatedly, one might think that deflationism about truth is inconsistent with truthmaker theory, and so one cannot employ truthmaker theory in arguing for deflationism about truth. The main reason, however, for thinking that truthmaking and deflationism form an inconsistent pair involves taking truthmaker theory to be some sort of substantive theory of truth, or a correspondence theory even. But that view is mistaken, for the reasons just discussed.36 We should be careful not to conflate a deflationary attitude toward the property truth with a generally deflationary attitude toward metaphysics in general. Deflationists accept that <Penguins exist> is true if and only if penguins exist, and think there's nothing more to the truth of the proposition than the existence of penguins. But it is no part of deflationism to deny that the proposition is true in virtue of penguins. The truth of <Penguins exist> depends upon the existence of the flightless birds, even if it doesn't depend upon the existence of a realm of facts and a correspondence relation. To say that truth is not a metaphysically substantive property is in no way to deny that truths have truthmakers, or that truths are true in virtue of the world. Rather, there are simply two distinct philosophical projects: giving an analysis of the property of truth, and giving an account of what it is in the world upon which certain truths depend. Deflationism about truth denies that the first project involves any sort of metaphysical analysis; it in no way rejects the second project, which does not even involve the attempt to say what truth is. A final objection that might be raised against my argument is that I have from the beginning mischaracterized the nature of metaphysically substantive theories of truth. Truth was never intended to be a property in any of the senses of 'property' relevant to the problem of universals. To this objection, I can reply only by asking: if a metaphysically substantive theory of the property of truth is not to be characterized in any of the familiar ways of characterizing 34 See Armstrong 2004, Lowe 2007, Merricks 2007, and Schaffer 2010 for competing accounts of the truthmaking relation. All employ an antecedent notion of truth. 35 See also Merricks 2007: 15. I develop this argument at greater length in my 2011. 36 Furthermore, the appearance of 'true' that we just saw in accounts of truthmaking is perfectly consistent with deflationary accounts of truth. See Lewis 2001. 18 metaphysically substantive views of properties, then how should it be characterized? Anyone who rejects my account faces the challenge of saying just what it is that a metaphysically substantive property of truth would be, if not a universal, set of tropes, or natural class. Furthermore, that account must make it explicit why deflationists are not entitled to a property of truth in that sense. For if deflationists can accept that truth is a property in that yet to be defined sense, then that notion of truth cannot be used to separate deflationists and substantivists. I take it that the various traditional theories-correspondence, coherence, pragmatic-are indeed committed to metaphysical substantivism; they just give different accounts of the nature of the property. If those views can be resuscitated in a way such that they are not committed to a metaphysically robust account of the property of truth, then they can deflect my argument. It's just not clear what such views would be, or why they would be anathema to deflationists. Besides, there is ample evidence that many theorists would accept my characterization of substantial truth as being a sparse property, however understood. Andrew Newman (2002) defends a correspondence theory in the context of realism about universals. Newman thinks that truth is a property, that there is something shared by all and only true things. Hence, given his defense of realism about universals, it seems likely that he is committed to thinking of truth as being one such universal. He even suggests that truth might be a natural kind (2002: 45). Richard Fumerton writes that "realists" about truth must think that there's a property of truth, but needn't be realists about universals (2002: 4). But if they are realists about universals, does that mean that they must think that there's a universal truth? Presumably, lest realism about truth turn out to be consistent with its deflationary opponent. More commonly, substantivist theorists about truth remain agnostic about the nature of properties. Gerald Vision (2004) defends the existence of a truth property, but is silent as to what kind of property it is. Michael Lynch (2009) is a pluralist (or functionalist) about truth in that he thinks truth sometimes consists in correspondence with the facts, sometimes in being superwarranted, and perhaps something else in other cases. Lynch is also silent about what he means by 'property', but he is very clear that truths are true in virtue of their having one of those properties: "Propositions about different subjects can be made true by distinct properties each of which plays the truth-role" (2009: 77).37 Others who shy away from correspondence accounts have endorsed the idea that truth is a property-and in so doing take themselves to be rejecting deflationism-but fall silent on what metaphysical story they think underlies the property (Alston 1996, Merricks 2007). 37 Lynch does discuss the nature of substantive properties somewhat in his 2006 and 2009. 19 Most theorists seem to prefer remaining agnostic about how we should understand the truth property, and hence they remain silent on what they mean by 'property'. If their views on truth do not turn on resolving the more general problem of universals, then this neutrality is appropriate. But substantivists do defend the view that truth is a substantive property, and so they must think that at least the disjunction of (S1) through (S4) is true, even while remaining neutral on the broader issue of realism and nominalism. What my arguments show is that regardless of which position is correct in the overall realism/nominalism debate, truth does not belong on the sparse side of the property divide. 6. Conclusion I have argued in favor of metaphysical deflationism, the thesis that there is no metaphysically robust property of truth. In doing so, I have remained neutral with respect to the second deflationary thesis, concerning the concept of truth's explanatory potency. Assuming that the traditional substantivist views are committed to metaphysical substantivism, the strongest remaining views, to my mind, are full bore deflationism (e.g., Horwich 1990, Field 1994, and Williams 1999 and 2002) and conceptual primitivism (e.g., Frege 1956, Davidson 1996, and Patterson 2010). Both views can accept that truth is not a metaphysically substantive property; their disagreement lies only with regard to the explanatory utility of the concept of truth. The primitivist thinks that our concept of truth is an explanatorily interesting notion, one that can figure into analyses of other notions (such as assertion or meaning) in ways that go beyond its expressive features. Truth cannot be analyzed in terms of any further notions-hence its primitive status-but it can be used to explain and analyze other things. The primitivist need not think that truth is a property in any metaphysically substantive sense; the foundational role it plays in our conceptual scheme is not one that needs the aid of any causal or truthmaking powers. Primitivism is indeed the view that I favor, though I must reserve its defense for another day. 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