Truthmakers Against Correspondence Jamin Asay University of Hong Kong asay@hku.hk Draft version; final version to be published in Grazer Philosophiche Studien Abstract Many philosophers think truthmaker theory offers a correspondence theory of truth. Despite the similarities, however, this identification cannot be correct. Truthmaker theory offers no theory of truth, nor can it be employed to offer an acceptable substantive theory of truth. Instead, truthmaker theory takes truth for granted. Though truthmaker theory is not a correspondence theory, it shares with it the same motivational basis-that truth is worldly-and better accounts for what is pre-theoretically compelling about correspondence theories. As a result, those at all attracted to correspondence theory (including many deflationists) should reject it and accept truthmaker theory instead. Keywords truth; correspondence; truthmaking; deflationism 1. Introduction The correspondence theory of truth is motivated by the idea that truth depends on reality. What it is to be true is to stand in the right kind of relationship to the world. Truth is explained by the world, not by our beliefs, desires, or evidence. This "worldliness" of truth is what sets correspondence theories apart from coherence, pragmatic, and epistemic accounts that don't define truth in terms of reality. It also explains why many have taken the recent resurgence of interest in truthmaker theory to be a revival of correspondence theory. For truthmaker theory, too, is motivated by the idea that truth depends on reality: truths are made true by the world. It is not uncommon, then, to find philosophers closely associating truthmaking and correspondence. 2 Julian Dodd, for instance, writes that "what I take to be the distinctive intuition motivating correspondence theories of truth [is that] every truth must have a truthmaker" (2000: 2). It's unsurprising, then, that many philosophers have taken truthmaker theory to be a contemporary form of correspondence theory. According to this view, truth can be defined in terms of truthmaking, thereby upholding and vindicating the main idea that drives correspondence accounts.1 I draw a very different moral from the close relationship between truthmaker theory and correspondence theory: truthmaker theory, properly understood, undermines correspondence theory by pulling the motivational rug out from under it. Because truthmaker theory captures the basic ideas behind correspondence theory at significantly less theoretical cost, we should reject correspondence accounts of truth. As I shall argue, traditional correspondence theory runs together two separate philosophical questions: (i) What is the nature of truth?, and (ii) What makes truths true? Once these questions are separated, we can develop a theory of truthmaking that does not embrace the perils of correspondence theory, and that can be paired with a more parsimonious deflationism about truth. If truthmaker theory can survive the rejection of correspondence theory, then it cannot be a form of correspondence theory, as many have previously argued (e.g., Oliver 1996: 69). Hence, after articulating how I understand the project of truthmaker theory, I argue that truthmaker theory itself does not offer a theory of truth, and, furthermore, that it cannot be used to offer an acceptable, non-deflationary account of the nature of truth (let alone a correspondence account). Truthmaker theory is best understood as presupposing the notion of truth, not helping to define it: truth is prior to truthmaking. While this claim has been asserted before, it has not received the dialectical scrutiny that it deserves. Then, having separated the theory of truth from the theory of truthmaking, I argue that those who are attracted to correspondence theories of truth should become truthmaker theorists, and reject correspondence theory in favor of either a deflationary or primitivist account of truth. Finally, I argue that deflationists, too, can and should uphold truthmaker theory, for they need it to capture the so-called correspondence intuition. 2. Theories of Truth and Theories of Truthmaking A theory of truth, as I shall understand it, attempts to reveal the nature of what it is, if anything, that truths share, in virtue of which they're true. The traditional, substantive theories of 1 See, e.g., Mulligan, Simons, and Smith 1984: 288-289, Read 2000: 67, Vision 2003: 140, Armstrong 2004: 16, and Cameron 2008: 412. 3 truth-correspondence, coherence, pragmatic, epistemic-define truth in terms of these further, more fundamental notions.2 Deflationists reject the idea that truths share any common nature: there is no common property shared by all and only truths (e.g., Horwich 1990). Pluralists argue that truth has multiple natures (or that its nature is realized differently in different domains) (e.g., Lynch 2009), while primitivists argue that truth's nature cannot be revealed in more fundamental terms (such as correspondence) (e.g., Asay 2013). While these characterizations are admittedly rather rough and ready, they are sufficient to identify my target. My interest is with the attempt to employ the notion of truthmaking to reveal the nature of truth in a manner similar to the traditional substantive theories. After all, if truthmaker theory just is a contemporary form of correspondence theory, then truth should be definable in terms of truthmaking, much as correspondence theorists think that truth is definable in terms of correspondence. My conclusion is that truthmaker theory cannot be employed for offering a substantive theory of truth that is a competitor alongside the traditional theories. To see why, it's important to appreciate some of the various desiderata to which the traditional theories are held. First, circularity is generally unacceptable: if truth is defined by X, then X had better not turn out to be defined by truth. This criterion is importantly related to the second, which is that the defining notions should be more fundamental than the notions doing the defining. In giving an analysis or definition, we're not interested in offering a synonym, or something that is merely coextensive. Rather, we want to understand the notion in question in more basic terms. The fundamentality desideratum also helps to explain what's problematic about circularity: if truth is analyzed in terms of X, then X is more fundamental than truth. But if X is in turn analyzed by truth, then truth is more fundamental than X. Circularity combined with (asymmetric) fundamentality leads to contradiction. Another feature that separates the traditional substantive theories from their deflationary competitors is that the former are finitely stateable. Paul Horwich's minimalist theory, for instance, maintains that truth is definable, albeit implicitly and infinitely (1990). Truth for the minimalist is defined by the infinitely many instances of the schema 'the proposition that p is true if and only if p'. As we shall see below, Horwich upholds the infinite nature of his definition because he believes that one can turn the schema into a proper, finitely stateable definition only at the expense of circularity. Now, it's understandable why a deflationist might rest content with an infinite definition of the nature of truth. For deflationists, truths don't share a common nature. Each truth is its own individual affair-the proposition that snow is white is true in virtue of 2 E.g., see, Rasmussen 2014, Walker 1989, Misak 1991, and Putnam 1981, respectively. 4 snow's being white, and the proposition that grass is green is true in virtue of grass's being green, and so on-and so one can't define the nature of truth without, in effect, going through all the infinitely many truths individually. But if truths do share a common nature, we should be able to identify it without having to resort to an infinite definition; otherwise the proposed definition offers no advance over the deflationary account.3 Another way to think about this desideratum is that an infinitely long definition is akin to a highly "disjunctive" account of truth. For example, something is true if and only if it expresses the proposition that snow is white and snow is white, or it expresses the proposition that grass is green and grass is green, and so on. There being a highly disjunctive account of some notion is of no help to those pursuing a metaphysically substantive account of it; such a definition can always be constructed by brute force. The substantivist's idea is that truth does have a genuine nature that can be captured without resort to such maneuvers. In what follows, I consider an adequate or acceptable substantive definition of truth to be one that finitely defines truth in more fundamental terms without circularity; in so doing I take myself to be respecting the standards already at play in the theory of truth.4 Traditional correspondence theory is one such attempt to offer an adequate substantive definition of truth. Truth is defined in terms of the more fundamental notions of correspondence and fact (or reality), which in turn are not to be defined in terms of truth, lest the account be circular or trivial. All truths must be explained in terms of correspondence; otherwise, the theory has holes. The theory of truthmaking also springs from the idea that truth depends on reality: when something is true, something in the world makes it true. How exactly that thought should be refined and/or qualified is a major part of truthmaker theory. Truthmaker theorists approach metaphysical questions by investigating what there is in the world that makes true all that is true. Any fully developed truthmaker theory offers accounts of (i) what the truthmaking relation is, (ii) which truths have truthmakers, and (iii) what objects play the truthmaking role. David Armstrong, for example, takes the truthmaking relation to involve metaphysical necessitation (such that where x is a truthmaker for y, it is metaphysically necessary that if x exists then y is true), believes that all truths have truthmakers, and employs states of affairs as truthmakers 3 See also David 1994: 107-110. 4 Which is not to say that these standards are indefeasible or universally recognized. Gupta and Belnap 1993, e.g., offers a circular account of truth. 5 (2004).5 As I shall be using the term, 'truthmaker theory' refers to the project of giving answers to these three theoretical demands. Because truthmaker theorists divide as to how these questions should be answered, they cannot be identified as such by their adherence to any one particular doctrine. For my purposes, then, what it is to be a 'truthmaker theorist' is to find the idea and language of truthmaking useful in philosophical inquiry, and to put it to work accordingly. According to correspondence theory, something is true just in case it corresponds to reality. According to truthmaker theory, truths are made true by reality. It's no wonder why many see an intimate relationship (if not identity) between the two. But the appearances here are deceiving. As I shall argue, truthmaker theory cannot offer an adequate theory of truth, let alone a correspondence theory. 3. Truth Before Truthmaking 3.1. Non-maximalist truthmaker theory To see why truthmaker theory itself is not in the business of offering a theory of truth, consider that truthmaker maximalism-the thesis that every truth has a truthmaker-would have to be not only true but a necessary part of truthmaker theory if truthmaker theory were to offer a theory of truth (cf. Smith and Simon 2007). If truth consists (even in part) in having a truthmaker, then every truth would have to have a truthmaker. Otherwise there would be truths whose truth could not be accounted for by truthmaking. But maximalism is not a sine qua non of truthmaker theory, and so truthmaker theory by itself offers no theory of truth.6 Though the matter is controversial, many truthmaker theorists reject maximalism (e.g., Bigelow 1988, Lewis 2001b, and Saenz 2014). The paradigm examples of truthmaker gaps-truths without truthmakers-are negative existentials. It's true that there are no hobbits, but it need not follow that there exists something making it true that there are no hobbits. To think otherwise is to suppose that one must ground one's "atheism" (about hobbits) with a separate kind of "theism" (about, say, negative facts, absences, or totalities)7. Regardless of whether this stance is 5 More precisely, Armstrong takes necessitation to be necessary but not sufficient for truthmaking, and does not hold that every truth needs a state of affairs for a truthmaker. The claim that penguins exist, for instance, is made true by penguins themselves. 6 Armstrong claims that most truthmaker theorists reject maximalism (2006: 245). 7 See, respectively, Russell 1985, Martin 1996, and Armstrong 2004. 6 the correct response to the problem of negative existentials, it is a defensible one, and one available to and used by truthmaker theorists. Since one may be a truthmaker theorist without being a maximalist, truthmaker theorists qua truthmaker theorists are not in the business of offering a theory of truth. Now, some claim that in abandoning maximalism, we abandon truthmaker theory altogether.8 On such a view, there simply is no room in truthmaker theory for non-maximalism. George Molnar writes that admitting that some truths do not have truthmakers is "the way of ontological frivolousness. It is a truly desperate resort" (2000: 85). But this response is too quick. The foundational idea underlying truthmaker theory is that truth depends upon reality. Truths are true in virtue of the way of the world. Negative existentials do, in at least one sense, depend upon the way of the world for their truth-they depend on there not being any of the relevant things around. The case is different for the suspicious phenomenalist and behaviorist counterfactuals that motivated contemporary truthmaker theory in the first place.9 In those cases, philosophers were positing truths that depended in no way upon the world for their truth. But such counterfactuals are nothing like the negative truths involving hobbits. The latter are still true in virtue of the way of the world, even if no particular entities exist that necessitate those truths. The truth that there are no hobbits admits of a perfectly worldly explanation; its truth is no metaphysical mystery. So not all truthmaker gaps are alike. Some are offensive to the spirit of truthmaking; others are not. Hence, there are reasons for rejecting maximalism that are not reasons for rejecting truthmaker theory itself. Non-maximalism may have its difficulties (see, e.g., Jago 2012), but it's not a non-starter. Since rejecting maximalism is no automatic offense to truthmaker theory, it follows that truthmaker theory is not in the business of giving a theory of the nature of truth. 3.2. Truthmaking, truth, and circularity Putting truthmaking to work as a theory of truth requires a commitment to maximalism. But not even maximalists can employ truthmaking in order to adequately say what truth is, for the truthmaking relation itself must be defined in terms of truth, and so any such analysis is 8 See, e.g., Cameron 2008: 412. Others argue for maximalism without requiring its being essential to truthmaker theory (e.g., Jago 2012). 9 See Armstrong 2004: 1-3. 7 circular.10 There are several accounts in the literature regarding the nature of the truthmaking relation. All of them employ an antecedent notion of truth. For most, truthmaking is (at least) a matter of necessitation: x is a truthmaker for y only if it is metaphysically necessary that if x exists, then y is true.11 Hence, the necessitation condition already employs the notion of truth. Other approaches share this same feature. On Lowe's "essential dependence" account, truthmakers are objects that are essentially related to truth bearers such that those truth bearers are true if those objects exist (2007). According to Schaffer, truthmakers are objects that provide grounds for the truth of truth bearers (2010). Any other analysis of the truthmaking relation is going to have to involve truth, for it must account for the truth of truth bearers, and not their other features (such as their existence or believability). On pain of circularity, anyone trying to build a theory of truth from a theory of truthmaking must somehow dispense with truth from the notion of truthmaking. The only theoretical option that avoids circularity is to take truthmaking as a primitive relation, and subsequently define truth in terms of it. Rodriguez-Pereyra (2005) takes truthmaking to be a primitive notion (though he cannot go on to define truth in terms of it, since he is not a maximalist). While this position is impossible to refute, it remains to be seen what the motivation is for taking truthmaking to be a more basic and more fundamental notion than truth. It's far more plausible, it seems to me, to take truth (a seemingly more basic and familiar notion) as primitive, and define truthmaking in terms of it. Even Rodriguez-Pereyra offers a gloss on the primitive truthmaking relation that appeals to truth, claiming that truthmakers are the objects in virtue of which truth bearers are true (2005: 18). Defending primitivism about some notion involves showcasing the many theoretical fruits that follow from it, as compared to other choices of primitives. The maximalist-cum-primitivist about truthmaking needs to show what those fruits are, if we are to take seriously the idea that truth is best defined in terms of a primitive notion of truthmaking. In particular, truthmaking primitivists must show that their overall view is superior to that of those who take truth to be the primitive, more fundamental notion here (e.g., Davidson 1996 and Asay 2013). 10 Merricks has also noticed this point with reference to his own account of the truthmaking relation (2007: 15; see also Schulte 2011: 420). I go further by arguing that any analysis of the truthmaking relation runs into the same problem, and then responding to potential objections against this line of thinking. The fact that philosophers such as Cameron (2008) and Jago (2012, 2013) persist in seeing a theory of the nature of truth within truthmaking, it's safe to conclude that they have not taken Merricks's brief discussion to be decisive. 11 E.g., Lewis 2001b, Armstrong 2004, and Merricks 2007. Merricks refers to necessitation being a necessary condition on truthmaking as "truthmaker orthodoxy" (2007: 5). 8 Setting aside the primitivist retreat, it appears that the attempt to define truth in terms of truthmaking runs straight into circularity. As a result, truth cannot be adequately defined in terms of truthmaking, and so truthmaker theory cannot be a kind of correspondence theory, which is an attempt to offer an adequate definition of the nature of truth. Suppose, however, that someone persists, and simply insists that maximalist truthmaker theory just is a kind of correspondence theory, one that takes the correspondence relation to be the truthmaking relation, and the set of corresponding objects to be the set of truthmakers. How can one deny that this truthmaker theory is a correspondence theory? Theorists of this stripe may call their theories whatever they wish; my argument is that they face a dilemma. This theory, regardless of what it's called, maintains that all truths, in order to be true, stand in a particular relation-the truthmaking relation-to some object or other. That relation is either defined in terms of truth, or is more fundamental than truth. The latter option, I have suggested, is unmotivated. The former option, if accepted, reveals that this "correspondence theory" is actually not a theory of truth at all, since it already presupposes the notion of truth. Whatever this theory accomplishes, it does not manage to succeed in answering the most basic question that correspondence theories have traditionally attempted to answer.12 Perhaps the circularity objection can be resisted another way. It might be thought that the appearance of truth in the above accounts of the truthmaking relation is innocuous, and that it can be dispensed with by utilizing familiar maneuvers from the deflationist's toolkit. For deflationary theories of truth, 'true' is primarily a logical device useful for expressing generalizations (among other things). For instance, instead of reasserting each and every individual thing that Kant ever wrote, I can simply say that everything that Kant wrote is true. So we might hold that we can give an account of the truthmaking relation that relies on 'true' only as 12 Hence, it's entirely possible that what some have defended in the name of correspondence theory cannot have ever been a theory of truth. If so, there is an important correction to be made to such views; calling them theories of truth was misleading and inaccurate. Armstrong himself struggles to formulate the relationship between his maximalist truthmaking theory and the correspondence theory of truth. On the one hand he presents his view as a kind of correspondence theory (1997: 128, 2000: 150, 2004: 16-17); on the other, he recognizes the threat of circularity, and so concludes that "A fundamental concept such as truth is likely to be so entwined with other fundamental notions that no total explication of it in terms of other concepts is possible" (2004: 17). What I offer in this paper is a resolution to this tension: truthmaker theory abandons the correspondence theory's pretensions of defining truth, but preserves its aim of grounding truth in reality. MacBride (2013) misses this tension by attending only to the former aspect of Armstrong's view. (See Simpson 2016 for criticism of MacBride.) 9 a device for generalization, and that hence can emerge truth-free.13 If so, we can use the notion of truthmaking to define truth without fear of circularity, despite initial appearances. This deflationist-inspired response, however, is not available to those who seek to use their truthmaker theory for revealing the nature of truth.14 For expository purposes, let us stick with the necessitation condition on truthmaking: (TM) For all x and y, x is a truthmaker for y only if it is metaphysically necessary that if x exists, then y is true. Equipped with TM, we may use it to give a necessary condition for our "truthmaking account of truth": (T1) For all y, y is true only if there exists some x such that it is metaphysically necessary that if x exists, then y is true. 'True' now appears in the definiens, which is the source of the circularity worry. The current thought is that by noticing the way that 'is true' is normally redundant, we may turn T1 into: (T2) For all y, y is true only if there exists some x such that it is metaphysically necessary that if x exists, then y. T2 avoids T1's use of 'true' at the fatal cost of unintelligibility. The quantifier accompanying 'x' is the ordinary objectual quantifier. If we also quantify over 'y' objectually-substituting it with names for truth bearers like sentences, beliefs, and propositions-then the final substitution will fail. We would have the following bit of nonsense as an instance: (1) 'Bill will kill Jill' is true only if there exists some x such that it is metaphysically necessary that if x exists, then 'Bill will kill Jill'. What we need at the end of the instance is a used sentence, not a mentioned one. For example: 13 For the generalizing role of 'true' in truthmaker theory, see Fox 1987: 189, Bigelow 1988: 125-127, Lewis 2001a: 278 and 2001b: 603-604, and Künne 2003: 164. 14 It is a perfectly fine response for those who are deflationists about truth and want to understand the theorems of truthmaker theory, as I discuss below. 10 (2) 'Bill will kill Jill' is true only if there exists some x such that it is metaphysically necessary that if x exists, then Bill will kill Jill. In order to derive theorems like 2, we need to trade in T2 for: (T3) For all y, 'y' is true only if there exists some x such that it is metaphysically necessary that if x exists, then y.15 To interpret T3, we need to employ both objectual quantification (for 'x') and substitutional quantification, for 'y' is now varying over sentential expressions. (Otherwise we would be unintelligibly quantifying objects into quotes.) There is a serious problem, however, with resorting to substitutional quantification here: the traditional semantics given for the substitutional quantifiers already employs the notion of truth. As Horwich notes: "the notion of substitutional quantification is trivially interdefinable with that of truth and itself requires theoretical elucidation" (1990: 27; see also Kripke 1976). A particularly substitutionally quantified sentence 'Σx(...x...)' is true if and only if there is an expression (from the relevant substitution class) such that substituting it for 'x' in '...x...' yields a true sentence. A universally substitutionally quantified sentence 'Πx(...x...)' is true if and only if every expression (from the relevant substitution class) is such that substituting it for 'x' in '...x...' yields a true sentence. Employing substitutional quantification to define the truthmaking relation still leaves us with a circular definition of truth.16 Thus, in order to rely on T3 to offer a 15 T3 is built for sentences. We could replace 'y' with 'the proposition that y' for a propositional version, or 'the belief that y' for a belief version. The problem persists despite what we take truth bearers to be. 16 It has been pointed out to me that defining truth in terms of objectual quantification, or even any logical connective for that matter, will also result in circularity as these notions may also need to be defined in terms of truth. If so, then there is no special problem with substitutional quantification. If these other logical notions are also defined in terms of truth, then so much the worse for anyone trying to define truth, including truthmaker theorists. I take this to be a strong argument in favor of primitivism. 11 truth-free truthmaker theory of truth, we have to formulate an account of substitutional quantification that in turn does not rely on the notion of truth.17, 18 Perhaps the answer for the truthmaker theorist seeking to analyze truth in terms of truthmaking lies not in substitutional quantification, but in infinite lists. Horwich (1990) thinks that truth cannot be defined finitely because he rejects as circular any substitutionally quantified truth schema. Truth is defined instead by the T-sentences, the infinitely many non-paradoxical instances of the propositional truth schema. Perhaps we can do the same for T1. Even if we cannot adequately remove 'is true' from T1, we can take its instances, pair them with the Tsentences, and derive both 2 and the following: (3) 'Jill will kill Bill' is true only if there exists some x such that it is metaphysically necessary that if x exists, then Jill will kill Bill. (4) 'Jill will thrill Bill' is true only if there exists some x such that it is metaphysically necessary that if x exists, then Jill will thrill Bill. Here we have some of the needed non-circular theorems of our truthmaker theory of truth. One could point to 2, 3, 4, and countless others and suggest that they are the key to understanding the nature of truth, just as Horwich points to the list of T-sentences and says that they are the key to understanding the nature of truth. Call this infinitary view 'T4'. T4 faces three major difficulties. First, anyone who advocates the view relinquishes the ability to give a finitely stateable theory of truth, a common desideratum for non-deflationary theories of truth. By "going infinite", a view concedes that nothing in general can be said about a particular notion-truth may be defined only implicitly, not explicitly. Such an attitude is appropriate for deflationary views of truth that deny that there is anything in common between 17 Hill (2002) has attempted such a project (though his interests are disconnected from truthmaking), which aims to offer an inferentialist treatment of substitutional quantification. This is not the place to evaluate Hill's proposal, but one may wonder whether the notion of inference will admit of a full elucidation without somehow relying on truth. Regardless of the success of a project like Hill's, truthmaker theorists who want their theory to serve double duty as a theory of truth have a steep hill to climb here (no pun intended). 18 One might respond by rejecting the semantics for the substitutional quantifiers given here, and taking them instead as logical primitives. This maneuver does sidestep the circularity worry, but invokes a theoretical primitive that requires further theoretical justification. It's unclear what could motivate taking on this additional primitive, given that the advocate of T3 doesn't get to say anything above and beyond what a deflationist who accepts truthmaker theory can say. 12 truths.19 Substantive theories of truth, however, do hold that there are important commonalities between truths, and thus the absence of an explicit, general statement of what it is in which truth consists is a serious shortcoming.20 Secondly, T4 exhibits a sort of motivational schizophrenia. Anyone who takes 2, 3, 4, and their cousins to constitute a theory of truth is advocating a union between anti-deflationist attitudes about truth (that it has an underlying nature, to be given by truthmaking) with deflationary maneuvers for dispensing with truth. It is deflationists who avail themselves of infinite lists, not those who think that the nature of truth can be analyzed into further, more basic notions. The tension between these competing attitudes can best be appreciated by noting how this view treats the two instances of 'true' appearing in T1 very differently. The first appearance of 'true' presents truth as something in need of further analysis-something that is to be more fully explained by the consequent of the conditional. But the second appearance of 'true' is treated as a mere logical device that is in principle dispensable. Finally, T4 stands in a problematic relationship to the T-sentences. We arrive at 2, 3, and 4 by deriving them from the circular instances of T1 and the T-sentences. For example, we can pair the following instance of T1 'Bill will kill Jill' is true only if there exists some x such that it is metaphysically necessary that if x exists, then 'Bill will kill Jill' is true with the T-sentence 'Bill will kill Jill' is true if and only Bill will kill Jill 19 Which is not to say that all deflationists are happy with the infinite approach. See Hill 2002 and Künne 2003. 20 There is another closely related worry about pairing a substantive theory of truth with the infinite list approach. If truth is defined by or in conjunction with an infinity of T-sentences, then truth appears to be defined in terms of all the many notions that appear in those T-sentences. This lead Gupta to charge that, according to infinitary deflationists, "an understanding of 'true' requires the possession of massive conceptual resources" (1993: 69). In short, you don't understand truth unless you understand everything. Deflationists may well find something right in this conclusion: you don't understand the truth of 'Electrons are negatively charged' unless you understand what electrons and negative charge are, for the truth of 'Electrons are negatively charged' consists in nothing more than the negative charge of electrons. Substantivists about truth say that its truth consists in something else (something that is common to all and only truths), like correspondence with the facts. So the thought, common to Horwich's minimalism and T4, that truth has to be defined in terms of everything does not sit well with substantive theories of truth. 13 in order to derive 2. To arrive at T4, then, we need to employ the T-sentences. Now, T4 cannot take the T-sentences to be the explanatorily basic facts about truth-that would be to concede deflationism-but neither can the advocate of T4 take them to be explained by T4, for that would involve an explanatory circularity. Moreover, most theorists of truth acknowledge what Tarski calls "Convention T", which holds that any adequate theory of truth must entail all the Tsentences (1956: 187-188). The idea is that the T-sentences provide a "check" on a theory of truth; any theory of truth that fails to produce the T-sentences is thereby defective as an account of truth. T4's relationship to the T-sentences, however, compromises the purpose of Convention T. T4 must be front-loaded with the T-sentences in order to derive its theorems, and so the convention provides no meaningful constraint on it. T4 trivially satisfies the constraint by taking all the T-sentences for granted. One might expect this result from deflationism, which takes the theory of truth to be exhausted by the T-sentences. But non-deflationary theorists of truth typically hold that their theories need to be derived independently of the T-sentences, lest they end up using truth to say what truth is. T4 is unique among theories of truth in virtue of its awkwardly taking the T-sentences for granted without taking them to be the explanatorily fundamental facts about truth. I conclude that we cannot use familiar deflationary tactics to allow truthmaker theorists to offer a non-circular truthmaker-based theory of truth. The proper way to understand 2, 3, 4, and the rest is not to think of them as revealing the nature of truth, of what the shared essence is between all and only truths. If any infinite list of theorems is to reveal the nature of truth, it's the list of T-sentences. What 2, 3, and 4 are, however, are theorems of how a deflationist unhappy with substitutional quantification should understand truthmaker maximalism. Because such theorems are available, the cogency of truthmaker maximalism is no immediate threat to deflationism. Deflationism about truth and truthmaker maximalism are perfectly consistent doctrines. The deflationary tactics we have employed show that deflationists may accept truthmaker maximalism; what the tactics cannot be used for is revealing any underlying essence to the nature of truth in terms of truthmakers. 4. Truthmaking, not Correspondence I have argued that truthmaker theory does not and cannot offer an adequate substantive theory of truth. A fortiori, truthmaker theory does not offer a correspondence theory of truth. Nevertheless, truthmaker theory and correspondence theory share much in common, given their shared motivational core that truth is "worldly". What I shall now argue for is the claim that 14 truthmaker theory, precisely because of its similarity to correspondence theory, actually serves to undermine the need for adopting any correspondence theory of truth. Truthmaker theory captures the theoretical motivations that underlie correspondence theories and make them seem so natural. But truthmaker theory can satisfy those motivations at lesser theoretical cost. Hence, those who are attracted to correspondence theories should become truthmaker theorists instead, and reject correspondence theories of truth. According to my reading, traditional correspondence theory conflates two separate philosophical questions. For some given truth p, we can ask (i) what its truth consists in, and (ii) what its truthmaker is. Correspondence theory answers the first question in terms of its answer to the second question: the truth of p consists in its correspondence to some fact, where the fact is also what makes it true. But these questions can be separated, and so they are distinct questions. One can hold, alongside deflationism, that truth doesn't consist in anything, that there is no common property shared by all and only truths.21 But that is not to say that truths don't have truthmakers. For example, one can maintain that the truth of that Socrates is a philosopher consists in nothing more than Socrates's being a philosopher (and nothing shared with the truth of, say, that Aristotle is a philosopher), but also claim that what makes it true is a state of affairs, trope, or Socrates himself under a counterpart relation.22 One can deny that the truth of that there are penguins and the truth of that there are puffins share a common core, and yet admit that both have truthmakers (namely, penguins and puffins). Hence, one can be a truthmaker theorist without being a correspondence theorist. I now argue that those who are attracted to correspondence theory should be truthmaker theorists, and not correspondence theorists. By this I mean that they should embrace the metaphysical project of offering a theory of truthmakers in the sense I outlined above, but without thinking that this project in any way elucidates the nature of truth itself. The reason behind my suggestion is that truthmaker theory is sufficient to account for the instincts that drive many to correspondence theory; those same instincts are precisely what make most everyone agree that correspondence 21 The word 'property' can be misleading. Even Horwich (1990) admits that truth is a "logical" property. I follow Edwards (2013) and Asay (2014) in maintaining that deflationists reject the view that truth is a "sparse" property in the sense of Lewis 1983, a property that captures genuine resemblances between the objects that share it. That truth is merely an "abundant" property is trivial. For criticism of this view, see Wyatt 2016). 22 See, respectively, Armstrong 2004, Lowe 2007, and Lewis 2003. 15 theory is the "default", "natural", or "intuitive" theory of truth (even if it is ultimately false or, perhaps, just empty and uninformative).23 A first reason to prefer truthmaker theory is that it can be more ontologically economical than correspondence theory. That is to say, truthmaker theory can offer a more parsimonious account when it comes to explaining the shared commitment to the idea that truth is worldly. Take, for example, the truth that there are penguins. The truthmaker theorist should say that this is made true by penguins: penguins themselves are sufficient for satisfying the "correspondence intuition" with respect to the truth that there are penguins. But on any correspondence account, for anything one takes to be true there must be some fact (or other relevant slice of reality) in one's ontology to which it corresponds. So to that there are penguins there must correspond some object-call it 'O'. If O is something like a fact (as it must be if the correspondence theory is of the familiar kind that maintains that all truths correspond to facts), then we have ontological overkill. What we need are penguins, not O, to satisfy the correspondence intuition with respect to the truth that there are penguins. But if O is just some penguin, then correspondence theory offers no advance over truthmaker theory. So in the case of many truths, truthmaker theory fares as well as or even better than correspondence theory in accounting for how truths are grounded in reality. Truthmaker theory also scores points for economy by speaking to a number of metaphysical concerns at once. Truthmaker theorists disagree as to what sorts of entities we should posit in order to serve as truthmakers. For example, is truthmaker theory better served by Armstrongian states of affairs or by tropes? Notice that these sorts of metaphysical posits are also front and center in the traditional debate over the existence of universals, and the debate over how to account for the genuine resemblances between objects and their causal powers. Tropes, as well as the universals that partially compose Armstrongian states of affairs, are the kinds of entities that metaphysicians posit in order to ground the objective resemblances between things, to solve the "problem of the one over the many", and to understand the nature of the powers that objects possess (see Lewis 1983). Truthmaker theorists can use their posited truthmakers to satisfy the correspondence intuition while at the same time tackling the problem of universals and accounting for causality. A familiar worry for the correspondence theorist's posits (assuming they go above and beyond the truthmaker theorist's) is that they are ad hoc: they 23 See, e.g., Blackburn 1984: 224, Horwich 1990, Grover 1992: 32, Wright 1992, and Hill 2002. Cartwright observes that "we are all inclined toward some form of "correspondence" theory of truth" (1987: 73). 16 serve no purpose other than their role in correspondence theory.24 It is not at all obvious, for instance, that facts can be used to account for genuine resemblances and causal powers. To be fair, correspondence theorists can use a realm of facts to account for resemblance and causality provided that they understand their posits in terms of universals and particulars, as does Armstrong. But recall that correspondence theorists who employ facts need more facts than does Armstrong-they need a fact to correspond to the truth that there are penguins, a different fact to correspond to the truth that there are aardvarks, and plenty more. What's unclear is what metaphysical role these facts are supposed to serve other than filling in the gaps of correspondence theory.25 Furthermore, if correspondence theorists are to make the case that their facts can be used to solve other metaphysical issues because their facts are composed of universals, then it looks like their hands are tied when it comes to the traditional questions concerning realism about universals. Correspondence theorists would not then be free to explore the merits of trope theory, lest they end up in ontological extravagance with a world made up by universals and tropes.26 Truthmaker theorists, by contrast, are not so constrained. They are free to explore the competing merits of universals and tropes (and other positions in the realism/nominalism debate) without being antecedently committed to a world of facts and universals. Truthmaker theory also provides greater theoretical flexibility than correspondence theory when it comes to accounting for traditionally problematic truths. Consider again the trickiest set of truths for truthmaker theory: negative existentials. What makes it true that there are no hobbits? Perhaps there are negative facts (Russell 1985), absences (Martin 1996), or one giant totality state of affairs (Armstrong 2004) that make it true. But we have seen another option: perhaps negative existentials don't have truthmakers at all (Bigelow 1988, Lewis 2001b). Truthmaker maximalism is not a sine qua non of truthmaker theory. It may be that the best response to negative existentials is not to ground their truth in the existence of specific existing entities. Thus, it may be that not all truths have truthmakers, a consequence that is perfectly consistent with the spirit of truthmaker theory. But if correspondence theory is the correct 24 E.g., Quine 1990: "facts contribute nothing beyond their specious support of a correspondence theory" (80). 25 It's also unclear how such "existential facts" can be composed of universals. Is there a universal existence? Correspondence theory now looks to be committed to the further view, not so popular nowadays, that existence is a property. 26 One might try to build a correspondence theory around truths corresponding to tropes rather than facts. (Something like this is operant in Mulligan, Simons, and Smith 1984.) This is a hard road to travel, for it's unclear how tropes can be used to account for negative existentials and general truths, for instance. 17 theory of truth, then every truth must have a corresponding object. There can be no "nonmaximalist" correspondence theory. Hence, correspondence theorists' hands are more tied than are truthmaker theorists' when it comes to handling negative existentials. There is a highly appealing route available to truthmaker theorists that is closed off to correspondence theorists. Finally, truthmaker theory avoids the traditional problem facing correspondence theory of giving a satisfying account of the correspondence relation. At least in its very simple version where for every distinct truth there is a distinct fact, correspondence theories offer an overloaded and unilluminating ontology. The world is a world of facts, and those facts come in various shades: positive, negative, conjunctive, disjunctive, existential, ethical, aesthetic, counterfactual, etc. A one-one correspondence relation comes with ontological extravagance, but a more subtle relation is notoriously difficult to articulate. The truthmaking relation, by contrast, is a many-many relation, and so we do not need a distinct kind of truthmaker for each kind of truth. Correspondence theorists must posit the existence of a similar relation, if they are to avoid ontological overload. This relation must exist in addition to the truthmaking relation since, as we have seen, correspondence cannot be defined in terms of truthmaking, on pain of circularity.27 So the correspondence theorist owes us an account of the correspondence relation that is above and beyond the truthmaking relation (while looking remarkably similar to it). Better to be a truthmaker theorist and avoid this burden altogether. Furthermore, the correspondence theorist owes us an account of what sorts of objects can enter into the correspondence relation. If the objects are limited to facts, then, since corresponding objects are understood as that which makes truths true, then it seems that such correspondence theorists must say that only facts can make truths true. But consider again the truth that there are penguins; it can be made true by just a simple penguin. If the world is more than a world of facts (a Moorean truth, I dare say), then the rest of the world provides truthmakers for truths, too. If other sorts of objects can stand in the correspondence relation, then it continues to resemble more and more the truthmaking relation, in which any object can (and does) stand. Take any existing entity x: x is a truthmaker for the truth that x exists, and so stands in the truthmaking relation to that truth. The world is a world of truthmakers; accordingly, the very idea of a truthmaker is not limited to any particular ontological worldview. Even the nominalist's world is a world full of truthmakers. So truthmaker theorists have far greater ontological flexibility and resources when satisfying the correspondence intuition. 27 See also David 2009, which argues that the correspondence relation and truthmaking relation are different. 18 In sum, correspondence theory at best offers no advance over truthmaker theory when accounting for the idea that truth depends on reality. One can develop a correspondence theory that looks strikingly similar to a certain kind of fully developed truthmaker theory (such as Armstrong's), but doing so is unmotivated, and adds no benefit above and beyond the benefits of "pure" truthmaker theory stripped away from any ambition of giving a theory of truth itself. At worst, correspondence theory offers a bloated ontology and little theoretical maneuverability. So the choice is clear. Rather than adding facts and a correspondence relation to our ontology, we need to account for the worldliness of truth via the theory of truthmakers. Truthmaker theory accomplishes that task without being biased as to the nature of what those objects are (for truthmakers are not limited only to certain kinds of ontologies), without relying on ad hoc posits, and without positing the existence of a one-one correspondence relation. (To the extent that correspondence theory can be developed without these things, it offers no benefit that truthmaker theory cannot claim for itself.) "Purified" truthmaker theory is the more economical, ontologically flexible, and theoretically desirable means for preserving the motivation behind correspondence theory.28 5. Truthmaking for Deflationists Truthmaker theory as I have defended it is in the business of accounting for what it is in reality that grounds or makes true all that is true; it is not in the business of saying what truth is. Deflationism is a view about the latter, and so there is no inherent inconsistency between truthmaking and deflationism. Since it is routinely thought that truthmaker theory presupposes a substantive theory of truth, it is natural to think that truthmaker theory and deflationism are at 28 Another line of response the correspondence theorist might take is charging that there are further motivations for correspondence theory beyond capturing the worldliness of truth. If so, these need to be articulated. One common thought seems to be something along the lines that correspondence truth is necessary for various forms of realism (e.g., Kitcher 2002). But realism is accounted for by way of correspondence theory's commitment to worldliness, and so also by truthmaker theory (cf. Asay 2012). Another thought might be that there are genuine resemblances between truths, and so we need a sparse account of truth to capture them. Such a view cannot be refuted, but I fail to see much plausibility in it. Truths run the gamut from aesthetics to morality to mathematics to zoology; they are disjunctive, atomic, counterfactual, and modal. In many cases, truths resemble falsehoods much more closely than they resemble other truths. So I doubt that there is any phenomenon of genuine resemblance that calls upon the need for a sparse account of truth. 19 odds.29 But this is not so; nothing about deflationism contradicts the idea that truths are made true by the world. Truths depend for their truth upon the world, even if there is no single property that all and only truths share. It is no tenet of deflationism that truths do not depend for their truth upon reality, or that truths "float free" independently of the way of the world. Even Quine was happy to declare that "No sentence is true but reality makes it so" (1970: 10). Deflationists maintain that each truth is its own individual affair: it is true that snow is white because snow is white, and it is true that grass is green because grass is green. Truthmaker theorists can agree, and offer individual truthmakers for individual truths. Hence, it is paramount to recognize that even if truth is not a metaphysically substantive property-a genuinely shared feature between all and only truths-it does not follow that truths themselves are not grounded in reality. A commitment to a set of truths must accompany an ontological commitment to what one takes their truthmakers to be, even if it doesn't require an additional commitment to a correspondence relation or a realm of facts.30 Deflationism about truth is no barrier to serious metaphysics.31 Should truthmaker theorists be deflationists, since they shouldn't be correspondence theorists? Truthmaker theory itself-even in its maximalist version-is not inhospitable toward deflationism. The appearance of 'true' in the definition of the truthmaking relation can be handled in standard deflationist fashion. (The problem from above, recall, was using these deflationary tactics for the non-deflationary purpose of building a substantive theory of truth out of truthmaking.) Furthermore, deflationism is hospitable toward truthmaking. Deflationism is a view about the lack of commonalities between truths. Truthmaker theorists can agree. That there are penguins is made true by penguins, and that there are electrons is made true by electrons. So while both are truthmakers, what we really have are a "there-being-penguins-maker" on the one hand and a "there-being-electrons-maker" on the other. The common term 'truthmaker' glosses over the differences between truthmakers just as 'truth' glosses over the differences between truths. Truthmaker theorists can subscribe to the same "piecemeal" approach to truths that deflationists have long advocated. 29 See, e.g., McGrath 2003 and Vision 2003. Thomas (2011) raises problems for pairing deflationism and truthmaker theory, but these involve misunderstandings about both enterprises that my present analysis avoids. MacBride (2013) also appears to resist my line of thinking, though his analysis depends on some sort of resolution to the objections I raised in section 2. 30 Cf. Rettler 2016. 31 I should emphasize that this paragraph represents my argument for the consistency of truthmaking and deflationism. I reject David Lewis's argument to the same conclusion (2001a, 2001b), as it relies on problematic claims and inferences concerning when sentences are "about" truth. David (2004) refutes his argument admirably. 20 Truthmaker theory, therefore, goes a long way toward vindicating deflationary analyses of truth. But we have not yet sealed the deal for deflationism, for at least one other view about truth remains, namely, the view that takes truth to be conceptually primitive (e.g., Davidson 1996 and Asay 2013). What separates deflationists and primitivists is not their (shared) rejection of the familiar substantive theories of truth, or the recognition that truth is not a metaphysically substantive property, but rather their disagreement over whether truth is an explanatorily potent concept. Primitivists take our concept of truth to be useful for explaining other important notions like successful action, belief, assertion, and others. Truthmaker theory is neutral on this score- we don't need anything more than a deflationary account of truth to give an account of the truthmaking relation, but it's no part of truthmaker theory to say whether or not there are explanatory demands elsewhere in philosophy that require something more than deflationary truth. Truthmaker theorists are free to choose between full-bore deflationism and conceptual primitivism. Truthmaker theorists can go in for deflationism (though they don't have to); they certainly shouldn't go in for correspondence theory. Should deflationists go in for truthmaker theory? Absolutely. Most opponents of correspondence accounts typically find something legitimate about them nevertheless, and go to some length in order to show how they too can maintain the "correspondence intuition". But deflationists cannot uphold what is right about correspondence theories merely via their own theories.32 This should be unsurprising, given how sparse and austere deflationary theories are. The theorems of deflationary theories of truth are typically just T-sentences, such as 'The proposition that snow is white is true if and only if snow is white'. This material biconditional makes no assertion whatsoever as to how truth depends upon reality. To say that the proposition is true if and only if snow is white is distinct from saying that the proposition has a truthmaker; it certainly offers no claim as to what that truthmaker is, or whether it even has one. T-sentences merely convey that some sort of equivalence holds between their two sides; they say nothing regarding how those two sides depend upon the world for their truth. We must not conflate the "semantic descent" expressed by a T-sentence with a claim about ontological grounding and truthmaking. My suggestion to deflationists is that they continue thinking that they too can account for what is right about correspondence theories. But to do so, they have to embrace some sort of theory of truthmaking. The worldliness of truth cannot be accounted for simply by the Tsentences alone, since they need to be supplemented by a theory of truthmakers. 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