University of Connecticut DigitalCommons@UConn Doctoral Dissertations University of Connecticut Graduate School 5-7-2014 Pluralism and the Absence of Truth Jeremy W. Wyatt University of Connecticut Storrs, wyattjww@gmail.com Follow this and additional works at: http://digitalcommons.uconn.edu/dissertations This Open Access is brought to you for free and open access by the University of Connecticut Graduate School at DigitalCommons@UConn. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of DigitalCommons@UConn. For more information, please contact digitalcommons@uconn.edu. Recommended Citation Wyatt, Jeremy W., "Pluralism and the Absence of Truth" (2014). Doctoral Dissertations. Paper 345. Pluralism and the Absence of Truth Jeremy Wyatt, Ph.D. University of Connecticut, 2014 In this dissertation, I argue that we should be pluralists about truth and in turn, eliminativists about the property truth. Traditional deflationists were right to suspect that there is no such property as truth. Yet there is a plurality of pluralities of properties which enjoy defining features that truth would have, were it to exist. So although, in this sense, truth is plural, truth is non-existent. The resulting account of truth is indebted to deflationism as the provenance of the suspicion that truth doesn't exist. But it would be hasty to simply classify the account as deflationary. Each of the 'truth-like' properties that it recognizes is highly substantive–that is, complex and explanatorily potent. So we should deflate truth by recognizing that it doesn't exist, but we should also recognize that one of the most vital tasks in truth theory is to discover the essences of the many truth-like properties. My aim here is to do precisely this. Pluralism and the Absence of Truth Jeremy Wyatt, Ph.D. B.A., Texas Christian University, 2008 M.A., University of Connecticut, 2011 A Dissertation Submitted in Partial Fullfilment of the Requirements for the Degree of Doctor of Philosophy at the University of Connecticut 2014 APPROVAL PAGE Doctor of Philosophy Dissertation Pluralism and the Absence of Truth Presented by Jeremy Wyatt, B.A., M.A. Major Advisor Michael Lynch Associate Advisor Jc Beall Associate Advisor Marcus Rossberg University of Connecticut 2014 ii To my family. iii ACKNOWLEDGEMENTS My greatest philosophical debt is due to Michael Lynch for his patience, encouragement, and honesty and most of all for his concern. He will serve for the rest of my career as a paradigm of the kind of person a philosopher ought to be; I'm fortunate to know him. Others at UConn, past and present, who deserve special thanks include my committee members Jc Beall and Marcus Rossberg as well as Don Baxter, Nilanjan Bhowmick, Tom Bontly, David Capps, Colin Caret, Aaron Cotnoir, Jon Gajewski, Michael Hughes, Casey Johnson, Scott Lehmann, Daniel Massey, Toby Napoletano, Dave Ripley, Yael Sharvit, Paul Silva, Lionel Shapiro, John Troyer, and Sam Wheeler. I began work on 'Minimizing moderate pluralism' while serving as a Visiting Research Fellow at the Northern Institute of Philosophy in the summer of 2013. The feedback that I received during a presentation in NIP's Pluralism seminar was integral to the development of that chapter. Thanks to everyone at NIP for an invaluable experience and especially to Carl Baker, Delia Belleri, Doug Edwards, Filippo Ferrari, Fed Luzzi, Giacomo Melis, Tim Sundell, Cory Wright, and Crispin Wright. I continued to develop this chapter while visiting Yonsei Universtiy for the remainder of that summer. Thanks to Nikolaj Pedersen and to the members of his Graduate Research Workshop, especially Junyeol Kim and Chulmin Yoon, iv for excellent feedback and to Nikolaj for ongoing and open conversation. Funding for my visit to Yonsei was provided by Yonsei University. Additional funding for both of these visits was provided by the UConn Philosophy Department and the UConn Graduate School. 'Domains, plural truth, and mixed atomic propositions' is a revised verison of an article of the same name, published in Philosophical Studies 166: 1. 255-36. An early version of this paper was presented to the Logic, Epistemology, and Metaphysics (LEM) Research Group at UConn. A later version was presented at the 1st Seoul Philosophy Graduate Conference at Yonsei University, funding for which was provided by the UConn Graduate School and Yonsei University. Thanks especially to Jinho Kang, Rune Nyrup, and Takashi Yagisawa for feedback. I presented part of 'Minimal pluralism' at the XVII Shapiro Graduate Philosophy Conference, held in 2012 at Brown University and at the 2013 meeting of the Pacific Division of the American Philosophical Association. Thanks to all in attendance and especially to Michael Conboy, Phil Corkum, Doug Edwards, and Blake Hestir for commentary. I'm highly indebted to the philosophy faculty at Texas Christian University, including Gregg Franzwa, Richard Galvin, Blake Hestir, and Bill Roche. Throughout my undergraduate career, they taught me that philosophy is challenging but immensely rewarding. Most importantly, they taught me to remain hungry for understanding. v Over the past six years, my family has contintually offered moral–and, when needed, financial–support. I wouldn't have made it without them. Finally, thanks to JoHannah and Leo for good company through the many hours of writing and revision. vi TABLE OF CONTENTS 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The essence question . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Deflationism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Pluralism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Going forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2. Why alethic pluralism? . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 Scope + Substance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.2 Substance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.1.3 Scope + Substance . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2 Alethic primitivisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.2.1 Anti-reductionism . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.2.2 Indefinabilism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.2.3 Anti-decompositionalism . . . . . . . . . . . . . . . . . . . . . . . . 61 2.2.4 Circularism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.3 Pluralism + Primitivism . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.3.1 The metaphysical instability challenge . . . . . . . . . . . . . . . . 67 2.3.2 Resisting the challenge: anti-reductionism and anti-decompositionalism 75 2.3.3 Circularism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 vii 2.4 Indefinabilism and the scope of the scope problem . . . . . . . . . . . 81 2.5 Explanatoriness and metaontology . . . . . . . . . . . . . . . . . . . 84 2.5.1 Indefinabilism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.5.2 Deflationism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 2.5.3 The metaphysical instability challenge . . . . . . . . . . . . . . . . 96 3. Domains, plural truth, and mixed atomic propositions . . . . . 99 3.1 Pluralism and truth-aptness . . . . . . . . . . . . . . . . . . . . . . . 101 3.2 Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.3 The problem of mixed atomic propositions . . . . . . . . . . . . . . . 112 3.3.1 Response: No domains . . . . . . . . . . . . . . . . . . . . . . . . . 114 3.3.2 Solution: Multiple domain membership, but one manifester . . . . 118 4. Minimizing moderate pluralism . . . . . . . . . . . . . . . . . . . 124 4.1 Moderate pluralism: core theses . . . . . . . . . . . . . . . . . . . . . 127 4.2 The alethic platitudes and platitude conformity . . . . . . . . . . . . 132 4.2.1 The need for platitudes . . . . . . . . . . . . . . . . . . . . . . . . 132 4.2.2 The need for neutrality . . . . . . . . . . . . . . . . . . . . . . . . . 138 4.2.3 Alethic properties and platitude conformity . . . . . . . . . . . . . 143 4.2.4 Overgeneration? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.2.5 Overly technical? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.3 The instability of moderate pluralism . . . . . . . . . . . . . . . . . . 158 viii 4.4 Sentence-truth, proposition-truth, and 'real truth' . . . . . . . . . . . 163 4.5 Miscellaneity: Proposition-truth, sentence-truth, and truth . . . . . . 169 4.6 Propositions and indicative sentence-tokens . . . . . . . . . . . . . . 176 4.7 Bearer-specific alethic properties . . . . . . . . . . . . . . . . . . . . 179 4.8 Truth as strongly general . . . . . . . . . . . . . . . . . . . . . . . . . 183 4.9 Unity: minimal pluralism vs. strengthened moderate pluralism . . . . 185 4.9.1 Ontological parsimony . . . . . . . . . . . . . . . . . . . . . . . . . 185 4.9.2 Unity, mixed discourse, and mongrel discourse . . . . . . . . . . . . 188 4.10 Mixed, general truth ascriptions and the meaning of 'true' . . . . . . 205 4.11 Core theses of moderate and strengthened moderate pluralism . . . . 210 4.11.1 Moderate pluralism . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 4.11.2 Strengthened moderate pluralism . . . . . . . . . . . . . . . . . . . 212 5. Minimal pluralism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 5.1 Minimal pluralism: overview . . . . . . . . . . . . . . . . . . . . . . . 213 5.2 Deflationism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 5.2.1 Pluralism and deflationism . . . . . . . . . . . . . . . . . . . . . . . 217 5.2.2 The need to disambiguate . . . . . . . . . . . . . . . . . . . . . . . 221 5.2.3 Varieties of substantiality . . . . . . . . . . . . . . . . . . . . . . . 223 5.2.4 Edwards on substantiality . . . . . . . . . . . . . . . . . . . . . . . 257 5.2.5 Minimal pluralism and deflationism . . . . . . . . . . . . . . . . . . 264 5.3 Proposition-truth and sentence-truth . . . . . . . . . . . . . . . . . . 283 ix 5.3.1 Necessity and contingency . . . . . . . . . . . . . . . . . . . . . . . 283 5.3.2 Propositions, sentence-tokens, assertions . . . . . . . . . . . . . . . 286 5.3.3 Priority: Properties and concepts . . . . . . . . . . . . . . . . . . . 294 5.4 The domain-specific alethic properties . . . . . . . . . . . . . . . . . 304 5.4.1 Unity and parsimony . . . . . . . . . . . . . . . . . . . . . . . . . . 305 5.4.2 Correspondence pluralism . . . . . . . . . . . . . . . . . . . . . . . 308 5.5 Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 5.6 Moving beyond truth . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 5.6.1 Minimal pluralism: core theses . . . . . . . . . . . . . . . . . . . . 335 Bibliography 338 x Chapter 1 Introduction 1.1 The essence question The traditional question in truth theory is the essence question: what is the essence of truth? This question has been taken to apply primarily at the level of properties. Most truth theorists, drawing upon our ordinary linguistic and cognitive practices, have supposed that in seeking after the essence of truth, we are seeking after the essence of a property truth which some entities have and some lack. The impression that this should be the object of truth theory is encouraged by the facts, for instance, (i) that in performing ascriptions and denials of truth, we very often use what looks to be a distinctive predicate, namely 'is true' and (ii) that this predicate looks to have a conceptual analogue, the concept truth, which we deploy when believing such things as that it is true that the Earth is spherical. Expressions that are predicates in a semantic sense have, according to a venerable tradition, properties as their semantic values. 'Is round,' for instance, has as its semantic value the property roundness. So if indeed we use a semantic 1 2 predicate 'is true,' then it is an important task for truth theorists to explain just what is the nature of the property truth that is the predicate's semantic value. This line of thought harbors an assumption that may, at first pass, seem rather unremarkable. This is that if 'is true' has a property as its semantic value, then there is exactly one property that is the semantic value of 'is true.' This assumption is characteristic of monism about truth. Monists about truth–or as they are sometimes called, alethic monists, the root of 'alethic' being the Greek word 'aletheia,' meaning truth–hold that there is one and only one property truth, whose essence truth theorists are tasked with discovering. And, so the tradition tells us, this task is a highly complicated one. The reason for this exceptional degree of complication is meant to be that the nature of truth exhibits a rather high degree of complexity, so that a thorough account of truth's nature will come only with a great deal of effort. 'And why think that truth's nature is impressively complex?' we might ask. One very good reason to think this, says the tradition, is that the notion of truth is ubiquitous in philosophy in a way that few other notions are. We take knowledge to be factive–one can only know truths, one cannot know falsehoods. Sound deductive arguments are ones that necessarily preserve truth and which have only true premises. A constitutive aim of belief is to believe only what is true. It is rational to endorse a scientific theory only if in doing so, one comes to know important scientific truths. And the list could be extended far further, or so 3 the tradition has it. The philosophical roles that truth plays look to be numerous and highly varied. Surely, the thought goes, the nature of the property that plays these roles must be very intricate indeed. In addition to the assumption of monism, the second assumption that has been traditionally made in truth theory is thus that truth is a substantive–that is, philosophically significant and thus highly complex–property. 1.2 Deflationism A growing number of philosophers have sharply criticized this second assumption. Early proponents of this movement held that, upon scrutiny, it becomes clear that 'is true' is not actually a predicate in the semantic sense. Frank Ramsey suggested that when I perform a truth ascription of the form 'It is true that p,' I am saying nothing more than I would have said were I to have simply uttered 'P.' What more am I really saying, Ramsey wondered, when I say 'It is true that Caesar was murdered' than that, well, Caesar was murdered? Adding that it is true that Caesar was murdered is, Ramsey thought, strictly redundant from a semantic point of view. Adding that a proposition is true, in other words, leaves the content of what I say unaltered–the content is just the same as it would have been, had I merely asserted the proposition itself. But if this is so, if 'is true' is not really a predicate in the semantic sense of denoting a property, then as Ramsey nicely puts the point, the motivations behind the essence question may be down 4 to a mere "linguistic muddle."1 For if 'is true' does not denote a property in the first place, then it is clearly no task for truth theorists to discover the essence of the property that it denotes. Better then, Ramsey and a number of like-minded philosophers have thought, to assume that there is no property truth and get on with more important business, such as discovering the meaning of 'is true' and similar expressions and determing the function that this predicate performs in English. The contingent of philosophers who followed Ramsey in urging that truth very probably does not exist ushered in a trend in truth theory that has come to be known as deflationism. Deflationists are so-called because their aim is to deflate the grand ambitions of traditional truth theorists to discover what they suppose is the highly complex essence of truth. If, as Ramsey thought, we had better suppose that there is no such property, then this traditional ambition is directly undercut. Contemporary deflationists, such as Paul Horwich, typically propose a somewhat midler deflation of the truth-theoretical tradition. Horwich has been especially forthright in allowing that truth does exist. But what he holds is that even though there is such a property, philosophers such as Ramsey were exactly right to deny that truth is a substantive–that is, a philosophically significant–property. The characeristic deflationary thesis about truth is thus that truth, if it exists at 1 [223, p. 157]. 5 all, is not a philosophically significant property. And this, they say, is precisely where the tradition in truth theory goes wrong. 1.3 Pluralism Ramsey's seminal paper was published in 1927, so it's fair to say that the deflationary movement in truth theory is fast approaching ninety years of age. Quite recently, in 1992, a countermovement in truth theory was sparked with the publication of Crispin Wright's landmark work Truth and Objectivity. Wright's major aim in this book is to develop a framework for the prosecution of debates between realists and non-realists in philosophy. Realists of a familiar sort claim of a particular kind of entity K that there are K's–that K's are real. Non-realists hold either that K's are not real (they are 'anti-realists' about K's) or refuse to weigh in on the issue as to whether K's are real (they are 'quietists' about K's). And there are further gradations of realism and non-realism still. What Wright proposed is that debates between realists and non-realists involve a number of 'realism-relevant criteria,' so that one's views regarding discourse about K's are more realist to the extent that they take such discourse to satisfy more of these criteria. What this points to, Wright says, is the possibility that some of the discourses in which we engage–for instance, physical and biological discourse–may satisfy more of the realism-relevant criteria (they may be 'more realist') than other discourses–for instance, moral or comedic discourse. The discourses in which we 6 engage, in other words, may vary to the extent that they conform to the model of discourse proposed by realists. This way of partitioning discourses, Wright points out, gives rise to an intriguing possibility regarding truth [274, pp. 37-8, see also pp. 24-5]: The proposal is simply that any predicate that exhibits certain very general features qualifies, just on that account, as a truth predicate. That is quite consistent with acknowledging that there may, perhaps must be more to say about the content of any predicate that does have these features. But is also consistent with acknowledging that there is a prospect of pluralism–that the more there is to say may well vary from discourse to discourse. . . Realists aboutK's hold thatK's are real. So if one discourse better conforms to the realist model than does another, then it is fair to say that the aim of the former discourse, moreso than that of the latter, is to describe what is real, i.e. to accurately describe the world. What this suggests, Wright urges, is that truth may be very different in the former sort of discourse than in the latter. For statements made within the former discourse to be true, they must succeed in their aim of accurately describing the world. But if this is not an aim of statements of the latter discourse, then it is inadvisable to require that they describe the world to be true. To make sense of how the latter sort of statement could be true in just as literal of a sense as the former sort of statement, we need, Wright says, to think of 7 truth in a 'very general' way. In doing so, we will be able to say that there is a very general notion of truth and that this general notion is applicable to statements from rather different discourses, though the conditions for its application–that is, what it is for different such statements to be true–differ across these discourses. In short, as Wright nicely puts it, the framework that he proposes for debates between realists and non-realists gives rise to a fascinating prospect of pluralism regarding the nature of truth. It also gives rise to the prospect that whereas the core notion of truth that applies across discourses is quite thin, the nature of truth, as it is instantiated by statements from a particular discourse, is quite substantive. In the intervening years, a number of philosophers–most notably Michael Lynch–have continued to develop this pluralist outlook on truth, which has come to be called alethic pluralism. Alethic pluralism, like alethic monism, is a propertylevel thesis about truth. Following Wright, alethic pluralists outline a very general conception of the sort of property that philosophers (and tacitly, ordinary cognizers) take truth to be. In contrast to traditional monists about truth, pluralists argue that there is not just one property that conforms to this conception, there is a plurality of such properties. Each of these properties is, in this sense, 'truthlike–'it behaves, at least sometimes, as our general conception of truth takes truth to behave. In advancing this thesis, pluralists also set themselves against mainstream 8 deflationists. Such deflationists claim either that there is no property that conforms to this general conception of truth or that there is exactly one such property, although it is a highly insubstantial property. So in holding that there is more than one such property, pluralists part company with both traditional deflationists such as Ramsey and more contemporary deflationists such as Horwich. Pluralists disagree with mainstream deflationists, that is, over the cardinality of the set of properties that conform to this general conception of truth. Pluralists also disagree with mainstream deflationists about the merits of asking after truth's essence. Mainstream deflationists are highly pessimistic on this score, arguing that such a question is confused, perhaps down to a mere 'linguistic muddle.' But the oversight inherent in this question, pluralists counsel, is not that it is a question about the essence of truth. It is perfectly in order, and terribly important, to speak of essences when discussing truth. The oversight stems from the fact that the question is put in terms of 'truth.' Posing the question in this way masks the fact that there is not just one 'truth-like' property, there are many such properties. So the better question is: What are the essences of the truth-like properties? To make headway in the essence project, as we might call it, what we need to recognize is that in pursuing this project, we are investigating not the essence of just one property, but the essences of many properties. So far from being deflated, the essence project is for pluralists even more rich, interesting, and potentially fruitful than traditional truth theorists recognized. 9 1.4 Going forward My aim in this dissertation is to articulate and defend what I regard as the most attractive variety of alethic pluralism. I'll begin by offering in chapter 2 what I take to be the strongest argument for alethic pluralism writ large, which draws upon and extends what Michael Lynch has called the 'scope problem.' This argument has proven to be very controversial, so I will venture to diagnose the weaknesses of the argument, as it has been formulated so far, and to show how they can be corrected. The remainder of the dissertation is devoted to the development of what I call minimal pluralism about truth. I'll concentrate in the third chapter upon two issues that arise not only for minimal pluralists, but for alethic pluralists in general. The first is the problem of articulating a precise conception of what Wright calls discourses, more commonly known as 'domains.' The second is a problem generated by atomic propositions which intuitively should be associated with more than one domain, so-called mixed atomic propositions. Since pluralists take truth's nature to vary across domains, the fundamental question here is what the truth-conditions of mixed atomic propositions might be, if they are indeed associated with more than one domain. These two problems, I'll argue, are intimately connected so that a solution to both substantially clarifies the form that a pluralist theory of truth ought to have. I then turn in the fourth chapter to the most influential family of pluralist 10 truth theories, representatives of what has come to be called moderate alethic pluralism. Being pluralists, moderate pluralists hold that there is more than one property which conforms to our general conception of the sort of property that truth is. But moderate pluralists are called 'moderate' because they privilege one of these 'truth-like' properties, holding that this property, in contrast to all of the others, should be accorded the distinguished title 'truth.' This much, moderate pluralists say, alethic monists get right–there is only one property truth, although there are other truth-like properties that don't merit this lofty title. Moderate pluralism, it has been thought, is able to thread a rather thin needle. Moderate pluralists recognize the diversity in truth's nature, but also posit significant unity in truth's nature, since they posit a single property truth. I'll argue, however, that when we pay careful attention to the mechanics of moderate pluralist truth theories, we see that they generate the result that there is more than one property which deserves to be called 'truth.' Since this result is incompatible with moderate pluralism, we must look for a way beyond moderate pluralism. And I hold that minimal pluralism is the way. The fifth chapter is devoted to an exposition of minimal pluralism. One of the chief aims of minimal pluralism is to preserve what I take to be central insights of deflationism while avoiding a commitment to deflationism writ large. At the level of properties, truth is deflated in the senses (i) that there is no such property as truth–Ramsey was right–and (ii) that the natures of the properties 11 which replace truth are rather minimal. We can save these insights, I explain, without going in for Deflationism with a capital 'D.' As I advance it, minimal pluralism is pluralistic not only with respect to the properties that replace truth, it is also pluralistic with respect to the notion of correspondence to reality. The truth of every truth-bearer should be explained in terms of correspondence to reality. But in some cases, the correspondence at issue is between propositions and facts whose existence depends upon our mental states–so-called response-dependent facts–whereas in other cases, the relevant sort of correspondence is a correspondence between propositions and responseindependent facts. In particular, I propose that we take propositions about taste– for instance, the proposition that beets are delicious–to be true if and only if they correspond to response-dependent facts. By contrast, it is more plausible to take chemical and biological propositions, e.g. the proposition that water is H2O, to be true iff they corrrespond to response-independent facts. So the minimal pluralist is a pluralist in two senses: (i) they deny that truth exists, positing instead a plurality of properties that have been erroneously identified with truth and (ii) they take the truth of some truth-bearers to be explicable in terms of–though not identical to–the property of correspondence with response-indendent facts, whereas the truth of other truth-bearers is explicable only in terms of correspondence with response-dependent facts. For the minimal pluralist, there are two pluralities of truth-like properties–one consisting of 12 rather minimal properties and the other consisting of response-dependent and response-independent correspondence. The way forward in the essence project is to investigate the essences of these properties, their relations to one another, and the important work that they do throughout philosophy. Chapter 2 Why alethic pluralism? The perfection of cognition requires that it be true. Truth is agreement of cognition with the object. But this is really only a nominal definition[;]this is one of the strangest phenomena in a science, when one cannot answer a question that constitutes the essence of the science. Such a question has long been posed in logic, namely, What is truth? Kant, Vienna Logic 13 14 2.1 Scope + Substance 2.1.1 Scope The traditional programme in truth theory is the monist-substantivist programme. The truth theories that emerge in the course of this programme, though they differ from one another in important respects, each entail a common thesis about truth:1 • (MS) There is one and only one 'truth-like' property–namely, truth itself– and truth is a rather substantive property. In the chapter 4, we will have occasion to carefully expand upon the notion of a 'truth-like' property. The guiding idea is that a property P is truth-like just if P has the features which the conception of truth that is pertinent to truth theory takes truth to have. A truth-like property is a property which, at least sometimes, behaves as this conception of truth takes truth to behave. Monist-substantivists hold that there is exactly one such truth-like property–truth itself. And as we'll see, a number of critics of monist-substantivism have called into question precisely this contention–that in our search for truth's essence, we will turn up only one property that conforms to our conception of truth. In chapter 5, we'll pay careful attention to the notion of substantiveness, as it applies to properties. For now, substantive properties can be thought of as 1 Throughout, I use italics to name properties, e.g. truth, and small captials when referring to the concept truth. When I wish to make a claim that is ambiguous between property and concept, I use the lowercase, unitalicized 'truth.' 15 being properties that have complex natures and are philosophically significant. We'll see that there is more than one interesting sense in which truth might be, or fail to be, a substantive property. So the sense in which traditional truth theories ential that truth is a 'rather substantive' property is that they entail that truth is substantive in more of the target senses than those in which it fails to be substantive. In chapter 5, we'll fill in the rest of these details. Alethic pluralists break sharply with the established tradition in truth theory. A highly influential pluralist challenge to (MS) has it that whichever rather substantive property is identified with truth, the resulting account of truth's nature will fail to satisfactorily apply to every entity that, intuitively, is capable of being true or false. The challenge, in other words, is that while traditional truth theories tend to enjoy considerable plausibility when applied to certain apparent truth-bearers, none enjoys plausibility in connection with all apparent truth-bearers. This would represent a systematic pattern of failure on the part of monist-substantivist truth theories that we should venture to diagnose. My aim in this dissertation is to articulate and defend what I regard as the most attractive variety of alethic pluralism. In this chapter, I want to focus on the general motivations for alethic pluralism by laying out what I think is the best general argument in its favor. This argument turns crucially upon the just-mentioned scope problem for monist-substantivist truth theories. And this is a liability for the argument, since the scope problem is actually not a problem 16 for substantivist-monist truth theories as such, but is rather a problem only for most such theories. So to offer a comprehensive critique of traditional monism, pluralists need a supplement to the scope problem. The supplement that I'll offer not only fulfills this need, it also serves as a further motivation for pluralism against a particular variety of 'deflationary' truth theory. So what I'll ultimately be arguing in this chapter is that once the scope problem is suitably supplemented, it forms a vital part of a systematic pluralist critique of competing truth theories. Correspondence theories We'll begin by considering several kinds of extant monist truth theory and showing why the plausibility that they enjoy is limited in scope. In what is the most detailed formulation of the scope problem to date, Michael Lynch [175, ch. 2] puts forward a critique of perhaps the most influential variety of monist truth theory, correspondence theories.2 In essence, a correspondence theory of truth is a theory of truth that takes being true to consist in instantiating a certain relational property correspondence.3 Lynch focuses in particular on the class of correspondence theories that characterize truth in terms of a certain naturalistic 2 Gila Sher has offered the related problem of the 'common denominator' [239] and her 'disunity challenge' [240]. 3 In general, n-ary relations can be treated as n−1-ary relational properties. In keeping with the model provided by (MS), we'll treat correspondence as a relational property in what follows. No issues of substance hang on this decision; we could just as well treat correspondence as a relation. 17 theory of reference. Hartry Field [96], in a seminal piece on correspondence theories, nicely articulates an attraction of accounts of truth which characterize truth in terms of a naturalistic theory of reference. Naturalism, broadly construed as the programme of using only those philosophical notions that are scientifically respectable, enjoys considerable and widely acknowledged philosophical advantages. Since the natural sciences don't explicitly investigate truth and reference, truth-talk and reference-talk is in prima facie tension with naturalism. One way to resolve this prima facie tension is to articulate a scientifically respectable account of reference and to then put this theory of reference to work in constructing an account of truth. The major ambition of the resulting metasemantics is, as Field [96, p. 373] puts it, to "explain the connection" between language and extralinguistic, extramental reality in a scientifically respectable way. For correspondence theorists moved by these considerations, the primary question is: how to explain what it is for a linguistic expression (and/or the concept(s) expressed by that expression) to refer? A number of naturalistic theories of reference take reference to be a causal relation.4 These theories take the reference of an expression x to consist in x's standing in a certain causal relation R 4 Proponents of such accounts of reference include Devitt [69]; Fodor [108]; Kripke [155]; Stampe [251]; and Putnam [219]. Teleosemantic accounts of reference, e.g. those defended by Millikan [188] and Papineau [200], form another influential class of naturalistic theories of reference. For present purposes, we can safely focus only on causal theories of reference. 18 to a distinct entity e (either directly or in virtue of the fact that x expresses a concept that itself stands directly in R to e). The proper name 'Barack Obama,' for instance, refers to a particular person: Barack Obama. A causal theory of reference attempts to explain this fact in terms of a particular causal relation in which 'Barack Obama' stands to Barack Obama. Perhaps, for instance, 'Barack Obama' refers to Barack Obama because Obama's parents, upon witnessing his birth, assigned him that name and the members of Obama's linguistic community have, for this reason, also consented to calling him 'Barack Obama.' With such a naturalistic theory of reference in hand, the prospects for a naturalistic account of truth look noticeably brighter. A causal theory of reference goes some way towards explaining the connection between language (and thought) and extralinguistic, extramental reality. If we were able to construct such a theory of reference for every sort of linguistic expression, we could then define in a familiar way what it is for a sentence consisting of such expressions to be true. The sentence 'Barack Obama is male.' is composed of the name 'Barack Obama' and the predicate 'is male.' These expressions refer–'Barack Obama' to Obama and 'is male' to the property maleness or perhaps to the class of males–and ex hypothesi, we can explain their reference along causal lines. What, then, is required for the sentence to be true? Its truth-condition looks to be that Obama instantiates the property maleness or alternatively, that Obama is a member of the class of males. Put more generally, the resulting account of truth will take the truth-conditions 19 for 'Barack Obama is male.' to be (i) that the sentence characterizes the world as being a certain way, in virtue of the fact that it is composed of expressions that refer to particular parts of reality and (ii) that its characterization of reality corresponds to the way that the world actually is. Though we've simplified its details, a correspondence theory along these lines is rather intuitive when we restrict ourselves to sentence-tokens like 'Barack Obama is male.' But what Lynch stresses is that a correspondence theory of this sort comes to grief in connection with certain other putative truth-bearers. For the sake of illustration, let our skeletal correspondence theory take indicative sentencetokens to be the sole bearers of truth. English appears to contain true sentencetokens about mathematics, e.g. '7+5=12.' Our theory has it that '7+5=12' is true only if its component expressions–'7,' '+' '5,' '=,' and '12' stand in certain (direct or indirect) causal relations to their referents. But it's difficult to see how this could be so. Numerals such as '7,' '5,' and '12' would presumably have to refer to numbers–to 7, 5, and 12, respectively. Likewise, '+' and '=' look to refer, if at all, to the addition function and the relation of numerical identity, respectively. The problem isn't hard to see: numbers, functions, and relations are presumably abstract, and thus acausal entities, but our theory entails that an expression refers to an entity e only if it stands in a particular causal relation to e. For this reason, our theory looks unable to accommodate mathematical reference. Since we've characterized truth in terms of a causal account of reference, our theory thus 20 looks unable to accommodate mathematical truths. Our everyday thought and discourse also evidences the fact that we take there to be truths about morality and taste. Suppose that someone presents me with slips of paper on which are written, respectively, 'Apartheid is unjust.' and 'Crème brulée is tasty.' Were they to ask me, 'Are these sentences true?' I would respond, 'Yes, of course.' I suspect that you would respond similarly about at least some moral and aesthetic sentences. But our skeletal correspondence theory also has trouble accommodating truths about morality and taste. The theory entails that 'Apartheid is unjust.' is true only if 'Apartheid' and 'is unjust' refer. The predicate 'is unjust,' if it does indeed refer, presumably refers to the property injustice or alternatively, to the class of unjust entities (acts, policies, persons, etc.). One problem here is similar to a problem involving mathematical reference: classes seem to exist over and above their members and are presumably abstract and properties, at least according to Platonist theories of properties, are also abstract. So it looks as though 'is unjust' couldn't refer to injustice or to the class of unjust entities, if reference is causal in nature. An additional problem is that it's proven notoriously difficult to 'locate' moral properties such as injustice in the world. G.E. Moore [191] famously argued that the property goodness, if it exists, must be 'non-natural,' and thus different in kind from a biological property like maleness. If cogent, then Moore's reasoning 21 would generalize to all moral properties, including injustice. It's also been pointed out that at least some moral disagreements seem to be rationally irresolvable. J.L. Mackie [181, pp. 36-7] famously takes this apparent fact about moral disagreement to constitute evidence that the world doesn't contain absolute, objective moral properties such as injustice. If it did contain such properties, the basic thought goes, then presumably we could rationally resolve disagreements about e.g. which acts are unjust. You and I can rationally resolve a disagreement about whether a yellowish substance is gold by determining its chemical composition. Similarly, the thought is, if there are absolute, objective moral properties, then presumably we could rationally resolve a disagreement about e.g. whether apartheid is unjust by determining whether apartheid does, indeed, instantiate the property injustice. But, of course, if there is no such property injustice, then 'is unjust' can't stand in a causal relation to the property. It's similarly plausible to think that at least some aesthetic disagreements are rationally irresolvable. John Bender [23, p. 371] offers a helpful case involving two highly experienced painting critics who disagree "whether a given painting is playful or merely trite, daring in its color treatments or just gaudy, serious or only self-absorbed, and so forth." Bender points out that such a disagreement may be generated because the critics operate with different aesthetic values, or perhaps because they operate with the same aesthetic values, but differ in the relative import that they assign to them. For this reason, it's a good question whether their 22 disagreement about the qualities of the painting could be rationally resolved. The basic thought is then essentially the same as in the case of moral properties: if there were absolute, objective aesthetic properties such as gaudiness, then presumably we could rationally resolve our disagreements as to whether certain entities are playful by determining whether those entities instantiate gaudiness. So if it is possible for us to have rationally irresolvable aesthetic disagreements, this looks to be evidence against the existence of absolute, objective aesthetic properties. So correspondence theories of truth founded upon causal theories of reference enjoy considerable plausibility when we restrict ourselves to truth-bearers about certain subject matters, such as biological sex, solidity, temperature, or chemical composition. But they come to grief in connection with truth-bearers about certain other subject matters, including mathematics, ethics, and aesthetics. Correspondence theorists can respond to this problem by way of several well-known strategies. First, they can deny that the problematic, putative truthbearers–e.g. indicative mathematical, moral, and aesthetic sentence-tokens–are capable of instantiating truth or falsity. In other words, they can deny that such putative truth-bearers are truth-apt. This is the strategy pursued by emotivists about moral discourse such as Ayer [12] and Stevenson [253], who hold that if one performs an assertion using moral vocabulary, one doesn't say anything apt for truth, but rather only expresses an emotion. This strategy is afflicted by well-known costs. It is error-theoretic, in that 23 it entails the falsity of strong intuitions held by competent speakers, evidenced by our practices of truth ascription, that the relevant kinds of truth-bearer are indeed truth-apt. It may also be revisionary, if it is leveraged to argue that we should alter our practices of truth ascription that are subserved by these intuitions. The proponent of this strategy might avoid this revisionary commitment by endorsing a fictionalist account of our practices of truth ascription, aiming to show why it is useful for us to ascribe truth to the problematic range of truth-bearers, even though these ascriptions are, strictly speaking false (though they may be 'true-in-the-fiction').5 This sort of fictionalism is clearly also error-theoretic, since it entails that we regularly perform false truth ascriptions and, like emotivism, entails that the strong intuitions of competent speakers that the problematic range of putative truth-bearers are truth-apt are simply false. A second strategy would be to attempt to bring the problematic truthbearers into the correspondence-theoretic fold by working at the linguistic end. They can attempt to systematically paraphrase the claims that we make with mathematical, moral, and aesthetic sentence-tokens in terms that are congenial to correspondence theories. A central problem for such a paraphrase strategy is that we have good reason to doubt that it is viable. We have yet to construct problem-free paraphrases of 5 For discussion of a thoroughly-developed fictionalism about truth see Armour-Garb and Woodbridge [5], [6] and Woodbridge [273]. 24 every sort of claim that causes trouble for correspondence theories–and not for lack of effort.6 A third strategy is to try to bring the problematic, putative truth-bearers into the correspondence-theoretic fold by working instead at the ontological end. Here, the strategy is to 'reduce' the problematic entities–numbers, moral properties, aesthetic properties, etc.–to entities that do have causal powers and can accordingly stand in causal relations.7 6 'Term formalist' analyses of mathematical discourse take e.g. numerals to be referential, but entail that numerals refer to particular expressions, perhaps to themselves. Term formalism is friendly towards correspondence theories that invoke some causal theory of reference, given that numerals are expression-tokens and thus presumably enjoy causal powers. For discussion of term formalism see e.g. Shapiro [237, ch. 6] and Weir [266]). Similarly, so-called contextualist analyses of predicates of personal taste (defended e.g. by Cappelen and Hawthorne [40, ch. 4] ) can also be seen as resulting in systematic, correspondencefriendly paraphrases of aesthetic claims. The basic contextualist proposal is that the content of an assertion of 'Licorice is tasty' by Jones, for instance, is that licorice is tasty, according to Jones' standards of taste. At the very least, then, contextualism about predicates of personal taste offers up the hope of adequately analyzing aesthetic claims while avoiding commitment to absolute aesthetic properties like tastiness. Broadly subjectivist interpretations of moral discourse can be seen as offering up correspondence-friendly paraphrases of moral claims. A simple version of subjectivism has it that an assertion 'Act A is right' by Jones means just that Jones approves of A. This analysis of rightness-ascriptions clearly avoids commitment to absolute moral properties such as rightness. 7 Though he doesn't advertise it in this way, Hartry Field [97]'s attempt to construct a nominalistic interpretation of Newtonian mechanics can be seen as a salvo in favor of the view 25 Such reductionist strategies also face a threat of viability. No attempt to that mathematical entities have causal powers. The details are delicate, but one of the most significant upshots of Field's programme, were it to succeed, would be that it serves as a challenge to the thesis that abstract mathematical entities are indispensable to mature science, which is often associated with Quine and Putnam (for discussion of the Quine-Putnam indispensability argument, see e.g. Colyvan [47] and Shapiro [237, ch. 8, § 2]). Given that one of our best apparent reasons to posit such entities is that they appear to be indispensable, the success of Field's programme would raise the question whether we ought to posit abstract mathematical entities or whether Field's nominalistic ontology of concreta might do. In this way, the success of Field's programme would offer some reason to think that mathematical abstracta can be reduced to regions of spacetime, relations between them, and etc. Hedonist-consequentialist normative theories, such as utilitarianism, aim to reduce moral properties to properties with causal powers, e.g. rightness to the relational property causing more pleasure than pain in all affected entities. This property clearly has causal powers: if an act instantiates it, then the act ipso facto causes more pleasure than pain in all affected entities. Hedonist accounts of beauty also attempt to articulate an intimate connection between beauty and pleasure/pain. Though the matter is contentious, it's fair to read Hume as advancing a dispositionalist account of beauty, according to which being beautiful consists roughly in being disposed to cause pleasure in competent critics. The following passage from the Treatise is instructive in this connection [135, 2.1.8.2] (italics removed): Beauty is such an order and construction of parts as, either by the primary constitution of our nature, by custom, or by caprice, is fitted to give a pleasure and satisfaction to the soul. This is the distinguishing character of beauty, and forms all the difference betwixt it and deformity, whose natural tendency is to produce uneasiness. Pleasure and pain, therefore, are not only necessary attendants of 26 reduce entities of these problematic kinds to entities with causal powers is widely accepted. Moorean considerations in connection with moral properties threaten attempts to reduce moral properties to properties that enjoy causal powers. Additionally, the putative existence of rationally irresolvable moral and aesthetic disagreements threatens attempts to reduce moral and aesthetic properties to absolute, objective, causally potent properties. While perhaps non-fatal, these considerations put considerable pressure on correspondence theories that characterize truth in terms of a particular causal theory of reference. And similar considerations can be raised against correspondence theories that invoke other naturalistic conceptions of reference.8 But Nicholas Smith [247, p. 292] has pointed to a structural flaw in this line of argument. Correspondence theorists (as Lynch [175, p. 35], [179] acknowledges), aren't committed, just in virtue of being correspondence theorists, to a naturalistic account of reference. It's also far from obvious that naturalistic theories of reference are the most attractive theories of reference on the market.9 The flaw in the above argument, then, is that the class of interesting correspondence theories looks to be considerably larger than the class of correspondence theories beauty and deformity, but constitute their very essence. 8 See Lynch [175, ch. 2]. 9 For a discussion of standard problems with naturalistic theories of reference, see [1] and [194]. 27 that invoke naturalistic theories of reference. So even if the latter are jeopardized by a problem of scope, this doesn't entail that correspondence theories as such are afflicted by the scope problem.10 Though its focus is objectionably narrow, Lynch's argument points toward a more general problem of scope for correspondence theories. Wolfgang Künne, in his excellent overview of the history of truth theory, divides the class of correspondence theories into object-based and fact-based correspondence theories.11 Restricting ourselves to indicative sentence-tokens formed from a single name and unary predicate, the distinctive thesis of an object-based correspondence theory is:12 • (OC) 'a is F' is true iff the property F-ness to which 'is F' refers corresponds to/fits a, the object to which 'a' refers. Object-based correspondence theories characterize truth in terms of a correspondence between the entities to which the proper parts of truth-bearers refer (e.g. the properties and particulars to which predicates and names respec10 This flaw in Lynch's rendering of the scope problem has also been pointed out by Julian Dodd [77, p. 315]. 11 See also Hill [119, ch. 1, § III]. Proponents of object-based correspondence theories include Bolzano and Kant and proponents of fact-based correspondence theories include Moore, Russell, and the early Wittgenstein 12 Künne [156, p. 108] characerizes object-based correspondence theories in terms of 'mental or verbal predications.' I use indicative sentence-tokens for the sake of convenience, even if doing so is somewhat anachronistic. 28 tively refer). By contrast, still restricting ourselves to 'name-predicate' indicative sentence-tokens , the distinctive thesis of fact-based correspondence theories is:13 • (FC) 'a is F.' is true iff 'a is F.' corresponds to a certain fact Φ. Considering object-based and fact-based correspondence theories in turn, we can see that each is afflicted by a particular problem of scope.14 Object-based correspondence theories, like correspondence theories which invoke a causal theory of reference, characterize truth's nature in terms of the referents of the proper parts of truth-bearers. So object-based correspondence theorists are committed to positing referents for the proper parts of the truth-bearers that they posit. For this reason, object-based correspondence theories are affected by the problem that Lynch details. Our ordinary practices of truth ascription (and denial) evidence the fact that we recognize the existence of truths about e.g. morality and taste. (OC) entails that these sentences are true only if the predicates they contain refer, respectively, to moral and aesthetic properties. But, as we saw, commitment to moral and aesthetic properties is notably problematic. Following Frank Jackson [136], we can say that object-based correspondence theorists must somehow locate very many sorts of entities in the world. The scope problem, as it affects object13 Again, I take some liberty with truth-bearers here, using indicative sentence-tokens for convenience. Künne [156, §§ 3.2.1-3.2.2] also draws a distinction between two notions of factbased correspondence, the 'Russellian' and 'Moorean' notions. For present purposes, it's safe to set this distinction aside. 14 Lynch [175, pp. 1-3] also briefly forwards this broader problem. 29 based correspondence theories, is the problem that the task of locating some such entities–e.g. physical and biological properties–looks to be more tractable than the task of locating others–e.g. moral and aesthetic properties. In short, the scope problem for object-based correspondence theories is a problem of referent location. By contrast, the fact-based correspondentist's characterization of truth avoids commitment to specific referents for truth-bearers' proper parts. What (FC) entails is that e.g. 'Apartheid is unjust.' and 'Crème brulée is tasty.' are true only if there are facts to which each corresponds. The former, being a moral sentence, would presumably correspond to a moral fact, and the latter, being an aesthetic sentence, to an aesthetic fact. The difficulty is that it's notably problematic to posit moral and aesthetic facts. The above considerations involving rationally irresolvable moral and aesthetic disagreement can be applied in this connection in much the same way. If the world contained moral and aesthetic facts, then one wonders why we couldn't rationally resolve our moral and aesthetic disagreements by discovering these facts. Additionally, if we take facts to be structured entities composed of particulars, universals, and relations, then the fact-based correspondence theorist faces a problem similar to the problem of referent location, namely how to locate the putative constituents of e.g. moral and aesthetic facts in the world. The scope problem, as it affects fact-based correspondence theories, is thus the problem that the task of locating some kinds of fact–e.g. physical and 30 biological facts–looks more tractable than the task of locating others–e.g. moral and aesthetic facts. We might call this the problem of fact location. Object-based and fact-based correspondence theorists also have recourse to the lines of response that we outlined above. But as we saw, each of these strategies is jeopardized by thorny problems. So object-based and fact-based correspondence theorists are each compelled to confront the fact that certain location problems threaten to attenuate the plausibility of their analyses of truth. Epistemic theories Being moved inter alia by these location problems, some truth theorists have put forward epistemic accounts of truth's nature.15 The most influential kinds of epistemic truth theory are coherence theories and pragmatic theories. In essence, coherence theories take being true to consist in being a member of a coherent system of truth-bearers.16 Pragmatic theories of truth in turn come in a variety of forms. Charles Peirce [214] is standardly associated with the view that true beliefs are those that would be held at an imagined end of scientific inquiry. William James [141] takes truth to consist in a certain sort of cognitive utility, which beliefs enjoy either by being verifiable or by being suitably related to beliefs that are verifiable. John Dewey [72], another well-known classical pragmatist, is sym15 For nice overviews of additional problems afflicting correspondence theories, see David [60, esp. §§ 5, 9]; Kirkham [150, ch. 4, esp. § 4.7]; and Kunne [156, ch. 3, esp. § 3.3]. 16 Brand Blanshard [25] and Harold Joachim [143] offer prominent coherence theories of truth. 31 pathetic towards the view that true truth-bearers are those that are 'warrantedly assertible.'17 Epistemic truth theories look to sidestep the location problems that afflict correspondence theories. If, for instance, being true consists in being a member of a coherent system of beliefs, we'll feel little pressure to posit extralinguistic, extramental facts as truthmakers. The more natural view, rather, would be that the truthmaker for a belief B is just the fact that B belongs to a coherent system of beliefs. Additionally, it would seem unnecessary to talk of the property to which a predicate refers 'corresponding to' or 'fitting' the object to which a name refers. If truth is coherence and we need not appeal to such notions in elaborating the nature of coherence, then it would seem that we can put forward an analysis of truth that is free of these notions. One reason to look closely at epistemic truth theories, then, is that they hold out the hope that we can avoid commitment to extralinguistic, extramental facts and to extralinguistic, extramental referents for e.g. names and predicates. For all of the diversity that the family of epistemic truth theories exhibits, Michael Lynch and Crispin Wright [274, p. 41]; [277, p. 765]; [278, p. 59] have pointed out that in locating truth theory so firmly within epistemology, truth theories of this sort carry commitment to a common, problematic thesis–that 17 Contemporary 'neo-pragmatist' positions on truth include the views of Brandom [28]; Price [217], [218]; Putnam [220], [221]; Rorty [226]; and Wright [277]. Dummett [84] puts forward a related epistemic theory of truth. 32 there is a global epistemic constraint upon truth. The problem is that while it's plausible to think that truth is epistemically constrained in some domains, it's highly implausible to think that this constraint applies across the board. To illustrate the problem, we can consider an epistemic truth theory discussed by Lynch that identifies truth with the property superwarrant.18 Superwarrant is maximally stable warrant: • (SW) The belief that p is superwarranted in world w =Df the belief that p is warranted without defeat at some stage of inquiry in w and would remain so at every successive stage of inquiry in w. Call the monist, epistemic truth theory that takes truth to be identical to superwarrant superwarrantism. Since the superwarrantist takes beliefs to be the bearers of superwarrant, they will likewise take beliefs to be the bearers of truth. Given that the superwarrantist identifies truth with superwarrant, superwarrantism entails that every instance of the following schema is true: • (TSW ) The belief that p is true in w iff the belief that p is superwarranted in w. Lynch draws upon two further assumptions, for which he offers independent motivation [175, pp. 7-9, 14]: 18 The notion of superwarrant is inspired by the notion of superassertibility, developed by Wright [274, ch. 2, §§ IV-VI], [277, §§ 4-5]. 33 • (TP ) 〈p〉 is true iff p • (Content) The belief that p is true iff 〈p〉 is true. Lynch's contention is that any proposition of the following form serves as a counterexample to superwarrantism:19 • (F) 〈p and no cognizer will ever have warrant for 〈p〉〉. What he aims to show is that no instance of (F) is superwarranted, though there are plausibly true instances of (F). I have two initial concerns here. The first is that (F) is objectionably inexplicit. Specifically, are we quantifying over all possible cognizers or only over all actual cognizers? We can assume for now that it is the latter; we'll have occasion later on to consider the former option. The second concern is that the instances of (F) are propositions. This is a problem because it would seem that the superwarrantist need commit only to beliefs being truth-bearers. It looks open to them to also take propositions to be truth-bearers, but they aren't obviously committed to doing so. It will be better, then, to consider a schema whose instances denote beliefs and to then ask after the truth and superwarrant of those beliefs. 19 I formulate Lynch's argument in terms of instances of schemas, rather than in terms of schemas themselves. This is because schemas are presumably apt neither for truth nor for superwarrant. We could also state the argument in terms of tokens of instances of schemas, given the arguments in § 5.3.3, but we can set this matter aside. 34 This concern also afflicts the assumptions (TP ) and (Content), since both appeal to the truth of propositions. Again, the superwarrantist might take propositions to be truth-bearers, but it's not obvious that they must. So in lieu of drawing upon (TP ) and (Content), we'll draw in what follows upon the equally plausible: • (TB) The belief that p is true in w iff p in w. So consider the following schema: • (F′) The belief that (p and no actual cognizer will ever have warrant for the belief that p). The Lynch-style contention here is that no instance of (F′) denotes a belief that is superwarranted, yet intuitively, some such beliefs are true. So, the argument goes, truth and superwarrant come apart–some beliefs are true but fail to be superwarranted, contra (TSW ). Let B be a belief denoted by an instance of (F′). Where 〈A〉 is a proposition, say that B is the belief that A and no actual cognizer will ever have warrant for the belief that A. Instantiating on (TB), we then have it that B is (actually) true iff A and no actual cognizer will ever have warrant for the belief that A. Given that our biconditional is transitive, it then follows from (TSW ) that B is superwarranted iff A and no actual cognizer will ever have warrant for the belief that A. 35 Could B be superwarranted? It's natural to assume that a conjunctive belief is superwarranted only if belief in each of its conjuncts is superwarranted:20 • (ConjSW ) If the belief that p and q is superwarranted in w, then the belief that p is superwarranted in w and the belief that q is superwarranted in w. So if B is superwarranted, then the belief that A is superwarranted. It follows from (SW) that the belief that A is warranted at some actual stage of inquiry, i.e. that some actual cognizer possesses warrant for the belief that A. But we know that B is superwarranted iff A and no actual cognizer will ever have warrant for the belief that A. It follows that B isn't superwarranted. So B isn't superwarranted and it follows from (TSW ) that B isn't true. But since B was arbitrary, it follows that no instances of (F′) denote true beliefs. The superwarrantist is committed to holding that every belief of the form given in (F′) is untrue. And by (TB), the superwarrantist is thus committed to holding that there are no states of affairs whose obtaining will forever outstrip the warrant of actual cognizers. As Lynch [175, pp. 43-4] points out, this result is quite problematic: [A]n evidential constraint seems plausible in the case of some normative truths at least. Be that as it may, it seems highly implausible 20 Notice that (ConjSW ) doesn't require that these beliefs are warranted at the same stage of inquiry. Lynch makes use of a similar principle, which takes the superwarrant of a conjunctive proposition to be a function of the superwarrant of its conjuncts. 36 that such an evidential constraint could be motivated across the board. Surely, one might think, there are at least some truths–perhaps about the distant past, or the far side of the universe, or the number of stars right now, for which no evidence will ever be available in principle. Humility in the face of the size of the universe seems to demand that. And yet [(TSW )] would seem to require us to deny this. And this seems implausible: surely there can be some truths for which we will never have warrant. Presumably, there is a determinate number n of stars currently in the universe. The superwarrantist must hold, then, that some actual cognizer will have warrant for the belief that the number of stars currently in the universe is n. But given the size of the universe and human finitude, this is rather dubious. It might be thought that this argument begs the question. Lynch [175, ch. 5] contends elsewhere that the superwarrantist should embrace intuitionistic logic.21 Let Excluded Middle be the schema 'S or not-S.' Proponents of intuitionistic logic deny that the instances of Excluded Middle are logical truths. But didn't we appeal to Excluded Middle in assuming that there is a determinate number of 21 Strictly, Lynch argues that discourse expressing propositions from domains where superwarrant manifests truth (see chapter 2 for an explanation of these aspects of Lynch's views) is governed by intuitionistic logic. Since the superwarrantist identifies truth with superwarrant, these considerations, if cogent, would show that the superwarrantist should take intuitionistic logic to govern all discourse. Pedersen [206, § 4] also offers a nice discussion of this issue. 37 stars currently in the universe? Not necessarily. We needn't suppose that it's a logical truth that there is a determinate number of stars in the universe, only that this is a truth–which it quite plausibly is. Even if the superwarrantist denies that the pertinent instance of Excluded Middle is a logical truth, she is compelled nevertheless to accept it on non-logical grounds. Another response for the superwarrantist would be to reconsider her quantifiers. We've supposed that she quantifies only over actual cognizers, i.e. that her quantifiers are actualist. What if they were possibilist? The resulting definition of superwarrant would be: • (SW?) The belief that p is superwarranted in w =Df the belief that p is warranted without defeat at some possible stage of inquiry s in world w′ and would remain so at every subsequent stage of inquiry s′ in w′. Now consider our belief B. Could B be superwarranted, in the sense of (SW?)? B is the belief that A and no actual cognizer will ever have warrant for the belief that A. So if B is superwarranted, then by (ConjSW ), the belief that A is superwarranted. So the belief that A is warranted without defeat at some possible stage of inquiry in world w′ and would remain so at every subsequent stage of inquiry in w′. It plainly doesn't follow from this that some actual cognizer will have warrant for the belief that A–w′ might be a merely possible world. Likewise, by (ConjSW ), B is superwarranted only if the belief that no actual cognizer will 38 ever have warrant for the belief that A is superwarranted. This, belief, too, might be superwarranted in virtue of the fact that it is warranted without defeat at some merely possible stage of inquiry in w′ and would remain so at every subsequent stage of inquiry in w′. So the superwarrantist can avoid Lynch's objection by endorsing (SW?) instead of (SW). Call this variety of superwarrantism possibilist superwarrantism. We might try to leverage a similar counterexample against possibilist superwarrantism involving a belief denoted by an instance of the following schema: • (F′′) The belief that p and no possible cognizer will ever have warrant for the belief that p. Where 〈A〉 is a proposition, let B′ be the belief that A and no possible cognizer will ever have warrant for the belief that A. We know that B′ is superwarranted iff A and no possible cognizer will ever have warrant for the belief that A. If B′ is superwarranted, then by (ConjSW ), the belief that A is superwarranted. So by (SW?), some possible cognizer possesses warrant for the belief that A. It follows that B′ isn't superwarranted. So B′ isn't superwarranted and from (TSW ), we get that B′ isn't true. Since B′ was arbitrary, it follows that the possibilist superwarrantist is committed to denying that any belief denoted by an instance of (F′′) is true. And by (TB), the possibilist superwarrantist is thus committed to holding that there are no states of affairs whose obtaining will forever outstrip the warrant of all possible cognizers. 39 This result, however, isn't obviously problematic. Human technology could have advanced far more rapidly than it actually did. So even if no actual cognizer will ever have warrant for believing that the number of stars currently in the universe is n, perhaps some possible cognizer does. And if there are possible cognizers with infinite cognitive capacities, then it's reasonable to hold that there is a possible cognizer who has warrant for every truth. So I think that the possibilist superwarrantist is invulnerable to Lynch-style counterexample. The trouble, I think, is that if the superwarrantist commits only to possibilist quantifiers, then it's no longer clear that their theory of truth is interestingly epistemic. The fact-based correspondence theorist, for instance, might happily admit that if there are possible cognizers with infinite minds, then for any given truth, there is a possible cognizer who has warrant for belief in that truth. This sort of 'epistemic constraint' on truth is pretty meagre. So by drawing upon the example of superwarrantism, we see that if the epistemic truth theorist appeals only to actualist quantifiers, then they face Lynch's problem–that while it's plausible to think that the truth of some beliefs is epistemically constrained, it's highly implausible to think that the truth of all beliefs is so constrained. They can escape Lynch's problem by instead invoking possibilist quantifiers. But in doing so, they drain the 'epistemic constraint' that they place upon truth of any clear interest. What this indicates is that if they are to put forward a robustly epistemic conception of truth, the epistemic, monist truth 40 theorist must grapple with the fact that the plausibility of their views is rather attenuated. Identity theories A third traditionalist camp is represented by identity theories, which take truth to involve identity to a fact. A serious shortcoming of extant presentations of the scope problem is that they leave identity theories of truth entirely out of account. If pluralists are to actually present an argument against traditional monism, it's imperative that they consider how the scope problem might affect identity theories. Identity theorists standardly take propositions to be the primary, though not necessarily the sole, truth-bearers. So identity theories, insofar as they offer an account of truth's nature, entail one of two distinctive theses:22 22 See Baldwin [13, pp. 35-6]; Beall [19]; Candlish [33, p. 339]; Candlish and Damnjanovic [37, p. 9]; [38]; [39, p. 2]; Dodd and Hornsby [78, p. 320]; Engel [93, p. 441]. Cf. Baldwin [13, p. 42] on the 'identity thesis,' which invokes identity with reality, in lieu of identity with a fact (though see [13, p. 49]); Candlish [34, p. 116], [35, p. 199, 203-4]; Dodd [73, p. 160], [74, p. 43]; Hornsby [125, p. 2]; [126, p. 241]. For discussion as to which fact ought to be mentioned in (ID1) and (ID1), see Beall [19] and Candlish [35, pp. 203-4]. Identity theories are sometimes taken to not be theories of truth's nature at all. Dodd and Hornsby, in particular, have been particularly vocal proponents of this contention; see Dodd [76, ch. 1, § 1; ch. 5, § 4] and Hornsby [125, § 1.2, incl. fn. 5], [126, p. 243]. McDowell [?] 41 • (ID1) Propositions are the sole bearers of truth and the truth of a proposition 〈p〉 consists in 〈p〉's being identical to a certain fact Φ; or • (ID2) The truth of a non-propositional truth-bearer a (a indicative sentencetoken, belief, judgment, or etc.) consists in (i) a having the content 〈p〉 and (ii) 〈p〉 being true, i.e. 〈p〉 being identical to a certain fact Φ. Fact-talk is significantly more natural in connection with certain subject matters than in connection with others. It's very natural to speak of the fact that tables are solid and the fact that 7 + 5 6= 13. But it tends to strike us as more problematic to speak of the fact that beets are tasty, the fact that charity is good, the fact that George Carlin's stand-up comedy is funny, or the fact that Rembrandt's work is beautiful. Since they take being true to consist either in being identical to a certain fact or in having propositional content that is identical to a certain fact, identity theorists are compelled to reckon with this attenuation in the plausbility of their views. The identity theorist might respond to this challenge by pointing out a also seems to think of his own identity theory of truth in this way, since he takes it to involve only 'truisms' (though as he points out, it may still be 'non-deflationary,' in the sense that the concept of truth enjoys "centrality and significance. . .in reflection about thought and language" [?, p. 87]. Burgess and Burgess [31, p. 70], David [59, p. 684], Künne [156, p. 6], and Vision [264, pp. 7-8] also define identity theories of truth so that they needn't entail any claims about truth's nature. Note that in the present context, we are interested in identity theories insofar as they do aim to describe truth's nature. 42 distinction, due to Julian Dodd, between robust and modest identity theories.23 Robust identity theories take facts to be worldly, in that their constituents are not senses, intensions, Kaplanian characters, or concepts, but extralinguistic and extramental particulars, universals, and/or relations. By contrast, modest identity theories take facts to be propositional, i.e. to have as their constituents senses, intensions, Kaplanian characters, or concepts. So both robust and modest identity theories are identity theories of truth in virtue of entailing either (ID1) or (ID2), but they differ as to which kind of entity they reduce to which other kind of entity. Modest identity theories reduce facts to true propositions–they posit entities with senses or etc. as constituents, rather than entities with worldly particulars, etc. as constituents. Robust identity theories, conversely, reduce true propositions to worldly facts.24 The modest identity theorist might insist that they actually avoid the scope problem. The reason is that the scope problem, as it affects identity theories, can be reasonably interpreted as trading upon a worldly conception of facts. Perhaps it is because most of us presuppose that facts are composed inter alia of worldly properties that we find it puzzling how there could be moral or aesthetic facts. It is a very good question, as we've noted, whether there are really such properties as tastiness, gaudiness, goodness, or beauty. But, the modest identity theorist may insist that they avoid commitment to such properties, since they reduce facts to 23 [73], [74, pp. 44, 227], [75, § II], [76]. See also Candlish [35, §§ IV-V]. 24 See also Candlish [35] and Engel [93] on this distinction. 43 true propositions, rather than reducing true propositions to worldly facts. But two major problems remain, affecting modest and robust identity theories respectively. Modest identity theories fail to offer an informative account of truth's nature. Since they reduce facts to true propositions, modest identity theories, insofar as they venture to describe truth's nature, turn out to entail one of two distinctive theses: • (MID1) Propositions are the sole truth-bearers and the truth of a proposition 〈p〉 consists in 〈p〉's being identical to a certain true proposition 〈p′〉 or • (MID2) The truth of a non-propositional truth-bearer a consists in (i) a having the content 〈p〉 and (ii) 〈p〉 being true, i.e. 〈p〉 being identical to a certain true proposition 〈p′〉. (MID1) is highly uninformative. It states that the truth of 〈p〉 consists in 〈p〉's being identical to a certain true proposition 〈p′〉. We know that every entity is numerically identical to one and only one entity–itself. So, in effect, what (MID1) says is that for 〈p〉 to be true is for 〈p〉 to be identical to the true proposition 〈p〉. Since all propositions are self-identical, this raises the notorious problem of how we should explain what distinguishes true from false propositions.25 Additionally, it's clear that (MID1) simply fails to say anything informative about truth–we were already quite aware that true propositions are true propositions! Any impression 25 For discussion of this problem, see Candlish [36, p. 234]; Dodd [74, pp. 42-3]; and Hornsby [125, p. 9]. 44 to the contrary can only be generated by a pernicious doublethink wherein we claim that true propositions are identical to facts but nevertheless conceive of them as distinct kinds of entity. (MID2) fares no better on this score. A modest identity theory whose distinctive thesis is (MID2) has it that the truth of e.g. a judgment consists in that judgment having a true proposition as its content. But again, all that we are told about the truth of propositions is what (MID1) tells us–that for 〈p〉 to be true is for 〈p〉 to be identical to the true proposition 〈p〉. This is entirely unhelpful, with the result that we also fail to be enlightened as to the nature of the truth of e.g. judgments. So modest identity theories, whether they entail (MID1) or (MID2), fail to say anything informative about truth's nature. Thus, if the identity theorist ventures to avoid the scope problem by endorsing a modest identity theory, they are saddled with an uninformative account of truth. The modest identity theorist may react to this shortcoming in their views by denying that it is possible to informatively describe truth's nature, thereby endorsing a primitivist position on truth.26 Alternatively, the modest identity theorist may stop short of endorsing primitivism about truth, instead arguing 26 Hornsby [125, p. 22] famously expresses sympathy with primitivism about truth. Candlish [35, n. 22, p. 220], Cartwright [43], and Johnston [144, §§ 2.3, 5.2; nn. 2, 4] also characterize identity theories of truth as primitivist theories. Interestingly, Moore and Russell also endorsed primitivist views of truth at the same time that they endorsed identity theories of truth. See also Engel [93, p. 446] on this issue. 45 that their inability to informatively describe truth's nature isn't much of a cost, since the project of doing so is less important than it seems. In adopting this stance, the modest identity theorist would embrace a deflationary position on truth.27 But the problem with both of these maneuvers is that in pursuing them, the modest identity theorist concedes that their 'identity theory of truth' collapses into either a primitivist or a deflationary theory of truth. The result would be that 'modest identity theories,' conceived as theories that analyze truth's nature in terms of the notion of fact-identity, are mere phantoms. And to accept this result is to concede the main point at issue–that while the modest identity theorist may avoid the scope problem, they do so at the cost of sacrificing an informative analysis of truth's nature. The scope problem, then, puts significant pressure on modest identity theories. But it would be unwise for the identity theorist to endorse a robust identity theory as a means of escape. Robust identity theories are afflicted by the scope problem in a way that by now familiar. Robust identity theories carry commit27 This is the position taken by Dodd [76]; see also Engel Engel01. Dodd and Hornsby [78, p. 321] point out that modest identity theories may still be 'substantial' theories that are relevant to debates about truth's nature (see also [74, p. 45]). This is because they "may be one part of a metaphysical stand in opposition to the one which a correspondence theorist obliges himself to take." But even if modest identity theories are substantial theories in virtue of their subversion of correspondence theories of truth, they still fail to provide an informative account of truth's nature. 46 ment to a worldly conception of facts, which takes facts to be composed inter alia of properties. So to accommodate moral and aesthetic truths, the robust identity theorist must commit to the existence of moral and aesthetic properties. But as we've seen, this commitment is notably problematic given e.g. Moorean considerations and apparent facts about moral and aesthetic disagreement. So in effect, robust identity theories face the scope problem in much the way that object-based correspondence theories do–each looks committed to positing kinds of property that is notoriously difficult to locate in the world. So we've seen that three families of monist truth theories–correspondence theories, epistemic theories, and identity theories–must reckon with a common problem. The accounts of truth proferred by the theories in these families fail to satisfactorily generalize over all apparent truth-bearers. Proponents of these theories may react to this problem in a number of different ways and in doing so, will invite further serious problems for their views. So the problem of scope that afflicts these varieties of traditional monism motivates the search for a theory of truth that can help us to both diagnose and avoid the shortcomings of these theories. 2.1.2 Substance An alternative to traditional monism that has garnered widespread acceptance among philosophers is a broadly deflationary stance on truth. In chapter 5, we'll 47 see that deflationism is a rather nuanced view–quite a bit more nuanced, in fact, than has been recognized. For now, it will be sufficient to note the general thrust of the deflationary view of truth. In contrast to traditional monists, deflationists hold that truth is not a substantive property. Some deflationists have flatly denied that there is a property truth. Others, notably Paul Horwich, have granted to traditional monists that there is such a property, but what these deflationists insist upon is that truth's nature is actually far more straightforward than traditional monists have thoght. Because truth is such a 'thin' property on this view, truth is simply devoid of any philosophical significance–it fails to be a substantive property. Deflationism, pluralists have been happy to admit, looks to avoid the scope problem. If we should indeed take truth as such to be devoid of philosophical significance, then presumably this will hold across the board, i.e. for all truthbearers. Nevertheless, pluralists have, by and large, been staunchly opposed to deflationism. Since we've elected to focus on the scope problem in this chapter, it will suffice for now to simply mention the misgivings that pluralists have had with deflationism, leaving more substantial discussion of deflationism to chapter 5.28 Lynch and Wright have argued that the normativity of truth poses a deep problem for deflationism. Wright makes this case via his well-known 'inflationary 28 For two recent proposals that are conciliatory towards both pluralism and deflationism, see Beall [21] and Kölbel [153], [154]. 48 argument,' which aims to show that certain facts about the normativity of truth and warranted assertibility respectively show that truth must, in fact, be a substantive property.29 Lynch has argued that Paul Horwich's version of deflationism, alethic minimalism, has particular difficulty in accounting for truth's normativity. According to Lynch, Horwich cannot satisfactorily account for the fact that not only is truth valuable, truth's value is final, i.e. not merely instrumental.30 Lynch has also charged that deflationists must reject truth-conditional theories of meaning and content, given that such theories presuppose that truth has explanatory power, something that deflationists characteristically deny.31 Truthconditional theories are by far the best developed theories of meaning and content currently on offer. So if deflationary truth theories are incompatible with taking meaning or content to be truth-conditional, this is a cost inherent to deflationism. 2.1.3 Scope + Substance Thus far, we've amassed a set of considerations that look to miliatate against an impressive array of truth theories that are competitors to alethic pluralism. And it's tempting to think that these considerations constitute a comprehensive criti29 [274, ch. 1]; [275, § 1]; and [276, § IV]. For discussion of the inflationary argument, see Horwich [129], [131, Postscript]; Kölbel [151]; Miller [187]; Rumfitt [228]; and van Cleve [263]. 30 [169] and [170, pp. 107-16]. See also [175, ch. 6, § 1] and [173]. 31 For differing views as to the compatibility of deflationism about truth and truth-conditional semantics, see Burgess [30]; Collins [45]; Dodd [77, pp. 317-18]; Dummett [82]; Horisk [123]; [124]; Kölbel [152]; Patterson [201]; and Williams [268]. 49 cal argument on behalf of pluralism. The field of competitors, this rationale goes, includes traditional monist truth theories and deflationary truth theories. The former are jeopardized by the scope problem. The latter look unable to accommodate the normativity of truth and truth-conditional accounts of meaning and content. So collectively, the tempting argument goes, these considerations motivate the search for a theory of truth that is an alternative to both traditional monism and to deflationism. Notably, for all of their differences, traditional monists and deflationists are agreed on one point: that either there is one 'truth-like' property– namely, truth–or there are no such properties (as some deflationists suspect). So an alternative to both monism and deflationism would be a theory of truth which took there to be more than one truth-like property. We can take this claim, then, to be the distinctive thesis of alethic pluralism: • (Plur) There is more than one truth-like property. Call the tempting argument for alethic pluralism the Scope + Substance argument. The reason that we should reject the temptations of Scope + Substance is that it is jeopardized by an inherent weakness in the scope problem. The upshot of the scope problem is meant to be that the plausibility of monist truth theories is attenuated–each fails to satisfactorily generalize over all apparent truth-bearers. But the scope problem suffers from its own problem of scope–it fails to satisfactorily generalize over every reasonable monist truth theory. The counterexample here is a particular variety of primitivism about truth. So to appreciate the prob50 lematically limited scope of the scope problem, we'll need to first think a bit more about what it might mean for truth to be a primitive property. I want first to highlight a distinction that is important to draw not only when thinking about primitivism, but when thinking about truth in general. The best-developed primitivist truth theories are theories at the level of concepts–they entail that truth is a primitive concept. This concept-level thesis doesn't commit the primitivist to holding that there is a property truth that is also primitive. Indeed, in his recent defense of primitivism about truth, Jamin Asay [8] aims to defend a primitivist account of truth and a deflationary, non-primitivist account of truth. So the distinction that we must be careful to draw here is the distinction between concept-level views of truth and property-level views of truth.32 As is codified in (Plur), alethic pluralism is a property-level view.33 Since primitivists about truth have, by and large, operated at the level of concepts, we face an initial difficulty–pluralists and primitivists seem to be speaking at cross-purposes, so it isn't straightforward to determine what a pluralist-primitivist dialectic might look like. To see that there is an interesting discussion to be had here, we'll first need to ask what a reasonable property-level primitivist view of truth might look like. 32 See Alston [2]; Asay [8, § 1.1.1]; Bar-On and Simmons [18]; and Devitt [70] for very useful discussions of the import to truth theory of the property/concept distinction. 33 See the recent work of Max Kölbel [153], [154] for a related, concept-level view. 51 In doing so, we'll see that the landscape of property-level primitivist views is quite complex. The ensuing dialectic between pluralism and primitivism is, in turn, more complex than we might expect. Most property-level primitivist views of truth are consistent with alethic pluralism, and interestingly so. But one such primitivist theory is inconsistent with pluralism. What's particularly interesting about this theory is that although it is monistic, it's immune to the scope problem. So this theory serves to show that the scope problem is not a problem for monist theories of truth as such. In turn, then, this species of primitivism about truth jeopardizes the Scope + Substance argument for pluralism. But I think that the basic rationale behind Scope + Substance survives this blow. The proper response, I think, is to supplement Scope + Substance by drawing on certain metaontological considerations. A deep difficulty for the offending variety of alethic primitivism is that it comports poorly with a very plausible metaontological norm. And, as it happens, these metaontological considerations bolster the pluralist's case against deflationism. They pose an additional deep difficulty for alethic minimalism, a leading variety of deflationism defended by Paul Horwich. So although we'll need to defer further assessment of deflationism until chapter 5, by the end of this chapter we'll be in a position to appreciate that Scope + Substance provides compelling and forceful motivation for alethic pluralism. 52 2.2 Alethic primitivisms To facilitate the pluralism-primitivism dialectic, we'll take alethic primitivism to be a property-level view of truth. We'll say that a truth theory is a species of alethic primitivism just when that theory entails that truth is, in some philosophically significant sense, a primitive property. This general primitivist thesis can be elaborated using any of four distinct notions of primitiveness, giving rise to four species of alethic primitivism. A unifying feature of the family of primitivist theories of truth is that they are all born out of a conviction that truth is, in one sense or another, unanalyzable. Primitiveness, so to speak, is precisely the antithesis of analyzability. So in sorting out the senses in which truth (or any other property) might be primitive, it will often prove helpful to ask in what philosophically significant senses truth might fail to be analyzable. 2.2.1 Anti-reductionism In his 'Logik,' Frege forwards a well-known contention about truth:34 Truth is obviously something so primitive and simple that it is not possible to reduce it to anything still simpler. 34 [112, pp. 128-9] 53 This contention forms the conclusion of an argument known as Frege's Treadmill, the aim of which is to show that 'true' isn't definable.35 Even as it is a linguisticor expression-level claim about truth, this remark by Frege is instructive when thinking about what a property-level primitivist view of truth might involve. What Frege's remark points to are two senses in which the property truth might be interestingly primitive. Fundamental physical entities are paradigm primitive entities. These entities would be primitive in that their natures would be irreducible to the natures of other entities–this is at least part of the reason that they are fundamental. The notion of reduction at play here operates at the level of properties, rather than at the conceptual or linguistic levels. So when we say that the nature of a fundamental entity is irreducible, we mean to invoke a distinctively metaphysical notion of reduction. We can characterize metaphysical reduction in terms of what Paul Horwich has called a constitution theory for properties. We'll take a metaphysically irreducible property P to be a property for which there is no true constitution theory, where a constitution theory for P has the following form (we stipulate, as Horwich no doubt intends, that constitution theories for properties 35 Frege's Treadmill is sometimes taken to be a regress argument and is accordingly called Frege's Regress. My own view is that Frege offers two distinct arguments for the indefinability of 'true,' one of which draws upon a putative regress and the other of which draws upon putative definitional circularity. For discussion of these arguments, see e.g. Asay [8, § 5.1], Carruthers [42], and Dummett [83]. For similar remarks by Frege, see [111, 60/327] and [112, 134]. 54 are non-circular, so that 'P′' may contain neither 'P' nor any synonym thereof):36 36 This isn't to contend, of course, that the present characterization is the one true characterization of metaphysical reduction, only that the characterization is prima facie attractive. See Kim [148, § 3] and Wedgwood [265, p. 42] for discussion of similar notions of property reduction. (CT) is a slight improvement upon Horwich's characterization of constitution theories. He specifically describes the form of a constitution theory for truth [131, p. 143]: • (CTT ) x is true = x is F . Generalizing from this description, a Horwichian constitution theory for a given property P has the following form: • (CTH) x's instantiating P = x's instantiating P′. Notice two difficulties that affect this account of constitution theories. The first is that it's not clear that (CTH) should really be called a theory about P's constitution. The reason is that (CTH) is a schema and thus doesn't entail any claims/propositions about P's nature. Suppose, then, that (CTH) is universally quantified to avoid the first difficulty (we might also take P's constitution theory to be the set of (CTH)'s instances, much as Horwich does in developing his minimal conception of truth). This yields: • (CT?H) For all x: x's instantiating P = x's instantiating P′. The second difficulty is that (CT?H) states that two states of affairs are numerically identical. (CT?H) is meant to be a theory of P's constitution. So (CT ? H) prejudges a resolution of the question as to whether constitution is identity. So far, the debate has been about material constitution of e.g. statues (see e.g. Johnston [145] and Noonan [196]), but it can be generalized easily enough to cover states of affairs. It would be preferable for a general characterization of the form of constitution theories for properties not to artificially resolve debates about the 55 • (CT) For all x: x's instantiating P consists in x's instantiating P′. This conception of metaphysical reduction goes at least some way towards capturing what we intend when we say that certain properties are metaphysically irreducible. Non-reductive materialism about mental properties serves as a helpful test case here. Jaegwon Kim characterizes non-reductive materialism as follows [148, § 3.2]: [Non-reductive materialism] is materialist in that it accepts ontological materialism (the view that all that exists is material) and supervenience (the claim that physical facts determine all the facts), and yet in denying the reducibility of mental and other special-science properties to physical properties, it is anti-reductionist, embracing a dualism of mental and physical properties. According to Kim, non-reductive materialism embodies a particular sort of dualism about mental and physical properties. This dualistic view is sometimes summarily described as the view that mental properties exist 'over and above' physical properties (even if, as non-reductive materialism has it, mental properties supervene upon physical properties). It's this idea that our notion of metaphysical reduction captures nicely. For property P to exist 'over and above' property P′ nature of constitution. Our description of the form of constitution theories avoids both of these difficulties. 56 is, in at least one good sense, for the instantiation of P to not just consist in the instantiation of P′. Our notion of metaphysical reduction generalizes this thought: property P is metaphysically irreducible iff there is no property P′ such that P fails to exist 'over and above' P′. The first respect in which the remark by Frege is instructive is that in invoking the notion of reduction, it directs us to the fact that one sense in which truth might be primitive is that truth is metaphysically irreducible. Primitiveness, recall, is antithetical to analyzability. One sense in which truth (or any property) could be analyzable is that it admits of metaphysical reduction, i.e. that there is a true constitution theory for truth (e.g. that offered by a correspondence theorist or that offered by an epistemic truth theorist). It follows that one sense in which truth might be primitive is that it doesn't admit of metaphysical reduction. We can call the view that truth is primitive in the sense of being metaphysically irreducible alethic anti-reductionism.37 37 An interesting detail in this connection is that Horwich, though he brands himself as a deflationist rather than a primitivist, is one of the most prominent supporters of the view that truth is metaphysically irreducible. This, I think, represents a serious concern for Horwich, which we'll have a chance to examine further in chapter 5. Dirk Greimann [113, esp. p. 141, §§ 6, 8-10] also develops a view, which he regards as a hybrid between primitivism and alethic minimalism, that incorporates an anti-reductive stance on truth. 57 2.2.2 Indefinabilism So one respect in which Frege's remark is instructive is that it points toward the fact that alethic anti-reductionism is a significant species of alethic primitivism. But recall that the stated purpose of Frege's Treadmill, as formulated in 'Logik,' is to show that 'true' is indefinable. That Frege takes 'true' to be primitive in virtue of being indefinable points toward a second sense in which the property truth might be interestingly primitive. Ernest Sosa and Donald Davidson are well-known proponents of broadly primitivist views of truth, which they summarily describe as follows:38 Truth is a primitive concept, and has no illuminating definition or Moorean analysis (Sosa [249, p. 15]). For the most part, the concepts philosophers single out for attention, like truth, knowledge, belief, action, cause, the good and the right, are the most elementary concepts we have. . .Why then should we expect to be able to reduce these concepts definitionally to other concepts that are simpler, clearer, and more basic? We should accept the fact that what makes these concepts so important must also foreclose on the possibility of finding a foundation for them which reaches deeper 38 Timothy Nulty [198, esp. p. 11] develops a view of truth which resembles those of Sosa and Davidson. See also the similar description of alethic primitivism (which he calls the 'property theory' of truth) by Stewart Candlish [34, p. 118]. 58 into bedrock (Davidson [67, pp. 264-5]). Sosa and Davidson are advancing primitivist views of truth at the conceptual level. Notice that in their remarks, they claim that truth is primitive because truth lacks an 'illuminating definition'/can't be 'definitionally reduced.' Both Sosa and Davidson take the primitiveness of truth to involve the fact that truth doesn't admit of a certain sort of definition. What's key here is to distinguish the above notion of metaphysical reduction from the notion of definition, as the latter applies to properties. A number of philosophers, in thinking about definitions, have articulated a distinction between nominal definitions and real definitions, which Kit Fine nicely summarizes:39 It has been supposed that the notion of definition has application to both words and objects–that just as we may define a word, or say what it means, so we may define an object, or say what it is. The concept of essence has [been] taken to reside in the "real" or objectual cases of definition, as opposed to the "nominal" or verbal cases. The purpose of a real definition of an entity e is standardly taken to be the description of e's essence, or essential nature. By contrast, the purpose of a nominal definition is to describe the meaning of a particular expression, or perhaps the content of a particular concept. A tried and true case that illustrates 39 [102, p. 2] 59 the distinction is the case of water. A real definition of water is 'water is H2O,' whereas a nominal definition of 'water' (or perhaps water) is something like 'water is the clear, odourless liquid that fills most terrestrial lake and river beds.'40 When Sosa and Davidson claim that truth doesn't admit of definition, then, they mean to invoke the notion of nominal definition, rather than that of real definition. Since we're interested to describe the respects in which the property truth might be interestingly primitive, however, the notion of definition that's of interest to us is that of real definition. So the distinction that we want to clarify at this stage is that between metaphysical reduction and real definition. To see that these notions come apart, notice that truth might fail to admit of metaphysical reduction, while nevertheless being susceptible to real definition. If this were so, there would be nothing in which the truth of truth-bearers nontrivially consists. But even if this were the case, it might still be possible to make informative claims about truth's essence. It's presumably part of a property's essence that it is instantiable only by certain kinds of entity. Part of the essence of being H2O, for instance, is that it is instantiable by liquids, but not by nonphysical souls or numbers.41 40 Notice that we'll take both real and nominal definitions to themselves consist of words. What distinguishes these two kinds of definition is what kind of entity they define, rather than what kinds of entity compose the definitions themselves. 41 This feature of being H2O 's essence presumably comprises part of what Kit Fine would call its 'consequential essence.' Fine distinguishes the consequential essence of an object from its 60 Likewise, it might be part of truth's essence that it is instantiable only by propositions, or only by indicative sentence-tokens, or only by judgments, or etc. And this might be so, even if there is no true constitution theory for truth. That truth is insuceptible to real definition is another sense in which truth might be a primitive property. The rationale here is the same as that involving metaphysical reduction. Primitiveness is antithetical to analyzability. To offer a real definition of truth is one way that one might analyze truth. So one sense in which truth might be primitive is that truth doesn't admit of real definition. Call the view that truth is primitive, in the sense of being insusceptible to real definition, alethic indefinabilism.42 'constitutive essence' as follows [103, p. 276] (the distinction could be easily carried over to the case of properties): A property belongs to the constitutive essence of an object if it is not had in virtue of being a logical consequence of some more basic essential properties; and a property might be said to belong to the consequential essence of an object if it is a logical consequence of properties that belong to the constitutive essence. 42 We showed above that alethic anti-reductionism doesn't entail alethic indefinabilism, but the converse doesn't hold. In the appendix, I outline the entailment relations in which the various primitivist theories of truth stand to one another. 61 2.2.3 Anti-decompositionalism In the above passage, Sosa claims not only that truth has no illuminating (nominal) definition, but also that truth is insusceptible to 'Moorean analysis.' He is referring here to a decompositional style of analysis, often associated with G.E. Moore's primitivism about the property goodness. When formulating his views on goodness, Moore remarks:43 And so it is with all objects not previously known, which we are able to define: they are all complex; all composed of parts, which may themselves, in the first instance, be capable of similar definition, but which must in the end be reducible to simplest parts, which can no longer be defined. But yellow and good, we say, are not complex: they are notions of that simple kind, out of which definitions are composed and with which the power of further defining ceases. According to Moore, goodness isn't susceptible to decompositional analysis because goodness has no proper parts into which it might be decomposed. Contrast goodness, as conceived by Moore, with an another tried and true case: the property being a bachelor. An object instantiates being a bachelor iff it instantiates the properties being male, being human, being unmarried, and being adult. It's thus reasonable to regard the latter properties as parts of being a bachelor : 43 [191, § 7]. See also [190, p. 182]. P.F. Strawson [257, pp. 17-18] also provides a very nice description of the aims decompositional analysis. 62 intuitively, we take being a bachelor to partly consist in being male, partly in being human, partly in being unmarried, and partly in being adult. So a further sense in which truth might be unanalyzable and thus primitive is that truth lacks proper parts that one could enumerate in offering a decompositional analysis of truth. Primitiveness in the sense of non-decomposability comes apart from both of the two notions of primitiveness that we've considered so far. First, truth could be primitive in the sense of being non-decomposable, while nevertheless being susceptible to metaphysical reduction. This is because a constitution theory for truth need not purport to enumerate proper parts of truth. Robust identity theories take being true to consist in being identical to a worldly fact. It's conceivable that the correct constitution theory for truth is given by a robust identity theory, even though truth lacks proper parts. The reason is that it's conceivable that numerical identity is itself primitive, in the sense that it is insusceptible to decompositional analysis. If this were the case and if being true consisted in being numerically identical to a worldly fact, then truth would in turn be insusceptible to decompositional analysis. Truth might also be non-decomposable while nevertheless being susceptible to real definition. It might be the case, for instance, that it's part of the essence of truth that truth and falsity are contradictory properties, in the sense that a truth-bearer is true iff it isn't false. But this putative relationship between truth 63 and falsity seems different from the relationship between being a bachelor and e.g. being male. We're inclined to say that being a bachelor partly consists in being male because being male is a necessary, though not a sufficient, condition for being a bachelor. By contrast, if truth and falsity were contradictory properties, lacking falsity would be both necessary and sufficient for being true. So it's not similarly tempting to say, in this case, that being true partly consists in lacking falsity–lacking falsity wouldn't be a proper part of truth in terms of which truth could be decomposed. So we should distinguish from our prior two senses a third sense in which truth might be interestingly primitive: truth might be insusceptible to decompositional analysis. Call the view that truth is primitive in this sense alethic anti-decompositionalism.44 44 Those sympathetic towards alethic anti-decompositionalism include the early Moore [192, p. 261] and Russell [229, p. 524]. Colin McGinn [185, pp. 104-5] advances a similar view at the conceptual level, according to which truth isn't susceptible to decompositional analysis. Paul Boghossian [26, p. 562] also seems sympathetic towards anti-decompositionalism, though it isn't altogether clear what he intends in suggesting that truth is a 'simple' property. Trenton Merricks [186, ch. 8, § IV] likewise seems sympathetic towards anti-decompositionalism, though he isn't very explicit as to the sense in which he takes truth to have 'no analysis.' 64 2.2.4 Circularism Douglas Patterson defends an intriguing primitivist view of truth at the conceptual level whose distinctive thesis is that45 the concept of truth is primitive in that its conception is circular: i.e., theres no true, non-circular statement of what it is one has to be disposed to accept about truth upon consideration in order to possess the concept of truth. . .[T]he view that there's no true conception of truth is unworkable, [so] on the view I endorse our conception of truth is circular. Patterson's view is that truth is a primitive concept in the sense that the set of claims that one must be disposed to accept after suitable reflection in order to possess truth (Patterson calls these claims 'conceptually analytic' for truth) themselves invoke truth. A property-level analogue of Patterson's view has it that truth is a primitive property in the sense that any comprehensive analysis of truth will contain at least one claim that refers to truth. This view, like alethic anti-reductionism, takes truth to be primitive in virtue of being fundamental, or basic. But the present view takes truth to be basic in a more encompassing sense than does anti-reductionism. The thought here is that the reason that truth is basic is that it is impossible to offer any sort of truth-free analysis of truth. To 45 [202, p. 13]. See also [202, n. 14, p. 22]. 65 reappropriate Davidson's metaphor, the present view has it that truth is basic in the sense that no analysis of truth will dig any deeper into metaphysical bedrock. It would be good news for anti-reductionism and anti-decompositionalism if truth were primitive in this sense. Recall that we stipulated, in venturing to articulate a suitable conception of metaphysical reduction, that the constitution theory for truth used in a metaphysical reduction of truth must be non-circular. So if truth isn't susceptible to any sort of non-circular analysis, then truth is metaphysically irreducible. A decompositional analysis of truth is presumably also non-circular. The aim of a decompositional analysis of truth is to enumerate truth's proper parts. But it's very plausible that no property is a proper part of itself–rather, every property is presumably its own sole improper part. It then that truth isn't a proper part of itself and thus that decompositional analyses of truth are meant to be non-circular. So if it were the case that truth isn't susceptible to non-circular analysis of any sort, this would also be a victory for the anti-decompositionalist. By contrast, that truth is primitive in the present sense is no victory for the alethic indefinabilist. This is because it is conceivable that the real definition of truth is circular. Fact-based correspondence theories hold that being true consists in corresponding to a certain fact. It's a good question, as modest identity theories bring out, whether in order to specify the nature of facts, we must mention truth. If so and if being true consists in corresponding to a fact, then a comprehensive 66 real definition of truth will be circular. Notice that a real definition of this sort needn't be entirely evacuated of content. We may be able to say quite a lot about the nature of facts in truth-free terms (e.g. that they are composed of worldly particulars, properties, and relations or senses, Kaplanian characters, or concepts), even if it to completely specify their natures, we must ultimately mention truth. Saying that being true consists in corresponding to a fact would, in this case, go some way towards informatively describing truth's nature. It's just that this description must ultimately rely upon an appeal to truth. So we should finally distinguish a fourth sense in which truth might be interestingly primitive: truth might be insuceptible to non-circular analysis. We can call the view that truth is primitive in this sense alethic circularism. So far, then, we've sketched four interesting species of alethic primitivism: alethic anti-reductionism, alethic indefinabilism, alethic anti-decompositionalism, and alethic circularism. Readers who are interested to get a full sense of the structure of this family of views should consult the appendix. We're going to turn now to the dialectic between alethic pluralism and alethic primitivism, asking what stance pluralists should take towards the respective species of primitivism. I'll argue that, somewhat surprisingly, the right attitude for pluralists to take towards three of these species is guarded conciliation. Each such species of alethic primitivism promises certain benefits when combined with alethic pluralism, which is why pluralists should be conciliatory 67 towards these views. But pluralists' conciliation should be guarded, since the commitments of these primitivist positions have yet to be studied in detail. We'll then see that the remaining species of primitivism–alethic indefinabilism–is inconsistent with alethic pluralism and that indefinabilism generates the scope problem from which the scope problem suffers. 2.3 Pluralism + Primitivism 2.3.1 The metaphysical instability challenge In thinking about the advantages that pluralists may enjoy by embracing either of alethic anti-reductionism or alethic anti-decompositionalism, it's helpful to consider a challenge to alethic pluralism that Pedersen [204] dubs the 'metaphysical instability challenge.'46 The challenge, in short, is that the metaphysics of alethic pluralism looks to collapse into a monist account of truth's nature. Alethic pluralists characteristically rely upon the scope problem in critiquing traditional monism. The charge of the scope problem is that at least most traditional monist theories can satisfactorily account for the truth of some, but not all, apparent truth-bearers. Pluralists often interpret the scope problem by invoking 46 Pedersen helpfully distinguishes two similar instability challenges that can be leveled against alethic pluralism. His 'linguistic instability challenge' invokes putative truth predicates, whereas his metaphysical instability challenge invokes truth(-like) properties. Christine Tappolet [259, § 3] also briefly raises the metaphysical instability challenge in connection with 'mixed conjunctions.' 68 the notion of a 'sector/region/area/domain of discourse.' The intuitive idea is that discourse is divided, for instance, into the physical, mathematical, ethical and aesthetic domains, and presumably many more besides. In the next chapter, we'll look more carefully at the natures of domains, but for now, this intuitive construal will suffice. Alethic pluralists, in responding to the scope problem, posit a plurality of truth-like properties T1, . . . , Tn, each of which is assigned to a proper subclass of the class of domains. The impetus for the metaphysical instability challenge is that it looks straightforward to define a disjunctive property in terms of T1, . . . , Tn and the domains D1, . . . , Dn that the pluralist posits. The form of this disjunctive property is being in D1 and being T1 or being in D2 and being being T2 or . . . or being in Dn and being being Tn. Call this disjunctive property TG. Given how we've defined TG, any truth-bearer that instantiates the member of T1, . . . , Tn that is assigned to its domain will also instantiate TG and vice versa. If, for instance, the truthlike property T1 is assigned to the physical domain, then 〈Tables are solid〉 will instantiate T1 iff it instantiates TG. Given that T1, . . . , Tn are truth-like properties (again, we'll have a closer look at the notion of truth-likeness in chapter 4), it's quite tempting to think that TG also qualifies as a truth-like property. The reason is that as we just noted, the instantiation of TG has a biconditional relationship with the instantiation of T1, . . . , Tn. To use Pedersen's formulation of the point, it's tempting to regard TG 69 as a truth-like property because the truth-bearers that instantiate TG are all and only the truth-bearers that instantiate the member of T1, . . . , Tn that is assigned to the domain with which the truth-bearer is associated. Given this and given that T1, . . . , Tn are all truth-like properties, it's hard to see how TG could fail to be a truth-like property. Now the pluralist can certainly point out at this stage that the distinctive thesis of their view is that there is more than one truth-like property. The existence of TG is, for this reason, strictly compatible with the letter of alethic pluralism. The deeper challenge that the pluralist faces, though, is that if they are committed to positing TG, then their views seem to mimic those of alethic monists. TG's nature is uniform across domains and, as we pointed out, TG is instantiated by all and only those truth-bearers that instantiate the pertinent member of T1, . . . , Tn. TG is, for this reason, a more general truth-like property than any of T1, . . . , Tn. The resulting picture looks suspiciously close to that forwarded by alethic monists, since it involves a single truth-like property that is instantiated by all and only those truth-bearers that we would customarily regard as constituting the class of truths. The challenge for pluralists is then to explain why their views are not best regarded as simply being species of alethic monism. Pedersen mentions two strategies that pluralists might use in responding to this challenge. The first is to endorse a rather conservative, sparse conception of properties. In his seminal work on the nature of properties, David Lewis [163], 70 [164, pp. 59-60] draws a contrast between the sparse and abundant conceptions of properties. Someone who holds an abundant conception of properties allows that corresponding to any consistent definition of a putative property there is, in fact, a property. Abundantists allow, for instance, that there is a property being a trout-turkey, since this property has a straightforward extensional definition: an entity e instantiates being a trout-turkey iff e is either a trout or a turkey. According to a sparse conception of properties, by contrast, the only properties that actually exist are those properties all of whose bearers exhibit a genuine resemblance/qualitative similarity in virtue of instantiating the given property. So the sparse theorist may refuse to posit a property like being a trout-turkey on the grounds that the bearers of this putative property wouldn't, in virtue of instantiating it, share a genuine qualitative similarity. The class of trout-turkeys, after all, is just the intersection of the class of trouts and the class of turkeys. And, the thought goes, a trout which belongs to this class doesn't enjoy a genuine qualitative similarity with a turkey that belongs to this class in virtue of the fact that they are both trout-turkeys. One maneuver for the alethic pluralist would be to endorse a sparse conception of properties and to refuse, on that basis, to posit TG. TG, the thought is, seems rather similar to being a trout-turkey, in that their respective bearers would fail to share any genuine qualitative similarity in virtue of instantiating these properties. So if a sparse conception of properties licenses refusal to posit 71 the latter, it should also license refusal to posit TG. The thrust of this maneuver is clear enough, but as Pedersen points out, its ultimate tenability will hinge upon the acceptability of the pertinent sparse conception of properties. Lewis, for instance, rejects sparse conceptions of properties on the grounds that abundant properties are particularly well-suited to serve as the semantic values of sentences. Also, as Lewis articulates the notion, a sparse conception of properties relies upon the notion of genuine qualitative similarities, or 'objective resemblances,' which entities are meant to exhibit to one another only rather selectively.47 It's not entirely transparent, however, that genuine qualitative similarity is all that hard to come by. The notion is often illustrated by invoking putative properties that would be rather extrinsic and/or gerrymandered, e.g. the property being within a 3.5 mile radius of the deepest point of the Atlantic Ocean.48 The standard contention is that the class of objects that instantiate this putative property wouldn't ipso facto exhibit a genuine qualitative similarity to one another. But we might want to ask with Lewis Carroll: 'Why is a raven like a writing desk?' The point is that if we take a pair of entities that are as dissimilar as you like, it will probably be straightforward enough to pinpoint certain respects in which they are intuitively similar. A hydrogen atom and a hardy crustacean that are both within 3.5 miles of the deepest point of the Atlantic Ocean do look to ipso facto resemble one 47 [163, pp. 346-7]. 48 This example is used by Asay [9, p. 149]. 72 another–they are both within 3.5 miles of this particular point–even if there are many other respects in which they fail to resemble one another. So qualitative similarity may actually come on the cheap, and it's not clear that we raise the price much, if at all, by adding that it must be 'genuine.' An advocate of a sparse conception of properties might respond by conceding that genuine qualitative similarity is easy to come by, but insist that some similarities–e.g. being within 3.5 miles of the deepest point of the Atlantic–are so insignificant as not to merit any attention. They might then revise their conception of properties and hold that the only properties that actually exist are those properties all of whose bearers exhibit a significant qualitative similarity in virtue of instantiating the given property. But the obvious problem is that significance is a highly interest-relative notion. This raises the possibility that the bearers of a putative property might enjoy a qualitative similarity that is significant to cognizers with one set of interests, though not to cognizers with a different set of interests. The particular difficulty for the pluralist would be to show either (i) that the qualitative similarity that bearers of TG enjoy in virtue of instantiating TG is insignificant according to any conceivable set of interests or (ii) that a particular set of interests Γ is somehow privileged and the bearers of TG fail to enjoy qualitative similarity in virtue of instantiating TG that is significant according to Γ. (i) is hardly plausible, since it looks easy to conceive of wildly divergent sets of interests that cognizers might 73 have and demonstrating (ii) would be, to say the least, a delicate task. For this reason, it's at best an open question whether the pluralist can resist the metaphysical instability challenge by endorsing a sparse conception of properties.49 According to Pedersen, the preferable strategy for the pluralist is to concede the existence of TG but insist upon an explanatory asymmetry in the instantiation of TG and the instantiation of each of T1, . . . , Tn. In general, it's highly plausible to think that the instantiation of disjunctive properties is explained by the instantiation of their disjunct properties, though not vice versa. Were a trout to instantiate being a trout-turkey, for instance, this would be explained by the fact 49 C.D. Wright [281, § 4] questions whether the metaphysical instability challenge is actually a challenge for alethic pluralism. Wright suspects that "[t]o show that the challenge necessarily arises, Pedersen would need to show that–by their theory of truth–pluralists are antecedently committed to an abundant conception of properties. . .But we have absolutely no reason to suppose that pluralists are antecedently committed to such a view [281, p. 100] [.]" But as we've seen, the dialectic needn't be conceived in this way. In essence, the metaphysical instability consists in the fact that TG is easily definable in terms of T1, . . . , Tn, which the pluralist posits. This generates a prima facie commitment on behalf of the pluralist to posit TG, which raises the question as to how alethic pluralism actually differs from alethic monism. What's key is that the pluralist does incur a prima facie commitment to TG, since, as Wright indicates, alethic pluralists have for the most part been inexplicit as to their conceptions of properties. The task for the pluralist is then to either endorse a sparse conception of properties and thereby show that they avoid an ultima facie commitment to TG or to posit TG and explain why their views are nevertheless importantly different from those of alethic monists. 74 that the trout instantiates being a trout (and similarly, were a turkey to instantiate being a trout-turkey). But even if being a trout-turkey is, in fact, a real property, it's highly implausible to claim that trouts instantiate being a trout because they instantiate being a trout-turkey. Pedersen's suggestion is that the pluralist apply this general rationale to the case of TG. The thought is that since TG is a disjunctive property defined in terms of the truth-like properties T1, . . . , Tn, if a truth-bearer a instantiates TG, this will be explained by the fact that a instantiates that member of T1, . . . , Tn which is assigned to the domain with which a is associated. The explanatory dependence here is meant to be similarly asymmetrical: it's not the case that if a instantiates the pertinent member of T1, . . . , Tn that a does so in virtue of instantiating TG. Pedersen's suggestion is that if TG's instantiation were explanatorily dependent upon the instantiation of T1, . . . , Tn in this way, then the pluralist would be able to resist the metaphysical instability challenge by securing a "a non-eliminable element of pluralism."50 The strategy that Pedersen puts forward is definitive of what has become the most influential variety of alethic pluralism, moderate alethic pluralism. In chapter 4, we'll show that moderate pluralism is, in fact, an unstable position. So in the end, Pedersen's strategy is undermined by the fact that the view of truth that it generates is unstable.51 Given this, the strategy can hardly be used to 50 [204, p. 103]. 51 Pedersen's views have changed over the years. In a recent manuscript, he argues with 75 show that alethic pluralism is a stable position. 2.3.2 Resisting the challenge: anti-reductionism and anti-decompositionalism Anti-reductionism Pluralists should respond to the metaphysical instability challenge by refusing to posit TG on metaontological grounds that commit them neither to a sparse nor to an abundant conception of properties. The basic reason that pluralists should refuse to posit TG is that TG, were it to exist, would lack explanatory power and it's incorrect to posit a property that lacks explanatory power, since such a property would burden one's ontology with dead weight. In § 2.5, I'll articulate this metaontological norm more exactly. For now, suffice to say that the pluralist can resolve the metaphysical instability challenge by drawing on metaontological considerations that enjoy independent import for pluralists. What I want to point out in the remainder of this section is that the pluralist can further remove her views from those of most traditional monists by endorsing either (or both) alethic anti-reductionism or alethic anti-decompositionalism. In choosing to endorse either of these varieties of alethic primitivism, the pluralist would distinguish her views from those held by many traditional monists. Though I won't ultimately go in for these views, what I want to stress is that it is open Seawha Kim that moderate pluralism is, even if stable, a false position. 76 to alethic pluralists to do so and that doing so brings with it a notable benefit. Many traditional monists–specifically, most correspondence and epistemic truth theorists–have sought to respond to the essence question by discovering the property in whose instantiation the instantiation of truth consists.52 An alethic pluralist can resist this common aspect of many traditional monist theories in one of two ways. They might include among the plurality of domain-specific truth-like properties T1, . . . , Tn a particular truth-like property Ti for which they refuse to offer a constitution theory. This maneuver is similar to the pluralist's diagnosis of the scope problem, that many traditional monist accounts of truth's nature can be plausibly applied to some, but not all, apparent truth-bearers. The contention here is that the methodology of many monist truth theories, which involves offering a constitution theory for truth, is more plausible in connection with some domains than in connection with others. Very briefly, one line of motivation for this maneuver would draw upon an apparent contrast between correspondence-theoretic and epistemic truth-like properties: (i) that there are apparently non-circular ways of detailing the nature of correspondence, e.g. in terms of the Tarskian notions of reference and satisfaction and (ii) that a number of philosophers have found it challenging to comprehensively analyze the epistemic notions of coherence and assertibility in non-truth-theoretic terms. (i) and (ii) could be used to argue that only some 52 Gerald Vision [264, ch. 1] offers a particularly helpful discussion of this point. 77 truth-like properties admit of constitution theories. The argument would be (a) that there are bona fide truth-bearers that can't instantiate any correspondencetheoretic truth-like properties (e.g. moral or arithmetical beliefs); (b) these truthbearers are, rather, true iff they instantiate some epistemic truth-like property; (c) but epistemic truth-like properties don't admit of constitution theories, since any such putative constitution theory would be circular and we know that by definition, constitution theories are non-circular; so (d) the pertinent truth-bearers are true iff they instantiate an epistemic truth-like property that is metaphysically irreducble. There's obviously much to wonder about in this argument. The key point for present purposes is that in advancing such an argument and thereby taking at least some truth-like properties to be metaphysically irreducible, the pluralist would adopt a truth-theoretic methodology that differs significantly from that of many traditional monists. Adopting such a methodology would furnish pluralists with a solution to the metaphysical instability challenge. Anti-decompositionalism Alethic anti-decompositionalism has much the same status in this debate. Many traditional monists–correspondence and epistemic truth theorists are again exemplars here–have sought to analyze truth's nature by offering a decompositional analysis of truth. Broadly speaking, correspondence theorists who analyze truth 78 in terms of a particular theory of reference hold that the truth of a truth-bearer a involves (i) a's proper parts referring to particular proper parts of the world and (ii) the claim that a thereby makes about the world corresponding, in some target sense, to a state(s) of the world. What's important in the present connection is that this is a decompositional analysis of truth. The analysis has it, in effect, that being true is decomposable into having referential proper parts and making a claim that corresponds to a state(s) of the world. Part of what is involved in making such a claim, according to the present theory, is having proper parts that refer. So if being true consists in making a claim that corresponds to a state(s) of the world, then part of being true is having referential proper parts. In other words, the analysis has it that the respective instantiation of the latter two properties is necessary to instantiate truth and that the instantiation of both is sufficient to instantiate truth. So an additional way that pluralists might distinguish themselves from traditional monists would be to contend that at least one truth-like property is nondecomposable. The most plausible strategy here would presumably be to claim that at least one of the more general truth-like properties (i.e. one of the truth-like properties that isn't one of T1, . . . , Tn) isn't susceptible to decomposition. According to the pluralist theory of truth that I'll be developing here, the basic nature of one such property is given by the following schema, made especially famous by Paul Horwich: 79 • (PT) 〈p〉 is true iff p. To specify the nature of this property, in other words, it is sufficient to state the schema (PT). Given this, it is arguably not possible to decompose the target property into proper parts. What would they be? So a second way that pluralists might respond to the metaphysical instability challenge would be to posit the arguably non-decomposable truth-like property that is specified by (PT). In doing so, they would break substantially with the trend among alethic monists of pursuing decompositional analyses of truth. 2.3.3 Circularism Finally, alethic circularism is also a significant potential ally to alethic pluralists. Lynch [175, ch. 8] contends that a coherence-theoretic property that he calls concordance should be assigned as the domain-specific truth-like property for the moral domain. Pluralists who posit a coherence-theoretic, domain-specific truthlike property should be attracted to alethic circularism for the simple reason that coherence is often analyzed in terms of consistency, which is itself standardly analyzed in truth-theoretic terms. Indeed, Lynch [175, p. 39] takes consistency to be among the 'coherence-making features' having which makes a belief system more coherent.53 53 Analyses of coherence which take a belief system to be coherent iff its component beliefs are mutually consistent include those offered by Bonjour [27]; Ewing [95]; and Sayre-McCord [233] 80 Recall that the distinctive thesis of moderate alethic pluralism, the variety of alethic pluralism endorsed by Lynch, is that there is a single property truth the instantiation of which is determined by the instantiation of the domain-specific truth-like properties T1, . . . , Tn. As Lynch has pointed out [175, pp. 83-4], [178, p. 39], it's very plausible to think that if the instantiation of truth is so determined, this is an essential, rather than a merely accidental, fact about truth. This looks, in other words, to be a fact about what it is to be truth, not merely a fact about how truth happens to be.54 So moderate pluralists take an aspect of truth's essence to be that truth's instantiation is determined by the instantiation of T1, . . . , Tn. Now suppose that among T1, . . . , Tn is a coherence-theoretic property Ti. Suppose further that coherence is analyzed truth-theoretically. The moderate pluralist is then committed to an analytical circle, for they propose to analyze truth's essence in terms of coherence and in turn analyze coherence in truth-theoretic terms. The moderate pluralist might attempt to avoid this analytical circle in at least three ways. But this proposal is counterintuitive and at the very least, its viability is unclear. The moderate pluralist might also contend that they can help themselves to a truth-free analysis of consistency. The trouble with this maneuever is that it is in tension with the typical, anti-deflationary claim (who invokes a notion of 'evidential consistency' the analysis of which looks to invoke the more familiar notion of propositional consistency). 54 In Fine's terminology, this can be plausibly thought of as a fact about truth's consequential essence. 81 of alethic pluralists (§ 2.1.2) that truth is an explanatory property. Third, the moderate pluralist might contend that coherence is a primitive property in the sense of being indefinable. This would raise the question as to whether coherence, if indefinable, could be an explanatory property. If not, then in positing coherence, the pluralist would violate a rather weak metaontological norm that we'll motivate in § 2.5. So moderate pluralists who posit a coherence-theoretic, domain-specfic truth-like property have reason to be attracted to alethic circularism. 2.4 Indefinabilism and the scope of the scope problem So we've seen that alethic pluralists have reason to take a friendly attitude towards three species of alethic primitivism. Since these three species of primitivism are potential allies to the pluralist, pluralists importantly incur no commitment to demonstrating why these views are unsatisfactory–each is strictly consistent with pluralism. So even if, as is probable, not every such species of alethic primitivism is afflicted by the scope problem, this is of no concern to pluralists. By contrast, our fourth species of alethic primitivism–alethic indefinabilism–does generate a significant problem for alethic pluralists on this score. Indefinabilists, being alethic monists, posit a property truth and argue that truth is insuceptible to real definition. Recall that the distinctive contention of moderate alethic pluralism is that there is a single property truth whose instantiation is determined by the instantiation of the domain-specific truth-like properties 82 T1, . . . , Tn. Moderate pluralists are 'moderate' because they concede to alethic monists that there is only one property truth. Strong alethic pluralists, by contrast, deny that there is a single property truth, positing instead only T1, . . . , Tn. So alethic indefinabilism is clearly inconsistent with strong pluralism, given that the former entails that there is a single property truth, while the latter entails that there is no such property. Alethic indefinabilism is also inconsistent with moderate pluralism, for a reason that we encountered just above. Moderate pluralists contend that the instantiation of truth is determined by the instantiation of T1, . . . , Tn. Recall that as Lynch points out, if this is a fact about truth, then it is presumably an essential fact about truth–it is a fact about what it is to be truth, not a fact about how truth simply happens to be. For this reason, moderate pluralists offer a putative (at least partial) description of truth's essence, i.e. a putative (at least partial) real definition of truth. Moderate pluralism thus entails that truth is susceptible at least to partial real definition and is, for this reason, at odds with alethic indefinabilism. So the result that we get is that alethic indefinabilism is inconsistent with alethic pluralism tout court. To motivate their views against those of alethic monists, then, pluralists must advance a principled critique of alethic indefinabilism. The trouble is that upon scrutiny, it's difficult to see why indefinabilists should be worried by the scope problem. The lesson that indefinabilism teaches pluralists is that the scope problem suffers from its own problem of scope–it fails to apply to every interesting 83 species of alethic monism. The scope problem is not an all-purpose objection to alethic monism. Perhaps the strongest considerations in favor of indefinabilism are methodological. It's not much of an oversimplification to say that the history of truth theory consists in unsuccessful attempts to answer the essence question. This can easily generate the suspicion that the essence project, as we might call it, is simply a degenerating research programme. Since the chief aim of the essence project is to describe truth's essence–that is, to offer a real definition of truth–the lesson to take away, it might be thought, is that truth is simply insusceptible to analysis of this sort. Now I am no indefinabilist, so it is certainly not my business to defend this inference. What's important for us is that whether or not the cogency of this inference isn't going to vary depending upon which domain is at issue. If the inference to indefinabilism from the problematic history of monism is compelling, that is, then it will be compelling in connection with every domain. And if it is not compelling, then it will be compelling in connection with no domains–the inference either holds across the board or it doesn't hold at all. Indefinabilism is not afflicted by the scope problem. So the Scope + Substance argument for alethic pluralism fails to carry conviction. But we shouldn't be too hasty here, since the argument does take pluralists rather far. What pluralists need, I think, is not a radically different argument for pluralism, but a supplement to the Scope + Substance argument. 84 And they have a potent supplement, I'll argue, in a certain metaontological norm. Considerations of metaontology serve not only as potent counterparts to Scope + Substance, they reinforce the 'Substance' stage of the argument by presenting a challenge for a leading variety of deflationism, Paul Horwich's alethic minimalism. And what's more, these considerations present yet another avenue for pluralists to escape the metaphysical instability challenge. So in the end, metaontology proves to be a boon for alethic pluralists. 2.5 Explanatoriness and metaontology In a discussion of deflationism, Lynch offers the following metaontological suggestion:55 [T]o the degree to which we come to believe that [property] P does no explanatory work, to that degree we will find ourselves doubting its reality. Accordingly, if we think that P is real, we'd be well advised to silence doubters by illustrating how it does explanatory work. Lynch is here alluding to a metaontological principle which closely resembles what David Armstrong calls the Eleatic Principle:56 55 [175, pp. 120], italics removed. 56 [7, vol. 2, p. 5]. Graham Oddie [199] considers and critiques various formulations of the Eleatic Principle. Mark Colyvan [46, p. 314] [47, p. 40] (tentatively) suggests a rendering very close to that given here. 85 • (EP) One ought to posit entity e only if e has causal powers and can thus be mentioned in the explanans of a true causal explanation. Armstrong contends on the basis of (EP) that one ought not posit e.g. classes, numbers, possible worlds, or propositions. These entities lack causal powers ex hypothesi and are thus unable to earn their keep by figuring in the explanans of causal explanations. So, Armstrong reasons, if one includes such entities in one's ontology, then one thereby commits to a certain amount of objectionable ontological deadweight. (EP) is a very plausible principle, at least at first pass. It codifies a standard philosophical practice of assessing the correctness of a posit by considering whether the posited entities enjoy explanatory power. Mark Colyvan [46], [47] has, however, pointed out an aspect in which (EP) is worringly restrictive: (EP) takes the correctness of a posit to be linked specifically to the causal-explanatory powers of the relevant entities. Colyvan offers several cases from the history of physics, including e.g. the bending of a beam of light when near a massive object, in which a given entity (in this case, the curvature of spacetime) is mentioned in the explanans of what looks to be a true, non-causal explanation. Colyvan suggests that to accommodate such cases, (EP) should be modified so as to allow Principles such as (EP) provide norms for positing; specifically, they each forward a necessary condition for a positing to be correct. For this reason, I take positing in what follows to be an intentional act. I mean to leave room for non-intentional 'ontological commitment,' incurred by e.g. use of a language containing quantifiers that range over particular classes of entity. 86 for the correctness of positing entities which enjoy non-causal, but nevertheless scientifically respectable explanatory powers. Building upon Colyvan's concerns, we should note that it has become increasingly common in contemporary metaphysics to speak of non-causal, metaphysical explanation–sometimes called, or at least closely associated with, grounding.57 A standard case of apparently non-causal, metaphysical explanation is the fact that the truth of its conjuncts and their manner of composition explains the truth of a conjunction. A true conjunction is true because all of its conjuncts are true and conjoined. Similarly, if normative consequentialism is true, then the rightness of an act is explained by the goodness of its consequences. But in neither of these cases do we seem to have instances of causal explanation. Normative consequentialists, for instance, don't hold that facts about the goodness of an act cause the act to be morally right. They tend to hold, rather, that the rightness of an act consists in the goodness of its consequences and that it is because of this that facts about the latter explain facts about the former. And the story about conjunction is presumably very similar. It's because of cases like these that (EP) is an objectionably narrow norm. The root intuition motivating (EP) is that in positing entities, one ought not burden one's ontology with entities that will be of no assistance when one performs explanations. If an entity e enjoys non-causal explanatory power, then e seems 57 See e.g. Clark and Liggins [44]; Fine [104]; and Rosen [227, § 7]. 87 just as capable of earning its keep as an entity that enjoys causal-explanatory power. So the fact that an entity enjoys non-causal explanatory power, no less than the fact that it enjoys causal-explanatory power, constitutes a reason to posit the entity. So following Colyvan, we should consider how (EP) might be broadened to allow for non-causal explanation. We might simply call this broadened principle the Explanatory Principle:58 • (XP) One ought to posit entity e only if there is an explanandum d that can be explained by (inter alia) mentioning e. (XP), note, captures the root intuition behind (EP)–that e is ill-suited to provide explanatory assistance, then to posit e is to add dead weight to ontology. The advantage of (XP) is that it recognizes not only the normative relevance of causal-explanatory power, but also that of non-causal explanatory power. We might also consider in this connection what is undoubtedly the most famous metaontological principle–Ockham's Razor. A standard rendering takes Ockham's Razor to lay down the following norm:59 58 Note that (XP) is weaker than Colyvan's suggested modification to (EP). 59 Ockham offers two formulations: "Pluralitas non est ponenda sine necessitate" and "Frustra fit per plura quod potest fiera per pauciora," translated respectively by Maurer [182, p. 483] as "A plurality is not to be posited without necessity" and "It is useless to do with more what can be done with fewer." 88 • (OR) One ought to posit entity e only if there is an explanandum d s.t. to explain d, it is necessary to mention e. It won't be my aim to take a hard line against Ockham's Razor. Indeed, I'll be drawing upon Ockham's Razor later on. What I want to highlight here is just how weak the norm laid down by (XP) is. Because this norm is so weak, it's going to be very difficult to oppose (XP). In particular, because (XP) is weaker than (OR), anyone who opposes (XP) is also committed to rejecting Ockham's Razor–and that, surely, is not a rejection to be taken lightly. To see (XP)'s weakeness relative to (OR), notice that (OR) issues a prohibition upon positing in a particular sort of case where (XP) permits positing. Let a case of 'explanatory overdetermination' have three basic features. First, there is at least one explanandum d that can be explained by (perhaps inter alia) mentioning entity e (d might be the shattering of a window and e a baseball). Second, there is an additional entity e′ such that a given explanandum d can be explained by (inter alia) mentioning e iff d can be explained by (inter alia) mentioning e′ (e′ might be the baseball's microscopic parts, which are arranged baseball-wise). Third, any explanans d that can be explained by mentioning one of e or e′ can't be explained in a way that mentions neither. There are thus explananda to explain The literature on Ockham's Razor is massive. For useful bibliographies citing both philosophical discussions of simplicity and complexity and appeals to considerations of parsimony in scientific papers, see <http://commonsenseatheism.com/?p=6670>, [14], and [106]. 89 which it's necessary to mention either e or e′. But it doesn't follow that there are explananda to explain which it's necessary to mention e, nor that there are explananda to explain which it's necessary to mention e′. For this reason, (OR) prohibits one from positing e and also prohibits one from positing e′. This prohibition by (OR) is, to my mind, quite plausible. One must appeal either to e or to e′ to explain an explanandum, but it's not the case that one must appeal to one of them, rather than the other. So the rational move, I should think, is to refrain from committing to the existence of either. The commitment that is warranted is to the weaker hypothesis that at least one of them exists. It's worth noting, though, that (OR)'s prohibition here might be resisted. Ted Sider [245] considers a case of causal-explanatory overdetermination in which the explanandum is the window shattering and the two available explanans are inter alia that the baseball impacted the window and that the baseball's microscopic parts impacted the window. Why not say, Sider asks, that both the baseball and its microscopic parts caused the shattering? After all, it's reasonable to take both the baseball and its microscopic parts to have impacted the window. So why isn't it then arbitrary to cite only one as the cause of the shattering? It seems clearly false that neither caused the shattering, so why is the right conclusion not that both caused the shattering? To defend (OR), we might question the contentious assumption that we are dealing with two coincident objects in this case–the baseball and the sum of the 90 baseball's microscopic parts, which are arranged baseball-wise. Indeed, we might ask, why not think that the baseball just is these parts so arranged? It would then be rather misleading to say that the baseball and its microscopic parts so arranged caused the window to shatter, since the baseball and its microscopic parts so arranged are one and the same. What this case points to is that (XP) is a weaker metaontological norm than (OR). Both (XP) and (OR) are what Robert Nozick [197, pp. 27-33] would call 'side constraints' on positing. Each lays down a condition that must not be violated if one's positing of an entity is to be correct. To satisfy (OR)'s side constraint, it must be necessary to posit e in order to explain some explanandum. To satisfy (XP)'s side constraint, it need only be possible to explain some explandum by (inter alia) mentioning e. As our case demonstrates, the latter constraint might be satisfied even though the former isn't. 2.5.1 Indefinabilism Given its weakness in relation to both (EP) and (OR), (XP) is a metaontological norm that is rather hard to deny. This should worry the indefinabilist. Indefinabilists contend that there is a property truth, while denying that truth's essential nature can be described. But if it's impossible to describe truth's essence, then it's difficult to see how truth could enjoy explanatory power. A number of philosophers have held, for instance, that by appealing to truth, 91 we can explain the normativity of belief. They contend that we can elucidate what is required for an act of believing to be correct by mentioning the truth of what is believed. As Pascal Engel [94, p. 128] points out, if it is indeed a fact about truth that it is a norm of belief, then this is presumably an essential, not a merely accidental, fact about both truth and belief:60 It seems extremely implausible to suggest that there might be as many different ways of believing and as many norms for belief as there are contents of beliefs. We would have to say that you do not believe in the same way when you believe that grass is green and when you believe that snow is white. The main reason why there has to be a central norm of truth is that belief in general aims at truth. Part of what it is for a mental state to be a belief, Engel points out, is that the mental state has truth as its aim in the sense that it is correct to have the mental state only if its propositional content is true. And this looks to be as much an essential fact about belief as an essential fact about truth: part of what it is for a property to be truth is that the property's instantiation by its propositional 60 Engel's misgivings here pose an intial problem for alethic pluralists, given that pluralists posit more than one truth-like property. Moderate pluralists mitigate these concerns by taking the single property truth to be the property at which beliefs aim. Given that beliefs have propositional content, I meet these concerns similarly, though as will emerge, the operative property on my own view is what I call proposition-truth. 92 content helps to determine whether it is correct to hold a belief.61 What this serves to suggest is that if we are to draw upon truth's nature to explain the sorts of phenomena in which philosophers are interested, we will do so by appealing to facts about truth's essence. But if truth's essence is indescribable, as the indefinabilist has it, then any such appeals to truth will simply fall flat. So the indefinabilist is committed to denying that truth lacks the explanatory power that it has traditionally been accorded. As such, indefinabilism falls foul of the weak norm on positing laid down by (XP). For the indefinabilist incurs both a commitment to truth's existence and a commitment to taking truth to lack explanatory power. And that is just what is prohibited by (XP). 2.5.2 Deflationism (XP) also presents a difficulty for a leading species of deflationism, Paul Horwich's alethic minimalism. Historically, deflationists have suspected that there is very probably no property truth. This denial is meant to deflate the traditional ambition to describe truth's essence. The ambition of the deflationist is not to provide a competing, constructive response to the essence question, it is to short-circuit the essence project outright. Traditional deflationists, in expresing sympathy towards the view that truth does not exist, famously run into the difficulty of explaining what we might be 61 Lynch [169], [170] also highights this point in a response to Horwich. 93 doing in peforming truth ascriptions and truth denials, if not asserting and denying, respectively, that truth-bearers have the property truth. I might, for instance utter assertorically 'What John said yesterday is true.' The natural analysis of this utterance is that in performing it, I say that what John said yesterday instantiates the property truth. But of course, if they deny that truth exists, then the deflationist cannot take it to be the semantic value of 'is true.' Unsurprisingly, deflationists have been quite sensitive to this difficulty and have proposed a number of inventive revisions to the natural understanding of truth ascriptions and denials.62 One of the most distinctive features of alethic minimalism is that it parts ways with deflationary tradition in allowing that there is a property truth. In a memorable passage, Horwich responds to a concern that might be raised for alethic minimalism [131, ch. 2, § 9]: 9. Even if we grant that, as predicates go, the truth predicate is highly unusual–even if we grant that its special function is to enable us to say certain important things while avoiding new forms of quantification–it surely does not follow that being true is not a genuine property. 62 These include Ayer [12] and Ramsey [223]'s redundancy theory; Strawson [256]'s performative theory; the disquotationalism of Quine [222], Leeds [159], and Field ( [98], [100]); Grover [116]'s prosentential theory; and Brandom's [28] anaphoric theory. See also Le Morvan [160] for a helpful discussion of Ramsey's views on truth. 94 Quite right. And it is not part of the minimalist conception to maintain that truth is not a property. On the contrary, 'is true' is a perfectly good English predicate–and (leaving aside nominalistic concerns about the very notion of 'property') one might well take this to be a conclusive criterion for standing for a property of some sort. The alethic minimalist, in contrast to most deflationists, posits truth, though they insist, as Horwich immediately points out, that truth is a merely 'insubstantive' property. Alethic minimalists, in other words, aim to deflate truth not by denying that it exists, but by assigning it a second-rank status among properties. What this amounts to for Horwich is that truth lacks, among other things, explanatory power.63 It's clear, Horwich will allow, that in performing explanations, it can be extremely beneficial to use the word 'true.' Suppose that you ask me why you should rely upon John's testimony that the blood sample found at the crime scene demonstrates that Sally was the murderer. I reply, 'Because John is a highly experienced and very reliable forensic scientist; all of his crime scene diagnoses have been true.' Since John has a lengthy track record of crime scene diagnoses, it would be highly inconvenient if, to convince you that you should trust John's testimony, I had to explicitly mention every such diagnosis. Luckily, in explaining why you should trust John's testimony, I can simply generalize over all of these 63 [131, ch. 3]; [133, pp. 6-7, 13-16]. 95 diagnoses and say that they are true. And since they take 'is true' to be an English predicate (in the semantic sense of 'predicate'), the alethic minimalist will also allow that in so using 'is true,' I am ascribing the property truth to all of John's past crime scene diagnoses. But what the minimalist denies is that in so using 'is true' in an explanation, I am drawing upon important facts about truth's essence. According to the minimalist, there simply are no such facts upon which one could draw in performing an explanation. It should now be clear, though, that in so setting themselves apart from both traditional deflationism and traditional substantivism, the alethic minimalist invites a serious metaontological difficulty. Unlike traditional deflationists, minimalists posit a property truth. Unlike traditional substantivists, they deny that truth enjoys explanatory power. But this is precisely what is prohibited by the weak norm on positing laid down by (XP). So in addition to other concerns that can be raised for deflationism, pluralists should draw in advancing the Scope + Substance argument upon the fact that deflationists must contend with a difficult dilemma. One horn of the dillemma consists in holding with traditional deflationists that there is no property truth. But then the challenge is offer a plausible revision of the natural understanding of truth ascriptions and truth denials. The other horn is to following alethic minimalists in positing truth. But since minimalists deny that truth has explanatory power, the deflationist who grasps this horn violates a very weak, and so not easily 96 denied, metaontological norm. Though the matter is delicate, as we'll see in chapter 5, pluralists are in a position to avoid this dilemma. Pluralists posit a plurality of truth-like properties and are accordingly free to assign a member (or members) of this plurality to serve as the semantic value of 'is true.' Pluralists are also free to oppose minimalists in holding that the truth-like properties that they posit enjoy explanatory power. So, at least at first pass, pluralists are in a position to endorse our natural impression that 'is true' is a predicate (in the semantic sense of 'predicate') and are also able to fully conform to the norm laid down by (XP). 2.5.3 The metaphysical instability challenge Finally, recall Pedersen's metaphysical instability challenge for alethic pluralism. The challenge is that in positing a plurality of domain-specific truth-like properties T1, . . . , Tn and a plurality of domains D1, . . . , Dn, the pluralist incurs a prima facie commitment to a disjunctive property TG, whose form is 'being in D1 and being T1 or being in D2 and being T2 or . . . or being in Dn and being Tn.' But if the pluralist accepts this commitment, then their views look to mimic those of alethic monists, given that TG is instantiable by truth-bearers belonging to any domain. The question is then: can the pluralist refuse to posit TG on plausible, principled grounds or must they allow that TG exists but explain why, even if it does, their views are importantly different from those held by monists? 97 We're now in a position to see that the pluralist does have plausible, principled grounds for refusing to posit TG: TG, if it existed, would lack explanatory power. To see this, consider first of all our other example of a disjunctive property, being a trout-turkey. Does being a trout-turkey have explanatory power? Suppose, for instance, that I tell you that it would be traditional for us to eat Harry during our Thanksgiving dinner. You ask me why eating Harry would be traditional and I reply: 'Because Harry is a trout-turkey.' Given that Harry is, in fact, a turkey, have I explained to you why it would be traditional for us to eat Harry on Thanksgiving? Intuitively, no, I haven't. The explanation for why it would be traditional to eat Harry is, of course, that Harry is a turkey. Similarly, we know that the instantiation of TG is biconditionally related to the instantiation of T1, . . . , Tn, so that a truth-bearer a instantiates TG iff a instantiates the pertinent member of T1, . . . , Tn. This should tip us off to the fact that in any instance where it might seem that an appeal to TG explains a given phenomenon, it is really a covert appeal to a member(s) of T1, . . . , Tn that is doing the explanatory work. Suppose, for instance, that I tell you that John ought to believe that tables are solid and you ask me why this is so. I reply: 'Because the content of his belief, 〈tables are solid〉, instantiates TG.' Have I explained why John ought to believe that tables are solid? Intuitively, no. The explanation, rather, is that 〈tables are solid〉 belongs to the physical domain and instantiates, say, the naturalistic 98 correspondence property that is assigned to that domain. Since TG is explanatorily impotent, were the pluralist to posit TG, they would violate the metaontological norm laid down by (XP). So pluralists should refuse to posit TG on the grounds that in doing so, they are better positioned to keep their metaontological house in order. To sum up, my main aim in this chapter has been to criticize and ultimately rehabilitate what I take to be the best argument for alethic pluralism, the Scope + Substance argument. In advancing this argument, I've said, pluralists should draw upon a metaontological norm that affords them other important benefits. In the end, the reason that we should be attracted to alethic pluralism is that it offers a way to salvage what was right all along about the essence project while avoiding the scope problem. Pluralism also, to my mind, is able to salvage the basic insights of deflationism–that truth doesn't exist and that the properties that we might be tempted to identify with truth have natures which are a good deal more straightforward than the tradition in truth theory leads us to expect. In the final chapter, we'll return to this latter point after closely examining the distinctive commitments of deflationism. Chapter 3 99 100 Domains, plural truth, and mixed atomic propositions There are logical truths. They are those that relate merely to the understanding and reason. From another side, we can think of an aesthetic and a practical truth. The former relates merely to the condition of taste, the latter on the contrary to the rules of the free will. Logical truth, however, is not always aesthetically true, and it does not always bring with it practical perfection. . .Much can be aesthetically true without being logically true[;]it may only stimulate and please. Thus it is, e.g., with novels. Even practical truth need not always be grounded on the understanding and on reason either. Kant, Blomberg Logic 101 3.1 Pluralism and truth-aptness In the remaining chapters, my aim will be to articulate and defend what I regard as the most attractive variety of alethic pluralism.1 I'll start in this chapter by focusing on two general concerns for pluralist truth theories: a concern about a key detail of these theories and a concern about their viability. The detail-related concern is that pluralists have relied heavily upon the notion of a domain, but it is not transparent what they take domains to be. Since the notion of a domain has been present in philosophy for some time, it's important for many theorists, not only alethic pluralists, to be clear on what domains are and what work they can do. The viability-related concern is that its not clear how a pluralist truth theory could explain the truth-conditions of mixed atomic propositions. To address this concern, alethic pluralists should recognize something to which they have not been sufficiently attentive: that some atomic propositions belong to more than one domain. But, recognizing this requires rethinking the relationships between the nature of propositions, their membership in domains, and their truth. I'll address these issues and propose an understanding of them that is preferable to the best existing account of them, that offered by Lynch. In the following chapters, we'll pay special attention to an issue that has 1 This chapter is a revised version of 'Domains, plural truth, and mixed atomic propositions,' Philosophical Studies 166: 1. 255-36. 102 been historically prominent in truth theory, but which has not received sufficient attention in debates about pluralism–the issue as to what kinds of entity bear truth. An alethic pluralist is not committed, just in virtue of being an alethic pluralist, to taking any particular kind of entity to be a truth-bearer. Any candidate from the standard list of potential truth-bearers–propositions, indicative sentence-tokens, judgments, indicative beliefs, assertions, and so on–is available to them. The most influential pluralist truth theories, versions of what has come to be known as moderate alethic pluralism, take propositions to be among the bearers of truth, and indeed to be the primary truth-bearers. I think that this is right and shall be assuming until turning in earnest to the issue of truth-bearing in the next chapter. One of the reasons that pluralist truth theories are especially interesting is that they promise to deliver two theses which seem, at first pass, to be in tension with one another: minimalism about truth-aptness and substantivism about truth. The latter thesis is, in essence, the negation of the core thesis of deflationism, that truth is not a substantive, i.e. philosophically significant, property. Set in a pluralist cast, the essential claim of substantivism about truth is that at least some properties which qualify, by the pluralist's lights, as truth-like properties are substantive. When placed into this cast, the core thesis of deflationism can be understood as holding that there are no properties which are both truth-like, in this sense, and also substantive. Every truth-like property, says, the deflationist 103 (and mainline deflationists take there to be either no such properties or one such property) is insubstantial; pluralists, in embracing substantivism about truth, deny just this claim. In an early statement of alethic pluralism, Crispin Wright articulates the core idea behind minimalism about truth-aptness [274, pp. 72-4]: [T]ruth is not intrinsically a metaphysically heavyweight notion–the mark of some profound form of engagement between language, or thought, and reality–for which certain areas of assertoric discourse, whatever internal discipline they manifest, may simply not be in the market. . . [A]ny assertoric discourse will permit the definition upon it of a minimal truth predicate. . . Here it is vital that, for the purposes of this claim, assertoric discourses are demarcated not by any deep feature of their contents which might be simulated or masked by surface syntactic features, but merely by their statements' being subject to acknowledged conditions of acceptance and their possessing the appropriate surface syntactic features. . . Wright's version of minimalism about truth-aptness has it that for a sentence 'S' to be truth-apt, only two conditions must be met:2 • (DS) 'S' has a indicative syntax : 'S' can be grammatically embedded under negation and propositional attitude verbs, serve as the antecedent of a 2 (Disc) is referred to as the discipline condition by Jackson, et. al. [137]. 104 conditional,. . . • (Disc) The use of 'S' is governed by acknowledged standards of warranted acceptability. The upshot is the possibility that not only discourse about ordinary, macroscopic objects, but, for instance, moral, aesthetic, and mathematical discourse might be truth-apt, even if the content of the latter is not about objective facts or response-independent properties. 'Random torture is immoral,' for instance, is just as embeddable under negation as 'The temperature today is 80◦ Fahrenheit.' The cost of entry into the truth game will have been substantially lowered, and if truth is substantive, it is surprising that entry is so cheap.3 Now, though an alethic pluralist posits more than one truth-like property, they need not go so far as to say that truth itself is plural. Indeed, an influential formulation of alethic pluralism due to Michael Lynch called manifestation functionalism has it that there is only one property that is identical to truth itself. Truth, on his view, is a functional property that is manifested by a plurality of substantive, truth-like properties which we can refer to as the manifesters. The manifesters manifest truth by instancing a certain functional role, the 'truth-role.' For a property to instance the truth-role is for it to satisfy a number 3 The pluralist truth theories of Lynch and Gila Sher also entail forms of minimalism about truth-aptness that are interestingly different from that advanced by Wright. These complexities are interesting, but we'll set them aside in what follows. 105 of platitudes that would appear to circumscribe our ordinary concept of truth. For instance, one platitude suggested by Lynch is (Objectivity) The belief that p is true iff with respect to the belief, things are as they are believed to be.4 The guiding thought here is that someone who possesses the concept of truth is, for that reason, disposed to accept highly general claims about truth such as (Objectivity). Any property, then, which satisfies such claims is behaving as our concept of truth tells us truth behaves–it is truth-like–and for that reason, manifests truth. Lynch suggests several properties that might be included as manifesters, but we will not need to consider these properties in detail just now.5 Rather, it will be important to note a distinguishing feature of manifestation functionalism. Manifestation functionalism is, as we will put it, a binary pluralist truth theory. That is, according to manifestation functionalism, there are two properties (other than truth itself) which, when instantiated by propositions, manifest truth. One of these is a representational, correspondence property which can be taken, following the early work of Field [96], to be underwritten by a causal theory of reference.6 4 See [175, ch. 1] and chapter 4 for further discussion of the platitudes about truth. 5 For further discussion, see [175, ch. 8], [178]. 6 See § 2.1.1. 106 The other is an epistemic, coherence-theoretic property, which is more nuanced than, though in the tradition of, the coherence properties which figures such as Blanshard [25] and Joachim [143] have taken to be identical to truth.7 3.2 Domains What, then, is supposed to determine which manifester a proposition must instantiate to be true? It is here that Wright's notion of a discourse promises to play a critical role: its membership in a certain discourse will determine the manifester that is assigned to a proposition. Wright says [274, pp. 37-8, see also pp. 24-5]: The proposal is simply that any predicate that exhibits certain very general features qualifies, just on that account, as a truth predicate. That is quite consistent with acknowledging that there may, perhaps must be more to say about the content of any predicate that does have these features. But it is also consistent with the possibility of pluralism–that the more there is to say may well vary from discourse to discourse. . . 7 See § 2.1.1 for a discussion of the related property of superwarrant. Given Lynch's definition of manifestation, not only do correspondence and coherence manifest truth, truth actually manifests itself. This is why, in defining 'binary pluralist truth theory' above, I include the parenthetical. 107 Wright is raising the possibility that the things we say (and think) comprise various discourses. This is not a novel contention. The conviction that there is more than one discourse underpins many debates about realism, antirealism, irrealism, error theory, fictionalism, cognitivism, and non-cognitivism. It is thus important for many philosophers, not only alethic pluralists, to be clear about what, exactly, a discourse is supposed to be. Discourses are presumably more inclusive than conversations. I could have a conversation about set theory at t1 and a conversation about arithmetic at t2. These would, in the operative sense, be instances of the same discourse: mathematical discourse. Discourses could, then, be thought of as (possibly soliloquized) conversation-kinds. The question then becomes how to individuate these conversation-kinds. A natural suggestion is to appeal to the kinds of entity that conversations are about. Lynch has recommended that discourse individuation take just this sort of trajectory. He sketches a procedure for individuating discourses, which he calls domains [175, pp. 77-80]: [A]n atomic proposition is true when it has the distinct further property that plays the truth-role–manifests truth–for the domain of inquiry to which it belongs. Not being true consists in lacking that property. . . [What determines whether a proposition is a member of one domain, rather than another, is] the kind of concepts (moral, legal, mathematical) that compose the proposition in question. . . One kind 108 of concept differs from another by virtue of (a) its relation to, and (b) the character of, the properties that kind of concept is a concept of. The view that Lynch is advancing here is clearly a development of that suggested by Wright. Call it domain pluralism, the view that propositions are members of distinct domains. As the above passage indicates, domain individuation is taken by Lynch to bottom out at the level of properties. A concept-kind K is individuated by: (i) the relations in which K-concepts stand to properties; and (ii) the 'character' of those properties. Though it is not absolutely clear what the character of a property is (presumably, a property's character is determined inter alia by whether it is physical or objective), this strategy for individuating concept-kinds appears to involve an appeal to property-kinds. Some conceptkinds are identical to others–trivially, every concept-kind is self-identical. Hence, some properties have the same 'character.' Presumably, this is enough for them to instance a property-kind (at least in some sense; perhaps these don't qualify as natural kinds, but there is no clear reason why they would need to). Propositionkinds are, in turn, defined in terms of concept-kinds. Propositions are taken to be composed of concepts, and proposition-kinds individuated by the kinds of concepts of which their instances are composed. Lastly, domains are individuated by appeal to proposition-kinds: one domain is identical to another iff all of its constituent propositions instance the same kind. 109 Atomic propositions have a distinctive status, on this view: they are taken to essentially belong to one and only one domain. Lynch says [175, p. 80]: Belonging to a particular domain is a feature an atomic proposition at least, has in virtue of being the sort of proposition it is. Propositions are the kind of propositions they are essentially; therefore, belonging to a particular domain is an essential fact about an atomic proposition.8 Lynch's method of domain individuation certainly goes further than Wright's, but it isn't quite adequate. I'll mention two concerns that arise for it. The first concern is that the view individuates concept-kinds too narrowly. According to Lynch, propositions are composed only of concepts. An account of propositional composition along these lines should take propositions to be composed not only of concepts of properties, but also of concepts of individuals and relations. 〈Brutus killed Caesar〉, for instance, should be taken to be composed of at least one individual-concept and either a property-concept or a relation-concept.9 8 Lynch [175, p. 81] carves out one exception: atomic propositions composed of vague concepts. Such propositions, he suggests, may not determinately be members of any domain; if so, their truth is likewise indeterminate. Vague propositions will be set aside in what follows. As the reader can verify, if this escape clause were used to respond to the problem of mixed atomic propositions, the resultant truth theory would be saddled with massive amounts of indeterminacy in truth-value. This result is questionable on its face, and it would certainly be in tension with minimalism about truth-aptness. 9 The options here are (brackets are used to denote concepts): 110 The second concern is that the notion of a domain is ambiguous. Domains have been described thus far as things of which propositions can be members– classes. This is one, but not the only, role that domains are supposed to play in Lynch's view. He also describes domains as 'subject matters,' e.g. mathematics and ethics.10 A subject matter would appear to be a kind of thing that one can think or talk about. But, one and the same thing cannot play both of these roles. Most of our thought and talk is not about (classes of) propositions, so propositions are not the subject matter of that thought and talk. This means that if domains are classes of propositions, the collection of all domains cannot exhaust the subject matters about which we think and talk. To resolve this ambiguity, we should recognize two distinct notions: that of a subject matter and that of a class of propositions composed of concepts of entities that instance that subject matter. There is, for instance, distinctively mathematical subject matter: sets, numbers, the successor function, and so on. There is also a class of propositions that are mathematical in kind: 〈The null set has zero members〉, 〈The successor of 1 is 2〉, and so on. These propositions are mathematical propositions because they are composed of mathematical concepts, • (B1) [Brutus], [ξ killed Caesar] • (B2) [Caesar], [ξ was killed by Brutus] • (B3) [Brutus], [ξ killed ζ], [Caesar] 10 [178, p. 14]; see also [175, p. 19]. 111 i.e. concepts about mathematical subject matter. To put the point another way, the identity of these propositions is determined by the identity of the subject matter they are about, not the other way around. To keep these notions separate, we can refer to subject matters as topics and classes of propositions as domains. Topics are individuated as follows: (Topic identity) Topic T is identical to topic T ′ iff the individuals, properties, and relations that instance T are numerically identical to those that instance T ′. With topics and domains disambiguated, the Lynchian view of domains that emerges is the One (Domain)-for-One (Atomic Proposition) strategy: • (1-1) (i) Domain D = domain D′ iff D exists and D′ exists and 〈p〉 ∈ D and 〈p′〉 ∈ D′ iff the concepts C1, . . . , Cn composing 〈p〉 and the concepts C1′ , . . . , Cn′ composing 〈p′〉 instance the same concept-kind K • (1-1) (ii) Concepts C and C ′ instance the same concept-kind K iff they bear the same relations R1, . . . , Rn to entities (objects, properties, relations) that instance the same topic • (1-1) (iii) Every atomic proposition essentially belongs to exactly one domain • (1-1) (iv) Every atomic proposition is assigned a manifester based upon its 112 domain-membership. Lynch points out three virtues of One-for-One [175, pp. 81-2]: • (V1) Proposition-kinds can be extracted from (1-1(i)). These kinds can be used to explain why there is more than one manifester property: because inter alia there is more than one kind of proposition • (V2) (1-1(i)) individuates domains in a 'natural' way • (V3) (1-1(iii)) rules out an unattractive possibility: that an atomic proposition might be both true and not true, in virtue of instantiating the manifester assigned to one domain, but not that assigned to another. 3.3 The problem of mixed atomic propositions One-for-One provides a clear and initially compelling way to think about how domains, propositions, and truth might be related, but it unfortunately has a fatal flaw. The Achilles' heel of One-for-One is the problem of mixed atomic propositions.11 Marian David [60, § 8.2] states the problem well:12 First, it seems difficult to sort propositions into distinct kinds according to the subject matter they are about. Take, e.g., the proposition 11 There are related problems in this vicinity, the problems of mixed compounds, mixed inferences, and mixed generalizations. These problems have been discussed much more extensively and we'll turn to them in the next chapter. 12 For similar remarks by David, see [61, pp. 744-5] and see also Sher [241, pp. 320-22]. 113 that killing is morally wrong, or the proposition that immoral acts happen in space-time. What are they about? Intuitively, their subject matter is mixed, belonging to the physical domain, the biological domain, and the domain of ethical discourse. It is hard to see how pluralism can account for the truth of such mixed propositions, belonging to more than one domain of discourse: What will be the realizing property? The problem is that some atomic propositions appear to be composed of concepts of different kinds, ones which bear relations to entities that instance different topics. Call these mixed atomic propositions. The identity-conditions for domains specified in (1-1(i)) do not range over such propositions, so One-for-One doesn't count them as belonging to any domain, and thus does not count them as truth-apt. This is in tension with minimalism about truth-aptness: 'Immoral acts happen in space-time.' clearly satisfies (DS) and (Disc). Moreover, if these propositions are composed of concepts of different kinds, it isn't clear how (11(iii)) could apply to them. Some of the concepts that compose them will be about one topic, some about another, so surely they cannot be members of only one domain, much less essentially members of only one domain. 114 3.3.1 Response: No domains How should alethic pluralists address the problem of mixed atomic propositions? One response is to substantially modify One-for-One by abandoning the notion of domains altogether. This is the response offered by Lynch in recent work [178, pp. 15-16]. The response might seem attractive, since mixed atomic propositions appear to certify the impossibility of cleanly sorting every proposition into one domain and assigning it a manifester on that basis. Why, then, keep domains around at all? Abandoning domains for this reason would, however, be a mistake. Without domains, it becomes difficult, if not impossible, to explain why a given proposition must instantiate a certain manifester, and not any other, to be true. Thus without domains, pluralists' ability to offer complete theories of truth will be jeopardized. Traditional truth theories, we saw, advance constitution theories for truth, which hold that the truth of a given truth-bearer a consists in a's instantiating property P. A truth theory that advances a constitution theory for truth is complete only if it also includes an explanation of why the truth of truth-bearers is so constituted, or if it includes an explanation of why this constitution theory is inexplicable. When available, explanation is preferable to mystery, so it is better for a truth theory to acheive completeness in the former way than in the latter. Pluralist truth theories have thus far been premised on precisely this promise of explicable constitution theories for truth. Thus their completeness will be called 115 into question if they are unable to provide explanations of them. To see the explanatory threat that is posed, consider a domain-free version of manifestation functionalism. Take the proposition 〈p〉. One and only one manifester P is assigned to 〈p〉. Why is P, and no other manifester P′, suitable for manifesting the truth of 〈p〉? The domain-free, manifestation functionalist's reply will be, 'Because 〈p〉 is composed of concepts C1, . . . , Cn, C1, . . . , Cn bear relations R1, . . . , Rn to x1, . . . , xn, and x1, . . . , xn instance topic T .' Notice that for the manifestation functionalist to fully explain why P is 〈p〉's manifester, they must also cite general facts about the concepts composing 〈p〉 and those entities of which they are concepts. Otherwise, they have only offered a brute claim that the composition of a proposition determines which manifester is suitable to manifest its truth. By way of analogy, suppose that a functionalist about mental states tells you: 'State S is a pain state iff S instantiates the property Ψ = being a C-fiberfiring state. Ψ manifests pain when instantiated by S because S also instantiates the property Ψ′ = being a human brain state.' This is clearly not a complete explanation of why Ψ manifests pain when instantiated by S. Why not? The reason appears to be that the mental state functionalist has, in effect, offered a claim of the form 'X determines Y ' that isn't conjoined with a conjecture as to how or why X determines Y . Call this a bare determination claim. To remedy this explanatory incompleteness, the mental state functionalist can replace their 116 bare determination claim with a claim of the form, 'X determines Y because Z' (X 6= Y 6= Z). They can, that is, claim instead that S's instantiating Ψ′ determines that Ψ manifests pain for S because. . .. Call a claim of the latter form a grounded determination claim.13 The lesson for manifestation functionalism is that manifestation functionalists should answer questions about the assignment of manifesters like the one above by advancing grounded, not bare, determination claims. But, as offered by a manifestation functionalist, a grounded determination claim will cite general facts about the kind(s) of the concepts of which a certain proposition 〈p〉 is composed. This entails that 〈p〉 instances a certain proposition-kind. Domains are just classes of propositions that instance a common kind, so domains then enter the picture straight away. This shows that manifestation functionalism should retain domains, even if the problem of mixed atomic propositions demonstrates that their characterization in One-for-One is inadequate. Put differently, because it retains domains, One-for-One has a further virtue: (V4) The kinds extractable from (1-1(i)) and (1-1(ii)) underwrite explana13 Of course, it is difficult to say just where complete explanations terminate, and why. It is also difficult to say how many hairs someone must have to not be bald. Still, we can say with confidence that someone with hair down to their ankles is not bald. Likewise, we can say with confidence that certain purported explanations are incomplete, even absent a final theory of explanatory completeness. 117 tions of why propositions are apt for certain manifesters, and not others. Since One-for-One has virtue (V4) and a domain-free version of manifestation functionalism does not, it's worth trying to salvage domains.14 14 An anonymous referee for Philosophical Studies suggested that a virtue sufficiently similar to (V4) can be preserved without mentioning proposition-kinds or domains. The thought is that one could explain why a given proposition 〈p〉 is apt for a certain manifester and no other manifester by citing facts only about the specific concepts composing 〈p〉, rather than any kinds that those concepts instance. Notice, however, that the suggested explanation is a bare determination claim: it has the form 'P is 〈p〉's manifester because 〈p〉 is composed of concepts C1, . . . , Cn.' Lynch has also suggested (pc) that the manifestation functionalist could allow that a given proposition 〈p〉 is apt for a certain manifester and no other manifester because there are certain general facts about the concepts composing 〈p〉, while denying that 〈p〉 belongs to a particular domain. The thought is that we might explain why e.g. 〈torture is wrong〉 is apt only for a coherence-theoretic manifester and not a correspondence-theoretic manifester by holding, following Moore, that there is no natural property wrongness and pointing out that [wrong] is a normative concept. But notice that this, too, is a bare determination claim. To convert it into a grounded determination claim, we would need to cite general facts about the pertinent kind of concept–namely, normative concepts–of which 〈p〉 is partially composed. This would entail that 〈p〉 instances a certain proposition-kind–〈p〉 is a proposition that is at least partially composed of normative concepts, i.e. 〈p〉 is a normative proposition. So 〈p〉 belongs to the domain of normative propositions. 118 3.3.2 Solution: Multiple domain membership, but one manifester To close this chapter, I will sketch a solution to the problem of mixed atomic propositions that retains domains. The guiding ideas behind the solution are first, that there are some concept-kinds K1, . . . , Kn such that if 〈p〉 is composed of K1or. . . , or Kn-concepts, then 〈p〉 cannot be true in virtue of representationally corresponding. Second, if 〈p〉 is composed of K1or. . . , or Kn-concepts then 〈p〉's manifester is an epistemic (e.g. coherence) property. Third, if 〈p〉 is not composed of K1or. . . , or Kn-concepts, then 〈p〉's manifester is representational correspondence. On this view, then, correspondence serves as a default manifester and other manifesters are introduced only to handle propositions that are truthapt, but are incapable of corresponding. To illustrate, consider 'Charlie is delicious,' where 'Charlie' is the name of a beet. This sentence is minimally truth-apt, and it presumably expresses 〈Charlie is delicious〉. 〈Charlie is delicious〉 is composed of the concept [deliciousness], which is plausibly non-representational. Thus, 〈Charlie is delicious〉 can't be true in virtue of representationally corresponding. This means that 〈Charlie is delicious〉 must be true, if it is, in virtue of instantiating another property. A plausible candidate is an epistemic, e.g. coherence-theoretic, property.15 15 My current aim is to outline a solution the problem of mixed atomic propositions on behalf of the manifestation functionalist. In chapter 5, we'll return to the issue of whether pluralists should include any epistemic properties in the class of domain-specific truth-like properties. An anonymous referee for Philosophical Studies suggested that for manifestation functionalism 119 Questions about this solution Finally, I will consider two illustrative questions about this proposal. Question #1: To which domain does 〈Charlie is delicious〉 belong, then? Answer: Every domain is pure–its membership-conditions specify a single kind of concept of which a proposition must be at least partially composed to be a member. 〈Charlie is delicious〉 is composed of two kinds of concepts, a 'macroscopic object' concept and a 'aesthetic' concept, so it is a member of both the 'macroscopic reality' domain and the 'aesthetic' domain. This is precisely the insight in David's description of the problem of mixed atomic propositions: alethic pluralists should not presuppose that every atomic proposition belongs to one and only one domain. It is also an insight that motivates Lynch's recent de-emphasis to address the problem of mixed atomic propositions, it is only necessary that some manifester be a default manifester, not that representational correspondence, in particular, be the default manifester. Suppose, then, that an epistemic, coherence property is the default manifester: it manifests truth for 〈p〉 unless 〈p〉 is composed of concepts that render 〈p〉 incapable of cohering with other propositions. Are there any such concepts? It would seem that even propositions that are entirely composed of representational concepts are capable of cohering with other propositions. This means that if coherence were the default manifester, coherence would manifest truth even for thoroughly representational propositions, e.g. 〈Snow is solid〉. Treating coherence as the default manifester, then, seems to give the upper hand to monist, coherence theories of truth. 120 of domains–though the de-emphasis is hasty, the insight is genuine. Lynch says [178, p. 16], "[T]here is no need for the pluralist to sort (atomic) propositions into strict domains. She takes each proposition as it comes, finding that, in fact, they come in groups, in bunches, in mobs." Lynch's second claim is exactly right: propositions must be taken as they come. Some come composed of concepts of entities that instance different topics, so that is how they must be taken. But, they can still be sorted into strict (that is, well-defined) domains. Question #2: Does the proposal preserve the virtues of One-for-One? Answer: (1-1(i)) will be replaced by (M-1) (i) Domain D = domain D′ iff D exists and D′ exists and there is a concept kind K such that 〈p〉 ∈ D iff 〈p〉 is (partially) composed of K-concepts and 〈p′〉 ∈ D′ iff 〈p′〉 is (partially) composed of K-concepts. (M-1) (i) allows us to distinguish, for instance, the 'macroscopic reality' domain and the 'aesthetic' domain, while allowing that 〈Charlie is delicious〉 is a member of both. The domains are distinct because a proposition composed only of aesthetic concepts, e.g. 〈Deliciousness is wonderful〉, is a member of the latter, but not the former. 121 The content of (1-1) (ii) and (1-1) (iv) will be retained as is. (1-1) (iii) will be replaced by (notice that there is no restriction to atomic propositions) (M-1 (iii)) Every proposition essentially belongs to those domains of which it is a member. The view that emerges can be called Many (Domains)-One (Manifester), since it allows that mixed atomic propositions can belong to more than one domain, though each such proposition is assigned only one manifester. Many-One, then, consists of the following four theses: • (M-1) (i) Domain D = domain D′ iff D exists and D′ exists and there is a concept kind K such that 〈p〉 ∈ D iff 〈p〉 is (partially) composed of K-concepts and 〈p′〉 ∈ D′ iff 〈p′〉 is (partially) composed of K-concepts • (M-1) (ii) Concepts C and C ′ instance the same concept-kind K iff they bear the same relations R1, . . . , Rn to entities (objects, properties, relations) that instance the same topic • (M-1) (iii) Every proposition essentially belongs to those domains of which it is a member • (M-1) (iv) Every atomic proposition is assigned a manifester based upon its domain-membership. 122 Many-One preserves (V1): proposition-kinds are extractable from (M-1) (i) (given the assumption that there is at least one domain), with mixed atomic propositions instancing more than one such kind. (V2) is also preserved: domains are individuated as naturally as by manifestation functionalism. (M-1) (i), like (1-1) (i), individuates domains according to the composition of their constituent propositions. (V3) is preserved: all atomic propositions, even mixed atomics, are still apt for only one manifester. Lastly, since a proposition's aptitude for a certain manifester is explained by the fact that the proposition instances a certain kind, (V4) is preserved as well. Many-One, then, does preserve all of the virtues of One-for-One, and has a further virtue, as well: (V5) The truth-conditions of all atomic propositions–mixed and unmixed– are explained. In sum, I have argued for two main claims in this chapter. The first is that domains are a vital detail of pluralist truth theories. The second is that the problem of mixed atomic propositions does not destabilize a suitably revised version of manifestation functionalism. Manifestation functionalism should allow for multiple domain-membership and should treat representational correspondence as the default manifester. Doing so preserves the virtues of the Lynchian formulation of manifestation functionalism while providing a more satisfactory resolution of the 123 problem of mixed atomic propositions. In this chapter, we've focused particularly upon manifestation functionalism because of its considerable influence in debates involving alethic pluralism. Manifestation functionalism is a member of a more general family of pluralist truth theories, each of which is a species of a more general outlook called moderate alethic plurailsm. In the next chapter, we broaden our focus to consider moderate pluralist truth theories as such. Chapter 4 Minimizing moderate pluralism When is a statement true? The temptation is to answer (at least if we confine ourselves to "straightforward" statements): "When it corresponds to the facts." And as a piece of standard English this can hardly be wrong. Indeed, I must confess I do not really think it is wrong at all: the theory of truth is a series of truisms. Still, it can at least be misleading. Austin, "Truth" Alethic pluralists hold that there is more than one truth-like property and that their denial of this thesis is the source of alethic monists' trouble with the scope problem. But as we've seen, some alethic pluralists are inclined to hold on 124 125 to alethic monists' contention that truth is one. Moderate alethic pluralists hold that monists are correct that there is only one property truth. Monists' fateful mistake, they say, is a failure to recognize that in addition to the focal truthlike property truth itself, there are other truth-like properties whose instantiation determines whether propositions are true. Truth, say moderate pluralists, is one, although the truth-like properties are many. We've looked thus far at one species of moderate pluralism, Lynch's manifestation functionalism. There are three further theories which, together with manifestation functionalism, make up the family of moderate pluralist truth theories. In his early work on functionalism about truth, Lynch [171] advocated an approach which takes truth to be a second-order property. This view is accordingly known as second-order functionalism. Nikolaj Pedersen [204], [210] has championed a moderate pluralist view that takes truth to be a disjunctive, rather than a second-order, property, which has come to be called alethic disjunctivism.1 And very recently, Doug Edwards [87], [90] has proposed a view according to which truth, whose nature is detailed by platitudes about truth, is 'conferred' upon a proposition in virtue of its instantiation of a further truth-like property. Crispin Wright [279] has also recently expressed sympathy towards this view, known as (simple) determination pluralism. 1 Readers familiar with the philosophy of mind can analogize second-order functionalism to 'role functionalism.' Manifestation functionalism, by contrast, is a form of 'specifier functionalism.' 126 So moderate pluralism has been a highly influential outlook among alethic pluralists. Indeed, it is safe to say that moderate pluralism is generally regarded as a paradigm for pluralist theories of truth. And this is no great surprise, since moderate pluralism's attractions are easy to appreciate. Moderate pluralist theories underwrite a diagnosis of monism's difficulties with the scope problem: monists confront the scope problem because they fail to recognize that there is, in addition to truth, a plurality of further truth-like properties. Yet in crediting to monists the insight that truth is one, moderate pluralists are well-positioned to accord univocality to the predicate 'is true.' 'Is true,' a moderate pluralist can say, always expresses the one property truth, so the predicate is straightforwardly unambiguous. This result is undoubtedly attractive. It is wise, as Paul Grice [115, p. 47] pointed out, to avoid positing unnecessary semantic ambiguity. So it is good methodology to posit as few semantic ambiguities as one can, lest some of them turn out to be fatuous. Another point of attraction is that in taking truth to be one, moderate pluralists secure a straightforward account of argumentative validity: validity, a moderate pluralist may say, is necessary preservation of truth and nothing more.2 Unfortunately, issues to do with truth-bearing show moderate pluralism to be an unstable, and so unavailable, position. But the bulk of moderate pluralism 2 Though moderate pluralists, like all alethic pluralists, do face questions as to which logics govern the various domains and, in turn, which logics govern discourse that cuts across domains. 127 can be salvaged so as to show that its apparent advantages were not quite as telling as they seemed. Truth cannot be both one and many, but this is no great loss, for as we shall see, truth may be many and many. And in taking truth to be many and many, we are in a position to better appreciate a rich range of issues to do with truth-bearing and the nature of truth. 4.1 Moderate pluralism: core theses We've seen that the manifestation functionalist takes there to be a plurality of domains, which we ought to treat as classes of propositions. This applies not only to the manifestation functionalist, but to moderate pluralists more generally. For all of their differences, moderate pluralists are agreed that propositions are the primary bearers of truth.3 So it is open to all moderate pluralists to adopt what we called the Many-One strategy of domain individuation. We can thus let the first two theses of moderate pluralism be: • (MAP1) Domain pluralism • (MAP2) Propositions are the primary bearers of truth. We've also alluded to the fact that alethic pluralists invoke the notion of truth-likeness, taking certain properties to qualify as truth-like. Intuitively, a 3 See, for instance, Edwards [87, p. 28]; Horton and Poston [128, p. 13]; and Lynch [172, p. 29], [173, pp. 291, 331], [174, p. 81], [175, p. 129], [178]. 128 truth-like property is a property which at least sometimes behaves as we ordinarily expect truth to behave. And moderate pluralists take our ordinary conception of truth to be codifiable by a collection of platitudes about truth.4 Lynch, recall, takes the following claim to qualify as one such platitude:5 • (Objectivity) The belief that p is true iff with respect to the belief that p, things are as they are believed to be. In § 4.2, we'll propose a definite collection of platitudes that codify our ordinary conception of truth. Assured that this collection is forthcoming, we can for now simply call the claims belonging to it the alethic platitudes and we can similarly call the properties that alethic pluralists take to be truth-like the alethic properties. Moderate pluralists, then, invoke the alethic platitudes to explain the natures of the alethic properties as follows:6 • (MAP?3) P is an alethic property =Df at least some instances of P conform to the alethic platitudes. Moderate pluralists propose a distinctive division between two 'levels' of alethic properties. Those properties on the 'lower' level are the domain-specific alethic properties, where a property P qualifies as a domain-specific alethic property by satisfying one of two conditions: 4 See Edwards [87, § 4]; Lynch [171, § III C, F]; [175, ch. 4]; [178, § 3, 5]; Pedersen and C.D. Wright [210, § 2.2]. 5 [175, p. 8]. 6 We star this thesis because we'll refine the notion of platitude conformity in § 4.2.3. 129 • (DS(i)) Only some possible instances of P conform to the alethic platitudes; or • (DS(ii)) Every possible instance of P conforms to the alethic platitudes, but P is plausibly assigned as an alethic property to only certain domains. Lynch holds [175, ch. 8]; [178], for instance, that a coherence-theoretic property satisfies (DS(i)). While he takes such a property to conform to the alethic platitudes when instantiated by moral propositions, he argues that a proposition solely about the physical properties of macroscopic objects, e.g. 〈Tables are not solid〉, might cohere in the target respect and yet for all that, be intuitively false.7 The latter instance of this coherence-theoretic property would fail to conform to the alethic platitudes. But since in connection with some domains, the property does behave as we expect truth to behave, it does qualify as an alethic property in connection with those domains. A property satisfying (DS(ii)) might be a (relational) correspondence property, underwritten by a causal theory of reference (cf. Field [96]). It may be that only certain kinds of belief–e.g. those whose propositional content belongs to the physical domain, though neither moral nor mathematical beliefs–are capable 7 Lynch sometimes speaks, e.g. at [175, ch. 6], of moral judgments, rather than moral propositions, cohering with a given system of moral judgments. It's certainly important to clarify which kinds of truth-bearer can cohere with which other kinds of truth-bearer, but since we won't commit to a detailed account of coherence, we'll set this issue aside. 130 of causally corresponding with the world. This points to a potential asymmetry between causal correspondence and coherence: that whereas a proposition may cohere in the relevant respect and yet fail to be true, every belief that causally corresponds to the world is true. It would then be the case that every instance of causal correspondence conforms to the alethic platitudes. Yet, being sensitive to the scope problem, we can still plausibly classify causal correspondence as a domain-specific alethic property. Here, the key idea is that causal correspondence is plausibly assigned as an alethic property to only certain domains, e.g. the physical domain. Moral and mathematical beliefs are simply not kinds of belief whose truth we intuitively expect to involve their causal correspondence to the world– hence the difficulty that these kinds of belief pose for monistic correspondence theories invoking a causal theory of reference. So given that these kinds of belief are truth-apt (which is secured by a belief-theoretic version of minimalism about truth-aptness), we have reason to resist the contention that they are true iff they causally correspond. We have reason, that is, to refrain from assigning causal correspondence as an alethic property to the moral and mathematical domains.8 So the fourth thesis of moderate pluralism is: • (MAP4) There is a plurality of domain-specific alethic properties. Only one property, say moderate pluralists, occupies the 'higher' level of alethic properties: 8 See Lynch [175, ch. 2]. 131 • (MAP5) There is a single general alethic property, an alethic property – (Gen(i)) Every possible instance of which conforms to the alethic platitudes and – (Gen(ii)) Which isn't plausibly assigned as an alethic property to only certain domains. In what follows, we'll simply call this putative general alethic property truth. In addition to positing these two levels of alethic property, moderate pluralists wish to explain how the 'higher-level' property truth is related to the 'lowerlevel' domain-specific alethic properties. Truth, they say, is both biconditionally related to and asymmetrically depends upon the latter:9 • (MAP6) If 〈p〉 ∈ D, then 〈p〉 instantiates truth iff 〈p〉 instantiates the domain-specific alethic property TD assigned to D • (MAP7) If 〈p〉 ∈ D and if 〈p〉 instantiates truth, then 〈p〉 does so in virtue of instantiating TD. For ease of reference, the core theses of moderate pluralism are listed in § 4.11.1. We've mentioned several times now pluralists' invocation of a collection of claims that they describe as platitudes about truth. How, though, are we to 9 We saw that the problem of mixed atomic propositions compels moderate pluralists to refine (MAP6) and (MAP7). We can set these complexities aside for now. 132 know whether a particular claim about truth belongs in this collection? Do the alethic platitudes share certain common features in virtue of which they qualify as platitudes about truth? And why should we think that there are any platitudes about truth, given how contentious the topic of truth has proven to be among philosophers? It is to these questions that we now turn, and we'll return to them in § 5.3.5. 4.2 The alethic platitudes and platitude conformity 4.2.1 The need for platitudes In Plato's Meno, Meno poses to Socrates the following concern about the very possibility of theoretical inquiry:10 How will you look for it, Socrates, when you do not know at all what it is? How will you aim to search for something you do not know at all? If you should meet with it, how will you know that this is the thing that you did not know? Meno points in this passage to two difficulties involving the development and evaluation of theories. His first query is how it is possible to begin to theorize about a particular topic M , given that at the beginning of such inquiry, one of course lacks a theory of M . To develop a theory of M , musn't one know what 10 Plato, Meno d [215]. 133 one is aiming to theorize about? But then mustn't one already have knowledge about M? How could this be so, if one lacks a theory of M? Meno's second query is how, if it is indeed possible to develop a theory of M , one is to evaluate whether a given theory is indeed a theory of M , rather than a theory about a distinct topic N? Of course, if one already possesses a theory T which one knows to be about M , then one could assess whether a distinct theory T ′ is about M by comparing the content of T ′ with that of T . But this of course only pushes the problem back: how did one come to know that the theory T is about M , rather than another topic? We can raise Meno's queries for the specific case of theories of truth. How is it possible to develop a theory of truth, absent such a theory? And how are we to know whether a given theory is really a theory of truth, rather than a theory of some other topic? Meno's first worry in this case is that it's not clear how one could begin to theorize about truth without already enjoying knowledge of truth. A natural response is that theoretical inquiry into M need not be guided by antecedent knowledge of M , only by antecedent beliefs that one has about M . Indeed, philosophers are very familiar with just this practice. A standard method for inquiring into a topic of philosophical interest, whether it be moral goodness, modality, epistemic justification, or etc., is to determine inter alia what pretheoretical beliefs, as we call them, one has about that topic. We typically elicit these beliefs by considering 134 relevant thought experiments. In the course of inquiry, one may find reason to revise certain of these beliefs so as to secure significant virtues for one's theory. Yet the initial mass of beliefs is crucially important–it serves, so to speak, as one's epistemic jumping off point. This methodology is in keeping with a philosophical programme known as the Canberra Plan, whose representatives include David Lewis [161], Frank Jackson [136], and Michael Smith [246].11 Canberra Planners propose that in developing philosophical theories, we should begin by drawing upon our pretheoretical beliefs about the topic of interest. These beliefs are often referred to as the platitudes about this topic. So our response to Meno's first query is that in developing a theory of truth, one ought to be guided inter alia by the platitudes about truth–the alethic platitudes provide an epistemic jumping off point for theories of truth. Meno's second query in this case is how we are to know whether a theory that bills itself as a theory of truth is, in fact, a theory of truth. Lynch has shown that the alethic platitudes can also be of service here. Lynch draws a distinction between two tiers of alethic platitudes–the 'core' alethic platitudes and the secondary, or peripheral, alethic platitudes. The core platitudes, which are meant to include (Objectivity) above, are those platitudes about truth that enjoy the most historical prominence in truth theory, while the peripheral platitudes 11 For an excellent discussion of the Canberra Plan, see Nolan [195]. 135 enjoy less historical prominence. In assessing whether a theory is a theory of truth, Lynch says, we should draw particularly upon the core platitudes. A theory T qualifies as a theory of truth iff for every core platitude π, T either (i) substantiates π, by explaining why π is true or (ii) explains π away, by explaining why π appears to be true, but is, in fact, untrue. The latter option would, of course, need to be taken only with great caution, since a core platitude would be a claim about truth that "cannot be denied without significant theoretical consequence and loss of plausibility. . .And denying many or all would mean that, at the very least, other users of the concept [truth] would be justified [in] taking you to be changing the subject [178, pp. 24-5]." So we can use the alethic platitudes to address Meno-like concerns for theories of truth. In what follows, we'll focus particularly upon the use of the platitudes in assessing theories as to whether they qualify as theories of truth. We'll focus, that is, upon the following feature that the core alethic platitudes are meant to have: • (F1) A theory T is a theory of truth iff (i) for every core alethic platitude π, T either (a) substantiates π, by explaining why π is true or (b) explains π away, by explaining why π appears to be true, but is, in fact, untrue and (ii) it is not the case that T explains away most of the core alethic platitudes. Truth theorists have long had the ambition of providing a comprehensive analysis of the ordinary concept truth and many such proposals have been put 136 forward. Most of these proposals have been reductive, in the sense that the aim of their advocates is to comprehensively analyze truth in a way that does not in its turn invoke the concept that they are trying to analyze. This reductive project has met with little success, which is what leads Davidson and Patterson to wonder whether truth might not be a bedrock concept that, as such, is simply insusceptible to reductive analysis. A natural worry for such primitivist proposals is that they seem to be conversation-stoppers. If truth constitutes conceptual bedrock, then when we reach truth, our spade is turned. So mustn't we abandon our ambitions to offer an informative, comprehensive analysis of truth? But Crispin Wright has pointed out that although reductive analysis may prove ineffectual here, analysis of truth as such may still be a healthy prospect [279, p. 128]: [T]he right thing to think about the quest for an analysis of the concept of truth might very well be that what the philosopher should do is to give a sensitive description of its constitutive connections with other concepts, which, when done sufficiently well and in a properly elaborated way, will identify that concept, or capture its conceptual essence, in an essentially relational or 'networking' way. Wright's proposal is that an analysis of truth should take the form of a comprehensive network the nodes of which are further concepts to which truth is 137 constitutively related. So rather than reducing truth to further concepts which one can grasp independently of one's grasp of truth, the aim of a network analysis of truth is to articulate the constitutive relations in which truth stands to the other nodes in the network. As Strawson [257, p. 21] points out, network analysis can thus be fairly thought of as a kind of 'connective analysis.' The questions for the networker then become: how are we to determine to which other concepts truth is constitutively related and how are we to determine in which relations truth stands to these concepts? Wright's proposal is that we should rely here upon the alethic platitudes. The alethic platitudes codify our pretheoretical beliefs about truth. So the nodes for our network analysis will be the concepts that the alethic platitudes invoke and the constitutive relations linking these concepts will be the relations in which the platitudes take them to stand. Our network analysis of truth, then, should in the end deliver up two crucial pieces of information: (i) which further concepts one must possess to possess truth and (ii) the relations in which truth constitutively stands to these concepts. Wright's proposal, then, is that the alethic platitudes have the following feature: • (F2) The alethic platitudes collectively specify truth's conceptual essence– the relations in which truth constitutively stands to other concepts. 138 4.2.2 The need for neutrality So the alethic platitudes afford avenues for addressing several central problems in truth theory. But this brings up a basic question: how are we to know whether a claim about truth qualifies as a platitude about truth? Cory Wright [211, § 4.3], [280] has aptly called this the criteria problem. Indeed, the problem is to articulate the criteria that a claim about truth must satisfy to be a platitude about truth. Absent such a set of criteria, any mention of the 'alethic platitudes' is merely an allusion to an underspecified set of claims. What I suggest is that we adopt a pragmatic approach to the criteria problem. When we introduce a collection of so-called platitudes about truth, our ultimate aim is use those platitudes to attain certain theoretical ends. We want inter alia to develop theories of truth, to assess theories that are advertised as theories of truth, and to develop a network analysis of the concept truth. So the ur-criteria that a claim must satisfy to be an alethic platitude are that: • (C1) It codifies a pretheoretical belief that cognizers have about truth; • (C2) It is a claim that any theory of truth must either explain or explain away (with the Lynchian proviso in (F1)); and • (C3) It partially specifies truth's conceptual essence (and the collection of alethic platitudes fully specifies truth's conceptual essence). In other words, the suggestion is that in thinking about what the alethic 139 platitudes must be like, we should think about what the alethic platitudes are meant to do. When we approach the criteria problem in this way, we come to see that in addition to (C1)-(C3), a claim about truth qualifies as an alethic platitude only if it satisfies a further criterion: • (C4) It is highly neutral as to what kinds of entity are capable of bearing truth. For convenience, let us call the issue as to what kinds of entity can bear truth the truth-bearer-kind issue. Suppose that we didn't impose (C4) as a criterion for being an alethic platitude, so that we allowed for the possibility that the platitudes are highly committal on the truth-bearer-kind issue. Suppose, for instance, that the alethic platitudes carried commitment to propositions being among the bearers of truth. It would then follow from the fact that the platitudes satisfy (C2) that a putative truth theory which took, say, indicative sentence-tokens to be the sole truth-bearers probably doesn't even qualify as a theory of truth! This is a very implausible result–consider, for instance, the contributions made by Sher's correspondence pluralism [239], [240], [241], [243], [244] and Fieldian and Quinean disquotationalism [100], [222], all of which deny that propositions are among the bearers of truth. Similar considerations would hold if the platitudes carried commitment to indicative sentence-tokens, assertions, judgments, or any other kind of entity being truth-bearers. For each such kind of entity, it's not difficult to locate or imagine a theory which denies that entities of that kind are 140 truth-bearers but which nevertheless strikes us as a bona fide theory of truth– albeit one that takes a stand on the truth-bearer-kind issue. An additional reason that the alethic platitudes should be highly neutral on the truth-bearer kind issue is that if they were committal on this score, they would generate problematic possession-conditions for truth. Suppose that the platitudes carried commitment to entities of a particular kind K being truthbearers, e.g. propositions, assertions, beliefs, or theories. A network analysis of truth resting upon the platitudes would then have it that truth is constitutively related to the concept of K's. This network analysis would thus entail that any cognizer possessing truth also possesses the concept of K's. The trouble, however, is that it is conceivable that a cognizer lacks concepts of any particular kind of truth-bearer while possessing certain rationally supported discriminative capacities, their possession of which would make it unacceptably arbitrary to deny that they possess truth. Let us stipulate that our cognizer S lacks concepts of any particular kind of truth-bearer. S possesses, however, the concept T, associated with which is the following distinctive condition: • (1) For all x: x is true iff x represents that p and p. For present purposes, T can be fleshed out using any concept of representation one likes (e.g. causal, teleofunctional, deflationary), as long as that concept isn't beholden to a particular kind of truth-bearer. What's important about T is 141 that its distinguishing condition (1) contains an objectual variable, rather than the more typical schematic letter standing in for a name of a particular kind of truth-bearer. For this reason, the content of T can be glossed as: something is true just when it represents that p and p. Because S possesses T, she enjoys certain discriminative capacities. If S were presented with a notecard telling her that a certain truth-bearer a (a proposition, perhaps–though S doesn't know that a is a proposition) represents that p and S happened to know whether p, S could competently classify a as 'true' or 'not true.' S, it is reasonable to say, is able to competently distribute truth-values across truth-bearers. S is also able to support her classification of a certain truth-bearer a as '(not) true' with a reason, namely that (i) a represents that p and (ii) (not-)p. It accordingly seems unacceptably arbitrary to deny that S possesses the concept truth. What this case suggests is that truth, although constitutively related to the rather coarse-grained concept bearer of truth, isn't constitutively related to concepts of any particular kind of truth-bearer. So given that they each have feature (C3), the alethic platitudes should be neutral on the truth-bearer-kind issue. Our pragmatic solution to the criteria problem thus has it that to qualify as an alethic platitude, a claim must satisfy all and only (C1)-(C4).12 In what 12 Notice that adopting this response to the criteria problem, we obviate Lynch's distinction between core and peripheral platitudes. 142 follows, it will prove useful to have a concrete list of alethic platitudes on hand. So I propose that we take the following three claims to be our alethic platitudes (these should be interpreted as closed sentences, not as schemas, a point that will be especially relevant in § 4.2.3): • (Reality) A truth-bearer is true iff it 'tells it like it is,' 'agrees with reality,' or 'corresponds to the facts' • (Covariance) The truth of a truth-bearer (i.e. whether a given truth-bearer is true) covaries with a distinct state(s) of the world 'determined' by that truth-bearer (that is: a given truth-bearer x is true iff the world is, or fails to be, in a distinct state(s) S which is (are) somehow determined by x) • (Inquiry) If a given truth-bearer is true, then it is ipso facto correct, to some extent, to endorse that truth-bearer when engaging in inquiry. This collection of alethic platitudes enjoys two particularly important virtues. Its constituent claims are highly similar to other claims that have been classified in the literature as platitudes about truth.13 Secondly, unlike many of the putative 13 See Edwards [87, p. 33]; Lynch [175, pp. 8-9, 12]; Pedersen [205]; Pedersen and C.D. Wright [210]; Vision [264, p. 33]; and Wright [274]; [276, p. 208]. Vision [264, p. 116] suggests that a claim similar to (Covariance) captures the core thought behind the various 'truth schemas,' including (PT) below. Hornsby [125, p. 7] tentatively takes it to be a platitude that "true sentences say how things are." And J.L. Austin [11, p. 115] takes it to be a truism that statements are true when they correspond to the facts. 143 platitudes proposed to date (e.g. Lynch's (Objectivity)), these three claims maintain the desired neutrality on the truth-bearer-kind issue. Accordingly, I propose that we call them the neutral platitudes. 4.2.3 Alethic properties and platitude conformity Thesis (MAP?3) of moderate pluralism states that for P to be an alethic property is for at least some instances of P to conform to the alethic platitudes. The intuitive thought is that alethic properties are those properties which at least sometimes behave as we pretheoretically expect truth to behave. But what, precisely, does this come to? What, exactly, is it for an instance of a property to conform to the alethic platitudes? I would also point to the literature on whether deflationary truth theories can accommodate the so-called correspondence intuition. The pretheoretical intuition here is the intuition that the truth of truth-bearers is explained by their relations to their truthmakers, or at least by the existence of their truthmakers. And this intuition entails, though it isn't entailed by, the covariance claim codified in (Covariance). Discussion of the correspondence intuition and its ramifications for deflationism include Douven and Hindriks [81]; Horwich [131, ch. 7], [133, ch. 14]; Stoljar and Damnjanovic [254, § 7.2]; and Wright [274, ch. 1, § IV]. Additionally, I take (Covariance) to capture the idea behind Aristotle's famous definition of truth (Metaphysics Γ, 7, 10011b, 26-8: To say of what is that it not, or of what is not that it is, is false, while to say of what is that it is, or of what is not that it is not, is true. 144 Doug Edwards [87] points out that the notion of platitude conformity is particularly troublesome for moderate pluralists.14 Lynch, for instance, advances a functionalist understanding of platitude conformity. Lynch takes the alethic platitudes to collectively specify a certain functional role (the 'truth role') that is occupied by both truth and the domain-specific alethic properties. The idea is that both truth and the domain-specific alethic properties are properties that conform to the 'job description' of truth collectively specified by the alethic platitudes.15 But Edwards wonders whether the job description of truth can really be the same as that of the domain-specific alethic properties. Isn't it a basic contention of moderate pluralism that whereas truth is the sole property that is 'truth-like,' no matter the domain to which its bearer belongs, the domain-specific alethic properties are 'truth-like' only when instantiated by propositions belonging to certain domains? How, then, could the domain-specific alethic properties satisfy the 'job description' specified by the alethic platitudes, if those platitudes aren't themselves explicitly relativized to a certain proper subset of the class of domains? But if the alethic platitudes are so relativized, Edwards asks, are they really platitudes about truth? Such relativized 'platitudes' would carry commitment to the theoretical construct domain. And as we know, this regimented, theoretical notion, in contrast to the ubiquitous, rough-and-ready notion of a 're14 Cf. David [62, §§ 2, 5]. 15 Though Lynch takes truth to play the truth role essentially, whereas the domain-specific alethic properties play the truth role only accidentally [175, p. 74-8], [178, p. 31]. 145 gion/sector/field of discourse,' is anything but uncontroversial. Thus if the alethic platitudes were committed to such a notion, then they would artificially rule out certain theories as not really being theories of truth. To escape this dilemma, Edwards contends, we should posit two sets of claims. What is distinctive about truth is that it conforms to the alethic platitudes, which are unrelativized. The domain-specific alethic properties, by contrast, conform only to weakenings of the alethic platitudes wherein they are relativized to particular domains.16 Once it is suitably clarified, (MAP?3) offers a way to slip through the horns of Edwards' dilemma. It offers an economical understanding of platitude conformity according to which we need only one set of claims, namely the alethic platitudes themselves, to identify all of the alethic properties. Let a property-instance (sometimes called a 'trope') consist in an individual a's instantiating a property P.17 Both my coffee table and a pen lying on it might 16 Edwards [87, § 4.4] calls the domain-specific alethic properties the 'truth-determining' properties. His solution is echoed by Pedersen and C.D. Wright [210, p. 92]. 17 Tropes are also standardly taken to be abstract particulars. I refrain from using the 'trope' label as I maintain neutrality on debates as to the nature of properties between e.g. trope theorists and realists about universals. Advocates of every theory of properties grant that properties have instances. What they differ over is the nature of property-instances–realists take property-instances to consist in the instantiation of universals, whereas trope theorists just take property-instances to just be properties themselves. For very helpful discussion of these issues, see Edwards [91] and Maurin [183]. 146 be black. We can capture this by saying that there are two instances of blackness, one consisting in my coffee table's instantiating blackness and the other consisting in the pen's instantiating blackness. To clean up (MAP?3), what we need is the notion of a property-instance satisfying an open sentence that contains an objectual variable x and a secondorder, property variable F (and no other free variables). We can represent a property-instance as a pair <a, P> whose members are an individual a and the property P that a instantiates. We'll then have it that a property-instance <a, P> satisfies '. . .x. . .F . . .' iff . . .a. . .P. . .. The neutral platitudes are closed sentences. This is important because presumably, neither open sentences nor schemas express propositions/make claims. But the alethic platitudes are meant to codify pretheoretical beliefs that we have about truth. If they are not closed sentences, then it is difficult to see how they could do so.18 So we should take the logical form of each of the neutral platitudes to be: 'For all x: if x is a truth-bearer, then. . ..' Call the mentioned universal quantifier the dominant quantifier of a given neutral platitude. Since our key notion is that of a property-instance satisfying an open sentence, we need a procedure for obtaining an appropriate open sentence from the neutral platitudes. This procedure has three steps: (i) remove the dominant quan18 Marian David stresses a related point [62, p. 45] in a very helpful, discussion of Lynch's manifestation functionalism. 147 tifier from each neutral platitude; (ii) replace 'true' in each neutral platitude with a property variable F and (iii) construct the needed conditional, the consequent of which is the conjunction of the open sentences obtained in (i) and (ii). We can call this conditional the open counterpart of the neutral platitudes. We then have the following cleaned-up definition of 'alethic property:'19 • (MAP3) P is an alethic property =Df at least some instances of P conform to the alethic platitudes, i.e. at least one instance <a, P> of P satisfies the open counterpart of the neutral platitudes:20 19 Thanks to Crispin Wright for prompting me to reflect further upon this definition. P's conforming to the alethic principles can be harmlessly described, following Lynch [175, pp. 71-3], as P's 'playing the truth-role.' The important detail in this connection is that to articulate the notion of conformity to the alethic principles, we need only appeal to the notion of satisfactionit isn't necessary to quantify over an entity called the 'truth-role.' Indeed, Lynch may not intend to quantify over such an entity. He suggests [175, pp. 71-2] that the notion of 'playing a role' is metaphorical and also clarifies that "[t]o play a functional role, in the sense intended here, is to satisfy a job description." So I suspect that for Lynch, talk of the 'truthrole' is an expository convenience rather than language carrying serious ontological commitment. Since it can easily seem otherwise, I find it preferable to speak instead of conformity with the alethic principles, thus avoiding the appearance of commitment to a 'role' that these principles specify. 20 Note that in constructing the open counterpart of the neutral platitudes, we don't prefix a quantifier to the second-order variable. For this reason, our procedure is distinct from Ramsification, which is integral to second-order functionalism (see Wright [280] and Lynch [172] for discussion of potential epistemic circularity in Ramsification, when used by second-order 148 If x is a truth-bearer, then (i) x is F iff x 'tells it like it is,' 'agrees with reality,' or 'corresponds to the facts;' (ii) whether x is F (i.e. x's instantiation of F ) covaries with a distinct state(s) of the world 'determined' by x; and (iii) if x is F , then it is ipso facto correct, to some extent, to endorse x when engaging in inquiry. (MAP3) shows how to slip through Edwards' dilemma. Recall how we've defined the notions of a domain-specific and a general alethic property: • P is a domain-specific alethic property =Df – (DS(i)) Only some possible instances of P conform to the alethic platitudes; or – (DS(ii)) Every possible instance of P conforms to the alethic platitudes, but P is plausibly assigned as an alethic property to only certain domains. • P is a general alethic property =Df – (Gen(i)) Every possible instance of P conforms to the alethic platitudes and functionalists to construct the truth-role). 149 – (Gen(ii)) P isn't plausibly assigned as an alethic property to only certain domains. We don't relativize the alethic platitudes to particular domains. Rather, we take the conformity of P to the neutral platitudes to consist in at least some instances of P satisfying the open counterpart of the neutral platitudes. This means that the putative general property truth, as well as the domain-specific alethic properties, qualify as alethic properties in virtue of meeting a common condition. Yet the domain-specific alethic properties qualify as domain-specific alethic properties because they satisfy (DS(i))-(DS(ii)), whereas truth qualifies as a general alethic property because it satisfies (Gen(i))-(Gen(ii)). We hereby capture the moderate pluralist's distinction between truth and the domain-specific alethic properties using only the unrelativized neutral platitudes. (MAP3) diverges from the account of platitude conformity recently advanced by Wright [279, § 5]. Wright takes the dominant quantifiers of the alethic platitudes to be universal, propositional quantifiers, in contrast to our universal, objectual quantifiers. Wright also offers a path out of Edwards' dilemma. He proposes to underwrite the distinction between truth and the domain-specific alethic properties by varying the range of the dominant propositional quantifiers of the platitudes. Let D be the class of all domains. Call a set of putative alethic platitudes the range of whose dominant quantifiers is D ⊂ D the D-restriction of these putative platitudes. Call the result of replacing each occurrence of 'true' in a set 150 of putative alethic platitudes with a property variable F (and performing no other variable replacements) their partially open counterpart. Wright's proposal is then that P is a domain-specific alethic property iff (i) P satisfies some D-restriction of the partially open counterpart of the alethic platitudes and (ii) P satisfies the partially open counterpart of the alethic platitudes only if it is D-restricted. Truth, by contrast, will be the sole property that satisfies the partially open counterpart of the alethic platitudes when their dominant quantifiers are allowed to range over the class of all propositions. My major concern with Wright's proposal is that in taking the dominant quantifiers of the alethic platitudes to be propositional, it fails to preserve the neutrality on the truth-bearer-kind issue which we know is highly desirable. Wright's proposal could be modified to take the platitudes' dominant quantifiers to be objectual, rather than propositional. Call this the objectual Wright proposal and, for the sake of concreteness, suppose that the proposal employs the neutral platitudes. According to the objectual Wright proposal: • (O-Wright) P is an alethic property =Df either (i) P satisfies the partially open counterpart of the unrestricted neutral platitudes or (ii) P satisfies some D-restriction of the neutral platitudes' partially open counterpart, but not the partially open counterpart of the unrestricted neutral platitudes. Truth will be the sole property that meets condition (i), whereas the domainspecific alethic properties will each meet condition (ii). 151 The objectual Wright proposal is elegant and I'm sympathetic towards it. (MAP3), however, provides a more straightforward response to a basic problem confronting alethic pluralism, and I prefer it over the objectual Wright proposal for this reason. This is the problem of accounting for the apparent unity exhibited by truth, given the diversity in truth posited by alethic pluralism.21 The problem of truth's unity has two basic faces. The first is the problem of explaining why the alethic properties form a unified–that is, a highly non-miscellaneous–class. The class of trout-turkeys, for instance, is a rather miscellaneous, disunified class. A trout-turkey is something that is either a trout or a turkey. The members of the class of trout-turkeys thus share at most the disjunctive feature being a trout or a turkey. For this reason, we don't take the class of trout-turkeys to be a very significant class–it's a mere hodgepodge. The challenge for the alethic pluralist is to explain why the class of alethic properties isn't a mere hodgepodge–why it is highly non-miscellaneous. We'll address the second face of the problem of truth's unity in § 4.9.2. (MAP3) offers a simple response to the first face of the problem of truth's unity. The alethic properties form a unified class because they share a common feature–they all have instances that conform to the alethic platitudes. The objectual Wright proposal takes the class of alethic properties to be more miscellaneous, since each alethic property shares, at most, the disjunctive feature detailed in (O21 See especially Lynch [175, Introduction, ch. 5] and Sher [239]; [240]; [243]; [244]. 152 Wright). So (MAP3) is preferable to the objectual Wright proposal on this score. (MAP3) therefore offers a definition of 'alethic property' that escapes Edwards' dilemma while avoiding the problems affecting Wright's account of the alethic properties and the variant of that account that employs objectual quantification. 4.2.4 Overgeneration? We've now articulated a collection of alethic platitudes, the neutral platitudes, and indicated how we can draw upon the neutral platitudes in understanding what it is for properties to qualify as alethic. We'll shortly be turning from these more general topics back to moderate pluralism, at which point we'll ask, given our reflections upon the former, whether moderate pluralism is a stable position. Before doing so, I'd like to address two concerns against the neutral platitudes that might be thought especially pressing. It might be worried, first, that given their high degree of neutrality on the truth-bearer-kind issue, the neutral platitudes drastically overgenerate kinds of truth-bearer.22 This concern is similar to an objection raised by Anil Gupta [117, pp. 363-4] against Horwich's position, alethic minimalism. According to alethic minimalism (which Horwich calls the 'minimal conception of truth') the so-called minimal theory of truth contains all of the most basic facts about truth. The minimal theory of truth, says Horwich, consists of the infinite class of instances 22 Thanks to Carl Baker and Cory Wright for pressing this concern. 153 of the following schema: • (PT) 〈p〉 is true iff p. Gupta criticizes alethic minimalists for failing to rule out the possibility that the Moon is true, given that the minimal theory itself offers no solution to the truth-bearer-kind issue. True enough, each instance of the minimal theory puts forward putative truth-conditions for a proposition, but what Gupta points out is that no class of such instances, no matter how large, entails that any proposition is, in fact, true. So no such class of instances of (PT) entails that propositions bear truth. Yet surely one of the basic facts about truth is that only certain kinds of entity (whatever they might be) can be true. This, then, is a basic fact about truth that is neither contained in nor derivable from the minimal theory of truth, contra alethic minimalism. However forceful one takes Gupta's objection against minimalism to be, it might be thought that in adopting the neutral platitudes as an epistemic jumping off point, we must grapple with a similar objection. One of the virtues of the neutral platitudes is that they invoke the general notion of a truth-bearer, rather than more specific notions of e.g. proposition, indicative sentence-token, judgment, or theory. The neutral platitudes are highly noncommittal on the truth-bearer-kind issue. But then the neutral platitudes fail to rule out certain wild possibilities, e.g. that blades of grass, or the Moon, are truth-bearers. Surely, the thought goes, we want our theory of truth to be strong enough to entail that these possibilities 154 don't obtain. And indeed we do want our theory of truth to do this. But what we must keep in mind is that the neutral platitudes are not themselves a complete theory of truth, they are the epistemic jumping off point for a theory of truth. The aim of our theory of truth, vis-à-vis the neutral platitudes, is to either explain or explain away each such platitude (and to not explain away all of them). So it's perfectly correct that the neutral platitudes are very neutral on the truth-bearer-kind issue– indeed, that's precisely the point. As we shall see, the theory of truth that they subserve will, by contrast, carry definite commitments on the truth-bearer-kind issue. But even before arriving at a full-blown theory of truth, we can meet the overgeneration worry by adding to the neutral platitudes a very widely held claim (a platitude, even) about truth-bearers. The neutral platitudes, together with this further platitude about truth-bearers, do provide reasons to deny that the Moon (blades of grass, and etc.) is a truth-bearer. Taken as a skeletal characterization of truth-bearers, the following claim is essentially uncontroversial:23 • (Bearer) Entities of kind K are truth-bearers only if some Ks can instantiate truth (are truth-apt). (Bearer), together with (Reality) and (Inquiry), delivers two reasons to exclude the Moon from the class of truth-bearers. From (Bearer) and (Reality), we 23 See e.g. David [60, § 2.1]. 155 can derive that Ks are truth-bearers only if Ks can 'tell it like it is,' 'agree with reality,' etc. But the Moon isn't a kind of thing that we intuitively regard as capable of 'telling it like it is' or 'agreeing with reality.' (Bearer) and (Reality) thus provide reason to deny that the Moon is a truth-bearer. From (Bearer) and (Inquiry), we can derive that Ks are truth-bearers only if there are Ks which it is correct, to some extent, to endorse when engaging in inquiry. But again, the Moon is not a kind of thing which we intuitively regard as being endorsable in inquiry, whether correctly or incorrectly. Were someone to say, 'I endorsed the Moon when engaging in inquiry,' we would either accuse them of a category mistake or charitably interpret them as claiming e.g. that they had discovered in the course of research that it is indeed the Moon, rather than Jupiter, that affects Earth's tides.24 So the neutral platitudes, together with a platitude about truth-bearers, are strong enough to stave off an overgeneration of truth-bearers. 4.2.5 Overly technical? It might also be worried that the neutral platitudes invoke rather technical notions such as 'truth-bearer,' 'correspondence to facts,' and 'determination of a state 24 Pairing (Covariance) with (Bearer) is somewhat trickier, since (Covariance) is highly noncommittal as to the sense in which a truth-bearer 'determines' a distinct state(s) of the world. But we've shown that (Reality) and (Inquiry), together with (Bearer), suffice to rebut the objection. 156 of the world.' Were we to read the neutral platitudes to an ordinary speaker and ask them whether these platitudes are true, they would presumably express puzzlement, owing to their lack of familiarity with such technical notions. But, the concern goes, how could the neutral platitudes really codify our pretheoretical beliefs about truth if ordinary speakers would have such a hard time understanding them?25 Here we should mark the distinction between beliefs that are held occurrently and those that are held tacitly. Following Lynch, we should take the neutral platitudes to codify beliefs that one who possesses the concept truth must hold tacitly, though not necessarily occurrently.26 To form a tacit belief about an entity e, it is plausibly necessary that one possesses a concept of entity e. But because the belief is tacit, it isn't necessary that one have facility with expressions in one's language that denote or express e.27 Intending to walk to the front door via the living room, a typical three-year-old child will, when approaching a coffee table that obstructs her path, alter her trajectory so as to avoid colliding with the table. We might explain this decision by hypothesizing that the child believes inter alia that the table is solid. If she does possess this belief, then she presumably possesses solidity. But the child may have yet to hear or use 'solidity' or 'solid.' In claiming that her belief is tacit, we mean to highlight the fact that although 25 Thanks to Doug Edwards for pressing this concern. 26 [175, pp. 7, 17]; [178, p. 23, 25]. 27 For helpful discussions of tacit belief, see Audi [10] and Lycan [166]. 157 she has never consciously attended to 〈the coffee table in my living room is solid〉, nor has she heard or used 'solid' or 'solidity,' were she apprised of the meaning of 'solid,' she would–with little, if any, hesitation–respond 'Yes' when asked whether the table is solid. Most ordinary speakers only tacitly believe the neutral platitudes and accordingly lack facility with technical vocabulary such as 'truth-bearer' and 'correspondence to fact.' But if, after being apprised of the meanings of 'truth-bearer' and 'correspondence to fact,' an ordinary speaker were asked, 'Is it the case that true (but not false) truth-bearers correspond to the facts?' I predict that they would–with little, if any, hesitation–respond 'Yes, of course.' The important upshot is that in classifying the neutral platitudes as platitudes about truth, we needn't take them to be occurrent beliefs of ordinary speakers, whose content they consciously endorse. It is far more plausible to think of the neutral platitudes as tacit beliefs of ordinary speakers. These tacit beliefs about truth, no doubt, substantially influence their evaluation of truth-bearers as true or false. Truth theorists seeking to provide an account of truth's nature accordingly have before them the task of discerning these tacit beliefs and the important roles that they play in our cognitive lives. Now that we have a better grasp of two central elements of moderate pluralism–the alethic platitudes and the notion of an alethic property–we are in a position to assess moderate pluralism for stability. 158 4.3 The instability of moderate pluralism Moderate pluralists claim that truth is both 'one and many.' Though they posit a plurality of domain-specific alethic properties, moderate pluralists concede to alethic monists that there is only one general alethic property truth. The view is, in this way, meant to capture core insights of both monism and pluralism. Unfortunately, however, moderate pluralism is infected with inextricable instability.28 Moderate pluralists take propositions to be the primary bearers of truth. What are the truth-conditions of propositions? Quite plausbily, they are codified in the following schema:29 • (PT) 〈p〉 is true iff p. Call the property whose instantiation-conditions are given in (PT) propositiontruth. Moderate pluralists are committed, then, to positing proposition-truth.30 28 The argument to follow is inspired by an argument developed by Pedersen [205, § 3]; (with Edwards) [207, pp. 220-22]; and (with C.D. Wright) [210, § 5.3, appendices A and B] on behalf of alethic disjunctivism. Since the argument to follow doesn't specifically invoke the machinery of disjunctivism, it sidesteps the concerns for Pedersen's argument raised by Lynch [176, pp. 263-4]. 29 In what follows, we will prescind from complications introduced by the semantic paradoxes. In the end, a complete theory of truth must be responsive to the paradoxes, but this task will have to wait for another day. 30 To say that proposition-truth is a property whose instantiation-conditions are given in (PT) isn't to presuppose that proposition-truth is a sparse property. We'll address this issue in § 4.5. 159 Moderate pluralists have a straightforward reason to posit indicative sentencetokens: it seems manifest that they exist. We appear to encounter them on a regular basis in both speech and writing, so much so that it wouldn't seem out of place to point to this page and affirm, in a Moorean spirit, 'Here's one indicative sentence-token and here's another.' And given that indicative sentence-tokens (in contrast to indicative sentence-types) are concrete–they are composed of e.g. graphite or ink marks or emitted sounds–their enjoy quite strong ontological credentials. If both indicative sentence-tokens and propositions exist, then it is essentially uncontroversial (prescinding from the precise nature of the expression relation) that indicative sentence-tokens express propositions. Indeed, one of the standard roles accorded to propositions is that they serve as the contents of certain sentence-tokens. Given this, moderate pluralists are committed to positing a further property, the instantiation-conditions of which are:31 • (ST) Sentence-token 'S' is true (in L and in the context of use c) iff 'S' 31 It might be worried that (ST) makes use of propositional quantification, which has proven controversial in truth theory. There are three ways that I might mitigate this concern: (i) by interpreting (ST) in terms of familiar objectual quantification; (ii) by interpreting (ST) in terms of propositional quantification, characterized inferentially (as in Hill [119]); or (iii) by interpreting (ST) in terms of objectual, propositional quantification (as in Künne [156]). For present purposes, I am neutral as between these three options. If pressed, I would say that there is no deep difference between (i) and (iii) and that I most prefer either of these. 160 expresses a 〈p〉 (in L and c) and 〈p〉 is proposition-true. Without prejudging any issues of substance, we can call this property sentence- (token-)truth. The trouble is that both proposition-truth and sentence-truth qualify as general alethic properties. Both behave, that is, just as moderate pluralists claim that truth behaves. A general alethic property is a property: • (Gen(i)) Every possible instance of which conforms to the alethic platitudes and • (Gen(ii)) Which isn't plausibly assigned as an alethic property to only certain domains. Proposition-truth and sentence-truth each satisfy both of these conditions. Consider (Gen(i)) first. We can show that proposition-truth and sentence-truth satisfy this condition by showing that the property-instances <〈p〉, propositiontruth> and <S, sentence-truth> satisfy the open counterpart of the neutral platitudes, no matter what 〈p〉 and 'S' happen to be. Suppose that 〈p〉 is propositiontrue. By (PT), we can infer that p. So, 〈p〉 'tells it like it is,' etc. If 〈p〉 doesn't 'tell it like it is,' etc., we can infer that not-p and, via (PT), that 〈p〉 isn't propositiontrue. So 〈p〉 is proposition-true iff 〈p〉 'tells it like it is,' etc. Moreover, 〈p〉's instantiation of proposition-truth covaries with a distinct state(s) of the world that is determined, in a certain sense, by 〈p〉. 〈p〉 is true iff p. Presumably, that 161 p, rather than some other state(s) q, is necessary and sufficient for the propositiontruth of 〈p〉 because of a fact about 〈p〉–that 〈p〉 is somehow 'about' or 'represents' the state(s) that p. Finally, given that p, it is ipso facto correct, to some extent, to endorse 〈p〉 when engaging in inquiry. Even if Jones possesses no justification for 〈p〉 and fails to know that p, if 〈p〉 is proposition-true, then Jones seems ipso facto to act correctly, to some extent, in endorsing (e.g. asserting or believing) 〈p〉. Now suppose that 'S' is sentence-true. Then 'S' expresses a proposition-true proposition 〈p〉. Given that 〈p〉 is proposition-true, we can infer via (PT) that p. Since 'S' expresses 〈p〉 and p, 'S' 'tells it like it is,' etc.32 If 'S' doesn't 'tell it like it is,' etc., then either (i) 'S' expresses no proposition or (ii) 'S' expresses 〈p〉, but 〈p〉 fails to be proposition-true. If 'S' expresses no proposition, then by (ST), 'S' isn't sentence-true. If 'S' expresses a proposition that isn't proposition true, then likewise, 'S' isn't sentence-true. So 'S' is sentence-true iff 'S' 'tells it like it is,' etc.33 Moreover, 'S"s instantiation of sentence-truth covaries with a distinct state(s) of the world that is determined, in a certain sense, by 'S.' By (ST) and 32 Of course, 'S' 'tells it like it is,' etc. because 'S' expresses 〈p〉 and 〈p〉 'tells it like it is,' etc. It might be worried that sentence-truth is, in this way, a merely 'derivative' alethic property. But as I'll explain in § 4.4, I don't think that this a serious concern. 33 The important detail that's brought out here is that our pretheoretical notions of 'telling it like it is,' 'agreeing with the facts,' and 'corresponding to reality' are general enough to apply both to proposition-truth propositions and to sentence-true sentence-tokens. 162 (PT), 'S' is true iff p. Presumably, that p, rather than some other state(s) q, is necessary and sufficient for the sentence-truth of 'S' because of a certain fact about 'S'–that 'S' expresses 〈p〉, which is proposition-true iff p. Finally, if 'S' expresses a proposition-true proposition, it is ipso facto correct, to some extent, to endorse 'S' when engaging in inquiry. Even if Jones possesses no justification for 〈p〉 and fails to know that p, if 〈p〉 is proposition-true, then Jones seems ipso facto to act correctly, to some extent, in endorsing a sentence that expresses 〈p〉 (e.g. by using the sentence to perform an assertion that p). So proposition-truth and sentence-truth both satisfy condition (Gen(i)). Moreover, both proposition-truth and sentence-truth satisfy condition (Gen(ii)). Proposition-truth is instantiable by propositions belonging to any domain, given that (PT) makes no reference to the domain-membership of 〈p〉. There is also no apparent reason that proposition-truth should be assigned as an alethic property to, say, the physical domain, but not to the moral or mathematical domains, nor vice versa. Every such domain is simply a class of propositions, all of which are apt for proposition-truth. Similarly, sentence-truth is instantiable by indicative sentence-tokens that express propositions, no matter the domains to which those propositions belong, since (ST) makes no reference to the domain-membership of 〈p〉. There is also no apparent reason that sentence-truth should be associated with, say, sentencetokens expressing propositions belonging to the physical domain, though not with 163 sentence-tokens expressing mathematical or moral propositions, nor vice versa. Every such sentence-token expresses a proposition that either is or fails to be proposition-true, meaning that the sentence-token is apt for sentence-truth. So both proposition-truth and sentence-truth thus qualify as general alethic properties, meaning that moderate pluralists are comittted to positing at least two general alethic properties. Moderate pluralists are also committed to positing truth, which was advertised as the one and only general alethic property. But then moderate pluralism is inherently unstable. Moderate pluralists are committed to positing truth, yet they are also committed to positing both proposition-truth and sentence-truth. Moderate pluralists are committed, that is, to both claiming and denying that truth exists. 4.4 Sentence-truth, proposition-truth, and 'real truth' In the remainder of the chapter, we'll consider five lines of response to the argument that we've just leveraged against moderate pluralism. The intent behind each of these lines of response is to put forward an account of truth that is rather similar to moderate pluralism but, unlike moderate pluralism itself, internally stable. What I'll argue is that one of these responses articulates a defensible and interesting successor to moderate pluralism, which I call minimal pluralism. In the final chapter, we'll turn to a more sustained examination of the implications of minimal pluralism. 164 We know that proposition-truth and sentence-truth each qualify as general alethic properties–they both behave as truth is meant to behave. But, moderate pluralists might fairly point out, describing the situation in this way obscures an important asymmetry. Part of the reason that sentence-truth qualifies as a general alethic property is that proposition-truth so qualifies–but not conversely. Proposition-truth, that is, qualifies as an alethic property all on its own. Why, then, can't the moderate pluralist insist that proposition-truth enjoys a privileged status that sentence-truth fails to enjoy?34 There are two things that might be meant by the claim here that propositiontruth enjoys a 'privileged status.' It might be thought that since sentence-truth is defined in terms of proposition-truth, though not vice versa, that sentence-truth, in contrast to proposition-truth, qualifies as an alethic property only in a manner of speaking. But this objection clearly rests upon an invalid form of inference: • (1?) P is a property of kind K, but not because P is defined in terms of a distinct K-property P′ • (2?) P′′ is only derivatively of kind K, i.e. P′′ is a K-property only because P′′ is defined in terms of P • (3?) Therefore: Whereas P is genuinely/really a K-property, P′′ isn't. It's easy to find counterexamples to this inference form. Consider the prop34 Thanks especially to Doug Edwards and Michael Lynch for pressing this concern. 165 erty of extrinsic value. Something is extrinsically valuable when it is suitably related (e.g. causally or constitutively) to something that is intrinsically valuable. Intrinsic value is a paradigm axiological, or value-related, property. We take extrinsic value to also be an axiological property because of the relation in which something that is extrinsically valuable must stand to something that is intrinsically valuable. Extrinsic value is an axiological property, that is, because for x to be extrinsically valuable is for x to stand in a suitable relation R to y, which instantiates intrinsic value. We thus take extrinsic value to be a 'derivatively axiological' property, whereas intrinsic value is a 'basically axiological' property. What we're not at all tempted to infer is that extrinsic value isn't 'really' an axiological property. Intrinsic and extrinsic value are both integral to the study of value and thus qualify as bona fide axiological properties. Basic and inferential doxastic justification, as detailed by foundationalist theories of epistemic justification, serve as an additional counterexample. According to epistemic foundationalism, both non-inferential and inferential justification are epistemic properties–they are both related to the acquisition of knowledge. Non-inferential justification is a 'basically epistemic' property, in that it is related to knowledge acquisition, but not because a non-inferentially justified belief b must stand in a suitable relation R to a distinct entity e that instantiates an epistemic property. By contrast, inferential justification is a 'derivatively epistemic' property, since b is inferentially justified iff b stands in a suitable inferential 166 relation to a distinct belief b′ that is non-inferentially justified. What foundationalists will deny is that because inferential justification is definable in terms of non-inferential justification, inferential justification isn't 'really' an epistemic property–both kinds of justification are integral to knowledge acquisition and thus qualify as bona fide epistemic properties. Sentence-truth is analogous to extrinsic value and inferential justification. We know that proposition-truth is a general alethic property, by the lights of moderate pluralism. Sentence-truth is the complex property expressing (in L) a proposition-true proposition 〈p〉. For a sentence-token 'S' to instantiate sentencetruth is for 'S' to stand in the expression relation to a proposition-true proposition 〈p〉. By contrast, according to (PT), a proposition-true proposition needn't be related to a distinct entity e that instantiates an alethic property. Sentencetruth is thus a derivatively general alethic property, whereas proposition-truth is a basically general alethic property. But why should it be any more tempting to infer that sentence-truth isn't really an alethic property than to infer that extrinsic value isn't really an axiological property or that inferential justification isn't really an epistemic property? So the thought that sentence-truth is somehow not 'really' an alethic property simply doesn't hold water. The moderate pluralist might grant this point–sentence-truth and propositiontruth are both general alethic properties, and that's a problem for the letter of moderate pluralism. But proposition-truth is a basically general alethic property, 167 whereas sentence-truth is a merely derivatively general alethic property. Isn't this reason enough to take proposition-truth to be the property that moderate pluralists should identify with truth? Why, that is, shouldn't the moderate pluralist hold that in addition to (Gen(i)) and (Gen(ii)), truth itself satisfies a further condition: • (Basic) Truth is the sole basically general alethic property? The trouble with this suggestion is that it should strike us as unacceptably arbitrary. Suppose that color scientists disover an intrinsic color property that a macroscopic object instantiates iff it reflects, independently of its relations to other macroscopic objects, light of a particular wavelength w. Call this property intrinsic blueness. After further research, the scientists discover that some macroscopic objects are not capable of instantiating intrinsic blueness, though they are capable of reflecting light of wavelength w if they are located within 1 meter of an intrinsically blue object. For some reason, being located near an intrinsically blue object alters the physical constitution of the latter objects in such a way that they are now able to reflect light of the target wavelength. The scientists call the property of reflecting light of wavelength w only when located within 1 meter of an intrinsically blue object extrinsic blueness. Question: Are extrinsically blue objects blue? I suspect that you will agree that they are, given that extrinsically blue objects enjoy the power that we associate with blueness–namely, being able to reflect light of the target wavelength w. Since both intrinsically and 168 extrinsically blue objects enjoy this power, the reasonable diagnosis is that both intrinsically and extrinsically blue objects are blue. It would be unacceptably arbitrary to exclude extrinsically blue objects from the class of blue objects–or, in other words, to say that intrinsic blueness is blueness itself, whereas extrinsic blueness is only an imposter. But the case of proposition-truth and sentence-truth is clearly very similar to that of intrinsic and extrinsic blueness. So the reasonable conclusion is that sentence-true sentence-tokens and proposition-true propositions are each and all true. Sentence-true sentence-tokens are really true, literally true, not merely true in a manner of speaking, just as extrinsically blue objects are really blue, really blue, literally blue, not merely blue in a manner of speaking. Sentencetrue sentence-tokens, no less than proposition-true propositions, conform to our pretheoretical understanding of what it is for a truth-bearer to be true. So just as it would be unacceptably arbitrary to identify intrinsic blueness with blueness, it would be unacceptably arbitrary to identify proposition-truth with truth. For similar reasons, it would be unacceptably arbitrary to identify sentence-truth with truth. It's worth stressing at this stage that sentence-truth and proposition-truth are distinct properties–neither can be reduced to the other. A sentence-token's being sentence-true partially consists in its expressing a proposition, whereas a proposition's being proposition-true doesn't consist in its expressing a proposi169 tion. This holds no matter how the expression relation is understood, e.g. along teleofunctional, inferentialist, causal-historical, or deflationary lines. In short, sentence-truth is more complex than proposition-truth. So sentence-truth can't be reduced to proposition truth. Likewise, of course, proposition-truth can't be reduced to sentence-truth. Since sentence-truth is defined in terms of propositiontruth, such a 'reduction' would be blatantly circular. Since they are distinct properties and since neither can be fairly identified with truth, the proper conclusion is that propositions can be proposition-true, indicative sentence-tokens can be sentence-true, and no truth-bearer can instantiate truth, for truth simply doesn't exist. 4.5 Miscellaneity: Proposition-truth, sentence-truth, and truth We've contended that moderate pluralists are committed to positing propositiontruth and sentence-truth. But this contention might seem too quick. It might be resisted by appealing to a highly influential distinction from the theory of properties. David Lewis [163] endorses class nominalism about properties, taking properties to just be classes. Class nominalism faces the concern that classes seem to be more abundant than properties. All that is needed for a class to exist is that its members exist.35 There is, then, a class of trout-turkeys, whose members are all and only those entities that are either a trout or a turkey. The class nominalist 35 Though a class is presumably a further entity, over and above the sum of its members. 170 is then forced to posit the disjunctive property being a trout-turkey, which looks to offend against scruples of ontological parsimony. Being sensitive to this problem, Lewis introduces a primitive notion of naturalness, taking some classes to be more natural than others. He also draws a related distinction between sparse and abundant properties. The maximally sparse properties, according to Lewis, are the perfectly natural classes, whereas the more abundant properties, e.g. being a trout-turkey, are the less natural classes. While Lewis takes the notion of naturalness to be primitive in the sense that it isn't analyzable, without remainder, into constituent notions,36 he offers heuristics that we can use to determine how natural a class is. A central such heuristic is the miscellaneity exhibited by a class–the more miscellaneous a class is, the less natural it is.37 The class of proposition-true propositions looks to be rather miscellaneous.38 Its members are all propositions, so perhaps it is not as miscellaneous as the class of trout-turkeys. But the instantiation-conditions for proposition-truth are: • (PT) 〈p〉 is true iff p. The class of proposition-true propositions thus presumably (and certainly, given minimalism about truth-aptness) contains propositions from very many different domains, e.g. 〈Penguins are flightless birds〉 and 〈Corporations should 36 Cf. § 2.2.3. 37 [164, pp. 59-60]. 38 This point is stressed by Jamin Asay [9], [8, pp. 116-18] and is alluded to by Edwards [89]. 171 be socially responsible〉. The proposition-truth of these respective propositions covaries with rather different states of the world, making the class itself look somewhat assorted. The class of sentence-true sentences also looks to be rather miscellaneous. The members of this class are all sentence-tokens, so perhaps it too isn't as miscellaneous as the class of trout-turkeys. But the members of this class express propositions from rather different domains and are, in turn, themselves associated with rather different domains.39 Moreover, the sentence-truth of the members of this class covaries, given (ST) and (PT), with rather different states of the world. Might the moderate pluralist endorse class nominalism but refuse, contra Lewis, to posit rather miscellaneous properties? Alternatively, might the moderate pluralist reject class nominalism (taking properties to be universals, perhaps) but refuse to posit properties whose extensions are highly miscellaneous? In endorsing either of these sparse conceptions of properties, the moderate pluralist could justifiably refuse to posit proposition-truth and sentence-truth. The trouble is that adopting such a sparse conception of properties would put the moderate pluralist in an untenable position. This is because the extension 39 For convenience, I speak of indicative sentence-tokens being 'associated' with domains. Propositions are taken, as in chapter 3, to literally be members of domains. A indicative sentence-token is then associated with domain D by expressing (in L) 〈p〉, which belongs to D. Whenever I wish to remain neutral as to which kind of truth-bearer is at issue, I speak neutrally of truth-bearers being associated with particular domains. 172 of truth (or alternatively, truth itself, if class nominalism is true) is rather miscellaneous. As (MAP6) codifies, the class of true propositions includes all and only those propositions that instantiate the domain-specific alethic properties assigned to the domains to which they belong. This class thus contains propositions from very many different domains. Moreover, the truth of these respective propositions covaries with their instantiation of rather different domain-specific alethic properties (e.g. correspondence and coherence). We can, in fact, prove two results which demonstrate that such a sparse conception on properties is closed to the moderate pluralist. We'll prove (i) that the class of truths is at least as miscellaneous as the class of proposition-true propositions and (ii) that the class of proposition-true propositions is at least as miscellaneous as the class of sentence-true sentences. We then see that were the moderate pluralist to refuse to posit either proposition-truth or sentence-truth due to their miscellaneity, or the miscellaneity of their extensions, they would commit to refusing to posit truth, thereby contradicting themselves. The proof to follow is somewhat involved and can be skipped without loss of continuity. We'll show first that the truths–the class of propositions that instantiate truth–would have to be at least as miscellaneous as the proposition-truths–the class of proposition-true propositions. We can abbreviate this claim as: Truths ≤M P-Truths. We'll then show that the sentence-truths–the class of sentence-true sentence-tokens–are at least as miscellaneous as the proposition-truths. 173 We'll begin by proving what we can call the Subset Principle, that subsets are at least as miscellaneous as their supersets: • (SP) For sets A and B, if A ⊆ B, then A ≤M B. If A ⊆ B, then either (i) A=B or (ii) A ⊂ B (A is a proper subset of B). Say that a set A is miscellaneous to degree n when A's members instance n kinds. We'll take the notion of kind as primitive, appealing to an intuitive notion according to which the class of trout-turkeys contains two kinds of entity: trouts and turkeys (assuming that there are no trout-turkey hybrids).40 If A=B, then obviously, A and B are miscellaneous to the same degree. Suppose, then, that A ⊂ B. There are then entities b1, . . . , bn that are in B, but not in A. For the sake of illustration, suppose that A is miscellaneous to degree 2–every member of A instances either kind K1 or kind K2. Each bi instances either K1, K2, or some distinct kind K3. If all of the bi instance either K1 or K2, then A and B are miscellaneous to the same degree, from which it follows that A ≤M B. If some of the bi instance kind K3, then since A ⊆ B, B is miscellaneous to degree m > n, from which it follows that A ≤M B. This suffices to prove the Subset Principle. 40 There are surely other renderings of miscellaneity that could be useful for certain theoretical purposes. The degree to which a set is miscellaneous might, for instance, be taken as a function not only of the number of kinds instanced by A's members, but also of whether those kinds are themselves unified under certain higher-order kinds. This notion could be used to capture the intuition that e.g. A = {a proton, a gluon, a positron} is less miscellaneous than B = {the Eiffel Tower, the number 16}. I leave such complexities aside here. 174 We can now prove that the truths are a subset of the proposition-truths. It will then follow from the Subset Principle that Truths ≤M P-Truths, which is what we wanted to show.41 The instantiation conditions for truth are: • (MAP6) If 〈p〉 ∈ D, then 〈p〉 instantiates truth iff 〈p〉 instantiates TD. Suppose that 〈p〉 ∈ D and that 〈p〉 instantiates truth. It follows by (MAP6) that 〈p〉 instantiates TD. TD is a domain-specific alethic property that is assigned to D. We thus know by (DS(i)) and (DS(ii)) (§ 4.1) that the instances of TD wherein TD is instantiated by a proposition in D satisfy the open counterpart of the neutral platitudes. Since 〈p〉 ∈ D, we know that <〈p〉, TD> satisfies the open counterpart of the neutral platitudes. Call the open sentence generated by removing the dominant quantifier of a given neutral platitude and substituting a property variable F for the occurrence of 'true' in that platitude the open counterpart of the platitude. <〈p〉, TD> thus satisfies the open counterpart of the (Covariance) platitude: • (CovarianceO) If x is a truth-bearer, then whether x is F (i.e. x's instantiation of F ) covaries with a distinct state of the world 'determined' by x. The state(s) of the world determined, in the target sense, by 〈p〉 is that p. So 〈p〉's instantiation of TD covaries with the worldly state that p. In other words, 41 Of course, the proof is self-evident if the class of truths is empty. For the sake of argument, we assume that it is non-empty. 175 〈p〉 instantiates TD iff p. Since we have it that 〈p〉 does, in fact, instantiate TD, we can infer that p. We can also infer, by (PT), that 〈p〉 is proposition-true. This shows that the truths are a subset of the proposition-truths. It therefore follows from the Subset Principle that Truths ≤M P-Truths. We'll finally show that the proposition-truths are at least as miscellaneous as the sentence-truths, which we'll abbreviate as: P-truths ≤M S-truths. We often speak as though sentences instance the same kinds as the propositions that they express. It's natural, for instance, to take 'Charlie is delicious' to be taste-related because it expresses 〈Charlie is delicious〉, which is itself taste-related. At the very least, sentences instance kinds that are counterparts of the kinds instanced by the propositions that they express–'Charlie is delicious' is a moral sentence at least in part because 〈Charlie is delicious〉 is a moral proposition. The kinds instanced by a indicative sentence-token 'S' that expresses proposition 〈p〉 (in L) are thus at least as numerous as those instanced by 〈p〉. Call this the Cardinality Principle. Now consider the class of sentence-truths and the class of proposition-truths that they express. Suppose that the P-truths are miscellaneous to degree n, i.e. that there are n kinds instanced by the P-truths. By the Cardinality Principle, the S-truths are miscellaneous to degree m ≤ n. That is, P-truths ≤M S-truths. We thus have it that Truths ≤M P-truths ≤M S-truths. Therefore, were the moderate pluralist to refuse to posit either or both proposition-truth and sentencetruth on the grounds that they, or their extensions, are highly miscellaneous, they 176 would be forced to refuse to posit truth. But then the moderate pluralist would invite into their views precisely the instability that they were trying to avoid. 4.6 Propositions and indicative sentence-tokens A third line of response would be to either deny that propositions exist or to deny that indicative sentence-tokens exist. If propositions don't exist, then no entity is proposition-true and no entity is sentence-true, given that only sentence-tokens which express proposition-true propositions are sentence-true. Likewise, if indicative sentence-tokens don't exist, then nothing is sentence-true, since sentencetruth is instantiable only by indicative sentence-tokens. Either of these strategies, then, would serve as a first step to constructing a stable descendant of moderate pluralism. But both come with serious costs. Were moderate pluralists to deny the existence of indicative sentence-tokens, they would thereby commit to a highly revisionary ontology. Indicative sentencetokens are also integral to truth-theoretic semantic theories, meaning that moderate pluralists would set themselves at odds with mainstream truth-conditional semantics were they to deny the existence of indicative sentence-tokens. This would undercut one of the most prominent objections leveled by moderate pluralists– specifically, by Lynch [175, ch. 6]–against deflationary theories of truth: that the latter, unlike moderate pluralism, are incompatible with truth-conditional theories 177 of meaning and content.42 Alternatively, moderate pluralists might posit indicative sentence-tokens, but refuse to posit propositions, offering in turn a non-propositional theory of meaning. Doing without propositions would mean abandoning the natural solution to the problem of domain-individuation that we developed in chapter 3. Were we to work instead with an ontology that contains indicative sentence-tokens but not propositions, we would presumably attempt instead to individuate domains in terms of indicative sentence-tokens. But this is a dicey option. The domainmembership of sentence-tokens would be rather less stable than that of propositions, meaning that individuation conditions for domains invoking the former will be considerably messier than the more familiar, proposition-theoretic individuation conditions. Consider, for instance, the written, English sentence-token 'There are ten chairs in the dining room.' I might use this sentence-token to perform assertions in more than one context. In the first context, you and I are setting up for a dinner party and I've lost my voice. To make the conversation run more smoothly, I've tried to anticipate the questions you'll ask and have written responses on slips of paper, which I display in response to your questions. While I'm setting out the cutlery in the dining room, you ask me from the kitchen, 'Have we set out the 42 This isn't to contend, of course, that this objection to deflationism is cogent, only that it is a central objection raised against deflationism by moderate pluralists that would be undercut, were moderate pluralists to refuse to posit indicative sentence-tokens. 178 chairs?' I walk into the kitchen and show you the slip of paper written on which is 'There are ten chairs in the dining room.' In the second context, you and I are seated at the dining room table after the party, taking a rest before clearing the place settings. You've now had a few drinks and because you've recently been converted to mathematical nominalism, you're insisting intently that numbers simply can't exist. Since I'm rather tired, I've let you go on for a while without responding. But when your monologue reaches a fever pitch, I become frustrated and hold up the slip of paper written on which is 'There are ten chairs in the dining room.'43 As used in the first context, in which the chairs are highly salient, it is natural to associate our sentence-token with the domain of discourse about middlesized, physical objects. As used in the second context, in which the putative reality of numbers is highly salient, it is natural to associate the sentence-token with the mathematical domain. In order to individuate domains in terms of indicative sentence-tokens, it thus looks necessary to account for such contextrelated complications. We can take propositions to be sufficiently fine-grained to rule out this kind of contextual variability. It's quite natural to interpret me as expressing different propositions in the above contexts. In the first context, I express 〈there is an x and 43 I'm indebted here to several conversations with Aaron Cotnoir, who mentions a similar case in an unpublished manuscript. 179 there is a y and . . . s.t. x is a chair in the dining room and y is a chair in the dining room and . . . and x 6= y 6= . . .〉, where the ellipses each contain eight additional objectual variables. In the second context, I express 〈there is a number, ten, and it is the number of the chairs in the dining room〉. The latter proposition looks to carry ontological commitment to numbers and to thus belong to the mathematical domain, while the former looks to avoid this commitment. These propositions' domain-membership will thus be more stable than would be that of the sentencetoken that I use to express them. So moderate pluralists have reason to retain their commitment to propositions: this commitment strengthens the prospects of a tidy account of domain individuation, which is a major desideratum for many truth theorists, moderate pluralists included. 4.7 Bearer-specific alethic properties Alternatively to the three prior strategies, we might retain a propositional account of domains and embrace the result of the instability argument, namely that there is not just one, but a plurality, of general alethic properties. The resulting view would retain theses (MAP1)-(MAP4), i.e. domain pluralism, the commitment to propositions as truth-bearers, the instance-based definition of 'alethic property,' and the plurality of domain-specific alethic properties. In lieu of positing truth, we would instead posit a plurality of general alethic properties that we can call bearer-specific. A bearer-specific alethic property is an alethic property that is 180 general, in the sense of (Gen(i)) and (Gen(ii)) (domain-general, so to speak), but is associated with exactly one kind of truth-bearer. Our plurality of bearerspecific alethic properties would, then, include (at least) proposition-truth and sentence-truth. So in lieu of (MAP5), we would endorse: 44 • (MP5) There is a plurality of bearer-specific alethic properties, containing (at least) proposition-truth and sentence-truth. Whereas moderate pluralists take truth to be 'one and many,' we would on this view take truth to be 'many and many.' We would also revise the truth-conditions put forward by (MAP6) to reflect the fact we posit proposition-truth and sentence-truth rather than truth:45 • (MP?6) (i) If 〈p〉 ∈ D, then 〈p〉 is proposition-true iff 〈p〉 instantiates the domain-specific alethic property TD; (ii) If 'S' expresses 〈p〉 (in L), then 'S' is sentence-true (in L) iff 〈p〉 is proposition-true. 44 Note that by definition, a bearer-specific alethic property is domain-general. The domainspecific alethic properties are thus not bearer-specific, in the present sense. This isn't to claim that the domain-specific alethic properties are instantiable by more than one kind of truthbearer. If the domain-specific alethic properties are instantiable only by propositions, for instance, then they are bearer-specific, in a wider sense. But in what follows, we'll use 'bearerspecific' in the narrower sense. 45 (MP?6) and (MP ?? 7 ) are starred because they are first approximations of theses that we'll state more exactly in § 4.9.2 and 5.1. 181 Finally, we can modify (MAP7) slightly, so that it specifically lays down an asymmetric dependence of proposition-truth upon the domain-specific alethic properties: • (MP??7 ) If 〈p〉 ∈ D and 〈p〉 is proposition-true, then 〈p〉 is proposition-true in virtue of instantiating TD. The present view is clearly indebted to the deflationary tradition in truth theory. Traditional deflationists such as Ramsey contended that a serious shortcoming of the essence project is that in seeking after truth's essence, truth theorists unjustifiedly presupposed that there is a property truth whose essence might be discovered.46 And according to the present view, they were exactly right: there is no such thing as truth. But rather than resting with this negative metaphysical thesis, we move one step further, positing in the place of truth a plurality of properties which equally deserve the title of 'truth,' namely proposition-truth and sentence-truth. The rationale here can be helpfully compared to a famous due to Paul Benacerraf [22] against Platonist, set-theoretic accounts of numbers. Benacerraf points out that there are at least two set-theoretic representations of the number 3, one due to Ernst Zermelo and the other due to John von Neumann. The Zermelostyle representation has it that 3 = {∅, {∅}, {∅, {∅}}}. The von Neumann-style representation has it that 3 = {{{∅}}}. The Zermelo set is distinct from the 46 This diagnosis is also proferred by Ayer [12]; Grover [116]; and Strawson [255]; [256]. 182 von Neumann set. But the trouble is that neither the Zermelo hierarchy nor the von Neumann hierarchy looks to enjoy virtues that the other lacks, making it impossible to non-arbitrarily claim that one, but not the other, identifies the true nature of the number 3. The Zermelo set and the von Neumann set, that is, have equally good claims to being the number 3. But since they are distinct, both cannot be 3. So, Benacerraf concludes, neither is 3. And, he says, we would get the same result, no matter how many other set-theoretic representations of 3 we considered, so the proper conclusion is that numbers are not sets. The thought behind the present view is much the same. One account of truth has it that truth = proposition-truth. Another has it that truth = sentence-truth. But proposition-truth and sentence-truth have equally good claims to being truth, since they are both general alethic properties. But since they are distinct, both cannot be truth. So neither is truth. And we will get the same result, no matter how many other bearer-specific alethic properties we care to posit–they will one and all be the general alethic properties, precisely the property that truth was meant to be. So better to conclude that none of these is truth and that in all likelihood, truth doesn't exist. So the present view is situated, in an important respect, within the deflationary tradition–it denies that truth exists. But as we'll see in § 5.3.5, to say flatly that this view is deflationary would be highly problematic. The basic reason is that although it does without truth, the alethic properties that it posits 183 are highly substantive. While it gives to deflationism with one hand, it withholds much from deflationism with the other. So rather than calling this view deflationary, I call it minimal pluralism. Minimal pluralism's account of truth is minimal in two senses. Its most basic general alethic property is proposition-truth, which is integral to Horwich's alethic minimalism. And its depiction of sentence-truth is in turn rather minimal, taking sentence-truth to amount merely to the expression of a proposition-true proposition. For convenience, minimal pluralism's core theses are listed in § 5.6 (we'll refine (MP?6) and (MP??7 ) in § 4.9.2 and 5.1). 4.8 Truth as strongly general Rather than endorsing minimal pluralism, it might be thought that the preferable strategy for moderate pluralists would be to retain their core contention that truth is one by taking truth to be general in a rather strong sense. The idea here would be that not only is truth a general alethic property in the sense of (Gen(i)) and (Gen(ii)), it is also general in the sense of being instantiated by all and only the true truth-bearers. Truth, on this way of thinking, is not only domain-general, it is also bearer-general.47 Call this view strengthened moderate pluralism. According to strengthened moderate pluralism, truth is a property • (SGen(i)) Every possible instance of which conforms to the alethic plati47 Thanks to Nikolaj Pedersen for pressing this response. Marian David [62, n. 3] also alludes to this sort of view. 184 tudes; • (SGen(ii)) Which isn't plausibly assigned as an alethic property to only certain domains; and • (SGen(iii)) Which is instantiated by all true truth-bearers. How, precisely, should we understand (SGen(iii))? The strengthened moderate pluralist endorses theses (MAP1)-(MAP4), thereby committing inter alia to propositions being truth-bearers. Given that (PT) codifies the truth-conditions of propositions, the ontology of strengthened moderate pluralism contains propositiontruth. For the same Moorean reason that moderate pluralists should posit indicative sentence-tokens, strengthened moderate pluralists should do likewise. Given that they commit to propositions, strengthened moderate pluralists should in turn take indicative sentence-tokens to express propositions and should thus posit sentence-truth. Clause (SGen(iii)) bifurcates, then, into (at least) two sub-clauses, taking truth to be a property • (SGen(iii)Prop) Which is instantiated by 〈p〉 iff 〈p〉 is proposition-true and • (SGen(iii)Sent) Which is instantiated by 'S' iff 'S' is sentence-true. So the core theses of strengthened moderate pluralism are (MAP1)-(MAP4)+ • (SMP5) There is a single, strongly general alethic property truthSG, which satisfies (SGen(i))-(SGen(iii)) 185 • (SMP6) (i) If 〈p〉 ∈ D, then 〈p〉 instantiates truthSG iff 〈p〉 instantiates TD; (ii) 'S' instantiates truthSG (in L) iff 'S' expresses 〈p〉 (in L) and 〈p〉 instantiates truthSG • (SMP7) If 〈p〉 ∈ D and 〈p〉 instantiates truthSG, then 〈p〉 does so in virtue of instantiating TD. For convenience, the core theses of strengthened moderate pluralism are listed in § 4.11.2.48 4.9 Unity: minimal pluralism vs. strengthened moderate pluralism 4.9.1 Ontological parsimony Minimal pluralism and strengthened moderate pluralism are, I think, the leading contenders to succeed moderate pluralism. Ultimately, I favor minimal pluralism on grounds of ontological parsimony. That minimal pluralism looks to be more 48 Note that the strengthened moderate pluralist can't refuse to posit proposition-truth and sentence-truth on the grounds that they are highly miscellaneous properties/have highly miscellaneous extensions. We showed (§ 4.5) that moderate pluralists can't refuse to posit propositiontruth and sentence-truth on grounds of miscellaneity, since the truths are at least as miscellaneous as the proposition-truths and the sentence-truths. The class of trueSG propositions is more miscellaneous than the truths, by the Subset Principle. So the strengthened moderate pluralist can't refuse to posit either or both proposition-truth and sentence-truth on grounds of miscellaneity without thereby committing herself to refusing to posit truthSG–which, of course, would be an untenable position. 186 ontologically parsimonious than strengthened moderate pluralism can be seen by considering how each view addresses a basic problem confronting alethic pluralism, which we first broached in § 4.2.3. This is the problem of explaining the apparent unity exhibited by truth, given the diversity in truth that alethic pluralism posits. I adopt a standard, Ockhamite characterization of ontological parsimony, taking ontological parsimony to be a comparative notion. Theory T is more ontologically parsimonious than theory T ′ just when T ′ carries a larger ontology that doesn't compensate for its size by offering greater explanatory power. More carefully:49 • (Parsimony) T is more ontologically parsimonious than T ′ =Df (i) T ′'s ontology–the set of entities to which T ′ is ontologically committed–is larger than T 's ontology, but (ii) there is no entity e in T ′'s ontology, but not in 49 In embracing (Parsimony) as a criterion for theory choice, I commit to the supposition that the phenomena related to truth's unity are not explanatorily overdetermined (see § 2.5 for discussion of explanatory overdetermination in connection with Ockham's Razor). Strictly speaking, we need only take the conditions given in (Parsimony) to be collectively sufficient for T to be more ontologically parsimonious than T ′. Since they are rather standard, though, I offer them as definitional of ontological parsimony. Note that (Parsimony) is neutral as to the nature of ontological commitment. Also, note that comparative ontological parsimony can't be determined merely by comparing the cardinalities of the pertinent theories' ontologies. For T to be more ontologically parsimonious than T ′ isn't just for T 's ontology to be smaller than T ′'s–it's for T ′ ontology to be larger than T 's, while failing to offer greater explanatory power. 187 T 's ontology, appeal to which can explain an explanadum d that can't be explained by appeal to entities in T 's ontology. First off, it's important to notice that strengthened moderate pluralism's ontology is larger than the ontology of minimal pluralism. We saw that strengthened moderate pluralism is ontologically committed to proposition-truth and sentence-truth and to truthSG. So strengthened moderate pluralism's ontology contains proposition-truth, sentence-truth, and truthSG, as well as the domainspecific alethic properties. By contrast, minimal pluralism's ontology contains proposition-truth, sentence-truth, and the domain-specific alethic properties, but not truthSG. This raises the question whether commiting to truthSG affords the strengthened moderate pluralist any explanatory advantages not available to the minimal pluralist. If no such advantages are apparent, then it is reasonable to credit minimal pluralism with the centrally important virtue of comparatively greater ontological parsimony. I stress that I won't venture to show that minimal pluralism delivers every explanatory benefit afforded by strengthened moderate pluralism's ontology, though I suspect that it does do this. After all, truthSG can be regarded as a disjunctive property whose disjunct properties are propositiontruth and sentence-truth–a trueSG truth-bearer is just a truth-bearer that is either proposition-true or sentence-true. And no truth-bearer is both proposition-true and sentence-true (we'll look at the possibility of such truth-bearers just below). 188 So any explanandum that can be explained by appealing inter alia to truthSG can be explained by appealing to one of proposition-truth and sentence-truth. The reasoning is somewhat quick, but it strongly suggests that minimal pluralism is the more ontologically parsimonious view. But as I say, I'll be defending a weaker contention here–that minimal pluralism is very probably more ontologically parsimonious than strengthened moderate pluralism. We can show this by considering the most central prima facie explanatory benefit yielded by strengthened moderate pluralism's commitment to truthSG and seeing why this explanatory benefit is, in fact, also yielded by minimal pluralism's truthSG-free ontology. Given current evidence, then, it's rational to refuse to posit truthSG. The strengthened moderate pluralist thus bears the burden of detailing further phenomena that they, but not the minimal pluralist, can explain. I predict that there are no such phenomena. 4.9.2 Unity, mixed discourse, and mongrel discourse It might seem obvious that the strengthened moderate pluralist, since they posit a single, strongly general alethic property, is better positioned than the minimal pluralist to account for truth's unity. Indeed, the problem of truth's unity has been a major driver of sympathy for moderate pluralism over strong alethic pluralism, which is identical to moderate pluralism except that strong pluralism doesn't commit to truth (nor to proposition-truth or sentence-truth). 189 One of the most central topics in this connection is mixed discourse, which constitutes the second face of the problem of truth's unity (we addressed the first face in § 4.2.3). In general, mixed discourse is discourse involving truth-bearers associated with different domains. Four varieties of mixed discourse have been especially prominent: (i) mixed inferences; (ii) mixed compounds; (iii) mixed atomics; and (iv) mixed generalizations.50 The key phenomenon for which alethic pluralists have tried to account is that truth is apparently unified across discourse, in the sense that both unmixed and mixed discourse can be analyzed and evaluated in truth-theoretic terms. As it relates to the four mentioned varieties of mixed discourse, this phenomenon imposes two basic tasks for alethic pluralists: (i) to specify a definition of validity that encompasses both mixed and unmixed inferences and (ii) to specify truth-conditions for logical compounds, atomic truthbearers, and generalizations that encompass both mixed and unmixed compounds, atomics, and generalizations. Mixed inferences Moderate pluralism's ontological commitment to truth is often thought to enable moderate pluralists to handle mixed discourse. If this is so, then the same should be true of strengthened moderate pluralism's commitment to truthSG. Consider first the mixed inference M : 50 For discussion of mixed discourse, see especially [20]; [49] [51]; [54]; [80]; [85]; [86]; [167]; [171]; [175]; [178]; [203]; [241]; [258]; [259]; [269]; and [282]. 190 • (1??) Donating to charity is admirable • (2??) Jane donated to charity • (3??) Jane acted admirably. (2??) and (3??) seem to be associated with different domains, since (3??) appears to be evaluative, whereas (2??) is non-evaluative. (2??) could be associated with the domain of purely descriptive discourse about human action and (3??) with the ethical domain. (1??), we can assume, is likewise associated with the ethical domain.51 The standard, truth-theoretic definition of validity has it that an argument is valid iff it is necessarily truth-preserving. But alethic pluralists initially seem committed to denying that a mixed inference such as M could be valid in this sense, given that its components are associated with different domains, which are in turn associated with different domain-specific alethic properties. Moderate pluralists respond to the problem of mixed inferences by defining validity as necessary truth-preservation.52 Strengthened moderate pluralists can 51 Though this wouldn't seem straightforward, since (1??) both mentions a type of act and evaluates that act. Note also that (3??) seems to both mention an act-token and evaluate that act-token and that (2??) invokes the concept charity, which might be fairly regarded, in Bernard Williams' terminology, as a 'thick concept.' See the discussions of mixed atomic propositions in chapter 3 and § 4.9.2. 52 Though, of course, they offer different accounts of truth nature. 191 likewise respond by defining validity as necessary truthSG-preservation. This definition will encompass both mixed and unmixed inferences, since by (SGen(iii)), all truth-bearers are apt for truthSG, no matter the domain with which they are associated. Theses (SMP6)-(SMP7) ensure, moreover, that the instantiation of truthSG by the premises and conclusion is suitably grounded in the relevant domain-specific alethic properties. Since they positt a plurality of bearer-specific alethic properties, rather than truth or truthSG, the minimal pluralist might seem incapable of offering a similar definition of validity. But this initial impression is misleading. The key detail in this connection is that a mixed inference such as M is presumably also unmixed, in a certain respect. M is mixed in the sense that (1??)-(3??) are associated with at least two domains. But M is also unmixed, in that (1??)-(3??) will be truthbearers of a common kind. We can continue to operate with two kinds of truth-bearer: propositions and indicative sentence-tokens. If an argument's premises and conclusion are propositions, then minimal pluralists take the argument to be valid iff it necessarily preserves proposition-truth. If an argument's premises and conclusion are indicative sentence-tokens, then minimal pluralists take the argument to be valid iff it necessarily preserves sentence-truth. So if (1??)-(3??) are propositions, then M is valid in virtue of necessarily preserving proposition-truth and similarly if (1??)-(3??) are indicative sentence-tokens. Theses (MP?6)-(MP ?? 7 ) ensure that the 192 instantiation by the premises and conclusion of the relevant bearer-specific alethic property is suitably grounded in the relevant domain-specific alethic properties.53 But, it might be asked, what entitles the minimal pluralist to the assumption that the premises and conclusion of an argument are truth-bearers of a common kind? Might there, for instance, not be an argument one of whose premises is a proposition and whose conclusion is an indicative sentence-token? Since the label 'mixed inference' is reserved for arguments whose component truth-bearers are associated with different domains and the putative argument just described need not (though it might) be mixed in this sense, we might call such an argument a mongrel inference. The minimal pluralist refuses to posit mongrel inferences and accordingly denies the need to account for their validity. One should refuse to posit mongrel inferences on grounds of ontological parsimony. We can see this by considering what might be initially classified as a case in which someone draws a mongrel inference and noting that the case can be easily reinterpreted as involving a nonmongrel inference.54 Suppose that propositions are the contents of propositional attitudes such as beliefs. Jane is a progressive member of Congress. She believes that a conservative 53 In § 4.9.2, we'll revise (MP?6) and (MP??7 ) in order to handle mixed atomics. The revised theses likewise take instantiation of the bearer-specific alethic properties to be grounded in instantiation of the doman-specific alethic properties. 54 Thanks to Junyeol Kim for suggesting a similar case. 193 politician John is a misogynist and also believes that misogynists shouldn't be allowed to legislate on women's reproductive rights. So when Jane receives an email from a fellow progressive Sally, asking 'Should I make John a member of my new committee on women's reproductive rights?' Jane types in response, 'No, he's a misogynist!' Jane's response might be explained by depicting her as drawing a mongrel inference. This inference would be (where (3???) is a sentence-token): • (1???) 〈John is a misogynist〉 • (2???) 〈Misogynists shouldn't be allowed to legislate on women's reproductive rights〉 • (3???) John shouldn't be allowed to legislate on women's reproductive rights. It's easy to see that Jane can also be depicted as drawing a non-mongrel inference whose premises and conclusion are all propositions.55 Jane produces the sentence-token (3???) in writing her email, but we can easily explain this decision by hypothesizing that (3???) expresses 〈John shouldn't be allowed to legislate on women's reproductive rights〉, which Jane infers from (1???) and (2???).56 Were 55 She might also be depicted as drawing an inference whose premises and conclusion are indicative sentence-tokens. This interpretation could be substantiated by hypothesizing that we think in Mentalese. 56 Indeed, if inference is a mental act and propositions are the sole objects of mental states, then this is presumably the only coherent explanation of the case. Thanks to Michael Lynch for 194 Jane to mistakenly cc John when replying to Sally, leading John to challenge Jane's email, Jane might defend her production of sentence-token (3???) in response to John's protestations. But again, this can be easily explained by hypothesizing that Jane believes the proposition expressed by (3???), which she believes can be validly inferred from other propositions that she believes, namely (1???) and (2???). What this case suggests is that a theory committed to mongrel inferences is less parsimonious than one which escapes this commitment. Barring further compelling reasons to posit mongrel inferences, the minimal pluralist therefore defines validity as follows: • (ValidMP ) An argument with premises x1, . . . , xn and conclusion y, each of which is a truth-bearer of kind K, is valid =Df necessarily, if x1, . . . , xn instantiate the bearer-specific alethic property TK assigned to K, then so does y. Mixed compounds Next, consider mixed compounds such as the mixed conjunction: • (J) Jane donated to charity and Jane acted admirably. The standard, truth-functional semantics for conjunctions has it that a conjunction is true iff all of its conjuncts are true. But the challenge facing alethic pointing this out. 195 pluralism is that the conjuncts of a mixed conjunction such as (J) are associated with different domains, which are assigned different domain-specific alethic properties (and similarly for other sorts of mixed compound, e.g. mixed disjunctions). How, then, could alethic pluralists endorse truth-functional semantics for logical compounds? And if they cannot, this looks to be a strike against alethic pluralists, given pluralists' emphasis upon the fact that they, unlike mainstream deflationists, take truth to be explanatory (§ 2.1.2). Moderate pluralists respond to the problem of mixed compounds by offering truth-functional semantics for compound propositions that invoke truth. A mixed, conjunctive propositions (as well as any unmixed, conjunctive proposition) is taken to instantiate truth iff all of its conjuncts instantiate truth (in virtue of instantiating the domain-specific alethic properties assigned to the domains to which they belong). Strengthened moderate pluralists can likewise offer a truth-functional semantics for conjunctions that invokes truthSG: a conjunction instantiates truthSG iff all of its conjuncts do. Since the minimal pluralist posits a plurality of bearer-specific alethic properties in lieu of truth or truthSG, it might seem that they are barred from embracing a truth-functional semantics for logical compounds. But the initial impression is again misleading. Minimal pluralists can pursue a strategy very similar to their strategy for defining validity. The key detail, as with mixed inferences, is that a mixed compound such as (J) is also presumably unmixed, in a certain respect. (J) 196 is mixed in that its conjuncts are associated with different domains. (J) is also unmixed, in that its conjuncts are truth-bearers of a common kind. Suppose that (J) is a proposition whose conjuncts are propositions. minimal pluralism then takes (J) to be proposition-true iff (J)'s conjuncts are propositiontrue (in virtue of instantiating the domain-specific alethic properties assigned to the domains to which they belong). Alternatively, suppose that (J) is a indicative sentence-token whose conjuncts are indicative sentence-tokens. minimal pluralism then takes (J) to be sentence-true iff (J)'s conjuncts are sentence-true (in virtue of expressing propositions that instantiate the domain-specific alethic properties assigned to the domains to which they belong). Again, it might be asked what entitles the minimal pluralist to the assumption that the major component truth-bearers of a logical compound are truth-bearers of a common kind. Might there not, for instance, be a conjunctive truth-bearer whose conjuncts are 〈Jane donated to charity〉 and 'Jane acted admirably'? We might call this a mongrel conjunction.57 57 Note that mongrel conjunctions would be distinct from the sort of 'mixed' truth-bearer that Horwich [131, § 31] calls 'mixed propositions.' Mixed propositions, in Horwich's sense, are propositions that are partially composed of Fregean senses and partially composed of Russellian referents. Horwichian mixed propositions, that is, are composed of different kinds of potential propositional constituents. Mongrel conjunctions, by contrast, are composed of different kinds of (complete) truth-bearer. 197 The minimal pluralist refuses to posit mongrel conjunctions and accordingly denies the need to specify truth-conditions for them. The reason for this refusal is the same as with mongrel inferences: there seem to be no phenomena that can be explained by appeal to a mongrel conjunction, though not by appeal to a non-mongrel conjunction. Thus, given that non-mongrel conjunctions manifestly exist, the minimal pluralist refuses to posit mongrel conjunctions on grounds of ontological parsimony (and similarly for other kinds of mongrel compounds, e.g. mongrel disjunctions). Though somewhat fanciful, the following case seems among the most reasonable cases that might lead one to posit a mongrel conjunction. Suppose that propositions are the contents of beliefs. Jane is talking to Sally, who is conveying information to Jane about an upcoming meeting of Committee A. Jane is typing this information into her phone and has gotten as far as 'The upcoming meeting of Committee A will be on 11-5-13 and', when her phone dies. She looks around in vain for a pencil or pen and decides to commit the rest of the information–that the meeting will be in Room 207–to memory. It might be suggested that Jane's behavior can be explained by positing a mongrel conjunction which has as conjuncts 'The upcoming meeting of Committee A will be on 11-5-13' and 〈the upcoming meeting of Committee A will be in Room 207〉, the latter being the content of Jane's memory. Notice that it's difficult to see how this sentence-token and proposition are meant to be conjoined. Jane types 198 a sentence fragment into her phone that contains 'and.' But it's very tempting to think that this token of 'and' can only conjoin a sentence-token to another sentence-token. So to explain this case by positing a mongrel conjunction, we would need an explanation of the 'coordinative glue,' so to speak, that is meant to conjoin its conjuncts. It's also easy to see how to explain the case while avoiding commitment to a mongrel conjunction. Jane types into her phone the sentence fragment 'The upcoming meeting of Committee A will be on 11-5-13 and'. She also forms a memory whose content is 〈the upcoming meeting of Committee A will be in Room 207〉 and a corresponding belief with the same content. Jane believes, as well, that the upcoming meeting will be on 11-5-13. We can appeal to this belief, as well as her belief that the meeting will be in Room 207, to explain Jane's future behavior, e.g. that she walks towards Room 207 on 11-5-13. Jane types a sentence fragment into her phone. We cannot evaluate this sentence fragment for sentence-truth nor sentence-falsity, since it is apt for neither. What we can do is evaluate the propositions that Jane believes for propositiontruth. Were she to plug her phone in and continue typing 'will be held in Room 207,' we could also evaluate the resultant conjunctive sentence-token for sentencetruth. This case and the problem of 'coordinative glue' provide grounds for refusing to posit mongrel conjunctions, and similar cases would provide grounds for 199 refusing to posit e.g. mongrel disjunctions or mongrel conditionals. Barring further compelling reasons to posit mongrel conjunctions, the minimal pluralist thus forwards the following truth-conditions for conjunctions: • (ConjMP ) A conjunctive truth-bearer x of kind K instantiates TK iff all of x's conjuncts instantiate TK . We can generate a complete, truth-functional semantics for Boolean compounds in the usual way, letting the following clause govern negated truth-bearers:58 • (NegMP ) A negated truth-bearer ¬x of kind K instantiates TK iff the negand of ¬x fails to instantiate TK . 58 If ¬x is the proposition 〈not-p〉, then its negand is 〈p〉; if ¬x is the sentence-token 'Not S,' then its negand is 'S.' Note that I am neutral here as to whether the instances of (ConjMP ), (NegMP ) and similar schemas are conceptual truths, necessary truths, or analytic truths. What I hold is that every instance of these schemas is sentence-true. Since I take it that no indicative sentence-token is a necessary existent (see § 5.3.1), I would say that no such instance is necessarily sentence-true. If pressed, however, I would say that the propositions expressed by these instances are necessarily proposition-true. But the issues as to whether the pertinent instances and the propositions that they express are conceptual, necessary, or analytic truths are side issues on which I needn't commit at present. 200 Mixed atomics The third major species of mixed discourse, which we first encountered in chapter 3, involves mixed atomics. For the sake of concreteness, we can work, as we did in chapter 3, with a broadly Fregean conception of propositions, according to which propositions are structured and have concepts as their constituents.59 Letting Charlie be a beet, 〈Charlie is delicious〉 is plausibly composed of the concepts [Charlie] and [deliciousness]. The first source of trouble is that [Charlie] is a concept of a macroscopic, physical object, whereas [deliciousness] is a tasterelated concept. It's thus tempting to take 〈Charlie is delicious〉 to belong both to the domain of discourse about macrophysical objects and to the domain of taste-related discourse. The second source of trouble is that it is, for this reason, unclear which domain-specific alethic property the proposition must instantiate to be true. In chapter 3, I articulated on behalf of the manifestation functionalist what I take to be the most attractive solution to the problem of mixed atomic propositions. Adherents of other varieties of moderate pluralism can take advantage of this solution, as well. A key detail is that moderate pluralist truth theories have tended to be binary truth theories. Moderate pluralists tend to foreground two domain-specific alethic properties, e.g. a (relational) correspondence-theoretic, 59 A Russellian conception of propositions, taking propositions to be composed of particulars and universals, would do as well. 201 domain-specific alethic property and an epistemic, domain-specific alethic property. They have tended to take propositions in only some domains to be apt for the former, whereas propositions in all, or at least most, domains are apt for the latter. Purely taste-related propositions, e.g. 〈Deliciousness is wonderful〉, will presumably be among the propositions inapt for the relevant sort of correspondence, since they are composed of taste-related concepts. Likewise, since 〈Charlie is delicious〉 is composed of the taste-related concept [deliciousness], it is presumably also inapt for such correspondence. Moderate pluralists should thus take 〈Charlie is delicious〉 to instantiate truth iff it instantiates the epistemic, domainspecific alethic property assigned to the domain of taste-related discourse. The core idea behind this solution is that correspondence is the default domain-specific alethic property. 〈p〉 instantiates truth iff 〈p〉 instantiates correspondence–unless 〈p〉 is inapt for correspondence, in which case 〈p〉 instantiates truth iff 〈p〉 instantiates the posited epistemic, domain-specific alethic property. Strengthened moderate pluralists can respond to the problem of mixed atomic propositions in a similar fashion. They can, for instance, take 〈Charlie is delicious〉 to instantiate truthSG iff it instantiates the domain-specific alethic property assigned to the domain of taste-related discourse. Likewise, they can take the English sentence-token 'Charlie is delicious.' to instantiate truthSG iff the proposition it expresses, 〈Charlie is delicious〉, itself instantiates truthSG. It should be clear that the minimal pluralist can adopt much the same 202 strategy. The key difference is that the minimal pluralist will take 〈Charlie is delicious〉 to instantiate proposition-truth iff it instantiates the posited domainspecific alethic property assigned to the taste-related domain.60 Similarly, the minimal pluralist takes the English sentence-token 'Charlie is delicious.' to instantiate sentence-truth iff 〈Charlie is delicious〉 instantiates proposition-truth. So to address the problem of mixed atomic propositions in full generality, the minimal pluralist revises (MP?6) and (MP ?? 7 ) as follows: • (MP6) (i) If 〈p〉 ∈ D and there is no distinct domain D′ s.t. 〈p〉 ∈ D′, then 〈p〉 is proposition-true iff 〈p〉 instantiates TD; (ii) If 〈p〉 ∈ D and 〈p〉 ∈ D′ (D 6= D′) and 〈p〉 is inapt for TD (TD′), then 〈p〉 is proposition-true iff 〈p〉 instantiates TD′ (TD); (iii) If 'S' expresses 〈p〉 (in L), then 'S' is sentence-true (in L) iff 〈p〉 is proposition-true • (MP?7) (i) If 〈p〉 ∈ D, there is no distinct domain D′ s.t. 〈p〉 ∈ D′, and 〈p〉 is proposition-true, then 〈p〉 is proposition-true in virtue of instantiating TD; (ii) If 〈p〉 ∈ D and 〈p〉 ∈ D′ (D 6= D′), 〈p〉 is inapt for TD (TD′), and 〈p〉 is proposition-true, then 〈p〉 is proposition-true in virtue of instantiating TD′ (TD). Importantly, minimal pluralism doesn't face even a prima facie threat from 60 In lieu of appealing to an epistemic property here, the minimal pluralist might also appeal to a distinct species of correspondence. I'll argue in favor of this sort of minimal pluralism in § 5.2. 203 'mongrel atomics.' A mongrel atomic would be an atomic truth-bearer that had truth-bearers of different kinds as proper parts, e.g. an atomic truth-bearer one of whose proper parts is a proposition and another of which is a indicative sentencetoken. But no atomic truth-bearer has a truth-bearer as a proper part, so 'mongrel atomics' are simply impossible. Mixed generalizations We come finally to mixed generalizations, which are generalizations about truthbearers that are associated with different domains. Suppose, for instance, that Jim asserted exactly two propositions on 3-11-2010: 〈Tables are solid〉 and 〈Deliciousness is wonderful〉. Then the English sentence-token 'Everything Jim asserted on 311-2010 is unsurprising' is a mixed generalization, since the quantifier phrase 'Everything Jim asserted on 3-11-2010' ranges over two propositions belonging to distinct domains. Alethic pluralists face the challenge of specifying truth-conditions for mixed generalizations, given that their quantifier phrases range over truth-bearers associated with different domains. Moderate pluralists offer truth-conditions for generalizations, whether mixed or unmixed, that invoke truth. Where U is the range of the quantificational concept [everything], these truth-conditions can be rendered as: • (AllMP ) 〈Everything is F〉 instantiates truth iff every object a ∈ U instanti204 ates the property F. Strengthened moderate pluralists can take a similar tack, reformulating (AllMP ) in terms of truthSG, rather than truth. Again, it might seem that the minimal pluralist will have a hard time here, since minimal pluralism posits a plurality of bearer-specific alethic properties, in lieu of truth or truthSG. But minimal pluralism's strategy for handling the problem of mixed generalizations is much the same as its strategies for handling mixed inferences and mixed compounds. As in the other cases, it's key to notice that a mixed generalization is also unmixed, in that it is a truth-bearer of a single kind K. Generalizations are either logically atomic or logical compounds. Since there are no 'mongrel atomics,' if generalizations are atomic, then they are truthbearers of a single kind. If generalizations are compounds, then the minimal pluralist takes them to be truth-bearers of a single kind, since they refuse to posit mongrel compounds. Where U is the range of the pertinent quantificational concept, minimal pluralists accordingly offer the following truth-conditions for universal and existential generalizations, whether mixed or unmixed:61 • (AllMP ) (i) 〈Everything is F〉 instantiates proposition-truth iff every object a ∈ U falls under the concept F; (ii) 'For all x: Fx' instantiates sentence-truth 61 Note that (AllMP ) and (SomeMP ) invoke the concept F, rather than following (AllMP ) in invoking the property F. The reason for this will emerge in the next section, when we consider mixed, general truth ascriptions. 205 iff 〈Everything is F〉 instantiates proposition-truth. • (SomeMP ) (i) 〈Something is F〉 instantiates proposition-truth iff there is an object a ∈ U that falls under the concept F; (ii) 'For some x: Fx' instantiates sentence-truth iff 〈Something is F〉 instantiates proposition-truth. To recap. we've shown in this section that minimal pluralism looks to be more ontologically parsimonious than strengthened moderate pluralism. Strengthened moderate pluralists are committed to a larger ontology, in virtue of their commitment to truthSG. But the strengthened moderate pluralist looks no better off for this commitment, since the minimal pluralist can straightforwardly account for the evaluability and analyzability of both mixed and unmixed discourse using its truthSG-free ontology. I conclude that minimal pluralism is the most worthy successor to moderate alethic pluralism. 4.10 Mixed, general truth ascriptions and the meaning of 'true' To close this chapter, we should consider a second aspect of the problem of mixed generalizations that bears directly upon minimal pluralism. We can make many general claims about truth-bearers, e.g. that everything Jim asserted on 3-112010 is unsurprising (disappointing, invigorating, etc.). A special case is a general ascription of truth to a particular class of truth-bearers, e.g. • (3) Everything that Jim asserted on 3-11-2010 is true. 206 (3) might be a mixed generalization, e.g. if the quantifier phrase ranges over 〈Tables are solid〉 and 〈Deliciousness is wonderful〉. A distinctive challenge raised for alethic pluralism by such mixed, general truth ascriptions is to specify a semantics for 'true' that encompasses its use in such truth ascriptions. Not only, then, must alethic pluralists offer truth-conditions for mixed generalizations, they must explain what 'true' means so as to account for the fact that 'true' can be used to perform mixed, general truth ascriptions. We can call this the ascription desideratum raised by mixed generalizations. Moderate pluralists and strengthened moderate pluralists will presumably address the ascription desideratum in a similar fashion. Moderate pluralists can take every instance of 'true' to express truth62 and strengthened moderate pluralists can likewise take every instance of 'true' to express truthSG. Minimal pluralists, by contrast, should take 'true' to express the concept truth, rather than a particular (bearer-specific or domain-specific) alethic property. In other words, whereas moderate and strengthened moderate pluralists will presumably offer what we might call a property-theoretic semantics for 'true,' minimal pluralists should analyze 'true' using a concept-theoretic semantics.63 62 See especially Lynch [171, p. 392], [175, ch. 4, n. 7]. 63 This isn't to contend, of course, that moderate and/or strengthened moderate pluralists must offer a property-theoretic semantics for 'true.' But it's easy to see how they can, so such a semantics should be attractive to a proponent of either view. 207 It's easy to see that the ascription desideratum would seriously compromise minimal pluralism, were minimal pluralists beholden to a property-theoretic semantics for 'true.' Where the quantifier phrase ranges over 〈Tables are solid〉 and 'Deliciousness is wonderful,' consider • (4) Every truth-bearer mentioned by Jim on 3-11-2010 is true. Given that tables are indeed solid and that deliciousness is indeed wonderful, (4) is intuitively true. Minimal pluralism's ontology contains proposition-truth, sentence-truth, and the domain-specific alethic properties. If 'true' expresses proposition-truth, then (4) is clearly false, since 'Deliciousness is wonderful' is inapt for proposition-truth. Similarly, if 'true' expresses sentence-truth, then (4) is false, since 〈Tables are solid〉 is inapt for sentence-truth. 〈Tables are solid〉 and 'Deliciousness is wonderful' are associated with distinct domains D and D′. The minimal pluralist should accordingly deny that this instance of 'true' expresses either of TD and TD′ . Suppose that 'true' expresses TD, the domain-specific alethic property assigned to the domain of discourse about physical reality, and that 'Deliciousness is wonderful' is inapt for TD (as is presumably the case). Then (4) is false. Suppose that 'true' expresses TD and 'Deliciousness is wonderful' is somehow apt for TD. Still, this analysis of 'true' is undesirable, since TD is a domain-specific alethic property assigned to D, but not to D′. So, even if 'Deliciousness is wonderful' instantiates TD, it isn't ipso facto sentence-true. Accordingly, that 〈Tables are solid〉 and 'Deliciousness is 208 wonderful' instantiate TD isn't what is required for every truth-bearer mentioned by Jim on 3-11-2010 to be true. Parallel reasoning shows that it is undesirable to take the instance of 'true' in (4) to express TD′ . But since this exhausts minimal pluralism's stock of alethic properties, minimal pluralists should favor a concepttheoretic, rather than a property-theoretic, semantics for 'true.'64 It might be worried that in endorsing a concept-theoretic, rather than a property-theoretic semantics for 'true,' the minimal pluralist sacrifices the ontological parsimony that they enjoy over strengthened moderate pluralism. Doesn't going concept-theoretic ontologically commit the minimal pluralist to the concept truth, a commitment avoided by the strengthened moderate pluralist? But aren't these views' ontologies then equal in size, since (i) they both contain the domain-specific and bearer-specific alethic properties; (ii) strengthened moderate pluralism's, but not minimal pluralism's, contains truthSG; and (iii) minimal pluralism's, but not strengthened moderate pluralism's contains truth? The minimal pluralist can respond to this concern in two ways. They can concede the point but respond that the argument of § 4.9.2 still provides substantial motivation for minimal pluralism. A tried and true method for motivating 64 Strictly speaking, minimal pluralism is consistent with semantics for 'true,' such as prosententialism, which take 'true' to express neither a property nor a concept. Absent motivation to do otherwise, the minimal pluralist should take 'true' to be predicative at the level of logical form, since 'true' is apparently syntactically predicative. They can do so by taking 'true' to express truth. 209 a philosophical position is to show that it doesn't succumb to the most salient problems affecting it. The argument of § 4.9.2 shows that minimal pluralism can accommodate mixed discourse, which has long been seen as one of the most difficult challenges facing alethic pluralism. But the minimal pluralist needn't be so concessive. They can also point out that the best developed varieties of moderate pluralism–most notably Lynch's manifestation functionalism–not only offer accounts of the nature of truth, but also offer accounts of the concept truth that rely upon the alethic platitudes. Indeed, the vast majority of truth theorists have thought it vital to address truth's nature, including deflationists who see no need to say much about truth's nature. The historical ubiquity of the project of describing truth's nature provides reason to think that doing so is an integral component of developing a truth theory. But then the strengthened moderate pluralist will need to forward an account of truth and thereby ontologically commit to truth. In § 5.3.5, I'll explain what I think the minimal pluralist should say about truth. My aim in this chapter has been to motivate minimal pluralism as against the most influential family of pluralist truth theories. To subserve the theoretical ends to which they have been put, the alethic platitudes must be neutral on the truth-bearer kind issue. But this spells trouble for moderate pluralism, as it shows their views to be inherently unstable. The way forward, I suggest, is to embrace pluralism not only at the level of domain-specific alethic properties, but also at 210 the level of general alethic properties, which we might simply call the level of truth. What I propose, in short, is that we should be pluralists about truth. The concluding chapter is devoted to a fuller articulation of minimal pluralism. 4.11 Core theses of moderate and strengthened moderate pluralism For ease of reference, I've compiled below the core theses of moderate and strengthened moderate pluralism. Where a particular claim is common to these positions, I've relabeled it as is appropriate. The core theses of minimal pluralism are detailed in § 5.6. 4.11.1 Moderate pluralism • (MAP1) There is more than one domain of discourse • (MAP2) Propositions are among the bearers of truth • (MAP3) P is an alethic property =Df at least some instances of P conform to the alethic platitudes–i.e. at least one instance <a, P> of P satisfies the open counterpart of the neutral platitudes: If x is a truth-bearer, then (i) x is F iff x 'tells it like it is,' 'agrees with reality,' or 'corresponds to the facts;' (ii) x's instantiation of F covaries with a distinct state(s) of the world 'determined' by x; and (iii) if x is F , then it is ipso facto correct, to some extent, to endorse x when engaging in inquiry. 211 • (MAP4) There is a plurality of domain-specific alethic properties – P is a domain-specific alethic property =Df ∗ (DS(i)) Only some possible instances of P conform to the alethic platitudes; or ∗ (DS(ii)) Every possible instance of P conforms to the alethic platitudes, but P is plausibly assigned as an alethic property to only certain domains. • (MAP5) There is a single (domain-)general alethic property truth – P is a (domain-)general alethic property =Df ∗ (Gen(i)) Every possible instance of P conforms to the alethic platitudes ∗ (Gen(ii)) P isn't plausibly assigned as an alethic property to only certain domains. • (MAP6) If 〈p〉 ∈ D, then 〈p〉 instantiates truth iff 〈p〉 instantiates the domain-specific alethic property TD assigned to D • (MAP7) If 〈p〉 ∈ D and 〈p〉 instantiates truth, then 〈p〉 does so in virtue of instantiating TD. 212 4.11.2 Strengthened moderate pluralism • (SMP1) There is more than one domain of discourse • (SMP2) Propositions are among the bearers of truth • (SMP3) P is an alethic property =Df at least one instance <a, P> of P satisfies the open counterpart of the neutral platitudes • (SMP4) There is a plurality of domain-specific alethic properties • (SMP5) There is a single, strongly general alethic property truthSG – P is a strongly general alethic property =Df ∗ (SGen(i)) Every possible instance of P conforms to the alethic platitudes; ∗ (SGen(ii)) P isn't plausibly associated only with certain domains; ∗ (SGen(iii)Prop) P is instantiated by 〈p〉 iff 〈p〉 is proposition-true; and ∗ (SGen(iii)Sent) P is instantiated by 'S' iff 'S' is sentence-true. • (SMP6) (i) If 〈p〉 ∈ D, then 〈p〉 instantiates truthSG iff 〈p〉 instantiates TD; (ii) 'S' instantiates truthSG (in L) iff 'S' expresses 〈p〉 (in L) and 〈p〉 instantiates truthSG • (SMP7) If 〈p〉 ∈ D and 〈p〉 instantiates truthSG, then 〈p〉 does so in virtue of instantiating TD. Chapter 5 Minimal pluralism There are many kinds of eyes–even the Sphinx has eyes. And there are many kinds of "truths" and consequently there is no truth. Nietzsche, The Will to Power 5.1 Minimal pluralism: overview My aim in the final chapter is to elaborate and further defend minimal pluralism. Minimal pluralism is situated to some extent within the deflationary tradition. As traditional deflationists suspected, truth does not exist. And this is because there is more than one property which behaves as truth was meant to behave. There is, for this reason, no single property that uniquely deserves to be called 'truth.' This result certainly deflates the ambitions of traditional truth theorists, whose principal aim was to discover the essence of truth. This ambition cannot be fulfilled, as there is no such property whose essence might be discovered. 213 214 But I'll argue that to break ranks in this way with the tradition in truth theory isn't yet to endorse Deflationism with a capital 'D.' For the contention here is not the simple one that truth doesn't exist. It is, rather, that there is a plurality of properties which enjoy equally strong claims to being called 'truth.' The question then arises whether these properties, proposition-truth and sentence-truth, are substantive or merely deflated properties. After proposing several diagnostics for determining how substantive a property is, I'll argue that proposition-truth and sentence-truth are as substantive as any property can be–they are maximally substantive properties. So although I wholeheartedly endorse a deflationary account of truth, I firmly resist a deflationary account of proposition-truth and sentencetruth. In positing proposition-truth and sentence-truth, we reap certain theoretical benefits. We put ourselves in a position to accommodate both the widespread intuition that there are necessary truths and the philosophically influential intuition that the existence of truths depends upon the existence of cognizers. We're also in a position to accommodate a set of pretheoretical convictions as to what bears truth. In particular, I'll argue contra Horwich and Austin that we pretheoretically take unasserted, indicative sentence-tokens to be bona fide truth-bearers. Additionally, in positing proposition-truth and sentence-truth, we are positioned to recognize a surprising asymmetry in their relative fundamentality. Propositiontruth is more basic than sentence-truth at the level of properties. But at the 215 level of concepts, things are different. The concepts proposition-truth and sentence-truth are equibasic–to possess either, one must possess the other. We might think of minimal pluralism as a metaposition about truth.1 To be a minimal pluralist is to hold that propositions are apt for proposition-truth, indicative sentence-tokens are apt for sentence-truth, no truth-bearer is apt for truth, and that propositions are proposition-true in virtue of instantiating particular domain-specific alethic properties. Accordingly, minimal pluralists can disagree among themselves as to the underlying natures of the domain-specific alethic properties. My view is that as Terence Horgan [16], [17], [121], [122] and Gila Sher [239], [240], [241], [243], [244] have proposed, the domain-specific alethic properties each constitute different species of correspondence. I argue, in particular, that propositions about taste are proposition-true because they correspond to response-dependent, worldly facts about taste. Other kinds of proposition-true proposition–e.g. chemical and biological propositions–are more plausibly taken to correspond to response-independent facts. So just as truth comes in different forms–proposition-truth and sentence-truth–so does correspondence to fact. Propositions are proposition-true because they correspond in a particular way to facts. What, though, is the force of this 'because?' In what sense, that is, does its correspondence to fact determine or explain that a proposition is proposition-true? 1 Thanks to Michael Lynch for suggesting this expression. 216 Alethic pluralists differ among one another as to the nature of this determination relation. I propose that the operative relation here is grounding. To close, I articulate several structural principles that govern grounding and describe precisely how proposition-truth is grounded in correspondence. Because a picture can often be as illuminating as thousands of words, I'll begin with a diagram representing the structure of minimal pluralism. Moving from bottom to top, 'Ti(〈p〉Di)' means that the proposition 〈p〉, which belongs to domain Di, instantiates the domain-specific alethic property Ti assigned to Di. 'PT(〈p〉)' means that 〈p〉 is proposition-true. 'E(S, 〈p〉, L, c)' means that the indicative sentence-token 'S' expresses 〈p〉 in L and c. 'ST<p>,L,c(S)' means that the indicative sentence-token 'S–'which expresses 〈p〉 in L and c–is sentence-true. A double arrow indicates a biconditional relationship between property instances. A dashed line indicates that the 'bottom' property grounds the 'top' property. ST〈p〉,L,c(S) ST〈q〉,L,c(S ′) ST〈r〉,L,c(S ′′) PT (〈p〉) E(S, 〈p〉,L, c) PT (〈q〉) E(S ′, 〈q〉,L, c) PT (〈r〉) E(S ′′, 〈r〉,L, c) T1(〈p〉D1) T2(〈q〉D2) . . . Tj(〈r〉Dj) Figure 1: Minimal pluralism 217 5.2 Deflationism 5.2.1 Pluralism and deflationism Alethic pluralists have, by and large, opposed the deflationary trend in contemporary truth theory. And if we consider the theories of truth that represent this trend, this isn't surprising, as the opposition between pluralism and deflationism seems rather clear-cut. Horwich [131, Postscript, § 5], in advancing alethic minimalism, holds that there is exactly one alethic property truth, which is implicitly defined by the infinite class of all non-pathological instances of (PT), i.e. by the non-pathological proper subclass of what he calls the minimal theory of truth. So the alethic minimalist and the alethic pluralist clearly differ over the cardinality of the set of alethic properties. The minimalist holds that it is 1 and the pluralist that it is greater than 1 (minimal pluralism takes it to be 4). It is also natural for advocates of two other leading deflationary views to hold that there is exactly one alethic property. Wolfgang Künne advances a variety of deflationism which differs from alethic minimalism as to how truth may be defined. The minimalist implicitly defines truth using the instances of (PT). By contrast, Künne puts forward an explicit definition of truth with the following form:2 • (OD) ∀x(x is true ↔ ∃p(x = 〈p〉 ∧ p)). Christopher Hill [119], [120] has also advanced an explicit definition of truth, 2 [156, p. 337]. 218 though Hill's definition has a somewhat different form:3 • (SD) ∀x(x is true ↔ Σp(x = 〈p〉 ∧ p)). The key difference between (OD) and (SD) is that (OD) contains an objectual quantifier that ranges over propositions, whereas (SD) contains a substitutional quantifier that is characterized inferentially by appeal to certain introduction and elimination rules. So we can call the view advanced by Künne objectual deflationism and that advanced by Hill substitutional deflationism. Objectual and substitutional deflationists both have reason to hold that there is exactly one alethic property truth that is characterized by (OD) and (SD), respectively. It's easy to see that both (OD) and (SD) entail that there is a property truth in the class nominalist sense of 'property.' (OD) and (SD) are explicit definitions. For this reason, they each carry commitment to a particular class, namely the class of entities that satisfy the conditions on the right-hand sides of their respective biconditionals. And the class specified by (OD) will, in fact, be identical to the class specified by (SD). An entity a is a member of this class iff there is a proposition 〈p〉 s.t. a is identical to 〈p〉 and p. Since class nominalists such as Lewis take properties to simply be classes and since (OD) and (SD) each entail that there is a class of truths, both (OD) and (SD) entail that there is a property truth in the class nominalist sense. 3 [119, p. 23]. Following Frege, Hill calls propositions 'thoughts.' 219 This isn't to contend, of course, that the objectual and substitutional deflationist are strictly committed to positing a property truth; they might resist class nominalism by adopting a sparse conception of properties. Since neither view comes equipped with a general account of properties, though, both the objectual and the substitutional deflationist are under pressure to posit a property truth, namely the class which they commonly regard as the class of truths.4 Were they to resist this pressure by e.g. advocating a sparse conception of properties, it would be most natural for objectual and substitutional deflationists to take the more traditional deflationary position that there are no alethic properties. As we've mentioned, the most prominent representatives of this tradition are Ramsey and Ayer's redundancy theory, Strawson's performative theory, Grover's prosentential theory, Brandom's anaphoric theory, and the disquotational theories of Quine, Leeds, and Field. Each of these views applies primarily at the linguistic level–the principal aim of each is to offer a semantics for 'is true' or for entire truth ascriptions which entails that in using 'is true'/in performing truth ascriptions, we are not using a truth predicate, in the semantic sense of 'predicate.' Truth predicates (in the semantic sense) are the common enemy of traditional deflationism. But the import of these projects extends beyond the linguistic level to the 4 And notice that this class is also identical to the class of proposition-true propositions. So in effect, objectual and substitutional deflationists are under pressure to posit proposition-truth (as understood by class nominalists). 220 level of properties. Of course, even if it were correct that no speaker uses a truth predicate, there might still be a property truth. And we might still be able to refer to that property, e.g. by using the common noun 'truth' or the definite description 'the property that a truth-bearer has iff it agrees with reality.' But if it turns out that truth ascriptions are semantically redundant, non-predicative endorsements, or prosentences, this will serve as a strong suggestion that our use of 'truth,' 'agrees with reality,' and the like can be analyzed in a similar fashion. It will suggest, that is, that all alethic discourse can be analyzed so as to avoid commitment to a property truth. And that result would undercut one of our strongest reasons for positing alethic properties, namely that our alethic discourse, in which we engage with considerable success, seems to carry commitment to them. So although traditional deflationists, operating mainly at the linguistic level, have tended to refrain from explicitly denying that there are alethic properties, the success of their linguistic projects would clearly speak in favor of this conclusion. To mark this fact, we should associate with traditional deflationism the thesis that there are no alethic properties. While this may not strictly be a commitment that traditional deflationists incur, their views push strongly in this direction. So if we characterize alethic deflationism by reference to leading deflationary truth theories, then deflationism will be squarely opposed to pluralism. Deflationists, on this understanding, hold either that there are no alethic properties or that there is exactly one alethic property. Pluralists, by contrast, hold that there is 221 more than one alethic property. 5.2.2 The need to disambiguate This description of the dialectic between pluralists and deflationists is fine as far as it goes. But the shortcoming of this way of thinking is that it generates a simplistic picture of the landscape of deflationary positions on truth. What it fails to account for is that there are several different axes upon which deflationism turns. For a deflationist like Horwich who posits an alethic property truth, the range of possible deflationary positions as to truth's nature is wide and interesting, indeed far more wide and interesting than has been acknowledged. So if we are interested to understand and evaluate deflationism, as nearly every truth theorist agrees that we should be, we must be sensitive to just how nuanced a position deflationism is. Coming to a more accurate understanding of deflationism will also help us to appreciate why minimal pluralism, although it sides with traditional deflationists in eliminating truth, is nevertheless not a very deflationary account of truth. Minimal pluralists deflate truth by eliminating it, but they do not deflate the alethic properties that they posit in its stead–each of these properties is as substantive as any property can be. That the nuances in deflationism have gone largely unnoticed isn't all that surprising. Deflationism is often offered more as a slogan (Wright [276, pp. 38-9] calls it a 'tendency') than as a concrete position on truth. The familiar deflation222 ary mantra is that 'truth is not substantive.' As with many slogans, this claim is highly suggestive, but it isn't transparent what it amounts to. For one thing, it's four-ways ambiguous: it might be a contention about theories of truth, the concept truth, the word 'true,' or the property truth. On any of these readings, the claim promises to be significant if true. Since alethic pluralism is a view at the level of properties, we'll confine ourselves to a property-theoretic understanding of deflationism in what follows. Even when it has been regimented in this way, however, the deflationary slogan is still difficult to understand, since it's not clear what it means to say that truth is not a substantive property. Of course, if truth doesn't exist at all, then it's not a substantive property–it's not a property at all. But if this were all that deflationists meant to say about truth (and we know that for Horwich, it isn't), then they would be advised to simply say that truth doesn't exist, without relying upon the notion of substantiality. The more interesting question is what a deflationist might mean in denying that truth is a substantive property were they to grant, as Horwich does, that there is a property truth. Call a deflationist who allows this a moderate deflationist. Substantiality, as it applies to properties, is clearly a theoretical notion.5 So in considering what the deflationist might mean here, it's useful to ask in what 5 Thanks especially to Jc Beall, Doug Edwards, and Michael Lynch for impressing upon me the importance of this point. 223 philosophically significant senses truth might fail to be substantive. When we frame the question in this way, we come to appreciate that deflationists have been highly equivocal on this point. There are, in fact, five senses in which deflationists have claimed that truth is not a substantive property which are frequently run together or erroneously assumed, as we'll see below, to be logically dependent upon one another. So in assessing the merits of moderate deflationism, our first task must be to distinguish between these five claims about truth. What we'll see is that four of these five claims are both distinctively deflationary and distinctively metaphysical claims about truth. These four claims are logically distinct from one another, in the sense that none entails any of the others. For this reason, it's best to understand moderate deflationists as advancing not a unitary thesis but a schematic claim about truth–that truth is insubstantive, in at least one of the target senses. A second result is that at the level of properties, the choice that truth theorists face is not so much whether to be deflationists or not, but how deflationary they wish their views to be. At the level of properties, being a deflationist about truth is a matter of degree, not a simple 'Yea' or 'Nay.' 5.2.3 Varieties of substantiality The theses about truth that have been associated with deflationism both by deflationists and by their critics are (i) that truth is a 'metaphysically transparent' property; (ii) that truth is not an 'explanatory' property; (iii) that truth lacks a 224 constitution theory; (iv) that truth is not a very 'natural' property; and (v) that truth is a 'logical' property.6 Each of these theses, if it is to be even partially definitive of deflationism at the level of properties, should enjoy at least two features: (a) it should be a distinctively deflationary thesis about truth (call this the Deflationary Constraint) and (b) it should be a distinctively metaphysical thesis about truth (rather than e.g. a disguised thesis about truth or 'true;' call this the Metaphysical Constraint). What will emerge below is that suitably understood, theses (i)-(iii) enjoy these two features. Thesis (iv), by contrast, fails to meet the Deflationary Constraint and thesis (v) fails to meet at least one of these constraints. For these reasons, we should take moderate deflationism to be defined, at the level of properties, only by theses (i)-(iii). Transparency When developing his critique of deflationism, Lynch offers the following account of property-level deflationary views of truth [175, pp. 106-7]: [D]eflationists share a metaphysical view: truth has no nature. Early deflationists sometimes put this by saying that the concept does not denote a property. But more contemporary deflationists wisely avoid this claim. Instead, they allow that the truth concept does express 6 Readers familiar with Doug Edwards' account of the metaphysics of deflationism [89] will notice my indebtedness to his work here. Section § 5.4.4 is a reply to the concerns that Edwards raises for (i)-(iii) and (v). 225 a property–in the same sense that the concepts of existence or identity express either a property or relation. Such properties, we might say, are metaphysically transparent or pleonastic properties. Metaphysically transparent properties have no underlying nature that isn't revealed in our grasp of the concept; grasping the relevant concept tells us the whole essence of the property. . .Contemporary deflationists can be understood as arguing that truth. . .is metaphysically transparent, in that we know all the essential facts about it–its real essence, as Locke might have said–just by grasping the concept of truth. Moderate deflationists, says Lynch, hold that truth is a metaphysically transparent property in the sense that "we know all the essential facts about [truth]. . .just by grasping the concept of truth." A couple of questions arise here. First, which truth concept is at issue? Clearly, the deflationist should have the ordinary concept truth in mind. One of the most significant consequences of truth's being metaphysically transparent would be methodological. Horwich formulates the idea well [131, p. 136]: What, then, from a minimalist point of view, is the basic theory of truth itself? Which body of fundamental facts about truth provides the best explanation of all the further facts about it? A natural conjecture is that, although there is always in principle a difference between the theory of the concept of X and the theory of X-ness itself, perhaps, 226 in the case of truth, these theories more or less coincide. Perhaps the axioms of the theory of truth are instances of the equivalence schema. . . If truth were metaphysically transparent, this would mean that to offer a comprehensive analysis of truth's essence, we would need only to offer a comprehensive account of the content of the ordinary concept truth. We would, that is, be able to do serious metaphysics by way of straight conceptual analysis. And, as Horwich points out, this would be a surprising result. In general, to investigate the nature of a property (think of being water or heat), it isn't sufficient to study the ordinary concept of the property. In general, we are inclined to say that the content of the ordinary concept of a property and the essence of the property may diverge, and perhaps sharply. But if truth were metaphysically transparent, then this distinction would hardly be worth making in truth theory. To secure this methodological upshot, moderate deflationists who hold that truth is metaphysically transparent should, in advancing this claim, have the ordinary concept truth in view. There is also a question as to whom 'we' are meant to be. In particular, does the definition of metaphysical transparency quantify over all possible cognizers or only over all actual cognizers? It's presumably contingent that our ordinary concept truth has the content that it does. It would seem that we could have possessed an ordinary truth concept whose content differs from that of our actual, ordinary truth concept. In § 5.4.5, I'll suggest that we should characterize the 227 ordinary truth concept using the alethic platitudes. But I'm happy to admit, as presumably most truth theorists will be, that had the percentage of philosophers in our species been larger, our ordinary truth concept might, for instance, have been a highly detailed, fact-based correspondence-theoretic concept. If enough of those extra philosophers were sympathetic towards fact-based correspondence theories, they might have been able to convince the general populace that truth is just fact-based correspondence. Given that it is contingent that our ordinary truth concept has the content that it does and that, by contrast, truth's essence is fixed across all possible worlds, it will be possible that truth is metaphysically transparent in the actual world, though not in some other possible world in which we possess a different ordinary truth concept, or vice versa. In light of this, when thinking in a general way about truth's metaphysical transparency, we should recognize that the conditions that must be satisfied for truth to be metaphysically transparent are schematic. In the sense articulated by Lynch, truth is metaphysically transparent in world w iff any cognizer in w who possesses the ordinary truth concept of w ipso facto knows all of the essential facts about truth. Presumably, however, our primary interest is to determine not whether truth is metaphysically transparent in some merely possible world, but whether truth is actually metaphysically transparent–even modal realists tend to have a special concern for the actual. So we can take the thesis that truth is metaphysically transparent, as formulated by Lynch, to amount to the following: 228 • (TransparencyL) Any actual cognizer who possesses the actual ordinary concept truth ipso facto knows all of the essential facts about truth. Nic Damnjanovic has also taken moderate deflationists (Damnjanovic calls them 'new wave deflationists') to hold that truth is metaphysically transparent. But Damnjanovic takes the operative notion of metaphysical transparency to be weaker than that specified in (TransparencyL). In Damnjanovic's terminology, property P is metaphysically transparent, relative to a particular concept C of P iff C is revelatory of P's nature. For C to be revelatory in this way is for it to be the case that "any subject S who grasps [C] is in a position to know the full nature of [P] without further empirical investigation or a priori argumentation."7 Notice that the question again arises as to whether we are quantifying over all possible, or only all actual, cognizers. I suspect that Damnjanovic intends the former, so that if a given concept C is revelatory of P's nature, then this will be a necessary truth about C. But for present purposes, either reading will do. So since we are principally interested in the actual metaphysical transparency of truth, we can again quantify only over all actual cognizers. Likewise, for the above reasons, we'll take it that the truth concept that is particularly relevant here is the ordinary concept truth. So for truth to be metaphysically transparent in the sense that Damnjanovic articulates would involve the following:8 7 [57, p. 48]. 8 Crispin Wright [277, p. 753] advances a similar conception of what it would be for truth to be metaphysically transparent. Horwich also famously contends that according to the minimal 229 • (Transparency) Any actual cognizer who possesses the ordinary concept truth is ipso facto in a position to know, without further empirical inquiry or a priori argumentation, all of the essential facts about truth. Damnjanovic points out why (TransparencyL) is a weaker thesis than (Transparency) [57, p. 48]: When a property is revealed to us by our concept of it, there is no more for us to learn about its nature. There is no more to learn either through empirical investigation or a priori reasoning. But that is not to say that grasping a revelatory concept is sufficient to know the nature of the property. It may be that some reflection on C is required, where such reflection falls short of a priori argument or reasoning. This is the point of saying that grasp of the concept only puts us in a position to know the nature of the property [Footnote: By 'being in a position to know that p' I mean roughly what Williamson [ [270, p. 95]] means; namely that 'no obstacle must block ones path to knowing p. If one is in a position to know p, and one has done what one is in a position to do to decide whether p is true, then one does know p.'] For truth to be metaphysically transparent in the sense of (TransparencyL), it must be the case that any actual cognizer who possesses truth knows every conception of truth, truth lacks a 'hidden structure' [131, pp. 2, 49]. 230 essential fact about truth, even if they have never reflected upon what essential features truth might have. By contrast, Damnjanovic's conception entails only that if truth is metaphysically transparent, then any actual cognizer who possesses truth is in a position to know every essential fact about truth without relying upon further empirical inquiry or a priori argumentation. And the important detail is that at t, S might be in such a position to know every essential fact about truth although S doesn't know at t every essential fact about truth. For S might be in a position satisfy the conditions for knowing every such fact although S hasn't as yet satisfied those conditions. So Lynch takes moderate deflationists to be committed to the stronger (TransparencyL), while Damnjanovic holds that they are committed not to (TransparencyL), but to the weaker (Transparency). To which of these theses, then, are moderate deflationists committed? In a sense, they are committed to neither. To see this, we can consider what the alethic minimalist should say about truth's metaphysical transparency. Horwich claims in the above passage that according to alethic minimalism, the proper account of truth and the proper account of truth basically coincide. As we explained in § 5.2.3, the minimalist should hold that to possess the ordinary concept truth, one must be disposed to accept every token of every instance of (PT) in every context and in the absence of supporting argumentation. And Horwich suggests that the fundamental, or essential, facts about truth are 231 just the facts that are expressed by the non-pathological instances of (PT). So it might seem that the minimalist should hold at least that a cognizer who possesses truth is ipso facto in a position to know every essential fact about truth without relying upon further empirical inquiry or a priori argumentation. For according to the minimalist, if S possesses truth, then S is disposed to accept every token of every instance of (PT) in e of supporting argumentation and in every contextthe absenc. But if the essential facts about truth are exhausted by the non-pathological instances of (PT), then S would be in a position to know every essential fact about truth without relying upon further empirical inquiry or a priori argumentation. To come to know these facts, all that S would presumably need to do is to competently reflect upon truth while considering the non-pathological instances of (PT). In doing so, S would come to believe the facts expressed by these instances and would thereby come to know these facts a priori. Or so the argument might go. The problem with this reasoning is that it overlooks a point that is due, in essence, to Anil Gupta [117] and Scott Soames [248] (we first encountered this point in § 4.2.4). Referring to Horwich's minimal theory of truth (whose axioms, recall, are just the instances of (PT)), as 'MT,' Gupta [117, pp. 363-4] notices: MT contains a biconditional for each proposition, but it does not imply that only propositions are true. Hence, even though we know that the Moon is not a proposition, we cannot deduce from MT that the Moon 232 is not true. The alethic minimalist holds that propositions are the sole bearers of truth. And as Gupta points out, given that this is a fact about truth, it's not a fact that we can deduce from any subclass of the instances of (PT). So the minimalist must take it to be, like the instances of (PT), a fundamental, essential fact about truth. But this is not a fact about truth that, according to the minimalist, anyone who possesses truth must be in a position to know, without relying upon further empirical inquiry or a priori argumentation. What we must ask is whether S's being disposed to accept every token of every instance of (PT) in the absence of supporting argumentation and in every context guarantees that S is in a position to know, without further empirical inquiry or a priori argumentation, that propositions are the sole bearers of truth? The answer is 'No.' The disposition here is a disposition to accept tokens of instances of (PT). But as Gupta points out, no class of such tokens entails that propositions are the sole bearers of truth. So in possessing truth, S isn't ipso facto disposed to believe, in the absence of further empirical inquiry or a priori argumentation, that propositions are the sole bearers of truth. And since belief is necessary for knowledge, S isn't ipso facto in a position to know, without relying upon further empirical inquiry or a priori argumentation, that propositions are the sole bearers of truth. So the minimalist must hold that there is an essential fact about truth–that propositions are the sole bearers of truth–which one who possesses truth is not ipso facto 233 in a position to know, without relying upon further empirical inquiry or a priori argumentation. For the minimalist, truth is not metaphysically transparent in the weak sense articulated by Damnjanovic. Thus for the minimalist, neither is truth metaphysically transparent in the stronger sense put forward by Lynch. Contrary to the standard assumption, then, moderate deflationists are not committed to holding that truth is metaphysically transparent. The alethic minimalist, in fact, is committed to denying that truth is metaphysically transparent. This is a rather important result, since it goes against the folk wisdom about deflationism. But this result shouldn't cause us to lose sight of the fact that both (TransparencyL) and (Transparency) are distinctively deflationary theses about truth. As we noted above, if truth were metaphysically transparent in either of these senses, this would severely deflate the importance of the essence project. For if we are even in a position to know every essential fact about truth without relying upon further empirical inquiry or a priori argumentation, the fact remains that we can comprehensively detail truth's essence through conceptual analysis alone. There would simply be no need to embark upon a separate metaphysical inquiry into truth's essence–studying the concept truth would be entirely sufficient. So (TransparencyL) and (Transparency), though moderate deflationists are not committed to them, are deflationary claims about truth that would be highly impactful if true. 234 My own preference is to associate (Transparency) with moderate deflationism, in lieu of (TransparencyL). This is because I see no reason that the moderate deflationist should commit to the stronger (TransparencyL), rather than to (Transparency). If true, (Transparency) would deflate the essence project in the way that moderate deflationists wish to deflate it. So absent any reason to go in for the stronger thesis, moderate deflationists who wish to claim that truth is metaphysically transparent should opt for (Transparency) instead. What I propose, then, is that (Transparency) is a thesis that we should associate with moderate deflationism because it satisfies the Deflationary Constraint. To endorse (Transparency) is to embrace moderate deflationism to some extent, though this isn't to say what we've seen reason to deny, that to be moderate deflationist, one must endorse (Transparency). In § 5.4.4, we'll look again at (Transparency) in connection with the Metaphysical Constraint. Explanatoriness Moderate deflationists regularly contend that truth is not an 'explanatory' property.9 This contention is part and parcel of deflationists' characteristic intention 9 For affirmations to this effect and contentions that this thesis is essential to alethic deflationism, see Bar-On, Horisk, and Lycan [15, pp. 13-14]; Brandom [29]; Devitt [71, pp. 31, 32, 34, 44, 83, 115-16, 188, 295]; Grover [116, § 3.1]; Horwich [131, ch. 3], [133, pp. 6-7, 13-16]; Lynch [175, pp. 107, 111]; and Williams [267], [268, pp. 547-48]. For related discussion, see Field [98, pp. 67, 76, §§ 4.2-5.4], [100, Postscript, § 7]; Ketland [147, p. 92]; Leeds [159, esp. §§ 235 to undercut the essence project. Traditional truth theorists sought to provide a constructive response to the essence question because they thought that if they could discern the nature of truth, then their understanding of other philosophically central topics–e.g. knowledge, rationality, epistemic justification, belief, assertion, theoretical success, communication, thought, ontology, and the list goes on–would improve appreciably. Moderate deflationists aim to dispel this hope by showing that upon scrutiny, truth's essence is far too simple and obvious for truth to enjoy any explanatory power. So the deflationary aim here is to show not only that we need not mention truth to explain philosophically significant phenomena, but that we can't explain such phenomena by mentioning truth–truth, the thought is, lacks explanatory power altogether. The thesis about explanation that moderate deflationists tend to advance, then, is the following: • (Explanation) There is a property truth, but there is no possible state of affairs ω whose obtaining, or failure to obtain, it is possible to explain by inter alia mentioning truth. So we have so far two senses in which truth might be less philosophically significant than the tradition in truth theory takes it to be. Truth might be insubstantial in virtue of being metaphysically transparent. Truth might also be insubstantial in virtue of being non-explanatory. These claims are often taken to be definitive of moderate deflationism, so that anyone who endorses moderate deIII and IV]; and Richard [225, p. 43]. 236 flationism must endorse both claims. But the point that I will stress as we consider the various claims about truth that are associated with moderate deflationism is that each of these claims is logically distinct from all of the others–no such claim entails any of the others, nor is it entailed by any of the others. And this calls into question the standard assumption that these theses come only as a package deal. What will emerge, in other words, is that the choice we face is not simply to accept or reject moderate deflationism. The interesting and highly consequential choice is to determine to what degree one accepts moderate deflationism. First, (Transparency) doesn't entail (Explanation). I'll demonstrate lack of entailment in what follows by appealing to countermodels. Talk of 'models' here is meant to be somewhat loose. In the present sense, a model is simply a logically possible state of affairs. Here, then, is a countermodel which demonstrates that (Transparency) doesn't entail (Explanation): • (i) Truth is metaphysically transparent because – (a) The only essential fact about truth is that being true consists in corresponding to a worldly fact and – (b) Our ordinary conception of truth (see § 5.4.5 for a more careful account of conceptions) entails this fact about truth • (ii) Truth enjoys explanatory power because we can explain certain phenomena, e.g. the nature and norms of belief, by appealing to correspondence to 237 a worldly fact. Conversely, (Explanation) doesn't entail (Transparency). Here's a countermodel: • (i) Truth lacks explanatory power • (ii) Truth isn't metaphysically transparent (truth is metaphysically opaque) because: – (a) The essential facts about truth are exhausted by the instances of:10 ∗ (1) For all x: x is true iff x represents that p and p, together with the fact that truth is instantiable only by propositions – (b) To possess the ordinary concept truth, it is necessary and sufficient to be disposed to accept every token of every instance of (1) in the absence of supporting argumentation and in every context. So we've now distinguished between two logically distinct senses in which truth might be an insubstantive property: truth might be metaphysically transparent or truth might be a non-explanatory property. Constitution Whenever he explicitly specifies the sense in which he takes truth to be an insubstantial property, Horwich explains that he regards substantial properties as those 10 We first encountered this schema in § 4.2.2. 238 properties "for which there might well be a constitution theory."11 Focusing on the opposition between deflationary and correspondence-theoretic views of truth, Julian Dodd [76, pp. 133-4] echoes Horwich's suggestion as follows: [According to the deflationist,] there can be no account of what truth consists in: there is no prospect of discovering a property F shared by all and only the truths, such that the truths are true because they are F . . .[T]he deflationist's contention is stronger than a mere rejection of correspondence: it is that the kind of project undertaken by a correspondence theorist–the search for a property F explanatory of truth–is misconceived. So Horwich and Dodd associate the following thesis with moderate deflationism: • (Constitution?) There is a property truth, but it is insusceptible to a constitution theory (i.e. truth exists, but there is no possible, true constitution theory for truth). 11 [131, p. 143]. For discussion of the thesis that truth is insubstantive in this sense, see David [58, pp. 65-6]; Devitt [71, p. 32]; Dodd [77, p. 298]; Field [98, p. 76]; and Horwich [134, p. 57]. For related discussion, see Burgess [32, pp. 259-60]; Devitt [71, p. 31]; Horwich [130, pp. 10, 29, 42, 104, 107, 113, 123], [132, p. 75], [133, p. 38]; Price [216, p. 250]; Richard [225, pp. 1-4, 42]; and Wright [276, pp. 34-9, n. 9]. 239 Recall that a constitution theory for a property P has the following form:12 • (CT) For all x: x's instantiating P consists in x's instantiating P′. As Dodd points out and as critics of deflationism are acutely aware, the intention behind (Constitution?) is to directly undermine the essence project, whose principal aim is to construct an accurate constitution theory for truth that will reveal truth's complex essence. So as with (Transparency), were we able to establish that (Constitution?) is true, the result would be a wholesale transformation of the traditional truth-theoretic programme. (Constitution?) is, then, clearly a deflationary thesis about truth. The trouble is that (Constitution?) doesn't quite capture what the moderate deflationist is after here. Notice first that (Constitution?) dovetails with a variety of alethic primitivism–alethic anti-reductionism–that we discussed in § 2.2.1. That (Constitution?) is a primitivist thesis about truth should serve as an initial tip that it may be too severe of a thesis even for the deflationist. For after all, deflationists tend to see their views as alternatives to, not species of, primitivism.13 And indeed, the alethic minimalist should actually reject (Constitution?). The form of a constitution theory for truth is: 12 For the reasons given in § 2.2.1, in what follows we'll take the form of constitution theories for properties to be slightly different from that which Horwich assigns to them. 13 Horwich [131, p. 10], for instance, (in)famously dismisses primitivist theories as the "resort only of those who feel that the decent alternatives have been exhausted." 240 • (CTT ) For all x: x's instantiating truth consists in x's instantiating P. By fiat, constitution theories for properties are non-circular, so 'P' cannot contain 'truth,' nor any synonym thereof. It is acceptable, however, for 'P' to be coreferential with 'truth,' and indeed if being true consists in instantiating P, it's natural to expect that these expressions will be coreferential. To see how the minimalist might go about replacing 'P,' consider the class of propositions that are denoted on the left-hand sides of the instances of (PT). Call these the minimally true propositions. Each member of this class bears a resemblance to every other member that no member bears to a non-member. Minimally true propositions are similar to one another in that for each such proposition 〈p〉, p. According to alethic minimalism, that is, truth is the property that 〈p〉 instantiates iff p. For minimalists, this definite desription–'the property that 〈p〉 instantiates iff p–'refers to truth. This description is free of the expression 'truth.' They also look to be non-synonymous expressions. The definite description contains the biconditional connective 'iff,' which surely has its own unique meaning. And it's rather implausible to regard the meaning of this connective as forming part of the meaning of 'truth.' When I ask, 'What is the nature of truth?' I don't seem to be invoking the notion of biconditionality. Since this definite description doesn't contain 'truth' and has a meaning distinct from that of 'truth,' there is an admissible constitution theory for truth that involves this definite description, namely: 241 • (CTM) For all x: x's instantiating truth consists in x's instantiating the property that 〈p〉 instantiates iff p. So minimalists should actually hold that truth is susceptible to a constitution theory. For this reason, (Constitution?) doesn't quite capture the point at which moderate deflationists diverge from traditional truth theorists as to truth's constitution. Where, then, is the actual point of divergence? What distinguishes a deflationary constitution theory for truth such as (CTM) from, say, a correspondencetheoretic constitution theory for truth such as the following: • (CTCorr) For all x: x's instantiating truth consists in x's being isomorphic to a worldly fact. What the moderate deflationist needs to capture, I think, is a sense in which (CTM) is more 'trivial' than (CTCorr). In doing so, they would secure the result at which they ultimately aim, namely to undermine the project of constructing non-trivial constitution theories for truth such as (CTCorr). But in what sense is (CTM) more trivial than (CTCorr)? Here's a suggestion: in judging that (CTM) is the more trivial claim, we're tacitly relying upon the notion of metaphysical transparency. We think that anyone who possesses the concept truth should, after reflecting upon this concept, find (CTM) obvious. And this in contrast to (CTCorr). Not only might one not find (CTCorr) obvious after reflecting upon truth, one might reasonably reject it (and indeed, I think that one will). 242 The notion of metaphysical transparency at play here is somewhat different from the notion that figures in (Transparency). When we say that (CTM) is transparent/obvious, what we're saying is that the fact about truth that (CTM) records is transparent/obvious. So whereas the notion of transparency in (Transparency) is property-theoretic, the notion that we're currently interested in is fact-theoretic. So let a fact F about truth qualify as metaphysically transparent (otherwise, metaphysically opaque) iff the following holds: • (TransparentF ) Any actual cognizer who possesses the ordinary concept truth is in a position to know F without further empirical inquiry or a priori argumentation. And call a constitution theory for truth opaque iff the fact about truth that it records is metaphysically opaque. The moderate deflationist thesis about truth's constitution is then: • (Constitution) There is a property truth, but it is insusceptible to an opaque constitution theory. So in opposing traditional accounts of truth's constitution, moderate deflationists invoke the notion of metaphysical transparency. This shouldn't lead us to think, however, that (Constitution) is logically dependent upon (Transparency), or vice versa. First, (Transparency) doesn't entail (Constitution). Here's a countermodel: 243 • (i) There is a true, opaque constitution theory for truth • (ii) Truth is metaphysically transparent because any actual cognizer who possesses truth is ipso facto in a position to know, without relying upon further empirical inquiry or a priori argumentation, (i) and all of the (other) essential facts about truth. Conversely, (Constitution) doesn't entail (Transparency). Here's a countermodel: • (i) Truth is insusceptible to an opaque constitution theory • (ii) Truth is metaphysically opaque because: – (a) S possesses the ordinary concept truth iff S is disposed to accept every token of every instance of schema (1) in the absence of supporting argumentation and in every context – (b) It's an essential fact about truth that truth is instantiable only by propositions (this fact, of course, isn't an instance of schema (1), nor is it entailed by the class of these instances). (Constitution) is also logically distinct from (Explanation). First, (Constitution) doesn't entail (Explanation). Here's a countermodel: • (i) Truth enjoys explanatory power because it's a fact about truth that truth is instantiable by propositions. So if John hypothesizes that the Pope 244 is virtuous, we can explain why what John hypothesized is truth-apt by drawing on the facts that John hypothesized a proposition and propositions are truth-apt • (ii) Truth is insusceptible to an opaque constitution theory. Conversely, (Explanation) doesn't entail (Constitution). Here's a countermodel: • (i) There is a true, opaque constitution theory for truth, e.g. that being true consists in being ideally rationally assertible (cf. Putnam [220]) • (ii) Truth lacks explanatory power because we are unable to explain any phenomena by appealing inter alia to ideal rational assertibility. And this because we are congenitally unable to fully grasp what the relevant ideal epistemic state would involve.14 So we've now identified three logically distinct 'insubstantiality theses' about truth: that truth is metaphysically transparent, that it is non-explanatory, and that it is insusceptible to an opaque constitution theory. 14 Recall that our 'models' are simply logically possible states of affairs. So this isn't to contend that we are unable to understand what an epistemically ideal state would involve, only that it's logically possible that we are; even Putnam's 1981 time-slice would grant that. 245 Sparseness In recent discussions of the metaphysics of deflationism, Doug Edwards [89] and Jamin Asay [9], [8, ch. 4] have proposed that the definitive moderate deflationist thesis about truth is that truth is not a very sparse property.15 The distinction between sparse and abundant properties was originally proposed by David Lewis [163] and has since been discussed rather extensively. According to Lewis, the sparse/abundant distinction is graded, with sparseness and abundance being inverses: properties are more or less sparse than other properties and the extent to which a property is sparse is inversely proportional to the extent to which it is abundant. At one extreme, Lewis contended, we have properties–presumably the properties taken to be fundamental by a final physics–which are maximally sparse or, in Lewis' terminology, perfectly natural. At the other extreme, we have properties–best exemplified perhaps by Nelson Goodman's famous property grueness–which are disjunctive and gerrymandered and thus maximally abundant. To properly describe this spectrum of properties, we need certain diagnostics by which we can determine how sparse a given property is. Edwards proposes three Lewisian diagnostics for sparseness, which have it that the extent to which a property P is sparse is determined by:16 15 Lynch [174, p. 68] once made a similar proposal, that deflationists take the truths to fail to constitute a 'minimally objective kind.' 16 [89, p. 12]. See also Dorr and Hawthorne [79, esp. § 2] and Schaffer [234] for very helpful discussion of the sparse/abundant distinction and the related Lewisian notion of naturalness. 246 • (S1) the length of P's chain of definability from the 'perfectly natural' properties (the length of this chain is positively correlated with P's degree of sparseness); • (S2) whether P grounds 'genuine similarities' among its bearers; and • (S3) whether P enjoys causal-explanatory power. So according to Edwards and Asay, the thesis about truth that moderate deflationists should be understood as advancing is: • (Sparseness) Truth is not a very sparse property. The trouble, however, is that the issue as to whether truth is rather sparse doesn't seem to be an issue in which moderate deflationists are especially interested. No moderate deflationist, to my knowledge, has explicitly discussed how long the definability chain connecting truth to the perfectly natural properties might be. What's more, even if moderate deflationists are committed to holding that the length of this chain is rather long, they are presumably not alone–many traditional truth theorists are presumably committed to the same. If the perfectly natural properties are those properties that the final physics will take as fundamental, it's reasonable to predict that the definability chain connecting the perfectly natural properties to say, superwarrant, ideal rational assertibility, worldly factidentity, or isomorphism to a worldly fact would be rather long. Substantivists about truth, that is, would seem to agree that truth can't be simply defined in 247 terms of the perfectly natural properties. So deflationism isn't the provenance of this claim. It might seem as though the issue as to whether truth grounds 'genuine similarities' among the truths is of particular concern to moderate deflationists. Dodd, recall, holds that according to deflationists, "there is no prospect of discovering a property F shared by all and only the truths, such that the truths are true because they are F ." Notice, however, that in making this claim, Dodd does not take deflationists to deny that truth grounds genuine similarities among the truths. According to Dodd, what deflationists deny is that there is a property– namely, that which would be mentioned on the right-hand side of a constitution theory for truth–whose instantiation by all and only the truths explains why the truths are true. What deflationists deny, according to Dodd, is that there is a property which grounds truth, not that truth fails to ground similarities among the truths. Still, it might be pointed out, moderate deflationists do characteristically deny that we can explain e.g. why all and only the true propositions are correct to believe by appealing to the nature of truth. Truth, moderate deflationists claim, fails to ground the sorts of similarities among the truths that traditional truth theorists have taken it to ground. But what's vital to appreciate here is why moderate deflationists tend to deny this. As we've seen, moderate deflationists tend to deny that truth grounds genuine similarities among the truths because 248 they tend to hold that we can't explain anything by appealing to truth–truth, they say, lacks explanatory power altogether. So the issue as to whether truth grounds genuine similarities among the truths isn't a matter of separate concern for moderate deflationists. It's an aspect of their more general concern with the explanatory power of truth. And the same goes for the issue as to whether truth enjoys causal-explanatory power. For one thing, as Nic Damnjanovic [56] and [57, esp. § 3.1] has stressed, whether truth enjoys causal-explanatory power depends to a significant extent upon controversial issues to do with the nature of causation, including the viability and import of the distinction, due to Jackson and Pettit [138], [139], between causal efficacy and causal relevance. Endorsing a moderate deflationist view of truth doesn't obviously commit one to a position on these issues about causation, so it's wise to refrain from associating with moderate deflationism a thesis as to the causal-explanatory power of truth. This shouldn't blind us to the fact, of course, that moderate deflationists are quite concerned with the explanatory power of truth. But again, the way to codify this is to associate with moderate deflationism the thesis that truth exists, but lacks explanatory power, i.e. (Explanation).17 17 Perhaps Edwards and Asay's intention is prescriptive rather than descriptive, so that their proposal is only that moderate deflationists ought to endorse (Sparseness), not that any extant moderate deflationists do endorse it. As best I can tell, the case for this recommendation would be that none of the other theses that have been associated with moderate deflationism are, in 249 So although the issue as to whether truth is rather sparse is an interesting one, the thesis that it isn't shouldn't be associated with moderate deflationism. The theses about truth that should be associated with moderate deflationism are (Transparency), (Explanation), and (Constitution). But to be fully entitled to draw this conclusion, we'll need finally to consider a fifth claim about truth that is often associated with moderate deflationism, the claim that truth is a merely 'logical' property. Logicality A number of deflationists have contended that truth is an insubstantial property in the sense that it is merely a 'logical' property.18 The difficulty in assessing this thesis is that it is rarely accompanied by an elucidation as to what is meant to distinguish logical from non-logical properties. To my knowledge, the most helpful discussion of this issue in the literature on deflationism is again due to Damnjanovic [57, § 2.1]. Damnjanovic's discussion brings into focus two important details. The first is that when they claim that truth is merely logical, deflationists are often advancing a thesis either at fact, definitive of the view. In § 5.4.4, we'll assess Edwards' arguments to this effect. 18 See Damnjanovic [56], [57]; Field [99, p. 322], [100, § 5], [101, p. 532]. For related discussion, see Beall [21]; Blackburn [24, p. 263]; Collins [45, p. 503]; Field [98, p. 76]; Hill [119, p. 22]; Horwich [131, pp. 2-5], [134, p. 78]; Horsten [127, §§ 5.1-5.2]; Künne [156, pp. 91, 338]; McGinn [185, ch. 5]; and Richard [225, p. 43]. 250 the linguistic level–i.e. a thesis about 'true' or 'is true–'or a thesis at the conceptual level–i.e. a thesis about truth. This again witnesses the importance of distinguishing between property-level, expression-level, and concept-level theses about truth. So in considering whether truth might be logical, the first task is to determine what feature might distinguish logical properties other than their merely being denoted by logical predicates or logical concepts.19 The second important detail that Damnjanovic brings to light is that when deflationists claim that truth is merely logical, they seem to be invoking a putatively pretheoretical understanding of what distinguishes logical properties (predicates, concepts) from non-logical properties (predicates, concepts). Damnjanovic is forthright on this score, as he ventures to clarify the pretheoretical notion of logicality by appealing to paradigm cases:20 I assume we would all agree that on the logical side of this distinction we have expressions like 'and,' 'every,' 'or,' 'not,', and on the nonlogical side we have expressions like 'blue,' 'tree,' 'magnetic,' 'justice,' and 'conscious.' Corresponding to these expressions, we have logical and non-logical properties and relations. Though the expression-property distinction is a bit too heavily lubricated here, the basic idea can be illustrated by considering the property being everything 19 Edwards [89, § 4] also offers helpful discussion of this point. 20 [57, pp. 46-7]. Cf. Field [99, p. 322]. 251 (in universe of discourse U). Were the quantifier 'every' to denote a property, it would presumably denote this property.21 The thesis that truth is a logical property is then to be understood as the contention that truth is relevantly similar to being everything (and relevantly dissimilar to e.g. blueness and being a tree). The question that arises at this point, of course, is: why is a raven like a writing desk? In what respects, that is, are truth and being everything meant to be similar? It's here that we have to buckle down and consider a candidate explanation of what distinguishes logical from non-logical properties. Otherwise, the claim that truth is a logical property looks to be either an expression-level or concept-level claim in disguise or else a property-level claim that is imprecise and thus unhelpful. Alfred Tarski offers what is perhaps the most influential account of the distinction between logical and non-logical properties. Tarski's view of what he calls 'logical notions' is inspired by the account of geometrical notions that falls out of Klein's Erlanger Programm. Klein's basic idea is that we can classify the notions that are distinctive to particular branches of geometry by reference to the sorts of transformations under which those notions are invariant. As the term is used in this context [261, p. 186], a transformation is a one-one function whose domain and range are each identical to the particular universe of discourse at issue. There are, for instance, transformations that preserve 21 The idea could also be illlustrated in reference to 'exists' and existence. 252 distance between points, which Tarski calls isometric transformations. A transformation f(x, y) is isometric just in case if (i) points a and b are in f 's domain, (ii) f maps a and b to points f(a) and f(b) in its range, and (iii) the distance between a and b is d, then (iv) the distance between f(a) and f(b) is also d. Tarski points out that all of the notions discussed in Euclidean geometry are invariant under all isometric transformations. And, as Tarski shows, we can characterize the distinctive notions of other branches of geometry by reference to other sorts of transformation. Tarski's key insight is that Klein's strategy can be generalized so as to generate an account of what makes a notion logical. As Tarski indicates, he uses the term 'notion' rather broadly [261, p. 147]: I use the term 'notion' in a rather loose and general sense, to mean, roughly speaking, objects of all possible types in some hierarchy of types like that in Principia mathematica. Thus notions include individuals (points in the present context), classes of individuals, relations of individuals, classes of classes of individuals, and so on. For Tarski, then, notions approximate to what we, speaking very generally, often call 'entities' or simply 'things.' Tarski then proposes to generalize Klein's strategy as follows [261, p. 149]: Now suppose we continue [Klein's] idea, and consider still wider classes of transformations. In the extreme case, we would consider the class 253 of all one-one transformations of the space, or universe of discourse, or 'world,' onto itself. What will be the science which deals with the notions invariant under this widest class of transformations? Here we will have very few notions, all of a very general character. I suggest that they are the logical notions, that we call a notion 'logical' if it is invariant under all possible one-one transformations of the world onto itself. So for Tarski, a notion counts as logical just if it is invariant under all possible transformations of the world onto itself. We might call this sort of transformation a total transformation, since it is simply a transformation of the world onto the world. Since our present aim is to specify what might be involved in truth's being a logical property, we can focus upon the case of properties. A property P will count as logical in the Tarskian sense just if where f(x) is a total transformation, if f(x) maps a to f(a) and a instantiates P, then so does f(a). Perhaps the clearest case of a property that is logical in this sense is the property being self-identical. Tarski points out that numerical properties, construed as second-order properties that are instantiable by classes of particulars, also clearly come out as logical on this account, given that transformations are stipulated to be one-one.22 It's also easy to see that the property being everything (in universe of dis22 Though as he points out [261, § 4]), this result doesn't strictly commit him to logicism. 254 course U) comes out as logical in the Tarskian sense. This property is instantiated by only one entity–the universe of discourse. So if we map the universe onto itself via a total transformation f(x), then it's clearly the case that if f(x) maps entity a to entity f(a) and a instantiates being everything, then so does f(a). For in this case, both a and f(a) are simply the universe, which alone instantiates being everything.23 By contrast, properties like blueness and being a tree clearly come out as non-logical in the Tarskian sense. There are total transformations which map the tree in my front yard to a spatial point three miles north of the tree's base and others which map the blue sweater in my closet to the green sweater in my closet.24 So far so good. We now have in hand a conception of what distinguishes logical from non-logical properties that we can use to clarify Damnjanovic's appeal to paradigm cases. The deflationary contention here is that like the property being everything, truth is a logical property in the Tarskian sense, i.e. • (Logicality) Truth is invariant under all possible total transformations. At first glance, (Logicality) may seem to be a distinctively deflationary thesis about truth. For the truth of (Logicality) would jeopardize many traditional 23 Existence will also come out as a logical property in the Tarskian sense, given (i) that there is a property existence and (ii) that the world contains no non-existent objects. 24 For further discussion of the Tarskian conception of logical notions and the related notion of formality, see Sher [238], [242], [243], [244]. 255 monist truth theories. Consider, for instance, a fact-based correspondence theory which takes the truth of a proposition to amount to its corresponding to a fact. Where 〈p〉 is a proposition that might be plausibly thought to correspond to a fact (e.g. 〈tables are solid〉), it's easy to see that there is a total transformation that maps 〈p〉 onto a proposition 〈q〉 that doesn't correspond to a fact (e.g. 〈7 + 5 = 13〉). Epistemic truth theories suffer a similar fate since as we saw, they take truth to be globally evidentially constrained. Where 〈p〉 is epistemically true (superwarranted, say), there is a total transformation that maps 〈p〉 onto a proposition that fails to be epistemically true, e.g. the proposition denoted by (4) above. (Logicality), however, doesn't threaten every sort of traditional monist truth theory. As we noted, numerical identity is a logical relation (or relational property, as per our going convention) in the Tarskian sense. So (Logicality) is clearly compatible with both modest and robust identity theories. Given that one of the major deflationary ambitions in truth theory is to upend traditional monism as such, this is reason enough to refrain from classifying (Logicality) as a distinctively deflationary thesis about truth. A second reason is that (Logicality), like (TransparencyL) and (Constitution ?), would jeopardize a paradigmatically deflationary theory of truth, namely alethic minimalism. For the minimalist, truth is the property that is instantiated by 〈p〉 iff p. If this were so, then truth would clearly be a non-logical property in the 256 Tarskian sense. There is, for instance, a total transformation on the actual world that maps 〈tables are solid〉 to 〈7+5 = 13〉. Since tables are, in fact, solid, 〈tables are solid〉 instantiates truth, according to the minimalist. But since seven added to five is not thirteen, 〈7 + 5 = 13〉 will fail to instantiate truth. This shows that for minimalists, truth isn't invariant under all possible total transformations. So in the end, I think that it is a mistake for moderate deflationists to contend that truth is a logical property. If what they really mean is just that 'is true' is a logical predicate that denotes truth or that truth is a logical concept that denotes truth, then they should dispense with the misleading, apparently metaphysical talk of 'logical properties.' Alternatively, if they mean that truth is a logical property in some sense other than the Tarskian one, then they should (i) specify what the intended sense amounts to and (ii) explain why the contention that truth is a logical property in this sense is, in contrast to (Logicality), a distinctively deflationary thesis about truth. At present, we should refrain from associating (Logicality) with moderate deflationism. We've distinguished, then, three senses in which the moderate deflationist may take truth to be an insubstantial property. They may take truth to be metaphysically transparent, non-explanatory, or insusceptible to an opaque constitution theory. Call this the multi-factor analysis of moderate deflationism. A consequence of the multi-factor analysis is that moderate deflationism cannot be reduced to a single, non-disjunctive thesis about truth. There are, rather, three 257 non-disjunctive theses about truth that are each partially but not exclusively definitive of moderate deflationism. If we wish to encapsulate moderate deflationism's view of truth in a single thesis, the best that we can do is the highly disjunctive: • (MD) Truth is metaphysically transparent or non-explanatory or insusceptible to an opaque constitution theory. But the more revealing way to think about moderate deflationism is to recognize that deflationism comes in degrees. The degree to which one endorses moderate deflationism is determined by how many of (Transparency), (Explanation), and (Constitution) one accepts. So in the end, the really interesting question is not 'Should we be moderate deflationists?' but 'To what extent should we be moderate deflationists?' In determining where they stand vis-à-vis moderate deflationism, truth theorists have options. 5.2.4 Edwards on substantiality My thinking about moderate deflationism is significantly indebted to recent work by Doug Edwards. But the conclusion of Edwards' discussion, as we've seen, is that (Sparseness) should be regarded as the definitive thesis of moderate deflationism. His case for this contention is mostly a negative one. What Edwards 258 argues is that (Transparency), (Constitution)25, and (Logicality) each fail to meet both the Deflationary and Metaphysical Constraints. Since I entirely agree that (Logicality) fails to meet these constraints (though for different reasons), I would like to explain why I don't find Edwards' cases against (Transparency) and (Constitution) compelling. Transparency The first concern that Edwards offers against associating (Transparency) with moderate deflationism is that [89, p. 5]: [Metaphysical] opacity and transparency are not, strictly speaking, metaphysical features of properties, [but] rather epistemic features which concern the ability of our concepts to fully reveal the nature of properties. The trouble with this objection is that it begs the key question–it rules out by fiat the possibility that a feature of a property could be both interestingly metaphysical and interestingly epistemic. And indeed, metaphysical transparency and metaphysical opacity are features that straddle metaphysics and epistemology. Whether truth is metaphysically transparent or metaphysically opaque is determined, in part, by the content of our ordinary concept truth. Given that 25 Though he seems to actually have (Constitution?) in mind; this won't matter for our purposes. 259 their instantiation is partially determined by the content of one of our concepts, metaphysical transparency and metaphysical opacity can be fairly regarded as epistemic features of properties. The key detail, though, is that whether truth is metaphysically transparent or metaphysically opaque isn't just a matter of what the content of truth happens to be. For truth to be metaphysically transparent, it must be the case that in possessing truth, a cognizer is in a position to know, without further empirical inquiry or a priori argumentation, every essential fact about truth. So truth's essence is also partially determinative of truth's metaphysical transparency. And surely essences are about as metaphysical as it gets. Edwards' second concern [89, p. 6] is that whether truth is metaphysically transparent seems to depend too heavily on which view is correct about the ordinary concept of truth, which makes the issue over what kind of property truth is secondary, and in a sense, epiphenomenal to this debate. Edwards' rationale here draws on two available accounts of the ordinary concept truth. One might be a deflationist about truth holding e.g. that to possess truth one must be disposed to accept every token of every instance of (PT) in the absence of further argumentation and in every context. Alternatively, one might endorse a substantivist view of truth holding e.g. that to possess 260 truth, one must be disposed to accept in the absence of further argumentation and in every context every token of every instance of the fact-based correspondence schema: • (FBC) 〈p〉 is true iff 〈p〉 is isomorphic to a fact Φ. Edwards' argument then proceeds as follows: • (1′) It is epistemically possible that the correct account of truth is deflationary while the correct account of truth is substantivist [Assumption] • (2′) Conversely, it is epistemically possible that the correct account of truth is substantivist while the correct account of truth is deflationary [Assumption] • (3′) In either case, truth is metaphysically opaque [(Transparency)] • (4′) So, truth is metaphysically transparent only if both the correct account of truth and the correct account of truth are deflationary or if both are substantivist [(1′)-(3′)] • (5′) Thus, to determine whether truth is metaphysically transparent or metaphysically opaque, all that we must determine is whether the correct account of truth is deflationary or substantivist [(1′)-(4′) (?)] • (6′) Therefore, the issue as to whether truth is metaphysically transparent 261 or metaphysically opaque actually arises at the level of concepts, not at the level of properties [(1′)-(5′)]. But the inference from (1′)-(4′) to (5′) is a non sequitur. As (1′)-(4′) bring out, for truth to be metaphysically transparent, it must be that both the correct account of truth and the correct account of truth are deflationary, or that both are substantivist. So to determine whether truth is metaphysically opaque or metaphysically transparent, we must determine not only who has the right theory of truth, we must also determine who has the right theory of truth. We must investigate, that is, at both the level of concepts and the level of properties. Thus despite Edwards' misgivings, I propose that we associate (Transparency) with the moderate deflationist conception of truth. Constitution Edwards [89, § 5] also finds it problematic to associate (Constitution) with moderate deflationism. His first concern that a property might have a true constitution theory while nevertheless not being very sparse in virtue of the fact that its extension is rather miscellaneous. Edwards draws here upon the property being jade. We know now that there are two chemically distinct minerals which we ordinarily call 'jade,' namely jadeite and nephrite. The extension of being jade is thus notably miscellaneous; its extension contains jadeite and nephrite, which are chemically distinct. But as Edwards points out, as long as we are willing to 262 countenance disjunctive properties, being jade does have a constitution theory. In fact, since we now know that there are two minerals which fit our ordinary conception of jade, being jade admits of an opaque constitution theory, namely: • (CTjade) For all x: x's instantiating being jade consists in x's instantiating being jadeite or being nephrite. So the problem is meant to be that a property might be susceptible to an opaque constitution theory while not being very sparse. The thought, I take it, is that if we took (Constitution) to be the defining thesis of moderate deflationism, then we would have to allow for the possibility that truth is substantial (i.e. that (Constitution) is false), but not very sparse. But if truth is rather abundant, the thought goes, then truth is like grueness–hardly among the elite, highly natural properties–so how could it be right to say that truth is a substantial property? But I don't see this as much of a concern. As we've noted, substantiality is a purely theoretical notion. Given that the moderate deflationist's principal aim here is to undermine the essence project, it is perfectly appropriate for them to take the issue as to whether truth is a substantial property to involve only (Transparency), (Explanation), and (Constitution). For if any of those claims were true, then the essence project would be severely jeopardized. By contrast, the truth of (Sparseness) wouldn't obviously have this effect. So while the fan of the sparse/abundant distinction may certainly introduce a notion of substantiality, according to which a property is substantial to the degree that it is sparse, it is 263 question-begging to impose this conception of substantiality upon the moderate deflationist.26 Edwards' final concern is that if (Constitution) is associated with moderate deflationism, then primitivist views of truth will be classified as deflationary, contrary to the intentions of primitivists. And we've seen that there is some truth to this. Alethic anti-reductionists contend that truth is insusceptible to any sort of constitution theory. So anti-reductionists are indeed committed to denying that truth is susceptible to an opaque constitution theory, i.e. to (Constitution). But I'm unmoved. For one thing, anti-reductionists are free to resist moderate deflationism on other fronts–namely, by taking truth to be metaphysically opaque or explanatory. So anti-reductionism doesn't simply collapse into moderate deflationism. Additionally, it's worth noting that anti-reductionism is deflationary, in the sense that if it were true–if there were no possible, true constitution theory for truth–then the essence project would be seriously jeopardized. The same goes for the other species of alethic primitivism–if any of them were true, this would threaten the viability of paradigmatic, traditional analyses of truth. And that would certainly be deflating. 26 Edwards raises the related concern that e.g. a fundamental physical property might be insusceptible to a constitution theory while nevertheless being intuitively 'substantial,' given that it is rather sparse. But this too presupposes a conception of substantiality that the moderate deflationist would reject. 264 5.2.5 Minimal pluralism and deflationism Is minimal pluralism a deflationary account of truth? With traditional deflationists, minimal pluralists refuse to posit a single, domain-general property truth. But unlike traditional deflationists, minimal pluralists posit two pluralities of alethic properties. So while it's clear that because it entails that truth does not exist, minimal pluralism is situated within the camp of deflationary truth theories, it would be hasty to simply classify minimal pluralism as deflationary and move on. To properly assess the extent to which minimal pluralism deflates truth, we should apply the multi-factor analysis in considering how substantial proposition-truth and sentence-truth–the properties with which minimal pluralists replace truth– turn out to be. Transparency Since the notion of metaphysical transparency involves the ordinary concept truth, we'll need to say a bit about the possession-conditions for truth. At several points, we've alluded to the distinction between a concept and the conception of that concept. Douglas Patterson [202, p. 13] nicely describes what the conception of truth amounts to: [T]heories of truth are supposed to state what anyone who has any beliefs that this or that is true must be at least disposed to accept about truth upon consideration; such claims are conceptually analytic. . .A 265 conception of truth is a set of putatively conceptually analytic claims for it. The aim in the theory of truth is to state the actual conception of truth, the one that includes all and only claims that anyone who has any beliefs that anything is true must be disposed to accept upon consideration. We can formulate the possession-conditions for truth by focusing upon truth's conception. Appealing to the propositions 〈p1〉,. . . ,〈pn〉 that constitute the conception of truth, we have it that a cognizer S possesses truth just in case S is disposed to accept φ1, . . . , φn upon suitable consideration. This proposal might look to generate a vicious infinite regress. We have it that suitable consideration of 〈p1〉,. . . ,〈pn〉 will cause S to accept 〈p1〉,. . . ,〈pn〉. Presumably, one of the questions that S will ask herself when engaged in such consideration is whether 〈p1〉,. . . ,〈pn〉 are true. In general, when I am determining whether to accept a particular proposition, I am concerned inter alia to determine whether it is true. I may also ask, for instance, whether I have warrant for believing the proposition or whether I know the proposition, but quite plausibly, the reason that I ask these questions is that I take warrant and knowledge to be intimately related to truth–I take warrant to be truth-conducive and knowledge to be factive. This may seem to present a problem for the strategy of formulating possession-conditions for truth by appealing to truth's conception. For it might be wondered: how could S engage in suitable consideration of 〈p1〉,. . . ,〈pn〉 unless 266 S already possesses truth? But wouldn't this mean that to suitably consider 〈p1〉,. . . ,〈pn〉, S must already satisfy the possession-conditions for truth? So aren't we off on a vicious infinite regress? We can mitigate this concern by distinguishing between the conceptual scheme that is used by the subject and the conceptual scheme that is used by the theorist. In the Warheitsbegriff [260], Tarski draws a similiar, highly influential distinction between the object language–the language about which one is speaking–and the metalanguage–the language in which one is speaking. When I point out, for instance, that 'La tierra es verde' means in Spanish that the land is green, I am using English as a metalanguage to make a claim about a sentence in the target object language, namely Spanish. We can similarly distinguish between the scheme of concepts that is possessed the cognizer about which we are theorizing and the scheme of concepts that we possess as theorists. We might call these the object scheme and the metascheme. The object scheme in the present case is that of a cognizer S who lacks the concept truth. S may possess other concepts, e.g. rudimentary sensory concepts such as concepts of the primary colors, the relative volume of noises in their immediate environment, heat and cold, etc. They may also have oveheard a fair amount of dialogue about truth between competent users of their home language, though not yet enough for our subject to gain mastery of truth. The proposal is that to possess truth, our subject must be disposed to accept the 267 propositions that constitute truth's conception upon suitable reflection. We've noted that in general, when you and I consider whether to accept a proposition, we ask inter alia whether it is true, so that we wouldn't count someone like us– roughly, a typical adult–as having suitably reflected upon the proposition unless they too asked whether it is true. But the key detail is that you and I, unlike the subject of our theorizing, possess truth. It's for this reason that we are able to ask whether propositions are true and to theorize about the role of truth in suitable reflection on our part. But it would hardly be plausible to suggest that in deciding whether they ought to accept a proposition, someone who lacks truth ought to ask whether the proposition is true, on pain of having reflected unsuitably upon it. For such a subject is simply incapable of asking whether propositions are true, given that they lack truth. So we should formulate the possession-conditions for truth in such a way that one who lacks truth could satisfy them: • (Truth) S possesses truth just in case S is disposed to accept the propositions 〈p1〉,. . . ,〈pn〉 constituting truth's conception upon suitable reflection, i.e. just in case for every such pi, S is disposed to accept that pi upon considering whether pi. Which propositions, then, constitute truth's conception? We've seen (§ 4.2.1) that the Meno problems which arise within truth theory can be handled by appealing to a collection of pretheoretical beliefs that are possessed by those 268 who possess truth. And we take these beliefs to be codified by the neutral platitudes–(Reality), (Covariance), and (Inquiry). The neutral platitudes, recall, are closed sentences that express propositions. So we can take the propositions that constitute truth's conception to be the propositions that the neutral platitudes express: • (TruthMP ) S possesses truth just in case upon suitable reflection, S is disposed to accept the propositions expressed by the neutral platitudes, viz. – (i) that a truth-bearer is true iff it 'tells it like it is,' 'agrees with reality,' or 'corresponds to the facts;' – (ii) that the truth of a truth-bearer covaries with a distinct state(s) of the world 'determined' by that truth-bearer; and – (iii) that if a given truth-bearer is true, then it is ipso facto correct, to some extent, to endorse that truth-bearer when engaging in inquiry. The neutral platitudes, that is, circumscribe the ordinary concept truth. We're now in a position to see that proposition-truth and sentence-truth are metaphysically opaque properties. It is an essential fact about proposition-truth that it is instantiable only by propositions. And likewise, it is an essential fact about sentence-truth that it is instantiable only by declarative sentence-tokens. To possess truth, it isn't required that S possess the concept proposition, 269 nor that S possess the concept indicative sentence-token. This clearly follows from (TruthMP ), since (TruthMP ) adverts to the general notion of a truth-bearer, rather than the more specific notions of proposition and indicative sentence-token.27 One who lacks proposition is not in a position to know, without relying upon further empirical inquiry or a priori argumentation, that proposition-truth is instantiable only by propositions. To know this, one must possess proposition and to possess proposition, one must engage either in empirical inquiry (investigating how fellow speakers use the word 'proposition') or a priori argumentation (reasoning e.g. that since what John said yesterday is true, then there must be something that John said–but what could that be?). For similar reasons, one who lacks indicative sentence-token would need to engage either in further empirical inquiry or in a priori argumentation in order to come to know that sentence-truth is instantiable only by indicative sentencetokens. There are, then, essential facts about proposition-truth and sentence-truth that one who posssesses truth needn't be in a position to know without relying upon further empirical inquiry or a priori argumentation. So while propositiontruth and sentence-truth are minimal properties, in the sense that they don't involve e.g. correspondence to a worldly fact or ideal rational assertibility, they 27 Also recall the case that we offered in § 4.2.2 when motivating the requirement that the alethic platitudes be neutral on the truth-bearer-kind issue. 270 are substantial in the sense of being metaphysically opaque. Constitution The minimal pluralist does take proposition-truth and sentence-truth to admit of constitution theories, namely:28 • (CTPT ) For all x: x's instantiating proposition-truth consists in x's instantiating the property that 〈p〉 instantiates iff p. • (CTST ) For all x: x's instantiating sentence-truth consists in x's instantiating the property that an indicative sentence-token 'S' instantiates iff 'S' expresses (in L, in c) a proposition-true proposition. Are (CTPT ) and (CTST ) opaque constitution theories? That is, do they respectively record facts about proposition-truth and sentence-truth that a cognizer who possesses truth may fail to be in a position to know, without relying upon further empirical inquiry or a priori argumentation? Yes, they do, and for reasons with which we're now familiar. The facts about proposition-truth and sentence-truth that are respectively recorded by (CTPT ) and (CTST ) are: • (2) The fact that for every entity x, x's instantiating proposition-truth consists in x's instantiating the property that 〈p〉 instantiates iff p and 28 (CTPT ) is, of course, identical to alethic minimalism's constitution theory for truth (§ 5.4.3). 271 • (3) The fact that for every entity x, x's instantiating sentence-truth consists in x's instantiating the property that an indicative sentence-token 'S' instantiates iff 'S' expresses (in L, in c) a proposition-true proposition. As we've seen, S may possess truth while failing to possess both proposition and indicative sentence-token. In order to know (2) and (3), one must possess the latter concepts–to know (2), one must possess proposition and to know (3), one must possess indicative sentence-token. And to come to possess these concepts, one must engage either in further empirical inquiry or in further a priori argumentation. So proposition-truth and sentence-truth are both susceptible to opaque constitution theories and are accordingly substantial in this sense. Explanatoriness Minimal pluralists take both proposition-truth and sentence-truth to enjoy explanatory power. To see how we may appeal to these properties in explanations, we can consider two cases. The first involves belief and the second involves assertion. We'll say that beliefs and assertions are each species of endorsement. Beliefs and assertions have propositional content. To believe that p is inter alia to endorse 〈p〉. Likewise, to assert that p is inter alia to endorse 〈p〉. If one performs an assertion in context c using an indicative sentence-token 'S' that expresses 〈p〉 in 272 L and in c, then one endorses 'S' in a derivative sense. Since 'S' expresses 〈p〉 in L and in c and one endorses 〈p〉, one endorses the use of 'S' to perform assertions in c, as well as its use in any other context in which it expresses 〈p〉. Roughly, if one uses 'S' to assert that p in c, then one commits to its being correct to so use 'S' and also commits to approving of other uses of 'S' to express 〈p〉. Recall that one of the neutral platitudes concerns the correctness of endorsing a particular truth-bearer: • (Inquiry) If a given truth-bearer is true, then it is ipso facto correct, to some extent, to endorse that truth-bearer when engaging in inquiry. The minimal pluralist accepts (Inquiry), taking truth to be normative over endorsement in the way that it states. More specifically, the minimal pluralist takes proposition-truth and sentence-truth to be normative over belief and assertion in the manner stated by (Inquiry). And in assigning proposition-truth and sentence-truth this normative status, minimal pluralists are in a position to explain the correctness of particular instances of endorsement. First, consider the case of belief. In the course of inquiry, S comes to believe that snow is white, thereby endorsing 〈snow is white〉. We intuitively classify S's belief as correct, at least to some extent. Why is it correct? Given that proposition-truth conforms to (Inquiry), we know that if 〈p〉 is propositiontrue, then it is ipso facto correct, to some extent, to endorse 〈p〉 when engaging in inquiry. We can thus explain why it is correct, at least to some extent, for S 273 to believe 〈snow is white〉–〈snow is white〉 is proposition-true, given that indeed, snow is white. We explain the correctness of a particular act of endorsement by appealing to the essence of proposition-truth–specifically, to its instantiationconditions. We can appeal to sentence-truth in explanations in much the same way. Consider the case in which S performs, in the course of inquiry, an assertion that snow is white by assertorically uttering the English sentence-token 'Snow is white.' Since sentence-truth conforms to (Inquiry), we know that if 'S' is sentence-true, then it is ipso facto correct, to some extent, to endorse 'S' when engaging in inquiry. So we can explain why it is correct, at least to some extent, for S to endorse 'Snow is white' when engaging in inquiry–'Snow is white' is sentence-true in English and in S's context of utterance. We can thus appeal to sentence-truth's essence–specifically, to its instantiation-conditions–to explain the correctness of particular acts of endorsement. So minimal pluralists take proposition-truth and sentence-truth to be substantial in the sense that they each enjoy explanatory power. What we have, then, is that according to minimal pluralists, proposition-truth and sentence-truth are maximally substantial. This shows that it would have been a serious mistake to simply classify minimal pluralism as a deflationary account of truth. What we now see is that yes, minimal pluralism is deflationary, in the sense that it eliminates truth. But it is also anti-deflationary, in the sense that it replaces truth with two 274 maximally substantial alethic properties, proposition-truth and sentence-truth. Better to say, then, that minimal pluralism is an eliminative, but nevertheless substantivist, account of truth. It gives to deflationism with one hand, but it withholds from deflationism with the other. Metaontology and metasemantics Minimal pluralists enjoy two significant advantages over mainstream deflationists in connection with the explanatory power of truth. The first is that minimal pluralism's metaontological commitments are more tenable than those of alethic minimalism. The problem for the minimalist, recall (§ 2.5.2), is that they posit truth but deny that truth has explanatory power. In turn, they violate a very weak, and thus difficult to deny, metaontological norm–namely: • (XP) One ought to posit entity e only if there is an explanandum d that can be explained by inter alia mentioning e. By contrast, minimal pluralists accord explanatory power to the properties with which they replace truth, proposition-truth and sentence-truth. So unlike alethic minimalists, minimal pluralists abide by (XP). Minimal pluralism's metaontological house looks to be in order. The minimal pluralist may also enjoy a metaontological advantage here over a variety of alethic pluralism recently detailed by Jc Beall [21]. Say that a unary 275 predicate T(x) is a transparent truth predicate for a language L iff T(x) satisfies the following two conditions: • (Pred) T(x) captures and releases for all sentences of L, i.e. for any Lsentence 'S,' (a) T('S') entails 'S' and (b) 'S' entails T('S') • (Trans) For all L-sentences 'S,' T('S') and 'S' are intersubstitutable in all nonopaque contexts (T(x) is transparent when applied to L-sentences). The deflated truth pluralist, says Beall, holds that the explanatorily fundamental truth predicate Tr(x) for English is a transparent truth predicate.29 The idea is that if there are any other truth predicates for English, they are truth predicates because they are defined in terms of Tr(x). By contrast, the transparent predicate Tr(x) isn't a truth predicate for English because it's defined in terms of some other truth predicate for English. Deflated truth pluralists are alethic pluralists at the linguistic level. They hold that in addition to its fundamental truth predicate Tr(x), there is at least one derivative truth predicate Tr1(x) for English that is defined in terms of Tr(x). Beall offers several paradox-related motivations that e.g. a paracomplete or paraconsistent logician could offer for positing a derivative truth predicate of this sort. 29 Beall [21, § 4.1] describes the deflated truth pluralist as taking 'our' fundamental truth predicate to be transparent; it's not obvious whether 'we' are meant to be English speakers, speakers of Indo-European languages, possible cognizers, or etc. This issue is significant, but we needn't settle it here. 276 For present purposes, the key detail is that deflated truth pluralists are deflationists [21, §§ 4, 4.1]. They hold that English contains Tr(x) because Tr(x) has certain distinctive logical features. We can use Tr(x), together with quantifier phrases, to perform generalizations that we couldn't otherwise perform (unless we had recourse to substitutional quantification). We can assert, for instance, 'Every possible token of the sentence-type ?S or not-S? is true' without (impossibly) asserting all of the infinitely many such possible tokens. English contains Tr(x), says the deflated truth pluralist, just because it is practical to have such an expression in the language. English doesn't contain Tr(x) because it denotes an alethic property that enjoys explanatory power–the deflated truth pluralist denies precisely that Tr(x) denotes such a property.30 It's here that metaontological considerations become particularly salient. Given that the deflated truth pluralist holds that Tr(x) is a predicate, they're under pressure to posit a corresponding property that this predicate denotes.31 The deflated truth pluralist denies that this property enjoys explanatory power. So 30 Beall [21, p. 336] does allow that the non-fundamental truth predicates may denote explanatory properties. He insists, though, that in appealing to these properties in explanations, we don't appeal to features of the properties which we come to know only via "analysis." The idea seems to be that in appealing to these non-fundamental 'truth properties' in explanation, we appeal only to features of the properties that are metaphysically transparent, in a sense similar to that outlined above. 31 And as Beall [21, n. 2] points out, it's quite important that deflationists take there to be a truth predicate for English, since a similar operator wouldn't afford the same expressive power. 277 again, given (XP), the minimal pluralist looks to enjoy the more secure metaontological footing. The deflated truth pluralist might suggest that they actually do have reason to posit an alethic property corresponding to Tr(x)32 This property, it might be thought, is expressively useful as indicated in the case above, even if it lacks explanatory power. But as is so often the case in truth theory, I think that it is vital to distinguish here between predicates, which in this case are expressions in a language, and the properties that they denote. Even as a substantivist about propositiontruth and sentence-truth, I'm happy to grant that having recourse to 'true' affords English speakers significant practical benefits, e.g. the ability to perform generalizations such as that mentioned above. But this is a point about a word–'true–'not a point about any particular property, e.g. proposition-truth or sentence-truth. The reason that I'm able to assert that every possible token of the type ?S or notS? is true without (impossibly) asserting every such token is that I have recourse inter alia to the quantifier 'every' and to 'true.' The practical, expressive utility, that is, stems from the lexical meaning of 'true,' rather than from features of some particular alethic property. So it can't be that we should posit a certain alethic property because the property affords us expressive benefits–that's not the sort of thing that properties do. 32 Thanks to Jc Beall for offering this response. 278 I think, then, that the deflated truth pluralist should go one of two ways. They should grant that the alethic properties that they posit enjoy explanatory power or they should offer an analysis of predication according to which predicates denote a kind of entity other than properties, e.g. concepts. To adopt the former strategy would be to embrace a less deflationary account of truth. If they opt for the latter strategy, then the deflated truth pluralist isn't obviously in competition with the minimal pluralist at the level of properties. Both would hold that 'true' denotes a concept and they could agree that all of the extant alethic properties enjoy explanatory power. The real conflict between the views may rather be over the issue as to what kinds of entity bear truth. The minimal pluralist takes 'sentence-true' to be a truth predicate for English in the sense of (Pred) (suitably augmented to account for context-sensitivity). And as best I can tell, 'sentence-true' is transparent when applied to English sentences. The minimal pluralist, though, doesn't take 'sentence-true' to be a fundamental truth predicate for English. 'Sentence-true' is a truth predicate for English because 'sentence-true' is defined in terms of 'proposition-true' and, according to the minimal pluralist, 'proposition-true' is a truth predicate for English. 'Proposition-true' isn't a truth predicate for English in the sense of (Pred), given that it is propositions, rather than sentences, that are proposition-true. But what this indicates, says the minimal pluralist, is that we should work with a broader notion of what it is to be a truth predicate. If we're to follow along 'capture279 release' lines (and I don't meant to suggest that we should), we should opt for the following conception: • (Pred?) T(x) is a truth predicate for L iff either (i) T(x) captures and releases for all sentences of L or (ii) T(x) captures and releases for all propositional designators (names and descriptions of propositions) in L, i.e. for any propositional designator '〈p〉' in L, (a) T(〈p〉) entails p and (b) p entails T(〈p〉). The disagreement here is, at bottom, a disagreement about what kinds of entity bear truth. Minimal pluralists take propositions and indicative sentencetokens to bear proposition-truth and sentence-truth, respectively. Deflated truth pluralists, by contrast, take only indicative sentences (presumably indicative sentencetokens, though Beall is inexplicit here) to be in the extensions of the truth predicates for English. It's clear, I hope, that I regard this as a highly significant issue. Since we're currently focused upon the explanatory power of the alethic properties, the key point at present is that minimal pluralism and deflated truth pluralism may actually be compatible at the level of properties, and if they aren't, then minimal pluralism has the metaontological upper hand. The second advantage that minimal pluralists enjoy over mainstream deflationists is that minimal pluralists are free to endorse a truth-conditional metasemantics. One of the basic questions in metasemantics is why meaningful expressions are meaningful. The seminal formulation of a truth-conditional approach to 280 this issue is due to Davidson, who nicely summarizes his proposal as follows [64, p. 310]: [A] theory of meaning for a language L shows 'how the meanings of sentences depend upon the meanings of words' if it contains a (recursive) definition of truth-in-L. And, so far at least, we have no other idea how to turn the trick. It is worth emphasizing that the concept of truth played no ostensible role in stating our original problem. That problem, upon refinement, led to the view that an adequate theory of meaning must characterize a predicate meeting certain conditions. It was in the nature of a discovery that such a predicate would apply exactly to the true sentences. Davidson's proposal is that we can give a theory of meaning for utterances in a given idiolect L by constructing a recursive definition of truth-in-L. Davidson [63] argues that one of the central desiderata for a theory of meaning is that it is compositional, that it explains how the meanings of sentences are systematically determined by the meanings of the subsentential expressions of which they are composed and their manner of composition. That meaning is compositional in this way is meant to explain how languages are learnable. The basic idea here is that in knowing the meanings of a finite stock of subsentential expressions and how to determine on this basis the meanings of sentences of which they composed, one has the ability to know the meanings of a potentially infinite number of sentences 281 by way of a finite stock of knowledge. To know the meaning of 'John sits,' it suffices to know the meanings of 'John' and 'sit' and how to determine the meaning of 'John sits' based upon the former knowledge and the manner in which these expressions are composed to form the sentence. And what Davidson points out is that by taking the operative notion in a theory of meaning to be that of truth-conditions, we look to be in a position to secure the compositionality of meaning. The idea is to explain why 'John sits' is meaningful by assigning it certain truth-conditions, namely that John sits. And we explain the meaningfulness of 'John' and 'sits' in turn by taking them to make certain contributions to the truth-conditions of 'John sits.' Roughly, 'John' denotes John and 'sits' denotes the property sitting. It is because they denote these entities and because they are combined as they are that the sentence they compose has the truth-conditions that John is sitting. Though this is a very quick gloss of the Davidsonian programme, it suffices to highlight the key point for our purposes. This is that a truth-conditional metasemantics enlists the notion of truth-conditions to explain why sentences are meaningful. And since they accord sentence-truth explanatory power, minimal pluralists are in a position to follow this strategy. For the minimal pluralist, an indicative sentence-token is meaningful because it has sentence-truth-conditions. The subsentential expressions of which it is composed are meaningful because they make distinctive contributions to the sentence-truth-conditions of the indicative 282 sentence-tokens of which they are composed. By contrast, mainstream deflationists are not in a position to follow this strategy, as Field [100] and Horwich [131] have pointed out. Minimalists (§ 5.2.2) deny that sentences (types or tokens) literally have truth-conditions, so the minimalist cannot explain meaning in terms of sentences' truth-conditions. And minimalists can't simply shrug this point off and explain meaning in terms of conditions for 'expressing a true proposition,' rather than in terms of conditions for sentences' literal truth. To do this would be to grant that truth, as the minimalist conceives of it, enjoys explanatory power–something that they explicitly deny. Likewise, disquotationalists such as Field who do recognize sentences as bona fide truthbearers deny that truth enjoys explanatory power. So they cannot explain why sentences are meaningful by appealing to conditions for truth, as they conceive of it. As Davidson pointed out and as is attested by their considerable successes, truth-conditional metasemantics look be among our best resources for securing the compositionality of natural language. If the theory of truth is capable of performing this important service, then why not enlist it? Why not recognize that truth enjoys explanatory power? 283 5.3 Proposition-truth and sentence-truth In positing proposition-truth and sentence-truth, we enjoy several significant theoretical benefits. These involve, respectively, the necessity and contingency of truth, our pretheoretical intuitions as to what bears truth, and the relative priority of proposition-truth and sentence-truth. 5.3.1 Necessity and contingency Many, probably most, cognizers would agree that there are necessary truths. Were you to ask them whether it might have been untrue that 7 plus 5 did not equal twelve, most people would give you a puzzled look and respond 'No, of course not.' The most natural way to accommodate this strong intuition is to posit certain truth-bearers which, if they exist, exist necessarily. Propositions, taken as abstracta, are commonly thought to be truth-bearers of this sort. So one advantage of positing proposition-truth is that we have a straightforward way of accommodating necessary truths–necessary truths are necessarily proposition-true propositions. No indicative sentence-token is necessarily sentence-true, even when we stipulate that such a sentence-token belongs to a particular language and consider only the range of contexts of utterance in which it expresses a particular proposition 〈p〉. The reason for this is straightforward. Indicative sentence-tokens are concreta–they are composed either of sounds or marks. So no indicative sentence284 token exists of necessity and it's thus not the case for any such sentence-token that it is true of necessity (this assuming that if an entity e fails to exist in world w, then e is not true in w, which seems quite right). What's interesting in this connection is that it can also strike us as quite compelling that if there were no cognizers, then there would be no truths. An especially forceful statement of this conviction is made by Davidson in the opening sentence of his Truth and Predication [68, p. 7]: Nothing in the world, no object or event, would be true or false if there were not thinking creatures. Granted, most cognizers will admit, if there had been no cognizers, then the world might have been a particular way–trees might have been solid, water might have been H2O, Jupiter might have been larger than Saturn. But with no cognizers around to remark on these states of the world, would it be true that Jupiter is larger than Saturn? Of course, given that we possess the concept truth, we take it to be true in our world that if there were no cognizers, then Jupiter might have been larger than Saturn. But the question that Davidson would press is whether it would be true that Jupiter is larger than Saturn in a world in which there were no cognizers. How could it be, given that no entity in that world holds beliefs or uses language to speak about the planets, that anything is true or false in that world? The final question makes explicit the source of this intuition. Davidson finds 285 it suitable to begin Truth and Predication by making this claim is that he has prior commitments as to what bears truth. Specifically, Davidson takes utterances in idiolects, understood as entities that a speaker of a language produces, to be the bearers of truth.33 Given this commitment, it is perfectly natural to wonder how, in the absence of cognizers, there could be true truth-bearers. And the important detail here is that in positing sentence-truth, we are in a position to accommodate this basic intuition. Consider the 'no cognizers' world that we've just mentioned. Since it lacks cognizers, no entities in the world are speakers of a language. So there are no indicative sentence-tokens in the world, which means that it lacks entities that are sentence-true. In positing sentencetruth, then, we are able to both endorse and appreciate the source of Davidson's intuition–the intuition is plausible to the extent, and only to the extent, that we fixate upon a kind of truth-bearer whose existence, and thus the truth of the instances of which, is contingent. The result here should be familiar. Alethic pluralism is motivated by the fact that the scope problem afflicts traditional monist truth theories. Alethic pluralists are able to both plausibly explain why this is so and offer a strategy for avoiding the scope problem. We've considered here two competing intuitions: the intuition that there are necessary truths and the intuition that in worlds where there are no cognizers, there are no true truth-bearers. Call these the necessity 33 This comes out especially clearly in [68, ch. 2]. 286 and contingency intuitions. What we've seen is that the pull of these intuitions depends upon what sort of truth-bearers are at issue. The necessity intuition is plausible given the supposition that there are truth-bearers which exist necessarily and the contingency intuition is plausible given the supposition that the bearers of truth are products of the activity of cognizers. The plausibility of the necessity and contingency intutions enjoy is notably attenuated. Because of its similarity to the scope problem affecting alethic monism, we can call this the modal scope problem. Because we posit both proposition-truth and sentence-truth, we have a ready solution to the modal scope problem. This is that both the necessity and the contingency intuitions are true. Each holds only in connection with a particular kind of truth-bearer–the necessity intuition in connection with propositions and the contingency intuition in connection with indicative sentence-tokens. We naturally save the appearances by appropriately delimiting their scope. 5.3.2 Propositions, sentence-tokens, assertions We take indicative sentence-tokens to be truth-bearers–specifically, sentence-truth bearers–because sentence-truth conforms to the core of our pretheoretical conception of truth, which is codified in the alethic platitudes. It might be objected that according to our ordinary conception of truth, indicative sentence-tokens are not actually bona fide truth-bearers, but only 'truth-bearers' in a manner of speaking. 287 One source of resistance here comes from propositionalists, those who take propositions to be the sole bearers of truth. Horwich [131, p. 16] puts the propositionalist's misgivings well:34 [I]f we agree with Oscar [when he asserts 'I am hungry' at midday on 1 January 1988], we attribute truth to what he said, to the proposition he asserted. Evidently the sentence-type of English that he used is not true; for that very sentence-type is used on other occasions to make false statements. Nor would one normally characterize the noises he made, or his belief state, as true. These entities are more naturally described as 'expressing a truth' and 'being of a true proposition.' No doubt we do attribute truth to statements, beliefs, suppositions, and so on; but surely what we have in mind is that the propositional objects of these linguistic and mental acts are true, and not the acts themselves. Horwich is quite right that sentence-types, whether indicative or in any other mood, shouldn't be classified as truth-bearers. If they were truth-bearers, then natural language would be shot through with truth-bearers that are both true and false. The indicative sentence-type 'I am sitting' has some tokens that are true in their contexts of utterance (when the speaker is sitting in that context) and some that are false in their contexts of utterance (when the speaker isn't sitting 34 Ayer [12, p. 87] makes similar claims. 288 in that context). So if we took the sentence-type to be a bona fide truth-bearer, the natural diagnosis would be that it is both true and false. And this would go for any sentence-type containing context-sensitive expressions. So we shouldn't take sentence-types to be truth-bearers. Horwich says about indicative sentence-tokens that it is more natural to describe them as capable of 'expressing truths' than to describe them as capable of being true. And it is quite plausible that when one ascribes truth to an indicative sentence-token, one says something notably complex–that it expresses a proposition and that this proposition is proposition-true. By contrast, when one ascribes truth to 〈p〉, one plausibly says something simpler–namely, that 〈p〉 is proposition-true.35 But Horwich's misgiving here rests upon an oversight. This is that according to our ordinary conception of truth, expressing a proposition-true proposition, is a way of being true. It is a derivative way of being true, just as being inferentially justified would be a derivative way of being justified and being extrinsically valuable is a derivative way of being valuable. So in claiming of an indicative sentence-token that it expresses a proposition-true proposition, one is claiming that it is true–specifically, that it is sentence-true. Other truth theorists such as Davidson take utterances–specifically, assertions, or statements–to be the bearers of truth. J.L. Austin [11, p. 113] nicely states misgivings that an assertivist, as we might call them, will raise for the idea 35 Cf. David [62, n. 3]. 289 that indicative sentence-tokens, whether asserted or unasserted, are bearers of truth:36 We may. . .genuinely say "His closing words were very true" or "The third sentence on page 5 of his speech is quite false": but here "words" and "sentence" refer, as is shown by the demonstratives (possessive pronouns, temporal verbs, definite descriptions, etc.), which in this usage consistently accompany them, to the words or sentence as used by a certain person on a certain occasion. That is, they refer (as does "Many a true word spoken in jest") to statements. Austin, like Horwich, concedes that we do appear to ascribe truth to indicative sentence-tokens, but proposes to explain this appearance away. Austin points out that when we apparently ascribe truth to indicative sentence-tokens, we often use expressions which suggest that we mean to refer to indicative sentence-tokens as asserted by a speaker in a particular context, rather than to the 'bare' indicative sentence-tokens themselves. This fact about ordinary language might be taken as strong evidence that according to our ordinary conception of truth, it 36 There is more than one way that one might think about assertions in this connection. Assertions might be conceived as sentence-tokens (typically, though not necessarily indicative) that are used assertorically by a speaker of the language to which they belong. They can also be conceived as acts–as the assertoric utterance of a particular sentence-token (typically, though not necessarily indicative). For the moment, we can safely set this distinction aside. 290 is only asserted indicative sentence-tokens that should be recognized as genuine truth-bearers. But I would sound two cautionary notes. The first is that the mere presence of the sorts of expression that Austin mentions in an ascription of truth to an indicative sentence-token doesn't show, all by itself, that we are considering that sentence-token as asserted by a particular speaker. Suppose that an undergraduate Jim sees you in the hallway and shows you a notebook that he found in a philosophy classroom. The notebook, he says, belongs to a philosophy student Jill, who has written at the top of page 1, 'Philosophers are stylish dressers.' Jim flips the notebook open and shows you that this indicative sentence-token is written at the top of page 1. He asks you, 'See what Jill has written there? Do you think that it's true?' Since Jim puts his question in terms of 'what Jill has written,' it might look as though he is asking you to assess the sentence-token, given that it is produced by Jill. But clearly, this isn't what Jim is asking. What Jim wants to know is whether you think that the sentence-token is true. And to determine this you don't need to know who, if anyone, used the sentence-token to perform an assertion. So the proper name and tensed verb in Jim's question are misleading–he could have simply asked you, pointing to the sentence-token at the top of page 1, 'Do you think that this sentence-token is true?' That is what he really wants to know. So Austin's manner of diagnosing the intent behind our truth ascriptions is 291 problematic. We can't simply read off the intent behind them by looking at the sorts of expressions we often use in performing them, for the presence of those expressions may be misleading. And there is a stronger point to be made here. In the opening section of Reason, Truth, and History, Hilary Putnam considers a case wherein an ant that is crawling on a patch of sand unintentionally traces marks with the shape 'WINSTON CHURCHILL.' Putnam asks whether these marks would refer to Churchill and returns a negative diagnosis. This seems quite right. The ant is not a speaker of English, nor of any other natural language in which 'Winston Churchill' is a referring expression. Putnam also points out that the ant, in producing these marks, has no intention to refer to Churchill; how could it, given that it is capable neither of recognizing Churchill himself as Churchill nor of recognizing a depiction (e.g. a painting) of Churchill as being a depiction of Churchill? Suppose now that John is an adult English speaker who regularly meditates. He has found it most effective to sit by the sea and drag his left index finger aimlessly through the sand, clearing his mind of all thought as he focuses on the feel of each individual grain of sand on his finger. By sheer chance, while meditating John traces marks in the sand with the shape 'HOSNI MUBARAK.' Not being aware that Hosni Mubarak is the erstwhile president of Egypt and having never encountered his name, John did not intend to refer to Hosni Mubarak in producing these marks. Question: given that John is a competent English 292 speaker, do the marks that John has produced refer to Hosni Mubarak? Here I suspect that intuitions will be more variable than in the case involving Putnam's ant. Similarly, suppose that John had traced the marks 'HOSNI MUBARAK WAS A DESPOT.' Not knowing of Mubarak, John does not intend in producing these marks to make a claim about him. Question: given that John is a competent English speaker, has he produced a true English sentence-token? Suppose that Sarah is walking along the beach as John finishes meditating. Being knowledgeable of Mubarak's presidential legacy, when she sees the marks that John has produced, Sarah says, 'Quite right; what you wrote there is exactly true, and it's wonderful that he was finally deposed.' Sarah's assertion seems entirely correct. Given that Mubarak was a despot, John has produced a true English sentence-token. So as the case involving the notebook brings out, we are quite accustomed to assessing indicative sentence-tokens for sentence-truth while abstracting away from our knowledge as to who asserted them. What the present case points to is that we are also entirely capable of assessing indicative sentence-tokens for sentence-truth when we know that no one has asserted them. Since John has never heard of Mubarak, he does not in producing the latter string of marks assert that Mubarak was a despot. Were Sarah to have believed that Mubarak was not a despot but a benevolent autocrat, she might have challenged John: 'So you say that Mubarak was a despot? Why so?' This challenge, of course, would 293 have been misplaced. John is under no obligation to defend his assertion that Mubarak was a despot. He has no idea who Mubarak is and has never even heard Mubarak's name, so he simply hasn't asserted that Mubarak was a despot. You and I are fully aware of this, yet it seems right for Sarah to say that what John has written is true, given that Mubarak was indeed a despot. So the assertivist is mistaken in claiming that according to our ordinary conception of truth, only asserted sentence-tokens can bear truth. There are indicative sentence-tokens which we know to be unasserted, but which we can nevertheless straightforwardly assess for sentence-truth. In positing sentence-truth, we are thus able to easily accommodate our pretheoretical conviction that unasserted, indicative sentence-tokens are bearers of truth. Indeed they are–they are bearers of sentence-truth. And we can also accommodate the propositionalist's view that propositions bear truth and the assertivist's view that asserted, indicative sentence-tokens bear truth. Propositions are bearers of proposition-truth. And asserted, indicative sentence-tokens, no less than unasserted, indicative sentence-tokens, are bearers of sentence-truth. That they are asserted certainly makes some difference. Given that 'S' is asserted by John, we can appropriately challenge John to provide reasons for thinking that 'S' and the indicative sentence-tokens that 'S' entails are true. But that 'S' is asserted makes no difference to its truth-conditions–'S' is sentence-true (in L and c) iff 'S' expresses a proposition-true proposition (in L and c). 294 5.3.3 Priority: Properties and concepts Sentence-truth is defined in terms of proposition-truth. (ST), of course, can be formulated without explictly using the expression 'proposition-truth.' Even so, (ST) defines sentence-truth as the property that an indicative sentence-token has (in L and c) iff it expresses (in L and c) a proposition-true proposition. For given that 'S' expresses 〈p〉 (in L and c), 'S' will be sentence-true (in L and c) iff p. 'S' will be sentence-true (in L and c), that is, iff the proposition that 'S' expresses (in L and c) is proposition-true. What this shows is that there is a sense in which we should take propositiontruth to be more basic than sentence-truth. Proposition-truth is ontologically more basic than sentence-truth; it is more basic, that is, at the level of properties. Following Schaffer [235], we can put this idea in terms of explanation. Suppose that 'S' is sentence-true in L and c. The explanation for this fact is that 'S' expresses a proposition 〈p〉 in L and c and 〈p〉 is proposition-true. But the condition for the proposition-truth of a given proposition 〈p〉 is just that p. So in general, we don't have it that if 〈p〉 is proposition-true, then 〈p〉 is proposition-true because some sentence-token 'S' is sentence-true (in L and c).37 37 Using notation that we'll introduce in § 5.5, we can also put the point by saying that every instance of (4) is sentence-true, whereas not every instance of (5) is sentence-true: • (4) |'S' is sentence-true in L and c| →F |'S' expresses 〈p〉 in L and c], [〈p〉 is propositiontrue| 295 Given that propositions are often treated as the primary bearers of truth even by those who recognize other kinds of truth-bearer, this result isn't too surprising. What's interesting is that when we carefully distinguish between proposition-truth and sentence-truth, we come to see the potential for an important asymmetry in their relative priority. We've said that proposition-truth is more basic than sentence-truth at the level of properties. But when we turn from the level of properties to the level of concepts–i.e. to the concepts propositiontruth and sentence-truth–we see that at this level, proposition-truth and sentence-truth look to be equibasic. At the level of concepts, that is, it seems that neither proposition-truth nor sentence-truth is prior to the other–to possess the former concept, one must possess the latter, and vice versa. Horwich puts forward a leading and quite plausible account of the possessionconditions for proposition-truth. He says:38 The basic thesis of deflationism, as I see it, is that the equivalence schema • The proposition that p is true iff p • (5) |〈p〉 is proposition-true| →F |'S' is sentence-true (in L, in c)|, ∆. 38 [130, pp. 103-4]. See also [133, ch. 2, § 6 and pp. 35-7] and [131, p. 135], where Horwich contends directly that "our concept of truth is engendered by our dispostion to accept instances of the equivalence schema." 296 is conceptually fundamental. By this I mean that we accept its instances in the absence of supporting argument. . .The evidence for this basic deflationist thesis is that our overall deployment of the truth predicate–the sum of everything we do with the word "true–"is best explained by taking the fundamental fact about its use to be our inclination to accept the instances of the equivalence schema. And the evidence for this explanatory claim is that that regularity is necessary and sufficient to account for the value of our concept of truth: its utility as a device of generalization. The concept proposition-truth is characterized by schema (PT), which Horwich calls the equivalence schema. According to Horwich, the sense in which (PT) characterizes proposition-truth is that to possess proposition-truth, one must be disposed to accept every instance of (PT) in the absence of supporting argumentation. So for Horwich, a cognizer S possesses proposition-truth iff the following holds: • (PT?C) S is disposed to accept every instance of (PT) in the absence of supporting argumentation. What, precisely, is required for S to have the pertinent disposition? What conditions must be met for S to be disposed to accept every instance of (PT) in the absence of supporting argumentation? Here it is important to notice what sort of 297 entity (PT) is. Just as we distinguish between sentence-types and sentence-tokens, so we should distinguish between schema-types and schema-tokens.39 Schema (PT), as it figures in (PT?C), is a schema-type. Horwich's contention is not, of course, that to possess proposition-truth, one must simply be disposed to accept every instance of the token of (PT) on p. 104 of some particular copy of Meaning. What he's claiming is that to possess proposition-truth, one must be disposed to accept every instance of the schema-type of which e.g. the schematoken on p. 104 of my copy of Meaning is a token. And what sort of entity is an instance of the schema-type (PT)? To obtain an instance of (PT), we uniformly substitute for 'p' synonymous indicative sentence-types, e.g. the sentence-type ∗Snow is white.∗ The result is an indicative sentence-type, e.g. ∗The proposition that snow is white is true iff snow is white.∗ So we have it that to possess proposition-truth, one must be disposed to accept every member of a certain class of sentence-types, each of which has the distinctive form 'The proposition that p is true iff p.' A problem with this proposal is that we don't, in general, accept/endorse sentence-types. Some sentence-types contain indexicals such as 'now,' 'here,' 'I' and 'yesterday.' Consider for instance, the sentence-type ∗I am sitting.∗ Do you accept/endorse this sentence-type? The question, of course, is misleading. If you are currently sitting, then you will accept it, but if you aren't currently sitting, then you won't. So in general, we don't 39 John Corcoran [50] calls schema-types 'template-texts' or 'scheme-templates.' 298 simply accept or reject sentence-types. We accept or reject (potential) tokens of sentence-types, which we take to exist in particular contexts. So the more accurate formulation of (PT?C) has it that S possesses proposition-truth iff: • (PTC) S is disposed to accept every token of every instance of (PT) in every context, in the absence of supporting argumentation. (PTC) has it that to possess proposition-truth, one must be disposed to accept, for instance, every token of ∗The proposition that snow is white is true iff snow is white,∗ ∗The proposition that I am sitting is true iff I am sitting,∗ and so on in every context, in the absence of supporting argumentation. What, in general, do we take into account when deciding whether to accept an indicative sentence-token in a particular context? Suppose that I write down an indicative sentence-token on a notecard without showing you which sentence-token it is. I ask you, 'Do you accept the indicative sentence-token that I've written on this notecard?' A natural response on your part would be: 'Well, is it true?' or 'Well, does it express a true proposition?' In general, that is, when competent speakers decide whether to accept a particular indicative sentence-token, they seek inter alia to determine whether it is sentence-true. It follows that given the possession-conditions (PTC) for propositiontruth, one possesses proposition-truth only if one possesses sentencetruth. For one possesses proposition-truth iff one is disposed to accept every token of every instance of (PT) in every context, in the absence of sup299 porting argumentation. One will be so disposed only if one is disposed to believe that every such sentence-token is sentence-true. But if one lacks the concept sentence-truth, then one is not disposed to believe that anything is sentencetrue. So given that (PTC) are the possession-conditions for proposition-truth, to possess proposition-truth, one must possess sentence-truth. To see that proposition-truth and sentence-truth are equibasic, it suffices to note that to possess sentence-truth, one must possess propositiontruth. Sentence-truth is characterized by schema (ST). So we can say similarly that S possesses sentence-truth iff the following holds: • (STC) S is disposed to accept every token of every instance of (ST) in every context, in the absence of supporting argumentation. We know that tokens of instances of (ST) are sentence-tokens that (explicitly or implicitly) mention proposition-truth, e.g. "Snow is white' is sentence-true (in L and c) iff 'Snow is white' expresses a proposition (in L and c) and that proposition is proposition-true.' If one lacks proposition-truth, then one will not be disposed to accept each of these tokens. Thus anyone who possesses sentencetruth also possesses proposition-truth. We have it, then, that sentence-truth and proposition-truth are equibasic. This is a surprising result, given that proposition-truth is more basic than sentence-truth at the level of properties. Thus, in positing proposition-truth and sentence-truth, we are able to appreciate the potential for an interesting 300 asymmetry in their relative priority. At the level of properties, proposition-truth is more basic than sentence-truth. But at the level of concepts, they look to be equibasic. It might be thought that by modifying (PTC) slightly, we can justifiably treat proposition-truth as more basic than sentence-truth. As we've seen, Horwich takes the axioms of the minimal theory of truth to be the propositions expressed by the infinitely many instances of (PT).40 Given that the instances of (PT) are sentence-types, indexicality again presents a difficulty. Sentence-types, e.g. ∗I am sitting∗, don't express propositions. Rather, tokens of sentence-types express propositions in certain contexts. If I assert a token of ∗I am sitting∗, that token expresses (in English) 〈Jeremy Wyatt is sitting〉, whereas if Sally asserts a token of this type, that token expresses (in English) 〈Sally is sitting〉. Accordingly, instances of (PT) don't themselves express propositions–tokens of these instances do. So it's preferable to take the axioms of the minimal theory to be the infinitely many propositions expressed by all possible tokens of instances of (PT). The axioms of the minimal theory will then include, as Horwich claims, 〈〈snow is white〉 is true iff snow is white〉, 〈〈beets are tasty〉 is true iff beets are tasty〉, 〈〈Sally is sitting〉 is true iff Sally is sitting〉, and so on. It would be in keeping with the spirit of alethic minimalism to propose possession-conditions for proposition-truth which make use of the axioms of 40 [131, ch. 2, § 2]. 301 the minimal theory, rather than tokens of instances of (PT). On this revised minimalist account, S possesses proposition-truth iff the following holds:41 • (PT??C ) S is disposed to accept every axiom of the minimal theory of truth in the absence of supporting argumentation. Since the axioms of the minimal theory of truth are propositions, it initially looks as though according to (PT??C ), S might fail to possess sentence-truth but nevertheless be sufficiently disposed as to possess proposition-truth. However, we should again ask: in virtue of what would S have this disposition? Given that the axioms of the minimal theory share a common form–〈〈p〉 is true iff p〉–it's quite plausible that if S is disposed to accept each such axiom, then this is explained by the fact that S is disposed to accept all propositions of that form–and precisely because they are of that form. The alternative view has it that for each axiom φ of the minimal theory, there is a unique explanation as to why S is disposed to accept φ. This account has it that, for instance, there is one explanation of why S is disposed to accept 〈〈snow is white〉 is true iff snow is white〉, an entirely distinct explanation of why S is disposed to accept 〈〈beets are tasty〉 is true iff beets are tasty〉, yet another of why S is disposed to accept 〈〈Sally is sitting〉 is true iff Sally is sitting〉, and so on. Since the minimal theory has infinitely many axioms, this account is extremely complex, highly disunified, and thus highly implausible. Much more plausibly, S's disposition to accept each axiom of the minimal theory 41 Thanks to Michael Lynch for pressing a similar response. 302 is explained by S's disposition to accept all propositions of the form 〈〈p〉 is true iff p〉, and precisely because they are propositions of that form. It's again crucial to notice what sort of entity '〈〈p〉 is true iff p〉' is. This expression is a schema. Specifically, as it figures here, it is a schema-type. The proposal under consideration–that (PT??C ) codifies the possession-conditions for proposition-truth–thus has it that to possess proposition-truth, S must be disposed to accept all instances of this schema-type in virtue of understanding the schema-type and recognizing that those instances are in fact its instances. This raises a question of general import: what is it to understand a schematype? Plausibly, it is (inter alia) to know how to generate admissible instances of that type. Where 'φ' is a sentential schematic letter, you and I understand the schema-type 'Either φ or not-φ.' And this is at least partly explained by the fact that you and I know how to produce admissible instances of that type–namely, by uniformly replacing 'φ' with synonymous sentence-types (of the same language). So for S to understand the schema-type '〈〈p〉 is true iff p〉' is (inter alia) for S to know how to produce admissible instances of that type. We produce these instances by uniformly replacing 'p' with synonymous sentence-types. It then follows that if the possession-conditions for proposition-truth are given by (PT??C ), then S possesses proposition-truth only if S possesses sentencetype. Further, S must be able to recognize the meanings of sentence-types in her language, else she wouldn't be able to ensure that the substituends for 'p' are 303 synonymous. It would run contrary to typical experience if S were able to recognize the meanings of the instances of (PT) that belong to her language yet had no inclination to accept tokens of these instances. Suppose that Sue Smith is an English speaker. You and Sue are sitting across from one another and you write on a notecard the sentence-token 'The proposition that Sue Smith is sitting is true iff Sue Smith is sitting.' Sue is disposed to accept 〈〈Sue Smith is sitting〉 iff Sue Smith is sitting〉 and she knows that 'Sue Smith is sitting' means that Sue Smith is sitting. So if you ask Sue, 'Do you accept what I've written on this card?' Sue will presumably respond, 'Yes, what you've written is true/what you've written expresses a truth.' Our normal course of experience suggests, that is, that given her other dispositions and her semantic knowledge, Sue is disposed to accept sentence-tokens of the form 'The proposition that p is true iff p.' And she is disposed to accept them because she takes them to 'express truths,' i.e. to be sentence-true. Accordingly, Sue must possess sentence-truth. So if (PT??C ) codifies the possession-conditions for proposition-truth, then one possesses proposition-truth only if one possesses sentence-truth. And as we've noted, since sentence-truth is defined in terms of proposition-truth, to possess sentence-truth, one must possess proposition-truth. So we again have it that proposition-truth and sentence-truth are equibasic. (PT?C) and (PT ?? C ) are two variants on a leading, minimalist conception 304 of proposition-truth. If we take the possession-conditions for propositiontruth to be given by either (PT?C) and (PT ?? C ), then proposition-truth and sentence-truth are equibasic. This strongly suggests that although propositiontruth is more basic than sentence-truth at the level of properties, proposition-truth and sentence-truth are equibasic at the level of concepts. 5.4 The domain-specific alethic properties Minimal pluralists posit a plurality of domain-specific alethic properties, and they are free to disagree among themselves as to these properties' natures. The most influential varieties of alethic pluralism–manifestation functionalism being the prime example–take some of the domain-specific alethic properties to be correspondencetheoretic and others to be epistemic. A problem with views of this sort is that they take the domain-specific alethic properties to be quite disunified, or so I'll argue. My view is that the domain-specific alethic properties are all species of correspondence. I won't be able to defend this view in detail–that would require another dissertation. I'll motivate the view by offering a correspondence-theoretic analysis of a kind of discourse that initially seems recalcitrant to this sort of treatment, namely discourse about what is delicious. 305 5.4.1 Unity and parsimony We've seen (§ 4.2.3) that alethic pluralists are compelled to explain why the class of alethic properties is rather unified, i.e. why it exhibits a low degree of miscellaneity. This is the first face of the more general problem of truth's unity. In addressing this problem, we appealed to a particular principle about the miscellaneity of sets–the Subset Principle–which states that subsets are at least as miscellaneous as their supersets: • (SP) For sets A and B, if A ⊆ B, then A ≤M B. It's straightforward to show, using this principle, that alethic pluralists are committed to taking the class of domain-specific alethic properties to be rather unified. This class, by all accounts, is a subset of the class of alethic properties. So by (SP), it's at least as miscellaneous as the latter class. The class of alethic properties will thus be highly unified (non-miscellaneous) only if the class of domain-specific alethic properties is highly unified. So pluralists are committed to taking the latter to be highly unified. It will thus be a distinct advantage if one pluralist truth theory takes the class of domain-specific alethic properties to be more unified than does another. This issue of unity owes its import to a more general issue related to theory choice. It's widely agreed that qualitative parsimony is a theoretical virtue. Lewis provides a well-known description of the notion of qualitative parsimony [162, p. 306 87]: A doctrine is qualitatively parsimonious if it keeps down the number of fundamentally different kinds of entity: if it posits sets alone rather than sets and unreduced numbers, or particles alone rather than particles and fields, or spirits alone rather than bodies and spirits. A theory T , then, is more qualitatively parsimonious than a theory T ′ iff T 's ontology contains fewer kinds of entity than does T ′'s ontology. When we appeal to qualitative parsimony in choosing between theories, we do so on the assumption that the theories enjoy equivalent explanatory power. Clearly, that theory T is more qualitatively parsimonious than theory T ′ doesn't always constitute a reason to prefer T to T ′: a theory with an empty ontology exhibits maximal qualitative parsimony but explains nothing and is thus about as bad as a theory can be. So the pertinent principle of theory choice is this:42 • (QP) If theories T and T ′ enjoy equal explanatory power and T is more qualitatively parsimonious than T ′, then T is preferable, to this extent, over T ′. In particular, if we have two pluralist truth theories T and T ′ which enjoy equivalent explanatory power and T is more qualitatively parsimonious than T ′, 42 Note that the operative notion of qualitative parsimony is that of ontological qualitative parsimony. Sam Cowling [55] offers a nice discussion of the distinction between ontological and ideological parsimony. 307 then this constitutes a reason to prefer T over T ′. And if the ontologies of theories T and T ′ contain the same kinds of entities, save that T ′'s contains more kinds of domain-specific alethic properties than does T 's, then T will be more qualitatively parsimonious than T ′. This shows that if theory T takes the class of domainspecific alethic properties to be more unified than does theory T ′ and T and T ′ enjoy equivalent explanatory power, then this constitutes a prima facie mark in favor of T . So given such an equivalence in explanatory power, we should prefer pluralist truth theories which take the class of domain-specific alethic properties to be highly unified. As a result, it's prima facie more attractive to take the domain-specific alethic properties to be species of a common genus, e.g. correspondence, than to suppose that they are heterogenous, e.g. taking some to be correspondencetheoretic and some to be epistemic. If we can explain the phenomena in which we're interested on the hypothesis that all of the domain-specific alethic properties fall under a common genus, then given (QP), we should. My own view is that the domain-specific alethic properties are all species of correspondence. I won't venture to show that it enjoys strictly equivalent explanatory power to, say, manifestation functionalism. What I'll argue is that it can account for the truth of a kind of proposition–namely, propositions about deliciousness–which, it might seem, could only be true in virtue of instantiating some epistemic alethic property. This result constitutes a strong reason to prefer 308 a purely correspondence-theoretic pluralist truth theory to one whose ontology contains both correspondence-theoretic and epistemic alethic properties. 5.4.2 Correspondence pluralism I take it that there are two species of correspondence, each of which involves a relation between a proposition and a fact or facts. What distinguishes these species of correspondence is that one involves correspondence between a proposition and only response-independent facts, whereas the other involves correspondence between a proposition and facts at least some of which are response-dependent. I'll argue that we can draw upon this distinction in analyzing the truth of taste-related propositions. I propose that taste-related propositions are proposition-true in virtue of corresponding to response-dependent, taste-related facts. In this respect, tasterelated propositions differ from e.g. biological and chemical propositions, which are more plausibly taken to correspond to response-independent facts. All of these propositions are true in virtue of corresponding to facts, but some correspond to different kinds of fact than do others. 309 Response-dependence and response-independence: facts and properties In the cases to follow, I take a fact to consist in the particulars a1, . . . , an instantiating the (possibly relational) properties P1, . . . , Pn. 43 I posit two kinds of fact: response-independent facts and response-dependent facts. A fact is responseindependent iff it consists in the instantiation of only response-independent properties. By contrast, a fact is response-dependent iff at least one of the properties in whose instantiation the fact consists is a response-dependent property. Ralph Wedgwood [265, p. 34] nicely articulates the general notion of a response-dependent property: [T]he response-dependence approach claims that objects are red, or good (or whatever), at least partly in virtue of some relation to some type of mental response on the part of thinking subjects [which] involves some sort of recognition or representation of something's being red or good. Following Wedgwood, we'll adopt the following conceptions of responsedependent and response-independent properties: 43 Cf. King [149, p. 26]. This isn't to contend, of course, that all facts have this form. There may be logically complex facts, facts which consist in first-order properties instantiating secondorder properties, and etc. But save in setting up an objection involving (10) below, we won't need to appeal to facts of these sorts. 310 • (RD) Property P is response-dependent =Df for any entity a, a's instantiation of (failure to instantiate) P is explained inter alia by the fact that there are cognizers who possess in circumstances C mental states about a's instantiating (failure to instantiate) P . • (RI) Property P is response-independent =Df there is no entity a such that a's instantiation of (failure to instantiate) P is explained inter alia by the fact that there are cognizers who possess in circumstances C mental states about a's instantiating (failure to instantiate) P . This conception of response-dependence is highly inclusive, the aim being to remain neutral on some prominent controversies surrounding responsedependence. We'll take the class of mental states to include both beliefs and experiences, so that a property may be response-dependent in virtue of its instantiation being explained by cognitive and/or affective states. We remain neutral on four particular issues: (i) whether it is knowable a priori whether a given property is response-dependent; (ii) whether response-dependent properties must be dispositional properties; (iii) whether properties are necessarily or contingently response-(in)dependent; and (iv) whether there is an important notion of responsedependence that applies at the level of conceptions, in addition to that which applies at the level of properties.44 44 For discussion of these issues, see Haukioja [118]; Jackson and Pettit [140]; Johnston [146]; Miscevic [189]; Wedgwood [265]; and Wright [274, ch. 3, appendix]. 311 I take it that deliciousness is a response-dependent property. Whether or not a is delicious depends upon how a would taste to actual cognizers. If a is delicious, this is explained by the fact that a would taste delicious to certain cognizers in certain circumstances. And if a is not delicious, this is explained by the fact that a wouldn't taste delicious to certain cognizers in certain circumstances.45 Taste and correspondence Absolutism has been largely ignored in the contemporary literature on taste discourse. The dominant approaches to taste discourse are each variants on two basic strategies. Content relativists, including contextualists, hold that taste-related propositions explicitly represent a cognizer or a cognizer's standard of taste. A content relativist about 'delicious,' for instance, might hold that if Jones asserts 'Beets are delicious,' Jones thereby expresses 〈Beets are delicious, according to Jones' standard of taste〉.46 Other influential accounts of taste discourse have it not that taste-related propositions are themselves relativized, but that the truth of taste-related truth-bearers (utterances, sentences, or propositions) is relative to a cognizer or to a cognizer's standard of taste. There are a number of interesting variants on this truth relativist approach to taste discourse, the most prominent 45 See Zangwill [283] for a recent defense of a response-dependent conception of aesthetic properties more generally. 46 See Cappelen and Hawthorne [40, ch. 4] for a defense of a more complex view along these lines. 312 being the proposals of Egan [92]; Lasersohn [157], [158]; MacFarlane [180]; Richard [225, ch. 5]; and Stephenson [252]. Despite their significant differences, each of these positions has it that whereas the structure of taste-related propositions is absolute, the truth of taste-related truth-bearers is relative. So all of the major analyses of taste discourse are, in one way or another, relativistic–either about the structure of taste-related propositions or about the truth of taste-related truth-bearers. Thoroughgoing absolutism about taste discourse has largely gone missing. And this isn't too surprising, since at first pass, absolutism looks highly unattractive. An absolutist analysis has it that, for instance, if Jones sincerely asserts 'Beets are delicious,' the sentence-token that Jones uses expresses 〈beets are delicious〉, which contains no reference to Jones, Jones' standard of taste, nor indeed to any cognizer or their standard of taste. And the truth-value of this proposition, says the absolutist, is absolute–the proposition is either absolutely true or absolutely false. Given that the conceptually fundamental truth-conditions for propositions are those codified by (PT), the absolutist is then committed to holding that either beets are delicious or they aren't. And this result looks quite problematic. If Sarah asserts 'Beets are not delicious' because beets don't taste delicious to Sarah, absolutism entails that Sarah expresses 〈beets are not delicious〉, which is proposition-true iff beets are not delicious. If beets are in fact delicious, then Sarah 313 has simply spoken falsely–she is wrong about whether beets are delicious and her assertion is presumably, to that extent, incorrect. But given that beets don't taste delicious to Sarah–she has an immediate urge to spit them out whenever she tastes beets–it seems as though Sarah is correct to assert 'Beets are not delicious.' And we confront a similar problem if we suppose that beets are, in fact, not delicious. Beets taste delicious to Jones. But according to the absolutist, when Jones sincerely asserts 'Beets are delicious,' he will simply be speaking falsely and his assertion will presumably be incorrect in this respect. But given that beets taste delicious to Jones, it would seem that it is correct for him to assert 'Beets are delicious.' So at first blush, absolutism about taste discourse looks unacceptable, making some sort of relativism seem inevitable. I think that absolutism is much more attractive than it initially seems. Suppose that taste-related propositions are structurally absolute, so that the English sentence-tokens 'Beets are delicious.' and 'Beets are not delicious.' express respectively 〈beets are delicious〉 and 〈beets are not delicious〉. The former proposition is proposition-true iff beets are delicious and the latter is proposition-true iff beets are not delicious. The question then becomes: what is it for beets to be, or to fail to be, delicious? Deliciousness, we noted, is a response-dependent property. If e is delicious (fails to be delicious), then this is explained inter alia by the fact that there are cognizers who would possess mental states about e's being delicious (failing to be 314 delicious) in certain conditions C. Specifically, we'll take it that if e is (fails to be) delicious, then this is explained inter alia by the gustatory experiences of e's being delicious (not being delicious) that certain cognizers would have. For such gustatory experiences to be explanatory of e's deliciousness (lack of deliciousness), they must occur in the right sort of setting. Suppose that beets taste delicious to Sue only if she has just brushed her teeth or eaten Synsepalum dulcificum (a berry which augments the perceived sweetness of foods). If Sue eats beets when she has a clean palate, has slept well, isn't distracted, and intends to assess the tastiness of beets, then beets taste disgusting to her. Is it right to say that beets taste delicious to Sue? Intuitively, no. It's right to say that beets taste delicious to Sue iff they taste delicious to her in the latter sort of circumstance. Call a circumstance of this sort–that is, a circumstance in which a cognizer hasn't just brushed their teeth or eaten Synsepalum dulcificum, in which they have a clean palate, have slept well, and etc.–a canonical circumstance. Being delicious and failing to be delicious, I suggest, then amount to the following: • (D) (i) Entity e is delicious iff there is at least one actual cognizer to whom e would taste delicious in canonical circumstances; (ii) K's are delicious iff every K is delicious • (ND) Entity e is not delicious iff there are no actual cognizers to whom e would taste delicious in canonical circumstances; (ii) K's are not delicious 315 iff no K is delicious We take facts to consist in the particulars a1, . . . , an instantiating the (possibly relational) properties P1, . . . , Pn. (D) and (ND) thus double as existenceconditions for the facts that e is delicious and that e is not delicious, respectively: • (FD) (i) It is a fact that e is delicious iff there is at least one actual cognizer to whom e would taste delicious in canonical circumstances; (ii) It is a fact that K's are delicious iff for every K entity e, it is a fact that e is delicious • (FND) It is a fact that e is not delicious iff there are no actual cognizers to whom e would taste delicious in canonical circumstances; (ii) It is a fact that K's are not delicious iff for every K entity e, it is a fact that e is not delicious. So thus far, we have it that 〈beets are delicious〉 is proposition-true iff it is a fact that beets are delicious and that likewise, 〈beets are not delicious〉 is proposition-true iff it is a fact that beets are not delicious. What is the order of explanation on these biconditionals? Following many truth theorists, I take it that the order is right-to-left: (i) if 〈beets are delicious〉 is proposition-true, then it is proposition-true because it is a fact that beets are delicious (and not vice versa) and (ii) if 〈beets are not delicious〉 is proposition-true, then it is propositiontrue because it is a fact that beets are not delicious.47 The guiding idea here 47 Note that since deliciousness is response-dependent, the order of explanation on (D), (ND), (FD), and (NFD) is also right-to-left. 316 is often called the correspondence intuition, which is the common intuition that "whenever a proposition. . .is true, it is true because something in the world is a certain way."48 Proposition-true propositions are proposition-true because the world contains certain facts, not the other way around. Why is it that for 〈beets are delicious〉 to be proposition-true, it must be a fact that beets are delicious, rather than, say, a fact that beets are not delicious? As Jeff King [149, pp. 1-4] points out, it is widely accepted that if propositions exist, then they must have certain features. One is that propositions are representational–propositions represent the world (not always accurately). And since distinct propositions have distinct truth-conditions, distinct propositions constitute distinct representations of the world. So I take it that in particular, 〈beets are delicious〉 represents beets' instantiating deliciousness. And it is because 〈beets are delicious〉 represents beets' instantiating deliciousness that for this proposition to be proposition-true, it must be a fact that beets are delicious (i.e. beets must instantiate deliciousness). Likewise, it is because 〈beets are not delicious〉 represents beets' failing to instantiate deliciousness that it is proposition-true iff it is a fact that beets are not delicious. For these propositions to be proposition-true, that is, they must correspond to certain facts. For 〈beets are delicious〉 to correspond to the fact that beets are delicious is for two conditions to be satisfied: (i) 〈beets are delicious〉 represents 48 Horwich [131, p. 104]. 317 beets' instantiating deliciousness and (ii) it is a fact that beets are delicious. And likewise for 〈beets are not delicious〉. Two questions arise regarding the claim that 〈beets are delicious〉 represents beets' instantiating deliciousness. First, can 〈beets are delicious〉 represent beets' instantiating deliciousness if beets do not, in fact, instantiate deliciousness? Second, what is it for 〈beets are delicious〉 to represent beets' instantiating deliciousness? The answer to the first question must be 'Yes.' Since all propositions are representational, to say otherwise would invite the result that every proposition is proposition-true. For present purposes, I remain neutral as to how propositions represent the world; it isn't my aim here to defend a particular theory of the nature of propositions. For the sake of concreteness, we can draw upon the account of propositions from chapter 3, according to which propositions are composed of concepts. On this account, 〈beets are delicious〉 is composed of the concepts [beets] and [ξ is delicious]. These respectively represent the class of beets and the property deliciousness and the proposition itself represents beets' instantiating deliciousness. So in sum, I propose the following account of discourse about deliciousness: • (AD1) Indicative, English sentence-tokens of the form 'a is (not) delicious.' express 〈a is (not) delicious〉 • (AD2) (i) It is a fact that e is delicious iff there is at least one actual cognizer to whom e would taste delicious in canonical circumstances; (ii) It is a fact 318 that K's are delicious iff for every K entity e, it is a fact that e is delicious • (AD3) (i) It is a fact that e is not delicious iff there are no actual cognizers to whom e would taste delicious in canonical circumstances; (ii) It is a fact that K's are not delicious iff for every K entity e, it is a fact that e is not delicious. • (AD4) (i) 〈a is (not) delicious〉/〈K's are (not) delicious〉 is proposition-true iff it corresponds to the response-dependent fact that a is (not) delicious/K's are (not) delicious • (AD5) If 〈a is (not) delicious〉/〈K's are (not) delicious〉 is proposition-true, then it is proposition-true in virtue of corresponding to the response-dependent fact that a is (not) delicious/K's are (not) delicious. A consequence of this proposal is that very many entities are delicious. Humans' tastes are highly varied, so that if an entity e is edible, then it's fair to predict that there is at least one actual human to whom e would taste delicious in canonical circumstances. Most edible entities, then, probably qualify as delicious. And no such entity qualifies as both delicious and not delicious. For e to be not delicious, there must be no actual cognizer to whom e would taste delicious in canonical circumstances. So given that most edible entities would taste delicious to at least one actual cognizer, it isn't the case that these entities are not delicious. 319 Chauvinism What about the initial misgiving with absolutist analyses of taste discourse? Beets taste delicious to me in canonical circumstances, so it follows that it is a fact that beets are delicious and that it is not a fact that beets are not delicious. By contrast, beets don't taste delicious to Sarah in canonical circumstances–whenever she eats beets, she wants immediately to spit them out. So were she asked whether beets are delicious, Sarah might assert 'No, beets are not delicious.' Since it is a fact that beets are delicious and thus not a fact that beets are not delicious, we must say that Sarah has spoken falsely and presumably that her assertion is, in this respect, incorrect. But given that beets don't taste delicious to her, this result seems counterintuitive; since they don't taste delicious to her, isn't it correct for her to assert that beets are not delicious? We should distinguish here between several assertions that Sarah might perform. Beets taste disgusting to Sarah. So if asked whether beets are delicious, Sarah might have responded, 'No, they're disgusting.' Sarah might also have been asked whether the particular beet that she has just put into her mouth is delicious, to which she might respond, 'No, this beet is disgusting.' Disgustingness, like deliciousness, is a taste-related, and thus responsedependent, property. Whether an entity is disgusting is at least partially explained by the fact that it would taste, look, smell, sound, or feel disgusting to certain cognizers. So we take the instantiation-conditions for disgustingness, in 320 the case of taste, to be much like those for deliciousness. Entity e is disgusting iff there is at least one actual cognizer to whom e would taste disgusting in canonical circumstances. Similarly, e is not disgusting iff there are no actual cognizers to whom e would taste disgusting in canonical circumstances. And the conditions for K's to be (fail to be) disgusting are likewise simlar to the conditions for K's to be (fail to be) delicious. We'll also treat sentence-tokens containing 'disgusting' as we treated those containing 'delicious,' so that an indicative, English sentence-token of the form 'a is (not) disgusting'/'K's are (not) disgusting.' expresses 〈a is (not) disgusting〉/〈K's are (not) disgusting〉. If Sarah asserts 'Beets are disgusting,' then this sentencetoken expresses 〈Beets are disgusting〉. And given that beets taste disgusting to Sarah, who is an actual cognizer, in canonical circumstances, this proposition is proposition-true. So in this respect, it is entirely correct for Sarah to assert that beets are disgusting. It is indeed a fact that beets are disgusting. It is also a fact that they are delicious, which is why I may truly assert that they are delicious. But it is neither a fact that they are not delicious nor a fact that they are not disgusting. Likewise, if Sarah tastes a particular beet B in canonical circumstances, then B will taste disgusting to her. So it is a fact that B is disgusting. Accordingly, if Sarah asserts that B is disgusting, then she will speak truly and in this respect, her assertion will be correct. 321 So the first point is that Sarah may correctly perform assertions that are similar to, though distinct from, the assertion that beets are not delicious. But it wouldn't be correct for Sarah to assert 'Beets are not delicious.' or for her to assert about a particular beet B that she has just tasted, 'This beet is not delicious.' I suspect that this diagnosis is less problematic than it initially appears. Suppose that you are dining with two friends: Bill, who is American, and Ren, who is Japanese. The waiter brings by a plate of sashimi, which you and Ren have eaten many times but which Bill has never tried. You each have a slice of sashimi and subsequently exchange glances indicating that you and Ren both find it rather nice, while Bill isn't so impressed. You proceed to ask Bill what he thinks and he responds, 'Sashimi isn't delicious at all!' I trust that Bill's response comes off as chauvinistic. By responding in this way, Bill is attending to his own gustatory experiences of sashimi while entirely overlooking yours and Ren's. It would have been preferable for Bill to respond that he doesn't find the sashimi delicious or that it doesn't taste delicious to him. When Sarah asserts that beets are not delicious or thatB is not delicious, she is also exhibiting chauvinism. She is privileging her own gustatory experiences of beets and ignoring those of others (I take it to be common knowledge that beets taste delicious to some people). Her assertion may not initially strike us as chauvinistic because unlike in the case just discussed, we imagine her responding to a query by a neutral party. For this reason, if she asserts that beets aren't 322 delicious or that B isn't delicious, she won't be guilty of ignoring the tastes of any nearby party. But she would exhibit chauvinism nonetheless.49 Absolutism expains the chauvinism that Sarah exhibits, as it takes her to overlook the fact that beets taste delicious to some humans, i.e. that beets are, in fact, delicious. It also entails that just as in the most recent case, Sarah could truly assert 'Beets don't (B doesn't) taste delicious to me' rather than 'Beets aren't (B isn't) delicious.' For given that beets don't taste delicious to Sarah in canonical circumstances, it is a (response-dependent) fact that they don't and that B wouldn't. Quantity and phantom implicatures There are several sorts of utterance which at first look rather difficult for the absolutist to accommodate. Sarah might assert one of the following sentences: • (8) Beets don't taste delicious to me, but they are delicious • (9) Beets are delicious, but they don't taste delicious to me. I trust that both of these assertions sound somewhat self-contradictory. But the absolutist takes (8) and (9), as asserted by Sarah, to express propositions which 49 She would also exhibit chauvinism were she to respond to the question 'Are beets delicious?' by asserting 'No, they're disgusting.' Saying 'no' would be chauvinistic, though it isn't chauvinistic for Sarah to assert 'Yes, beets are disgusting' if she's asked whether they're disgusting. And likewise if Sarah responds to the question 'Is B delicious?' by asserting 'No, B is disgusting.' 323 are not only consistent but proposition-true. According to the absolutist, (8) and (9) express the same proposition: • (10) 〈beets are delicious and they don't taste delicious to Sarah〉. Given that beets do taste delicious to some humans, though not to Sarah, there is a fact which consists in beets' being delicious and their not tasting delicious to Sarah. This is the (response-dependent) fact that (10) represents, so (10) corresponds to a fact and is thus proposition-true. The first problem, then, is how to explain the intuition that (8) and (9) are self-contradictory. To see a similar problem, consider Bill, who has never tasted beets. Bill might assert: • (11) Beets are delicious, but I've never tasted them. Like Sarah's assertions of (8) and (9), Bill's assertion of (11) sounds selfcontradictory. Again, though, the absolutist takes (11), as asserted by Bill, to express a proposition-true proposition, namely 〈beets are delicious and Bill has never tasted beets〉. How, then, to explain the intuition that Bill's assertion is selfcontradictory? In each of these cases, I think that the explanation is pragmatic. Paul Grice famously articulates several maxims which he takes to govern rational, cooperative conversational behavior. These maxims are rules that one ought to follow in conversation in order to abide by the general conversational principle that Grice [114, p. 26] calls the Cooperative Principle: 324 • (CP) Contribute to a conversation at t what is required at t, given the accepted purpose of the conversation. Among the maxims that Grice proposes is the Quantity maxim [114, p. 26]:50 • (Quantity) Make your contribution to a conversation at t as informative as is required, given the accepted purpose of the conversation. Grice applies his conversational maxims in explicating the notion of a conversational implicature. A well-known case involves professors from two philosophy departments speaking about whether a student Jim, currently studying in one department, should be admitted into the other.51 Professor A asks, 'Should I admit Jim?' to which Professor B responds, 'He certainly has wonderful handwriting.' What has Professor B said? In one sense, he has said that Jim has wonderful 50 Grice's other maxims are [114, p. 27]: • (Quality) Try to make your contribution one that is true (do not say something that you believe to be false or for which you lack adequate evidence) • (Relation) Be relevant • (Manner) Be perspicuous (e.g. avoid obscurity of expression and ambiguity and be brief and orderly). 51 [114, p. 33]. The case that Grice considers is somewhat different, though not significantly so. 325 handwriting–this is the proposition expressed by the sentence-token that he uses. In another sense, he has said that Professor A shouldn't admit Jim–this is what Professor B implies in responding as he does. The question is then how to explain the fact that Professor B implies this particular proposition. The accepted purpose of A and B's conversation is to determine whether Jim should be admitted into Professor A's department. So in evaluating B's response, A will reason as follows: 'Now I asked B whether I should admit Jim. B replied that Jim has wonderful handwriting, which isn't the information that I require. I know that B is Jim's thesis advisor and that he knows the aims of my department, so he surely has a belief about whether I should admit Jim. B intends to contribute what is required at this stage in the conversation. So B must intend to communicate more than the proposition he asserted, though he is reluctant to assert this further proposition. He has no reason to be reluctant about asserting that I should admit Jim, so he must intend to communicate that I shouldn't.' In this way, Professor A is able to determine that Professor B implied that Professor A shouldn't admit Jim. Had Professor B not implied this, his response would have violated the Quantity maxim; yet it is common knowledge among A and B that they both intend to abide by the Cooperative Principle and thus by the Quantity maxim. Consider now a typical conversation about deliciousness. Bill has never tasted beets, so he's not sure how beets will taste to him. He knows that Jones 326 has tasted beets, so he decides to ask Jones, 'Should I buy myself some beets at the grocery store? Are they delicious?' Since beets taste delicious to Jones, Jones responds, 'Oh yes, beets are very delicious.' If you asked Bill and Jones what the purpose of their conversation was, what do you suspect that they would say? Presumably, Bill would say that he was trying to determine whether he should buy some beets for himself and Jones would say that he was recommending to Bill that he do so. Absolutism about 'delicious' has it that the sentence-token that Jones uses expresses 〈beets are delicious〉. This proposition is proposition-true iff beets would taste delicious to at least one actual cognizer in canonical circumstances, not necessarily to Bill. So that this proposition is proposition-true doesn't settle the issue in which Bill and Jones are principally interested: whether Bill should buy himself some beets. For this reason, in responding as he does, Jones implies that beets taste delicious to him and that his tastes, as far as beets are concerned, are similar to Bill's. In implying this, Jones' abides by the Quantity maxim, which he would otherwise have violated. In typical conversations about what is delicious, speakers are trying to determine whether one or more of them should eat a particular food. Given this, if S asserts 'a is (K's are) delicious' in such a conversation, S implies that a tastes (K's taste) delicious to S and that S's tastes, as far as a is (K's are) concerned, are similar to those of the other participants in the conversation. 327 Return now to Sarah's assertions of (8) and (9) and to Bill's assertion of (11). When we consider these assertions, performed independently of any conversation, we hear them as self-contradictory. The explanation for this, I propose, is that we hear Sarah and Bill, given that they each assert that beets are delicious, as implying that beets taste delicious to them. We hear Sarah as implying that beets taste delicious to her and we hear Bill as implying that beets taste delicious to him. That we interpret Sarah and Bill in this way is understandable–in a typical conversation about the deliciousness of beets, they would imply these respective propositions. But Grice's maxims govern conversational behavior, not isolated assertions. Since their respective assertions are performed in isolation, neither Sarah nor Bill implies that beets taste delicious to them. What we sense, then, is a contradiction between the propositions that they actually assert and the propositions that we mistakenly take them to imply. We sense a contradiction, that is, between the asserted propositions and a phantom implicature. Just as a phantom limb is a limb that seems to be attached to one's body but isn't, so a phantom implicature is a proposition that a speaker seems to imply but doesn't. We hear phantom implicatures in other cases as well. Suppose that Sue is eating dinner at her dining room table and that she asserts, looking at the salt shaker on the other side of the table, 'I can't reach the salt.' Most English speakers, I take it, will hear Sue as implying that she would like someone to pass her the salt. It's understandable that we seem to hear an implicature here, for 328 typically, when one asserts that they can't reach the salt while eating dinner and looking at a distant salt shaker, they are accompanied by other diners and they do indeed imply that they would like one of their companions to pass them the salt. In familiar contexts of this sort, that implicature is explained by the Quantity maxim. If, during dinner, S is asked whether she would like anything and S responds by asserting that she can't reach the salt, then S implies, lest she violate (Quantity), that she would like someone to pass her the salt. Because this is the normal run of things, it's predictable that we hear the phantom implicature when we consider the assertion in isolation. So the absolutist can explain why we hear (8), (9), and (11) as self-contradictory. The propositions that (8), (9), and (11) express are internally consistent and proposition-true. The source of our intuition that they are self-contradictory is the understandable but erroneous sense that assertions of these sentences generate implicatures that are inconsistent with the propositions that they express. Correspondence pluralism? Does absolutism about taste discourse help to motivate a distinctively pluralist conception of correspondence? Absolutism takes propositions about deliciousness to be proposition-true iff they correspond to response-dependent facts. By contrast, purely chemical propositions are proposition-true iff they correspond to response-independent facts. 〈Water is H2O〉, for instance, is proposition-true iff 329 (i) it represents water's being H2O and (ii) it is a response-independent fact that water is H2O. But, it might reasonably be wondered, why isn't this a monist conception of correspondence? After all, the possibility remains that the nature of representation is uniform across all domains. So why not say that there is a single correspondence relation–representation of a fact–though propositions can represent different kinds of fact? This concern is generated by an overly narrow understanding of the identity of relations.52 The operative thought is that the identity of a relation doesn't depend upon the kinds of relata that it relates. Consider the relations being born in a large town and being born in a small town. Are these the same relation? Clearly not. To stand in the former, one must have been born in a large town, whereas to stand in the latter, one must have been born in a small town. But if, when individuating relations, we ignore the kinds of relata that relations relate, then we will incorrectly classify these as the same relation. We'll say that they are both the relation being born in. So to properly individuate relations, we must use individuation-conditions with a finer grain. We must be attentive to the kinds of relata that relations relate. It's this that explains why being born in a large town and being born in a small town are not the same relation. The 'leftmost' relatum of both is an animal. And their 'rightmost' relata are similar, though not identical. The rightmost relatum of the former must be a large town, whereas the 52 Recall that for the sake of convenience, we're assimilating relations and relational properties. 330 rightmost relatum of the latter must be a small town. Since they relate different kinds of relata, they are distinct relations. And the situation regarding correspondence is much the same. The proposal is that some kinds of proposition, including taste-related propositions, are proposition-true iff they stand in the relation correspondence to a response-dependent fact. By contrast, other kinds of proposition, including chemical propositions, are proposition-true iff they stand in the relation correspondence to a responseindependent fact. The kinds of leftmost relata that these relations take are similar, though different. The former takes e.g. taste-related propositions, whereas the latter takes e.g. chemical propositions. Likewise, the kinds of rightmost relata that they take are simlar, though different. The former takes response-dependent facts, whereas the latter takes response-independent facts. And since they relate different kinds of relata, these relations are distinct.53 53 This is a crucial respect in which the present view differs from the pluralistic correspondence theory defended by Horgan and colleagues [16], [17], [121], [122]. As his most recent articulation of the view makes clear, he takes truth to be a single relation, ideologically-mediated correspondence. The sense in which Horgan's view is pluralistic is that he takes the degree to which truth is ideologically mediated to differ across domains. But just as one can hold that there is only one property heat and that some entities are hotter than others, so Horgan holds that truth is a single, degreed, relation. Gila Sher, by contrast, advances a correspondence theory that is closer to the present view. Sher agrees that correspondence is a genus with multiple species, the species being numerically distinct correspondence relations. She [243] has classified these species as 'direct correspondence' 331 Being born in a large town and being born in a small town are rather similar relations–they both involve an animal's being born in a particular town. Likewise, response-dependent correspondence and response-independent correspondence, as we'll call them, are rather similar–they both involve a proposition's correspondence to fact. And that is precisely the point. There is more than one property which behaves as truth is meant to behave in connection with some, though not all, domains. Though distinct, these properties are importantly similar and accordingly form a highly unified class. So while truth is diverse across the various domains of discourse, it nevertheless retains a high degree of unity. and 'indirect correspondence' and most recently [244] as 'non-composite correspondence' and 'composite correspondence.' As the latter descriptions make clear, Sher takes correspondence in some domains to be a composite relation that involves a truth-bearer, certain entities that humans posit, and a truthmaker (Sher [243, § 4] specifically mentions laws and entities instantiating properties as truthmakers). By contrast, in other domains, correspondence is a non-composite relation that involves only a truth-bearer and its truthmaker. A key difference between Sher's view and my view, then, is that I take the species of correspondence to all be non-composite relations that are distinct in virtue of relating different kinds of fact. This leaves open the possibility that, as Sher thinks, truth in the mathematical, logical, and ethical domains involves some sort of composite correspondence. Were this so, the species of correspondence would be more numerous, but they would nevertheless be species of a common genus. For further discussion of Sher's views, see [239]; [240]; and [241]. 332 5.5 Determination My view is that there are two domain-specific alethic properties, response-dependent correspondence and response-independent correspondence. Whether a given proposition is proposition-true is determined by its instantiation of one of these properties. But what, precisely, does this talk of 'determination' come to? I take the determination relation in play here to be the 'in virtue of' relation, often called grounding. Grounding is governed by certain structural principles, due to Gideon Rosen [227, § 5], which articulate its formal features:54 • (Strong asymmetry) If |p| ← |q|, Γ, then it is not the case that: |q| ← |p|, ∆ 54 Strictly, I take these to be the formal features of grounding as it figures in minimal pluralism. I don't contend that there is a single relation with these features that can do all, or even most, of the work that grounding has been thought to do. In particular, I'm open to the possibility that there is a single relation grounding which lacks e.g. irreflexivity (strong or weak) and/or transitivity (strong or weak) (in this connection, see Fine [104], Jenkins [142], Litland [165], Raven [224], and Schaffer [236]). I'm also open to the possibility that, as Jessica Wilson [271] argues, there isn't a single ('big-G') grounding relation, only a plurality of ('small-g') grounding relations. What I claim is that there is a dependence relation which exhibits the pertinent formal features in connection with the alethic properties. We'll take pairs of vertical lines, when suitably combined with bare schematic letters (and logical symbols), to be schematic names for facts. We'll take '←' to denote our grounding relation, so that e.g. '|p| ← |q|' means that the fact that q (fully) grounds the fact that p. Γ and ∆ are (perhaps empty, perhaps infinite) classes of facts. 333 • (Strong irreflexivity) It is not the case that: |p| ← |p|, Γ • (Strong transitivity) If |p| ← |q|, Γ and |q| ← ∆, then |p| ← |q|, Γ, ∆. So we take grounding to be strongly asymmetric, strongly irreflexive, and strongly transitive. To precisely describe the grounding of proposition-truth in the domain-specific alethic properties, we can draw upon a distinction between full grounds and partial grounds :55 • (FG) |q| is a full ground for |p| =Df |p| ← |q|, ∅ • (PG) |q| is a partial ground for |p| =Df |p| ← |q|, Γ and |q| isn't a full ground for |p|. We earlier described proposition-truth's grounding in the domain-specific alethic properties as follows: • (MP?7) (i) If 〈p〉 ∈ D, there is no distinct domain D′ s.t. 〈p〉 ∈ D′, and 〈p〉 is proposition-true, then 〈p〉 is proposition-true in virtue of instantiating TD; (ii) If 〈p〉 ∈ D and 〈p〉 ∈ D′ (D 6= D′), 〈p〉 is inapt for TD (TD′), and 〈p〉 is proposition-true, then 〈p〉 is proposition-true in virtue of instantiating TD′ (TD). 55 Γ is a non-empty, possibly infinite class of facts. See Fine [104], [105, § 1] for an alternative rendering of this distinction. 334 We appealed here to partial, rather than full, grounding. If 〈p〉 is propositiontrue, then there are two facts that explain why this is so: (i) the fact that 〈p〉 belongs to a particular domain(s) and (ii) that 〈p〉 instantiates the pertinent domainspecific alethic property. So the more exact formulation of (MP?7) is (where ←F is the relation of full grounding and ←P is the relation of partial grounding): • (MP7) – (i) If 〈p〉 ∈ D, there is no distinct domain D′ s.t. 〈p〉 ∈ D′, and 〈p〉 is proposition-true, then (a) |〈p〉 is proposition-true| ←P |〈p〉 ∈ D and there is no distinct domain D′ s.t. 〈p〉 ∈ D′|; (b) |〈p〉 is propositiontrue| ←P |〈p〉 instantiates TD|; and (c) |〈p〉 is proposition-true| ←F |〈p〉 ∈ D and there is no distinct domain D′ s.t. 〈p〉 ∈ D′|, |〈p〉 instantiates TD|; – (ii) If 〈p〉 ∈ D and 〈p〉 ∈ D′ (D 6= D′), 〈p〉 is inapt for TD (TD′), and 〈p〉 is proposition-true, then (a) |〈p〉 is proposition-true| ←P |〈p〉 ∈ D|; (b) |〈p〉 is proposition-true| ←P |〈p〉 ∈ D′ (D 6= D′) and 〈p〉 is inapt for TD (TD′)|; (c) |〈p〉 is proposition-true| ←P |〈p〉 instantiates TD′ (TD)|; and (d) |〈p〉 is proposition-true| ←F |〈p〉 ∈ D|, |〈p〉 ∈ D′ (D 6= D′) and 〈p〉 is inapt for TD (TD′)|, |〈p〉 instantiates TD′ (TD)|. 335 5.6 Moving beyond truth The traditional project in truth theory is the essence project, whose central aim is to discover the complex essence of truth. This project is severely jeopardized by the scope problem, which indicates that the traditional accounts of truth's essence are plausible only in connection with certain domains. The diagnosis of mainstream deflationists is that it was simply misconceived to frame the problem in terms of essences. I have argued to the contrary that the fateful misstep was to presuppose that there is a property truth whose essence we can discover. In fact, there was no such property to begin with, so it's no surprise that we haven't discovered its essence. There is no such property as truth because there is more than one property that behaves as truth is meant to behave. It can't be that all of these properties are truth, so we should conclude that none of them is. The way forward is to seek a more comprehensive understanding of the essences of these properties, the essences of the truth-like properties that ground them, and the important explanatory work that they can do in philosophy. So the essence project is perfectly healthy. What we must recognize is that it is even more complex, and thus even more exciting and potentially fruitful, than we took it to be. 5.6.1 Minimal pluralism: core theses • (MP1) There is more than one domain of discourse 336 • (MP2) Propositions are among the bearers of truth • (MP3) P is an alethic property =Df at least one instance <a, P> of P satisfies the open counterpart of the neutral platitudes • (MP4) There is a plurality of domain-specific alethic properties whose members are response-dependent and response-independent correspondence • (MP5) There is a plurality of bearer-specific alethic properties, containing (at least) proposition-truth and sentence-truth – P is a bearer-specific alethic property =Df ∗ (BS(i)) P is a domain-general alethic property ∗ (BS(ii)) P is associated only with truth-bearers of kind K • (MP6) (i) If 〈p〉 ∈ D and there is no distinct domain D′ s.t. 〈p〉 ∈ D′, then 〈p〉 is proposition-true iff 〈p〉 instantiates TD; (ii) If 〈p〉 ∈ D and 〈p〉 ∈ D′ (D 6= D′) and 〈p〉 is inapt for TD (TD′), then 〈p〉 is proposition-true iff 〈p〉 instantiates TD′ (TD); (iii) If 'S' expresses 〈p〉 (in L), then 'S' is sentence-true (in L) iff 〈p〉 is proposition-true • (MP7) – (i) If 〈p〉 ∈ D, there is no distinct domain D′ s.t. 〈p〉 ∈ D′, and 〈p〉 is proposition-true, then (a) |〈p〉 is proposition-true| ←P |〈p〉 ∈ D and 337 there is no distinct domain D′ s.t. 〈p〉 ∈ D′|; (b) |〈p〉 is propositiontrue| ←P |〈p〉 instantiates TD|; and (c) |〈p〉 is proposition-true| ←F |〈p〉 ∈ D and there is no distinct domain D′ s.t. 〈p〉 ∈ D′|, |〈p〉 instantiates TD|; – (ii) If 〈p〉 ∈ D and 〈p〉 ∈ D′ (D 6= D′), 〈p〉 is inapt for TD (TD′), and 〈p〉 is proposition-true, then (a) |〈p〉 is proposition-true| ←P |〈p〉 ∈ D|; (b) |〈p〉 is proposition-true| ←P |〈p〉 ∈ D′ (D 6= D′) and 〈p〉 is inapt for TD (TD′)|; (c) |〈p〉 is proposition-true| ←P |〈p〉 instantiates TD′ (TD)|; and (d) |〈p〉 is proposition-true| ←F |〈p〉 ∈ D|, |〈p〉 ∈ D′ (D 6= D′) and 〈p〉 is inapt for TD (TD′)|, |〈p〉 instantiates TD′ (TD)|. 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(2000) Skin deep or in the eye of the beholder? The metaphysics of the aesthetic and the sensory. Philosophy and Phenomenological Research 61: 3. 595-618. 356 Appendix 1: Primitivist truth theories Readers with a strong interest in alethic primitivism may desire a more precise picture of the family of primitivist theories of truth. In this appendix, I'll provide such a sketch. The arrows in Figure 1 represent entailments, so the figure itself represents the relative strengths of the views in this family. Indefinabilism Circularism Anti−Decompositionalism Anti−Reductionism Figure 2: Primitivist truth theories The strongest of these four primitivist theories is indefinabilism, since it entails the three additional theories in the family but is entailed by none of them. Indefinabilism entails alethic anti-reductionism. Alethic indefinabilism is the view that it isn't possible to describe the essence of truth. It is highly plausible to interpret a constitution theory for a property P as purporting to describe P's essence. Consider, for instance, the constitution theory for water which states that x's being water consists in x's being H2O. The aim of this constitution theory is presumably not to describe a contingent fact about water, but to describe the essence of being water. However, alethic indefinabilism is the view that it's impossible to describe truth's essence. So, alethic indefinabilism entails that there is no true, constitution theory for truth and thus entails alethic anti-reductionism. Alethic indefinabilism also entails alethic anti-decompositionalism. This is 357 because it is similarly plausible to interpret a decompositional analysis of a property P as purporting to describe certain essential facts about P. A decompositional analysis of being the current US President, for instance, might take this complex property to have as proper parts the properties being at least thirty-five years old, being a US resident for at least fourteen years, being unable to hold one's current occupation for more than eight years, etc. The aim of this analysis is to describe the essential proper parts of being the current US President. This shows that alethic indefinabilism entails that there is no true, decompositional analysis of truth and thus entails that alethic anti-decompositionalism is true. Finally, indefinabilism entails alethic circularism a fortiori. The second strongest of these five views is alethic circularism. As we explained in § 2.2.4, circularism doesn't entail indefinabilism but does entail both anti-reductionism and anti-decompositionalism. The third strongest view in this family is alethic anti-reductionism. As we explained in § 2.2.2, anti-reductionism doesn't entail indefinabilism. Antireductionism also fails to entail circularism. Even if there is no true constitution theory for truth, there might still be a true, non-circular description of truth's essence, e.g. 'truth is essentially instantiable by declarative sentence-tokens.' By contrast, anti-reductionism does entail anti-decompositionalism. This is because a decompositional analysis of truth looks to entail that there is a true, constitution theory for truth. A decompositional analysis of property P aims to 358 identify certain properties P1, . . . ,Pn which are proper parts of P. As is suggested by our sample decompositional analysis of being the current US President, the properties identified by a decompositional analysis will often be properties in whose collective instantiation being P is taken to consist. An exception to this rule would be, for instance, a decompositional analysis of being solid or being liquid into being solid and being liquid. Notice, though, that this analysis does purport to identify two properties P1 and P2, one of which must be instantiated for the disjunctive property P to be instantiated. So it entails that a's being solid or liquid consists in a's being solid or a's being liquid. Consequently, a decompositional analysis of a disjunctive property P entails that P is constituted (and similarly for decompositional analyses of negative or conditional properties). For this reason, alethic anti-reductionism entails truth is non-decomposable. Finally, the weakest view in this family is alethic anti-decompositionalism, which entails none of the other three views and is entailed by all of them. We saw in § 2.2.3 that anti-decompositionalism entails neither anti-reductionism nor indefinabilism. It also fails to entail circularism. Anti-decompositionalism fails to entail indefinabilism because truth might be non-decomposable even though there is a true constitution theory for truth. Since constitution theories for properties are, by stipulation, non-circular, it follows that truth might be non-decomposable though nevertheless non-circularly analyzable.