The Philosophical Quarterly Vol. 66, No.262 2016 ISSN 0031 8094 doi: 10.1093/pq/pqv063 Advance Access Publication 27th August 2015 DEFLATIONISM, CONCEPTUAL EXPLANATION, AND THE TRUTH ASYMMETRY By David Liggins Ascriptions of truth give rise to an explanatory asymmetry. For instance, we accept <Rex is barking> is true because Rex is barking but reject Rex is barking because <Rex is barking> is true. Benjamin Schnieder and other philosophers have recently proposed a fresh explanation of this asymmetry: they have suggested that the asymmetry has a conceptual rather than a metaphysical source. The main business of this paper is to assess this proposal, both on its own terms and as an option for deflationists. I offer a pair of objections to the proposal and defend them from counter-objections. To conclude, I discuss how else to explain the asymmetry, and set out the implications for deflationism and correspondence theories of truth. Keywords: truth, conceptual explanation, grounding, deflationism, correspondence theory. I. THE TRUTH ASYMMETRY Suppose there is a dog called Rex. Furthermore, suppose that <Rex is barking> that is, the proposition that Rex is barking is true. Why is it true? The obvious explanation is that Rex is barking. If Rex is barking, it is no surprise that <Rex is barking> is true. Suppose we now turn our attention to Rex s behaviour and ask for an explanation of why he is barking. There may be many possible explanations: perhaps he has smelt a canine rival, or perhaps he is reminding his owner it is dinnertime. However we explain Rex s barking, we will not point to the possession of a semantic property by an invisible, intangible entity. In particular, we will not explain Rex s behaviour by pointing out that <Rex is barking> is true. Thus, we have an explanatory asymmetry: we accept (A) <Rex is barking> is true because Rex is barking. C The Author 2015. Published by Oxford University Press on behalf of The Scots Philosophical Association and the University of St Andrews. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
THE TRUTH ASYMMETRY 85 but reject (ConA) Rex is barking because <Rex is barking> is true. It is important that because is read here as indicating an explanation. Perhaps there is another sense of because in which (ConA) is true say, a sense in which because marks a valid inference. Substituting other truths for Rex is barking yields many similar cases. I call this phenomenon the truth asymmetry. 1 That there is an explanatory asymmetry here is not particularly surprising: there are few if any cases where we explain why p by pointing out that q and also explain why q by pointing out that p. If there are virtuous explanatory circles, they have a greater radius than that. But the asymmetry gives rise to an interesting question: Why does the explanation run in the direction it does? In other words, why is (A) right and (ConA) wrong? To answer these questions is to explain the truth asymmetry. Many philosophers are attracted to deflationist accounts of truth. One deflationist, Paul Horwich, offered an explanation of the asymmetry in his 1998, but Horwich s explanation is widely believed to fail (as I will discuss in Section II). More recently, Benjamin Schnieder and other philosophers have offered a fresh explanation of the asymmetry: they have suggested that the asymmetry has its source in the concept of truth (Section III). The main business of this paper is to assess this proposal, both on its own terms and as an option for deflationists. I will offer a pair of objections to the proposal (Section IV) and defend them from counter-objections (Section V). To conclude, I discuss how else to explain the asymmetry, and set out the implications for deflationism and correspondence theories of truth (Section VI). II. HORWICH S EXPLANATION Horwich s deflationism has four tenets. (i) Truth has no underlying nature. (ii) To possess the concept of truth is to be disposed to believe the T-biconditionals. (iii) The function of true is expressive. (iv) The T-biconditionals explain the phenomena of truth. Let me briefly introduce these. Some philosophers think that truth is correspondence to fact. Others think that truth is membership of a coherent set. Horwich rejects all such identifications and maintains that we can explain the phenomena of truth without 1 It was noted by Aristotle: see Künne (2003: 150).
86 DAVID LIGGINS their help. This is what is meant by the claim that truth has no underlying nature tenet (i) (cf. Horwich 1998: 141 5). Where the concept of truth is concerned, Horwich is similarly economical (1998: 136, 2001: 158, 159, 164 n. 23). He holds that to possess the concept of truth is to be disposed to believe the propositions expressed by instances of the schema: (E) <p> is true iff p. (where iff expresses the material biconditional). This is tenet (ii). Following David (2005), I ll call these propositions T-biconditionals. Tenet (iii) concerns the predicate true. Deflationists face the question of why we bother applying this predicate to anything, and their answer (following Quine 1970: 10 13) is that the predicate true performs an expressive function. The idea is that the function of true is to allow us to generalize and thus enhance our expressive power. For instance, What John said is true gives me a quick way of endorsing John s claim, however long and complicated it was, and regardless of whether I know what he said, or even am in a position to understand it. Horwich (1998: 33) claims that we have the predicate true because it performs this function. That is how I will understand (iii). (Note that Horwich s view is nothing to do with the position in metaethics known as expressivism ; in particular, Horwich does not deny that ascriptions of truth are truth-evaluable.) Tenet (iv) is that the T-biconditionals explain the phenomena of truth: for instance, that material implication preserves truth, that true beliefs tend to lead to success in action, and that true theories yield accurate predictions. According to Horwich (1998: 23 5), we need assume no more about truth than the T-biconditionals to explain such phenomena. We may need to invoke principles that do not concern truth, but the only claims about truth required are the T-biconditionals. Given tenet (iv), we would expect Horwich to offer an explanation of the truth asymmetry which appeals to no claims about truth other than T-biconditionals. This is what Horwich does: he argues that his deflationist theory leads to something very similar to (A), namely: (1) <Snow is white> is true because snow is white. Horwich writes: In mapping out the relations of explanatory dependence between phenomena, we naturally and properly grant ultimate explanatory priority to such things as the basic laws of nature and the initial conditions of the universe. From these facts we attempt to deduce, and thereby explain, why, for example, (2) Snow is white.
THE TRUTH ASYMMETRY 87 And only then, invoking the minimal theory, do we deduce, and thereby explain, why (3) <Snow is white> is true. (Horwich 1998: 105, numbering altered) This is how Horwich offers to explain the direction of the truth asymmetry. Notice that (1) explains the truth of <Snow is white> in terms of snow s being white; so the part of Horwich s account which concerns how to explain why snow is white is irrelevant. The same account should apply even if the colour of snow could not be explained in Horwich s way, or even if it could not be explained at all (Künne 2003: 156, 157; Wright1992: 27). Stripped of irrelevance, Horwich s argument is that his theory explains (A) because the following deduction is valid: (2) Snow is white. (E-Snow) <Snow is white> is true iff snow is white. (Instance of (E)). Therefore, (3) <Snow is white> is true. The problem with Horwich s argument is that, since (E-Snow) is a biconditional, the following deduction is also valid: (3) <Snow is white> is true. (E-Snow) <Snow is white> is true iff snow is white. Therefore, (2) Snow is white. So if Horwich s theory implies (A), it implies (ConA) as well. But this means it cannot explain the asymmetry (Rodriguez-Pereyra 2005: 27). Moreover, this casts doubt on Horwich s claim that his theory implies (A), because (as we have seen) it is implausible that both (A) and (ConA) hold. It was never very plausible to think that the mere deducibility of (3) gives us (1): a familiar point from the philosophy of science is that entailment is insufficient for explanation (see Bromberger 1966). So Horwich s discussion of (A) does not indicate any way for deflationists to explain the truth asymmetry. 2 The failure of Horwich s explanation should make us doubt that his form of deflationism can be used to explain the truth asymmetry. Horwich s starting point is the T-biconditionals, and these are entirely symmetrical. Even if Rex is barking, there is no way to get from the symmetrical biconditional 2 For further discussion of Horwich s argument, see Wright (1992: 27), Künne (2003: 156, 157), and Vision (2004: 121 3). Having responded to Horwich, Wright (1992: 27) tries to secure (A) for deflationism; difficulties are pointed out at Vision (2004: 116 20) andkünne (2003: 157). See Douven and Hindricks (2005) for commentary on both Horwich and Wright.
88 DAVID LIGGINS <Rex is barking> is true iff Rex is barking. to the asymmetrical explanation <Rex is barking> is true because Rex is barking. (Künne 2003: 151, 152; Vision 2004: 118, 119). So the T-biconditionals do not suffice to explain the asymmetry. But if Horwich employs other claims about truth to explain the asymmetry, then he renounces his deflationism by renouncing tenet (iv). III. THE PROPOSED CONCEPTUAL EXPLANATION OF THE ASYMMETRY As Gupta (1993) and David (2002) have argued, it is very hard to explain the phenomena of truth using only the T-biconditionals and principles that do not concern truth. Let us consider a weakened version of Horwich s view, which I ll call mild deflationism. This is just the same as deflationism except that tenet (iv) that the T-biconditionals explain the phenomena of truth is replaced with (iv ) The phenomena of truth can be explained by the T-biconditionals and tenets (i) (iii). Spelled out more fully, (iv ) says that we need assume no more about truth than the T-biconditionals and tenets (i) (iii) to explain the phenomena of truth; we may also need to invoke principles that do not concern truth. Can mild deflationism explain the truth asymmetry? It is hard to see how truth s lack of underlying nature [tenet (i)] or the expressive function of true [tenet (iii)] could help explain the asymmetry, but tenet (ii) (that the T-biconditionals exhaust the concept of truth) is more promising. Expanding on a suggestion in Künne (2003: 154, 155), Schnieder (2006b: 35, 36, 2006a: 404 6) offers an explanation of the truth asymmetry of this sort. Dodd (2007: 399, 400) makes similar claims, and Horwich himself has recently done so as well, albeit in just two sentences (2008: 266 n. 13). The most developed explanation is Schnieder s. I will argue that it is unacceptable. (I should mention, for the record, that Schnieder does not commit himself to deflationism.) Schnieder isolates a class of explanations which he dubs conceptual explanations. His examples of conceptual explanations include: (E1) Xanthippe became a widow, because Socrates died. (E2) This vase is coloured because it is red. Schnieder (2006a: 32) tells us that conceptual explanations are non-causal and are based on certain conceptual relations. For instance, we can relate
THE TRUTH ASYMMETRY 89 the concept widow to other concepts by analysing it as woman whose husband has died. According to Schnieder,(E1) is based on these conceptual relations. He holds that not all conceptual explanations rest on a conceptual analysis. For instance, the concept being coloured cannot be analysed in terms of the concepts of particular colours, but (E2) is still a conceptual explanation, since it is based on a conceptual relation: that being red is sufficient for being coloured. Although Schnieder does not use the term analytic, it seems fair to report him as believing that for every conceptual explanation there is a corresponding analytic truth a sentence true in virtue of its meaning which records the conceptual connection on which the explanation rests: for instance, Something is a widow if and only if it is a woman whose husband has died for (E1), and If something is red, it is coloured for (E2). In both (E1)and(E2), the concepts invoked in the explanandum are arguably more complex than those invoked in the explanans. Schnieder holds that this holds more generally: [A]s the order of explanation (explanations are in general asymmetric) is determined, in the case of causal explanations, by the order of the causal relation itself, it will be owed to factors of conceptual complexity and primitiveness in the case of conceptual explanation. In general, statements involving complex or elaborated concepts are explained with recourse to more primitive concepts (which may or may not enter into an analysis of the complex concepts). (Schnieder 2006a: 406) This principle offers mild deflationists a possible explanation of the truth asymmetry. According to Schnieder, the explanation flows in the direction it does because of the conceptual relations between true and other concepts. He claims that it is constitutive of our mastery of the concept of truth to accept instances of (E) <p> is true iff p. 3 He continues: This fact about the concept of truth gives rise to the correctness of (T) [ p: Ifitistrue that p at all, then it is true that p, because p] and its instances. The explanatory force of (T) is comparable to that in the examples of conceptual explanations discussed so far; it is an explanation of a proposition employing a logically elaborate concept, the concept expressed by true, by a conceptually simpler proposition. This latter proposition does not employ concepts which enter into an analysis of the concept expressed by true ; truth is not analysable in terms of the concepts expressed by white and snow, because someone can have a grasp of the concept of truth without knowing anything about snow or the colour white. But mastery of the concept is constituted by the ability to relate statements involving it to statements involving only conceptual resources already at hand. (2006a: 36, footnotes removed) 3 Actually Schnieder talks about instances of It is true that p p, but that amounts to the same thing.
90 DAVID LIGGINS Schnieder s idea is that, although none of the T-biconditionals is a conceptual analysis of true, each of them is an analytic truth. To use a phrase of Künne s (2003: 155), the right-hand side of each one elucidates the sense of the left. For instance, Snow is white elucidates the sense of <Snow is white> is true. Speaking schematically: if p, then the explanation <p> is true because p is based on the conceptual relations which underpin the sentence <p> is true iff p. For instance, (A) is based on the conceptual relations which underpin the sentence <Rex is barking> is true iff Rex is barking. And the explanations run in the direction they do Schnieder claims because <p> is true is of greater conceptual complexity than p. IV. TWO PROBLEMS FOR THE CONCEPTUAL EXPLANATION It would be good to be given a fuller account of just what conceptual complexity is, and to be told more about how to compare the conceptual complexity of two statements. But Schnieder s account is detailed enough to be going on with. I ll argue that even if we grant Schnieder all his claims about conceptual complexity, his explanation of the asymmetry runs into two major difficulties. The first difficulty for Schnieder s explanation is that, although the instances of (E) are often assumed to be analytic, they are actually poor candidates for analyticity. To see this, note that if such a sentence as (E-tiger) <All tigers are tigers> is true iff all tigers are tigers. is analytic, then so is the logical truth All tigers are tigers. But these jointly logically entail that <All tigers are tigers> is true. And that entails that there is something, namely <All tigers are tigers>. So if (E-tiger) is analytic, we have a purely conceptual proof that there is something rather than nothing. (For a similar argument, see Halbach 2001: 179.) But this is fishy. It is plausible to think that the lesson of the ontological argument is that conceptual truths lack ontological entailments. Field (1989: 5) puts the point well: An investigation of conceptual linkages can reveal conditions that things must satisfy if they are to fall under our concepts; but it can t yield that there are things that satisfy those concepts (as Kant pointed out in his critique of the ontological argument for the existence of God). If Field is right, the instances of (E)arenot conceptual truths, because they logically entail existence claims. That means that the conceptual connections required to support conceptual explanation are absent. And in that case Schnieder s account of the asymmetry fails. There are further reasons to doubt the analyticity of the instances of (E). On many accounts of propositions, some propositions contain contingently existing things and are therefore contingent existents themselves. For example,
THE TRUTH ASYMMETRY 91 if Rex is a component of <Rex is barking>, then<rex is barking> would not have existed if Rex had not. And the same goes for <Rex does not exist>. But that means that the sentence <Rex does not exist> is true iff Rex does not exist. is only contingently true: it would not have been true if Rex had failed to exist,forifrexhadfailedtoexist,thesentencewouldnothaveexpresseda proposition. (Fine 1977: 136, makes a similar point.) Since the sentence does not possess any of the familiar sources of contingent analyticity (for example, it is free of indexicals), its contingency casts doubt on its analyticity (see David 2005: 387 92). 4 The plausibility of these popular accounts of propositions therefore challenges the analyticity of the instances of (E). The second difficulty for Schnieder s explanation of the truth asymmetry concerns the very idea of conceptual explanation. Let us go back to Schnieder s initial examples: (E1) Xanthippe became a widow, because Socrates died. (E2) This vase is coloured because it is red. It is appealing to think that these explanations rest on conceptual relations. But it is striking that the explananda have nothing to do with concepts: they concern a particular woman and a particular vase. It is hard to see how the fact that the concept widow can be analysed as woman whose husband has died bears on the explanation of why Xanthippe became a widow. Similarly, even though it is a conceptual truth that everything red is coloured, it remains to be seen how that conceptual connection is relevant to the explanation of why the vase is coloured. Prima facie, these facts about concepts are irrelevant to the phenomena to be explained. Admittedly, Xanthippe falls under the concept widow and the vase falls under the concept coloured, but then each thing falls under many concepts. How do concepts help us to explain why someone is a widow or why a particular vase is coloured? For a parallel, let us switch from concepts to predicates. Each thing satisfies many predicates: for instance, Xanthippe satisfies the predicate is a widow and the vase satisfies the predicate is coloured. These predicates are related to others: for instance, something satisfies is a widow just in case it satisfies is a woman whose husband has died, and something satisfies is coloured if it falls under is red. But it is far from clear how these relations between predicates could help explain the phenomena allegedly explained in (E1) and(e2). Schnieder and other proponents of conceptual explanation make the surprising claim that concepts do help. They need to explain 4 David (2005: 409 16) contains further arguments against the analyticity of the instances of (E).
92 DAVID LIGGINS how they help and it is not clear how to go about doing this. The point is independent of any particular theory of the nature of concepts. Some philosophers regard concepts as abstract objects; others think of them as mental representations or mental capacities (see Margolis and Laurence 2007). In each case, we are entitled to an account of the relevance of these entities. Let me emphasize that my aim is not to cast doubt on (E1) and(e2), but on whether facts about concepts give rise to their correctness (as Schnieder puts it). Consider: (E1-C) Xanthippe falls under widow, because Socrates died. (E2-C) This vase falls under coloured because it is red. These seem to be good explanations. The explananda are closely related to the explananda of (E1) and(e2). In (E1-C)and in (E2-C), we explainwhy a certain concept applies to an object by citing the fulfilment of a sufficient condition for its application. Take (E1-C). For someone to fall under the concept widow, it is sufficient for them to be a woman whose husband has died. That follows from the fact, highlighted by Schnieder, that widow can be analysed as woman whose husband has died. To anyone who knows that Socrates was Xanthippe s husband, (E1-C) explains the applicability of widow by citing the fulfilment of the condition. Similarly, (E2-C) explains why the vase falls under coloured by appeal to a sufficient condition for falling under coloured being red. Its sufficiency follows from a fact about conceptual relations, namely, the fact that falling under red is sufficient for falling under coloured. My purpose in introducing these explanations is to explain away the appeal of the idea that (E1) and(e2) are conceptual explanations in Schnieder s sense. There are good explanations in the vicinity which rely on conceptual relations, namely, (E1-C) and (E2-C). The difference between (E1-C) and (E1) is subtle, as is the difference between (E2-C) and (E2). For most purposes, the distinction between being a widow and falling under widow is of no importance, for instance. So it is plausible that our intuitive feeling that (E1) and(e2) must have something to do with conceptual relations really stems from the fact that (E1-C) and (E2-C) do have to do with conceptual relations (in the manner just described), combined with a failure to register the usually unimportant distinctions between (E1-C) and (E1), and between (E2-C) and (E2). Let us call this the conceptual proposal. Consider also these explanations: (E1-P) Xanthippe satisfies is a widow, because Socrates died. (E2-P) This vase satisfies is coloured because it is red.
THE TRUTH ASYMMETRY 93 These are further examples of good explanations which owe their success to conceptual relations. Suppose the predicate F applies to all and only the things which fall under the concept Fness, and suppose the predicate G appliesto all and only the things which fall under the concept Gness. Suppose furthermore that Fness and Gness are related in such a way that falling under Fness is sufficient for falling under Gness (for instance, perhaps Fness can be analysed as Gness). Then satisfying F suffices for satisfying G. That means, in turn, that we can explain why something satisfies G by describing it as F (that is, by applying F to it). Explanations(E1-P) and (E2-C) thus trade on conceptual relations. Now such distinctions as the distinction between being red and satisfying red are typically of no importance. So we have another reason to expect that we will be tempted to regard (E1) and(e2) as having something to do with conceptual relations: (E1-P) and (E2-P) trade on conceptual relations and the respective differences between these and (E1) and(e2) are unimportant, so it is no wonder that we might think that (E1) and(e2) rely on conceptual relations for their correctness. Let us call this the metalinguistic proposal. (The metalinguistic proposal expands on a suggestion of Mark Johnston s; see his 1993: 330.) One of Künne s examples of conceptual explanation is as follows. (R ) He is your first cousin because he is a child of a sibling of one of your parents. Regarding (S ) The statement that snow is white is true, because snow is white, Künne (2003: 155) writes: [W]e can understand (S ) along the same lines as (R ). Why is it correct to say of him that he is your first cousin? The second clause of (R ) gives the answer. Why is it correct to say of the statement that snow is white that it is true? The second clause of (S )givestheanswer. Notice that Künne writes Why is it correct to say of him that he is your first cousin?, not Why is he your first cousin?, and Why is it correct to say of the statement that snow is white that it is true?, rather than Why is the statement that snow is white true?. Elsewhere, Künne maintains: [I]f the statement that there are no Martians is true, then it is true because there are no Martians. This claim explains why true is correctly applied to a certain statement if it is applied to it at all... (p. 165). These passages suggest that Künne has confused the explanation of why something is true with the explanation of why true applies to it. My challenge to Schnieder is to establish that his explanation of the truth asymmetry does not rely on any such confusion.
94 DAVID LIGGINS V. REPLIES TO OBJECTIONS V.1. A severe confusion? Schnieder (2010) contains, in effect, a defence of conceptual explanation against the second objection I have given. The defence is partial because Schnieder only considers the metalinguistic proposal, not the conceptual proposal, and because he does not consider the role of concepts in giving rise to the correctness of metalinguistic explanations such as (E1-P) and (E2-P). In addition, he presupposes that advocates of the metalinguistic proposal will deny (E1) and(e2) and will try to explain away their apparent truth. The objection I am exploring here does not involve denying (E1) or(e2), although it does involve denying that facts about concepts give rise to their correctness. Still, the proposals are sufficiently similar that it is worth assessing whether Schnieder s defence causes my objection any trouble. Schnieder offers two main counter-arguments, the first of which rests on the idea that the metalinguistic proposal attributes to us an unacceptably severe confusion. Schnieder suggests that, according to that proposal, we confuse with (B1) A bachelor is a bachelor because he is an unmarried male. (B1 ) A bachelor is correctly called bachelor because he is an unmarried male. and also confuse with (B2) Donald is a bachelor because he is an unmarried male. (B2 ) Donald is correctly called bachelor because he is an unmarried male. But if we ignore sceptical arguments about apriority (B1) is a priori, whereas (B1 ) is a posteriori. Moreover, (B1) is necessary, whereas (B1 ) is contingent. Schnieder writes (2010: 334): The confusion that is ascribed to people who mistake [(B1)] for [(B1 )] or [(B2)] for [(B2 )] is quite a severe one. And he implies that it is wrong to ascribe such a degree of confusion to us. Let me make two comments on this argument. Firstly, (B2) and(b2 )are red herrings. Since they both imply that Donald is a bachelor, both of them are contingent and a posteriori. We can run them together without falling into modal or epistemological confusion. Secondly, even if we concede the differences in modal and epistemological status between (B1) and(b1 ), it should be unsurprising that we are prone to confuse claims which differ in this way. A disposition to make use mention errors is widespread, as every philosophy teacher knows, and it is clear that such errors lead us to confuse claims which differ in modal and epistemological
THE TRUTH ASYMMETRY 95 status. For instance, it is a priori and necessary that everything is self-identical, but it is a posteriori and contingent that everything is correctly called selfidentical so if one confuses being self-identical with being correctly called self-identical, one will confuse an a priori necessity with an a posteriori contingency. Only if we are not prone to make use mention confusions is it wrong to portray us as liable to confuse claims which differ in modal and epistemological status. But we are prone to make use mention confusions, so it is not wrong to portray us as liable to confuse claims which differ in modal and epistemological status. It is therefore not at all clear that my objection attributes to us an unacceptable degree of confusion. V.2. Overgeneration? The second counter-argument (Schnieder 2010: 334, 335) maintains that the metalinguistic proposal makes an erroneous prediction. It predicts that we will accept (D1) Donald is an unmarried male because he is a bachelor. because we accept (D1 ) Donald is correctly called unmarried male because he is a bachelor. and mistake being an unmarried male for being correctly called one. In fact Schnieder claims we reject (D1), causing trouble for the metalinguistic proposal. I am prepared to grant to Schnieder that we reject (D1). But I think that this rejection is entirely compatible with the metalinguistic proposal. To explain why (E1) and(e2) seem to have something to do with conceptual relations, for instance, it is enough to say that we are disposed to confuse them with explanations which do have to do with conceptual relations, such as such as (E1-P) and (E2-P), and make this confusion on the basis of a tendency to blur use and mention. There is no need to make the stronger claim that we make such confusions in every case. This reply will not be satisfying, however, until it is explained why (D1)isan exception. But here I can appeal to some claims made by Schnieder himself. Schnieder (2010: 333) reports that he has observed a number of (philosophically trained) people going metalinguistic when asked to justify (B1), and argues that this observation gives little if any support to the proposal, because our inclination to do so can be explained away. This can be done by noting that explanations such as (B1) can be used in teaching someone part of the language: for instance, someone who has not yet mastered bachelor will find (B1)helps them to learn the meaning of the word. This follows from the more general point that by using a word, we can help other people learn how to use it. As
96 DAVID LIGGINS Schnieder observes, this is far from showing that everything we say is covertly metalinguistic. I have no quarrel with these comments of Schnieder s. Rather, my point is that they help to defuse his second counter-argument against the metalinguistic proposal. We were wanting a reason to expect that we will not be led to accept (D1) even though we accept (D1 ). The reason is that (D1) would be of little use in teaching someone the word bachelor : (B1) would be much more helpful. Someone who does not understand unmarried male is unlikely to understand bachelor, so they are unlikely to receive much help from (D1). More generally, we teach the less familiar expressions by using more familiar ones. Since (D1) is not appropriately assertible in language-learning contexts, and it is hard to think of other contexts where it would be appropriately assertible, we probably reject (D1) on the grounds that it is not assertible. For these reasons, I am unpersuaded that Schnieder s counter-arguments to the metalinguistic proposal cause my objections any trouble that cannot be overcome. V.3. Avoid the instances of (E)? Schnieder might reply to my objections by modifying his explanation of the truth asymmetry. Instead of appealing to the instances of (E), he might appeal to other principles which are more plausibly regarded as analytic, and claim that these record the conceptual connections on which explanations such as (A) are based. Consider (E-tiger )If<All tigers are tigers> exists, then: <All tigers are tigers> is true iff all tigers are tigers. and the other instances of (E )If<p> exists, then: <p> is true iff p. (The colon indicates that If... then is the main connective.) These are much more promising candidates for analyticity than the instances of (E). Because they are conditional on the existence of propositions, they cannot be used to show that propositions exist (compare Field 1989: 168, 169). And they avoid the contingency objection: if Rex is a component of <Rex is barking>, then the sentence <Rex does not exist> is true iff Rex does not exist. is only contingently true, but the corresponding instance of (E ) If <Rex does not exist> exists, then: <Rex does not exist> is true iff Rex does not exist. is still necessary (Fine 1977: 136).
THE TRUTH ASYMMETRY 97 It is hard to see how the instances of (E ) could underpin explanations of the truth of propositions. The reason is that Schnieder s examples of conceptual explanations involve a conceptually sufficient condition for the explanandum (see Section III), whereas instances of (E ) do not do this. For instance, (E2) This vase is coloured because it is red. is supposed to rest on the conceptual relation that being red is sufficient for being coloured but no instance of (E ) states a conceptually sufficient condition for the truth of the proposition whose truth is supposed to be being explained. However, notice that each instance of (E ) entails an instance of (E ): (E )Ifp and <p> exists, then: <p> is true. and this provides a sufficient condition for <p> s being true. If these instances are analytic, then perhaps the conceptual connections they record give rise to conceptual explanations of the truth of propositions. Such explanations would take the following form: <p> is true because p and <p> exists; for instance: <Rex is barking> is true because Rex is barking and <Rex is barking> exists. It might then be claimed that (A) is an abbreviated version of this explanation. The problem with this proposal is that the existence of the proposition does not help to explain why it is true. Once we have pointed out that Rex is barking, we have explained the truth of <Rex is barking>. Although the existence of the proposition is a necessary condition of its truth, the existence of the proposition is not part of the explanation. So this modified version of Schnieder s explanation fails. It is plausible that explanations such as (A) have a contrastive element: Rex s barking explains why <Rex is barking> is true rather than untrue. From this perspective, it is unsurprising that the proposition s existence is not part of the explanation, for it is clear that the proposition s existence does not help to explain why it is true rather than untrue. Contrastive explanation has been discussed in the literature on causal explanation, largely thanks to Lipton (1990), but should be taken into account in non-causal cases as well.
98 DAVID LIGGINS VI. IMPLICATIONS VI.1. Implications for deflationism It is hard to see how Horwich s deflationism could explain the truth asymmetry. The asymmetry cannot be explained using the only allowable resources concerning truth, the (symmetrical) T-biconditionals (Section II). Mild deflationists allow themselves to appeal to tenets (i) (iii) in order to explain the phenomena of truth, but it is hard to see how any of these apart from (ii) could help. And I have argued that the most developed appeal to (ii) runs into serious problems and thus cannot be regarded as a successful explanation for the mild deflationist to use (Sections IV and V). I conclude that the asymmetry is a serious problem for both deflationism and mild deflationism. My arguments carry over to other forms of deflationism. For instance, I have taken propositions as truthbearers, but the same objections can be made to forms of deflationism, such as Field s (1994), which take sentences instead. Some deflationists, such as Hill (2002: ch.2)andkünne (2003: section 6.2)tryto generalize the T-biconditionals and thereby give an explicit definition of truth: but I do not see how that would help them to explain the truth asymmetry or evade my arguments against the proposed conceptual explanation. 5 Deflationists may try to avoid the problem by denying that there is an asymmetry: if there is no asymmetry, then there is no asymmetry to be explained. Presumably they will not want to endorse both (A) and (ConA), for then they would be saying that explanation runs in both directions. A deflationist who denies the asymmetry is much more likely to deny both (A) and (ConA), and find some way to explain why we are tempted to think that there is an asymmetry. Such a response would fail. I assume that deflationists think that some propositions are true; to deny (A) would leave them with the task of explaining why they are true. But the obvious explanations of why propositions are true take the form of (A): there are no other credible candidates. (This is not to deny that (A) can be deepened by appending an explanation of why Rex is barking.) Once the deflationist has denied (A), they will be at a loss to find an explanation. And I do not think that it at all comfortable to say that there is no explanation of why (for example) <Rex is barking> is true. Perhaps some will claim that, according to deflationism, for <Rex is barking> to be true just is for Rex to be barking, so the proposition s truth has been explained once we have explained the behaviour of the dog. But that would be to confuse deflationism with the redundancy theory, which should be rejected in any case (see Künne 2003: 34 53). 5 Hill (2002: 56, 57) prefers to call his theory quasi-deflationist and Künne (2003: 19, 20) thinks the term deflationism should be banned. But their views resemble Horwich s deflationism, and it is hardly unfair to deflationism to consider whether they can explain the asymmetry.
THE TRUTH ASYMMETRY 99 A more radical response for the deflationist is to deny that anything is true and thus deny (A) and (ConA). There is a question about whether the resulting theory would count as a form of deflationism, but, setting that terminological matter aside, it would clearly be a very different theory to the forms of deflationism currently under discussion, and I will not say any more about it here. VI.2. A metaphysical explanation of the asymmetry Deflationism aside, how might one go about explaining the truth asymmetry? An attractive way is to make some claims of grounding. Let me briefly introduce this term. The notion it expresses is familiar, though our theoretical understanding of it is fairly dim as yet. It is the notion we have in mind when we say that the existence of Socrates singleton set depends on the existence of Socrates; when we say that containing vodka makes a drink alcoholic; when we speak of the mass of an object being owed to the masses of its parts; and when we describe something as flexible in virtue of its microphysical properties, or beautiful on account of its colour. Grounding is referred to in many different ways in philosophy too: it is variously known as non-causal dependence, ontological dependence, ontological priority, and priority in nature. 6 I will assume that explanations work only in virtue of the determinative relations that exist in the world.... [W]e explain something by showing what determines that thing to be as it is (Ruben 1990: 231; see also Kim 1994; Rodriguez-Pereyra 2005: 27, 28). From this perspective, the direction of explanation is determined by the direction of grounding, just as we causally explain events by pointing to their causes, not their effects. It is controversial whether grounding is a relation and, if it is, what it relates: I will assume that it is a relation between facts, and I will write thefactthatp as [p]. We can now see a natural way to explain the truth asymmetry: claim (for instance) that (A) is underpinned by some relevant grounding, whereas (ConA) is not. More precisely, claim that [<Rex is barking> is true] is grounded by [Rex is barking], whereas [Rex is barking] is not grounded by [<Rex is barking> is true] (indeed, for no proposition x is [Rex is barking] grounded by [x is true]). On this view, the explanatory asymmetry is explained by a metaphysical asymmetry. The same strategy could be applied to the many similar pairs. The metaphysical doctrine that [<p> is true] is generally grounded by [p], but not vice versa, is enough to explain the truth asymmetry. Although this explanation is attractive, it is unavailable to deflationists, since it involves grounding claims which go beyond the T-biconditionals (and their 6 For more on the notion of grounding, including further examples, see Correia (2005), Schaffer (2009), Rosen (2010), Correia and Schnieder (eds) (2012), and Clark and Liggins (2012). Audi (2012) defends the coherence of the notion against sceptical attacks.
100 DAVID LIGGINS generalizations). Anyone who invokes grounding to explain the phenomena of truth has left deflationism behind. It is worth noting that the explanation also puts pressure on the deflationist doctrine that truth has no underlying nature. If one asserts that [<p> is true] is generally grounded by [p], one should ideally offer to explain this correlation and it seems likely that any explanation will appeal to some feature of truth itself. For instance, one might say that it is part of the nature of truth that facts of the type [<p> is true] are grounded in this way (compare Fine 1994, 1995). But then truth has an underlying nature. If the truth asymmetry is to be explained by appeal to grounding, then it seems that not much of deflationism will be left. The explanation is compatible with other accounts of truth. For instance, take the following formulation of the correspondence theory: For all propositions x, x is true iff there is a fact to which x corresponds. This formulation needs to be clarified: what is it for a proposition to correspond to a fact? The following constraint may be part of the answer to this question: If x corresponds to [q], then [x is true] is grounded by [q]. If the theory incorporates this constraint, then it entails the claims about grounding which can explain the asymmetry. But I do not claim that the correspondence theory is the only theory which can explain it. Any theory which makes the relevant grounding claims will suffice. VII. CONCLUSION No satisfactory deflationist explanation of the truth asymmetry has yet been provided, and there is reason to suspect that none can be provided. We are able to explain the explanatory asymmetry by pointing to an underlying metaphysical asymmetry but deflationists are barred from endorsing this explanation. The simplicity of deflationism makes it an appropriate starting-point, but we must now turn to consider accounts of truth which invoke the notion of grounding. 7 7 I would like to thank all the philosophers who have given up their time to help me with this work. Particular thanks to Chris Daly, Marian David, Julian Dodd, Gonzalo Rodriguez-Pereyra, and Benjamin Schnieder. I gratefully acknowledge an AHRC Research Leave Award which supported the writing of this paper.
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