A Dilemma for the Weak Deflationist about Truth 1 Introduction The deflationist about truth is committed to a triviality or transparency thesis: the content of the truth predicate is exhausted by its involvement in some version of the truth-schema [P] is true iff P (where '[P]' stands for any declarative propositional object and 'P' stands for '[P]'s object-level equivalent). Within this classification, deflationists can usefully be divided into two camps according to the extent of their ontological commitment: a strong camp and a weak camp. Strong deflationism holds that the truth predicate doesn't designate a property or that there is no property of truth (e.g., Ramsey (1927), Ayer (1946), and Grover, Camp and Belnap (1975)). Weak deflationism holds that the truth predicate does designate a property (e.g., Horwich (1998a, 1999), Sosa (1993) and Soames (1997, 1999)). It is just that the property of truth, on weak deflationism, is deflated in some sense, e.g., it is not substantial, theoretically important, interesting, explanatory, a natural kind, or anything in this general vicinity. For example, Horwich, in making the latter kind of claim, denies that truth is "an ordinary sort of property ― a characteristic whose underlying nature will account for its relations to other ingredients of reality" (1998a, p. 2). As things currently stand, the consensus is that weak deflationism is the superior deflationary alternative. The problem with strong deflationism is that its 2 ontological thesis  that truth is not a property  seems to be underwritten by a semantic claim that is widely regarded as indefensible: 'is true' does not function semantically as a predicate (i.e., it does not denote a property). Among others, Horwich (1998a, p.3) and Gupta (1993, pp. 366-7) have persuasively argued the speciousness of this thesis on the grounds that '[P] is true' and 'P' are not synonymous,1 implying that 'is true' is ineliminable, and correspondingly, that it must designate a property of some sort.2 In opposition to the prevailing view, I argue here that weak deflationism's initial promise is illusory, that it falls short of being a viable alternative to strong deflationism and to inflationary theories of truth (theories according to which truth is a substantial property of truth bearers). Weak deflationism, it turns out, is on shaky ground since it is vulnerable to an inexorable instability objection the general form of which has been highlighted by Boghossian (1990) and Wright (1992, 1996). Contra Boghossian and Wright, though, it turns out that the strongest variation of the instability objection gives rise to a dilemma concerning truth-property ascriptions rather than the concept of truth. 1 Gupta appeals primarily to the indispensable generalizing function of the truth predicate to undermine the synonymy claim. Horwich appeals to the denominalizing function of the truth predicate in general to undermine the synonymy claim. 2 See Horwich (1998a) for the general line of argument thought to undermine strong deflationism's ontological thesis: "... '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 of standing for a property of some sort" (p. 37); "No doubt truth is very different from most properties insofar as it has no underlying nature; but in light of the inferential 3 2 The Dilemma Weak deflationism (hereafter 'WD'), unlike strong deflationism, is a theory of truth that takes the ontological middle road. It is committed to a two-pronged ontological thesis: truth is both i) a property and ii) deflated. It has been speculated that WD's ontological thesis generates an incoherence or instability in its view of truth of the following basic form: either truth is a property in which case 'is true' is susceptible to explicit analysis or truth is not a property in which case 'is true' is not susceptible to explicit analysis.3 For example, Boghossian (1990) advances an instability objection to WD along such lines on the basis of the conceptual import of the T-schema, while Wright (1992, 1996) advances an instability objection to WD along such lines on the basis of the normative import of the concept of truth (i.e., on the basis of the fact that truth is a distinct norm from justification). Perhaps the most potent variation of the instability objection, though, gives rise to a truth-property ascription dilemma that in effect calls into question the very coherence of the notion 'deflated property'. Of course, instability/incoherence dilemmas are not entirely new for the notion 'deflated property'. It has been relatively widely speculated that for any property P there role of 'true' as a logical predicate, it is nonetheless a 'property', at least in some sense of the term" (p. 125). 3 In the postscript to his (1998a), Horwich attempts to short circuit the instability objection by qualifying WD's (or 'minimalism's') ontological thesis, claiming that WD does not in itself answer the question of whether or not truth is a property, but does so only in conjunction with particular conceptions of property (p. 141): 4 must, metaphysical speaking, be some basis for ascribing P to any entity E that bears it, but that the deflationist about any property P does not have the explanatory resources necessary to supply us with the basis for such ascriptions. In other words, it has been surmised, contra the deflationist about properties, that to supply the metaphysical basis for ascribing a property P to any entity E, P must be inflated. The instability dilemma for WD fits this general mold. While its details need some spelling out (see §3), the instability dilemma for WD can be framed in simple terms: Assuming truth is a property, like other properties, it is attributable to entities paradigmatically thought to bear it (propositions, sentences, beliefs, etc.). For example, if truth is a property it is attributable to the following statements: (S1) snow is white, (S2) grass is green, (S3) the earth is round, and the like. WD, in view of its ontological thesis, is thus subject to the following desideratum: its proponent must furnish us with the basis, metaphysically speaking, for truth-property ascriptions of this kind. In particular, she must answer the following question: what is the basis for ascribing the property of truth to all the statements in question? Or to put the point another way, what prevents us from ascribing some other property to the statements in question, or from ascribing a different property to each statement (since each statement has a different truth condition)?4 Minimalism does not involve, in itself, any particular answer to this question. For it may be combined with a variety of different conceptions of property, some of which will yield the conclusion that truth predicate does stand for a property, and some that it doesn't. 5 The quagmire is that there appears to be only two basic maneuvers available to the proponent of WD in this case, neither of which seems to enable her to retain her unique, two-pronged ontological thesis about truth ― i) that it is a property and ii) that it is deflated. Either 1) she must argue that there is no metaphysical basis for the ascription of a property of truth to truth bearers (there is nothing that makes them all true) in which case she relinquishes thesis i), or 2) she must argue that there is some basis for truth-property ascriptions in which case she relinquishes thesis ii). 3 First Horn of the Dilemma To begin, consider the first (minor) horn of the dilemma. To elude this horn, the proponent of WD must argue that there is no metaphysical basis for ascribing truth to truth bearers. In other words, what must be argued in this case is that for each and every truth-bearer, e.g., [snow is white], [grass is green], etc., there is nothing that makes them true, nothing by virtue of which we can ascribe a property of truth to them. Such a maneuver is clearly a non-starter, though, one that surely will not tempt the proponent of WD. Indisputably, if there is nothing that makes alleged truth bearers true by virtue of which we can ascribe a property On the surface, though, such a maneuver does not appear to confront the heart of the instability objection. Horwich's maneuver, it would seem, can be glossed as follows: depending on what conception of property is endorsed, WD implies either i) that truth is a deflated or 'logical' property or ii) that truth is not a property. The problem is that on i), WD is committed to truth being a deflated property of some kind in which case it still gives rise to the instability objection, and on ii), WD is committed to there being no property of truth in which case WD looks indistinguishable from strong deflationism or the so-called 'redundancy theory of truth', a theory widely regarded as patently untenable (see Horwich, note 2). 4 In other words, ascribe [snow is white] property A, [grass is green] property B, [the earth is round] property C, etc. (where none of A, B, C and the like are the property of truth). 6 of truth to them, entitlement is relinquished for ascribing the property of truth to them. A cursory examination of property ascriptions bears this point out. The following seems to be a standard principle constraining property ascriptions: (POP) To be justified in ascribing some property P to an entity or set of entities E relevant grounds G must be available to license the ascription by explaining why or how E possesses P. It seems uncontroversial, viz. (POP), that property ascriptions require relevancy grounds. For example, to be justified in ascribing the property of tallness to Evan and Sally one must supply some reason explaining why Evan and Sally are tall, to be justified in ascribing the property of heaviness to Rasheed and Joseph one must supply some reason explaining why Rasheed and Joseph are heavy, etc.5 But assuming the legitimacy of (POP), it plainly is not a maneuver available to the proponent of WD to contend that there is no basis for truthproperty ascriptions ― that there is nothing that makes truth-bearers true (by virtue of which we can ascribe the property of truth to them). The problem is that claiming there is no basis for truth-property ascriptions violates (POP), since by failing to furnish the basis for truth-property ascriptions, the proponent of WD 5 This seems to follow regardless of which account of the notion property one embraces (i.e., no matter what properties are, ontologically speaking) - whether properties are particulars, 7 fails to provide any grounds for ascribing the property of truth to truth-bearers, let alone relevant grounds. In short, WD cannot elude the first horn of the truth-property ascription dilemma since by claiming there is no metaphysical basis for truth-property ascriptions ― nothing that makes alleged truth bearers true ― the proponent of WD, assuming the judicious (POP), relinquishes entitlement for ascribing the property of truth to any statement or for claiming that any statement is true. The implication in this case is that WD's view of truth collapses into that of strong deflationism: i.e., no property is ascribed to statements when we describe them as 'being true' (that is, there is no property of truth). 4 Second Horn of the Dilemma Next, consider the second (major) horn of the dilemma. To elude this horn, the exponent of WD must argue that there is a basis for ascribing a property of truth to truth bearers ― there is something that makes truth bearers true that licenses the ascription of a property of truth to them. Crucially, what requires underscoring at this stage is that there is a widely held, intuitively appealing perspective from which it would appear WD will not be able to invoke this maneuver either. This perspective can best be appreciated by looking more closely at (POP): to be justified in ascribing some property P to universals, tropes, the meanings of the predicates that designate them, or something else. For more 8 an entity or set of entities E relevant grounds G must be available to license the ascription by explaining how or why E bears P. A natural extension of (POP), one that the proponent of WD will reject, is (POP*): to be justified in ascribing some property P to an entity or set of entities E relevant grounds G must be available to license the ascription by explaining why E bears P, where in order for G to explain why E bears P, G must refer to one or more sortals (i.e., defining characteristics) of E by virtue of which E bears P. (POP*) stipulates, for example, that to be justified in ascribing the property of tallness to Evan and Sally one must refer to one or more sortals characterizing Evan and Sally by virtue of which the property of tallness can be ascribed to them (e.g., they both measure at over six feet in height), to be justified in ascribing the property of heaviness to Rasheed and Joseph one must refer to one or more sortals characterizing Rasheed and Joseph by virtue of which the property of heaviness can be ascribed to them (e.g., they both weigh over two hundred pounds).6 The intuitive plausibility of (POP*) stems from its pre-reflectively appealing view of what relevant grounds for property ascriptions must look like. In on the different theories of properties see Mellor and Oliver's anthology (1997). 6 Of course, (POP*) does not imply that supplying relevant grounds for ascribing a property to an entity or set of entities must involve appealing to a separable property Pii of the entity in question in virtue of which the original property Pi is instantiated. Instead, (POP*) implies that the grounds licensing the ascription of a property to an entity must refer to sortals individuating the property as such, whether such sortals are themselves property constituting or not. The disclaimer renders (POP*) at least prima facie plausible by rescuing it from a prompt rebuttal to the effect that if property ascriptions must be grounded in the isolation of a separable property of the target of the ascription a vicious, infinite regress of ascriptive justification will be generated. (POP*), in conformity with this concern, suggests that the regress of ascriptive justification terminates eventually in the isolation of sortals by virtue of which the property of truth is instantiated but that are not themselves property constituting. 9 particular, (POP*) endorses a supposition about property-ascription justifications that is difficult to resist ceteris paribus: i.e., relevant grounds G for ascribing a property P to an entity E must explain why or how E bears P. Relevant grounds for property ascriptions would seem to need to be explanatorily relevant in some sense. It is surmised, though, that the only sorts of grounds G that seem capable of explaining why (or how) an entity E bears P must make reference to one or more sortal characteristics of E. The crucial point is that it is difficult to fathom what might distinguish E as bearing P without recourse to some kind of sortal categorization of E, in which E comes out as a subset of P things. At the very least, this view of things seems prescribed by ordinary canons of explanation and analysis which dictate that only explanations (or analyses) drawing out explicit sortal connections between explanans and explanandum can be sufficiently illuminating. From the intuitive, (POP*)-based perspective, though, WD's justifications for truth-property ascriptions plainly do not satisfy the explanatory relevancy criterion for property ascriptions. In particular, WD cannot justify the ascription of the property of truth P to a statement or set of statements S by appealing to sortal characteristics of S that explain why S bears P. The problem for WD is that it holds that truth is an indefinable and unanalyzable property ― a property whose explanatory role is exhausted by its involvement in the schema: [P] is true iff P. This means the exponent of WD is forbidden from providing justifications for 10 truth-property ascriptions with the explicit form deemed necessary for explanatory illumination: justifications that draw out explicit sortal connections between explanans and explanandum. 5 Second Horn of the Dilemma Revisited Unquestionably, though, the challenge remains of examining whether the intuitive, (POP*)-based perspective obstructing our opponent's evasion of the second horn of our dilemma is in fact a viable one. In particular, to assess the legitimacy of this intuitive perspective, it is important to examine WD's specific proposal(s) for grounding truth-property ascriptions to determine whether it satisfies uncontroversial requirements for explanatory relevance (e.g., those stipulated by (POP)). In my view, only one basic option is available to the advocate of WD in this case. This option is pursued in a proposal made by Horwich (1998a, chapter 7).7 Horwich proposes that the basis for truth-property ascriptions is in effect that truth bearers in a specific sense 'legitimately instantiate the T-schema' (not the standard reading of this phrase): [P] is true iff P. In particular, Horwich claims that the license for ascribing the property of truth to a proposition, sentence or belief is that it legitimately instantiate the T-schema in the following sense: i) it can be plugged into the schema, and ii) the right-hand side of the schema in some 11 sense comes to pass. In other words, the license for ascribing the property of truth to [snow is white] derives from the legitimacy of the corresponding T-sentence ― [snow is white] is true iff snow is white ― and that snow is white, the license for ascribing the property of truth to [grass is green] derives from the corresponding T-sentence ― [grass is green is true iff grass is green] ― and that grass is green, and so forth. To be sure, this maneuver is a fortiori plausible. It supplies us with the only justification for truth-property ascriptions that seems permissible on the terms of WD: a statement must legitimately instantiate the T-schema. Upon closer examination of the functioning of the T-schema, though, ― how it functions, in conjunction with actualities (e.g., that snow is white) to pick out certain kinds of statements and not others as true ― it becomes less manifest that the grounds supplied by Horwich for truth-property ascriptions satisfy uncontroversial criteria for explanatory relevancy (stipulated by (POP)). A potential concern with Horwich's maneuver in this case is that any explanation of the T-schema, how it functions to only pick out true propositions, must amplify the material equivalence of the '[P]' and 'P' upon which our understanding of the T-schema is founded, if it is to be minimally comprehensible and thus satisfy an indisputable relevancy requirement (stipulated by (POP)). For example, consider one such explanation of the T-schema: 7 Horwich's explicit formulation of the proposal differs somewhat from that given in the text. But 12 (TS) A statement is true (i.e., legitimately instantiates the T-schema) if and only if what it says to be the case is in fact the case (compare with Boghossian, 1990). To be sure, there are other ways of explaining the T-schema, but if I am correct an explanation of this general form will be needed: an explanation deploying semantic notions or phrases such as 'saying what is the case', 'expressing what is the case', 'facts', and so forth. The problem with any such explanation, of course, is that it incurs ontological commitments forbidden by WD, since it says things about truth its advocate is not permitted to say (given her ontological thesis),8 things that would seem to commit her to truth being a property with an underlying nature (i.e., some sort of correspondence between statements and facts). Patently, to analyze truth (or derivatively truth-bearing) via the deployment of semantic explanans is to commit oneself to an inflationary view of truth. Not surprisingly, Horwich has a reply to this kind of objection to his proposal for justifying truth-property ascriptions (1998a, pp. 34-35 and 50-51): the notion of legitimately instantiating the T-schema does not require amplification since the T-schema is explanatorily basic or primitive. In addition to Horwich, Soames (1999, p. 231) also endorses some such form of the so-called 'primitivist thesis' regarding the T-schema. Horwich's basic line of reasoning is captured by our formulation of the proposal. 8 Refer back to section 1. 13 The question is: what might be meant by the claim that the T-schema that truth bearers must legitimately instantiate is explanatorily basic? The primitivist thesis is difficult to pin down but is typically fleshed out in the following way (Horwich (1998a, pp. 50-1, 121) and (1998b)): the T-schema is explanatorily basic in the sense that the need to explain its functioning does not arise. The interpretation of the T-schema, according to this line of argument, is not a thing it is possible to explain inasmuch as it is already implicitly fixed by our dispositions to assent to its instantiations.9 If the interpretation of the T-schema is implicitly fixed by our dispositions to assent to its instantiations, the obligation to explicitly explain it, i.e., by importing inflationary semantic notions or phrases such as 'saying something to be the case', 'expressing the fact that', etc. will be discharged. The snafu is that the Horwichian dispositionalist defense of the primitivist thesis about the Tschema flies wide of the mark: dispositions to assent to the instances of the Tschema seem not to implicitly fix its meaning. Apparently, there are a wide variety of questions regarding how any version of the T-schema (e.g., the disquotational schema, the equivalence schema, etc.) is to be read that are not resolvable by appeal to dispositional assent. 9 And in effect, according to this line of argument, such dispositions fix the meaning of the word 'true'. This is the sense in which, for Horwich, the dispositions to assent to the instances of the Tschema (in his case, the equivalence schema) are supposed to be truth constituting (1998a, pp. 3435). Many of the background assumptions underlying this line of argument can be found in Horwich's (1998b). Soames does not make this sort of claim in defense of the explanatory primitiveness of the T-schema. But since neither Soames nor any other proponent of WD provides an alternative defense of the primitivist thesis, we can restrict our examination to Horwich's dispositionalist defense. 14 Consider Horwich's version of the T-schema, the equivalence schema: (ES) <P> is true iff P (where '<P>' stands for 'the proposition that P' and 'P' stands for <P>'s object-level equivalent). Instances of this schema include (ESI) the proposition that snow is white is true iff snow is white, (ESI) the proposition that grass is green is true iff grass is green, and the like. As it has recently been argued (e.g., Collins (2002, pp. 668-674), Davidson (1990) and Wiggins (1980)), one crucial aspect of how to read the equivalence schema (and its various instances) that is not fixed by our disposition to assent to propositions such as these is how to read the 'iff' operator in it. There are a variety of ways in which the 'iff' operator might be read in the equivalence schema (or in any version of the T-schema). Does it represent extensional equivalence, intensional equivalence, cognitive equivalence, etc.?10 Dispositions to assent to the instances of the equivalence schema are of no help at all here in isolating which of these readings is the correct one. Indeed, our disposition to assent to the instances of the equivalence schema seems at least partly to be a function of how the 'iff' operator is to be interpreted, implying a fortiori they 15 cannot be constitutive of its interpretation. For example, if the 'iff' operator in the equivalence schema only represents extensional equivalence, we will be more disposed to assent to the propositions that instantiate it. If, on the other hand, 'iff' represents cognitive equivalence (a stronger relation), we will be less disposed to assent to the propositions that instantiate the equivalence schema. In short, bare dispositional assent does not implicitly fix the meaning of the equivalence schema in view of the widely acknowledged fact that there are crucial aspects of its interpretation that bare dispositions tell us nothing about such as the question of how the 'iff' operator is to be read in it.11 The same point applies mutatis mutandis to any other version of the T-schema. Perhaps, then, since bare dispositions will not suffice to fix the meaning of the T-schema, the dispositionalist might appeal to patterns of sets of dispositions to assent to the instances of the T-schema to fix its meaning (e.g., to distinguish between different readings of the 'iff' operator). One question this proposal raises is: what are 'patterns of sets of dispositions'? Presumably, they are sets of dispositions with structural relations to one another. The crucial difficulty with such a proposal is that patterns of sets of dispositions (or dispositions with structural relations to one another) is plainly not a natural kind: mere dispositions do not stand in explanatory or structural relations to one another. Indeed, as 10 There is no standard reading of 'iff' the proponent of WD can appeal to in this connection. 11 Aside from questions concerning the proper interpretation of the equivalence schema, another important question the Horwichian dispositionalist defense of the primitivist thesis leaves open is why we should have dispositions to assent to true statements and not false statements, or statements bearing some other kind of property. 16 Collins has pointed out (2002, pp. 672-3), the only way to discern the structural relations between sets of dispositions is to appeal to an underlying theory of semantic competence ― a theory of what it is to competently speak and understand a language. Plainly, though, in this case the theory of semantic competence would be doing the explanatory work. In short, the problem is that the only proposal available to the defender of WD that I am aware of (and the only proposal on the table) involves justifying truthproperty ascriptions via Horwich's criterion of legitimately instantiating the Tschema, and then claiming that the T-schema does not need to be explained (to satisfy the relevancy requirement) since it is in some sense explanatorily primitive. But it would seem that no version of the T-schema can be explanatorily primitive in the way this line of argument requires: its interpretation is not implicitly fixed by dispositional assent (either bare dispositional assent or patterns of sets of dispositional assent). The implication is that WD seems unable to forestall the requirement of explicitly explaining how the T-schema functions, in conjunction with actualities, to discriminate between true and false statements, and that it needs to invoke inflationary semantic notions to do so. Sustained reflection thus bears out our intuitive supposition that the defender of WD seems unable elude the second horn of the dilemma: she cannot furnish us with a justification for truth-property ascriptions that satisfies basic relevancy 17 requirements without recourse to inflationary explanans. The implication in this case is that WD's view of truth collapses into some form of inflationism. 6 Conclusion In the end, then, WD is on shaky ground: it appears to be fundamentally unstable. The problem is that WD's ontological thesis about truth  that it is both a property and deflated  generates a troublesome truth-property ascription dilemma the proponent of WD is at pains to circumvent. In attempting to elude the first horn of the dilemma, WD's view of truth collapses into that of strong deflationism. In attempting to elude the second horn of the dilemma, WD's view of truth collapses into that of some form of inflationism. Importantly, the deficiency in WD's ontological thesis seems to issue from its failure to conform to a view regarding the nature of property-ascription justifications that is difficult to dismiss. Intuition and sustained analysis seem to bear out that the justification of property ascriptions are governed by (POP) and its natural extension (POP*): to be justified in ascribing some property P to an entity or set of entities E relevant grounds G must be available to license the ascription by explaining why E bears P, where in order for G to explain why E bears P, G must make reference to one or more sortals of E (by virtue of which E bears P). (POP*)'s legitimacy implies the folly of taking the ontological middle road when it comes to alethic theorizing ― of claiming that truth is both a 18 property and deflated. More generally, though, (POP*)'s legitimacy implies the folly of taking the ontological middle road when it comes to theorizing about properties in general (of claiming that anything can both be a property and deflated), and for this reason, has enormous bearing on the prospects for deflationary metaphysical positions. References Ayer, A.J. (1936) Language, Truth, and Logic, Penguin, London. Boghossian, P. (1990) 'The Status of Content', Philosophical Review 99, pp. 157184. Collins, J. (2002) 'On the Proposed Exhaustion of Truth', Dialogue 41, pp. 653679. Davidson, D. (1990) 'The Structure and Content of Truth', Journal of Philosophy 87, pp. 279-328. Field, H. (1994) 'Deflationist Views of Meaning and Content', Mind 103, pp. 249-258. Grover, D.L., Camp, J.L., and Belnap, N.D. (1975) 'A Prosentential Theory of Truth', Philosophical Studies 27, pp. 73-125. Gupta, A. (1993) "Minimalism", Philosophical Perspectives 7, pp. 359-369. Horwich, P.G. (1998a) Truth, second edition, Clarendon Press, Oxford. ― (1998b) Meaning, Clarendon Press, Oxford. ― (1999) 'The Minimalist Conception of Truth', in S. Blackburn and K. Simmons (eds.), Truth, Oxford University Press, Oxford, pp. 239-263. Mellor, D. H. and Oliver, A. (eds.) (1997) Properties, Oxford University Press, New York. Ramsey, F.P. (1927) 'Facts and Propositions', Proceedings of the Aristotelian Society 7. 19 Soames, S. (1997) 'The Truth About Deflationism', in E. Villaneuva (ed.), Philosophical Issues 8, pp. 79-94. ― (1999) Understanding Truth, Oxford University Press, New York. Sosa, E. (1993) 'The Truth of Modest Realism', in E. Villaneuva (ed.), Philosophical Issues 3, pp. 77-95. Tarski, A. (1983) Logic, Semantics, Metamathematics, 2nd ed., Hackett, Indianapolis. Wright, C. (1992) Truth and Objectivity, Harvard University Press, Cambridge. ― (1996) 'Response to Commentators', Philosophy and Phenomenological Research 56, pp. 863-868, 911-941. GLEN HOFFMANN Department of Philosophy Ryerson University <ghoffman@ryerson.ca> Acknowledgments I would like to thank Matthew McGrath, Danny Goldstick, Joe Millum and anonymous referees for helpful comments on this paper. I owe a special debt of gratitude to Gurpreet Rattan whose valuable feedback heavily influenced the direction of this paper.