Replacing Truth?* Matti Eklund [Published in Burgess & Sherman (eds.), Metasemantics, OUP 2014] 1. In this paper I will discuss whether, for theoretical purposes, the concept of truth should be replaced by some other concept – still a broadly truth-like concept, but distinct from the ordinary concept of truth. I will first make some general remarks on this issue. Then, later, I will discuss the question as it arises specifically in connection with the kind of inconsistency theory of truth that I and a number of other theorists have defended in face of the semantic paradoxes. 2. David Chalmers (2011) forcefully stresses what seems to me to be a good and important point concerning philosophical methodology: while philosophers often have been concerned with our actual concepts or the properties or relations they stand for, philosophers should also be asking themselves whether these really are the best tools for understanding the relevant aspects of reality, and in many cases consider what preferable replacements might be. Philosophers should be engaged in conceptual engineering.1 Compare: when physicists study reality they do not hold on to the concepts of folk physics but use concepts better suited to their theoretical purposes. Why should things stand differently with what philosophers study? It would be Panglossian to suppose that the concepts we find ourselves with are the ones that are best suited to the purposes in question. In this paper, I discuss this general point as it applies to the case of truth. One possible route to go when doing conceptual engineering would be to simply get rid of all concepts of a particular kind. In the case of truth there is the possibility of (like some logical positivists at a certain point) urging not only that we get rid of the ordinary concept of truth but also, more generally, that we ought not to employ any truth-like concepts at all. However, in this paper, I will not discuss that kind of radical stance. I will assume the legitimacy of truth-like concepts. The * Many thanks to Alexis Burgess, Colin Johnston, David Liggins, Kevin Scharp and Bret Sherman for helpful comments on an earlier version. 1 Chalmers does not himself use the locution "conceptual engineering". I take that locution from Blackburn (1999). 2 question is whether there might be a case for replacing the concept of truth by some other truth-like concept.2 One natural, albeit vague, source of unease with the general idea of conceptual engineering in philosophy is that the concepts that are at the center of philosophical disputes – truth, knowledge, justification, rightness,... – are in some way basic or fundamental, in such a way that one cannot very well replace them. I am doubt if there is a way to make good on this general sense of unease. At any rate, I will not discuss this general worry. Instead I will discuss some problems specific to the case of truth. Given facts specific to the case of truth, the case for replacing it is somewhat problematic. I will not attempt to survey all theoretical projects for which one might want to replace the concept of truth, or all views on the role of the concept of truth. Instead I will discuss some prominent projects and views and discuss the problems that arise in those contexts. A number of theorists, including myself, hold that the liar paradox and related semantic paradoxes show the ordinary concept of truth to be in some sense inconsistent.3 It is natural to think that if any version of the inconsistency view we defend is correct, then the ordinary concept of truth ought to be replaced by some sanitized counterpart, at least in theoretical contexts. I will critically discuss this thought later. But many of the considerations I will bring up in the paper are independent of the fate of the inconsistency view. What might be an example of a truth-like concept that could serve to replace the ordinary concept of truth? If we look at the liar literature, we can find some concrete suggestions. To take a historically important example, Tarski's (1935) hierarchy of truth predicates was meant to serve as a replacement for the ordinary concept of truth, which Tarski deemed to be inconsistent.4 Moreover, in the contemporary literature one finds a whole variety of theories – versions of Kripke's theory, various revision theories, various paraconsistent theories, etc.5 All of these theories describe possible 2 What conditions must a concept satisfy to count as truth-like? How similar to the ordinary concept of truth must it be, and how is similarity to be understood here? These are certainly reasonable questions, but I will not pause to answer them. I think it should be clear that the proposed replacements I go on to talk about satisfy any such conditions. 3 See, e.g., Azzouni (2006, 2007), Burgess & Burgess (2011), Eklund (2002), Johnston (forthcoming), Ludwig (2002), Patterson (2007, 2008, 2009), and Scharp (2007, 2008, 2013a, 2013b). 4 See Tarski (1935). The formulation in the text slides over an issue orthogonal to present concerns but important in the bigger picture. What Tarski deemed inconsistent was not specifically the concept of truth but natural language. Natural language is inconsistent, Tarski held, because of how the truth predicate works together with facts about what logic it obeys and what expressive resources it has. Tarski's preferred cure involved replacing the truth predicate with a hierarchy of truth predicates, and this is why it is natural to single out truth, but strictly it is wrong to say that Tarski held truth to be inconsistent. The same point applies generally to the inconsistency views discussed here. 5 For just a small sampling of some important theories on offer, see, e.g., Field (2008), Gupta and Belnap (1993), Maudlin (2004), McGee (1991), Priest (2006), and the essays collected in Martin (1984). 3 concepts of truth, even if at most one of them can successfully describe the ordinary concept.6 Whichever ones of these theories fail to describe the ordinary concept describe possible replacement concepts. Here is a general way to look at the liar paradox literature since Tarski. Tarski proved an impossibility theorem, showing that there cannot be a language simultaneously satisfying a number of natural desiderata: having a truth predicate that obeys the standard truth rules (the ascending rule from p to infer 'p' is true and the descending rule from 'p' is true to infer p), being classical, and being able to speak of its own syntax. Much of the formal literature since then serves to map out various ways of attempting to approximate satisfying these desiderata. Even completed, that map still leaves open two types of questions. One concerns what conditions our language, and its truth predicate, satisfies. Another concerns what conditions a language, and its truth predicate, should satisfy in order to be ideal for such-and-such a theoretical purpose.7 The above paragraph also indicates what types of alternatives to the ordinary concept of truth I will consider in my discussion: alternative truth-like concepts that differ in that they obey different logical principles. Obviously one can also imagine comparing truth-like concepts that differ also along other dimensions. For example, one might look at the debates over truth in the more metaphysics-oriented literature and conclude that there are correspondence concepts of truth, coherence concepts of truth, epistemic concepts of truth, deflationist concepts of truth, etc., and hold that while our actual concept is of one of these types, the best truth concept to use is of another type. 3. In this section I will start problematizing the project of replacing the concept of truth for theoretical purposes. Take the following, relatively standard justification of truth-theoretic semantics. People have tacit knowledge of the referents of words. They know facts such as that "Newt Gingrich" refers to Newt Gingrich, "dog" refers to dogs, etc. They know the syntactic structure of sentences, and they know the composition rules corresponding to the syntactic structures. This lexical and compositional knowledge allows them to grasp the truth-conditions of sentences they hear, and express propositions they want to express. Truth-conditional semantics states what speakers have tacit knowledge of, and thus provides a psychological explanation of how our knowledge of language allows us to gather information about the world, and communicate it as well. This helps provide a generally successful account of linguistic activity – successful as evidenced by the advances in the 6 Well, one possibility is that the ordinary concept is indeterminate in such a way that there are different best theories of its behavior. Then several of the theories currently on offer may be among those "best theories". 7 A nearby question concerns what conditions the logical expressions of a language must meet in order for the language to be ideal for such-and-such theoretical purposes. I will however do my best to suppress this question, in an attempt to have fewer moving parts. 4 relevant parts of linguistics and philosophy of language. For future reference, call this kind of justification for the use of truth in semantics a cognitivist justification. The cognitivist can be seen as treating semantics as a branch of psychology.8 If this is how the project of truth-theoretic semantics is motivated, then what justifies the employment of the concept of truth in semantics is that speakers have tacit knowledge of contents involving this concept. The concept of truth employed in semantics must be the concept of truth that occurs in the contents that speakers have tacit knowledge of. Speakers must have this concept of truth. Given the cognitivist justification for theoretical employment of the truth predicate, there is then a problem for the idea that the ordinary concept of truth ought to be replaced for theoretical purposes. This justification demands that the concept of truth used in truth-theoretic semantics be a concept speakers already have. This might seem to immediately doom the replacement idea, for it might seem as if this immediately demands that it be the ordinary concept of truth that is used in truth-theoretic semantics. But there are some complications. For example, it may be that we have one concept of truth that is lexicalized in ordinary language and that is employed consciously in thought and another one, drawn upon in semantic processing, of which our grasp is normally only tacit. In this scenario, one can consistently endorse both the cognitivist justification for truththeoretic semantics and some version of the replacement idea. The idea would be that what justifies using a replacement concept rather than the ordinary concept of truth in truth-theoretic semantics are considerations to the effect that the concept we tacitly use is not the ordinary concept of truth but some other one. Anyone who embraces this idea would need to provide arguments to the effect that the ordinary concept of truth and the tacitly used concept differ in relevant respects. Of course since we already have the tacitly used concept there is a sense in which capturing it would not strictly be a replacement strategy. But still, the project would be one of finding a concept that better suits the theoretical purposes at hand than the ordinary, lexicalized concept does. One reaction to the problem noted is to say that when the truth-theoretic semanticist ascribes tacit knowledge of truth theories to ordinary speakers, this must be understood in the right way: no psychological realism is assumed, instead all that is meant is that the ascriptions fit speakers' dispositions to behavior. Given this more deflationary understanding of the ascriptions of tacit knowledge, one can ascribe to speakers a concept of truth they would find foreign, such as a given replacement concept of truth. Moreover, a natural objection to the cognitivist conception is that it is psychologically implausible. Do really all language users, including, for example, very young children, possess a concept of truth? If no psychological realism is assumed, this objection does not arise. So there may be reasons to go this alternative route. However, if the truth-theoretic semanticist takes 8 See, e.g., Larson and Segal (1995), Pietroski (2000), and Stanley (2005). 5 this route, she abandons the cognitivist justification of truth-theoretic semantics. This justification crucially relies on a psychologically realist understanding of what is going on. 4. To stress, all I have done in the previous section is to display the problems relating to the project of replacing the concept of truth given one kind of justification of truth-theoretic semantics, the cognitivist justification. Let me briefly provide an account of an outlook better suited to the replacement project. It is easier to justify replacing the concept of truth given a deflationary understanding of the use of a truth predicate in a theory of meaning. Take, to consider a worked example, the deflationary understanding of the use of a truth predicate in a Davidsonian theory, such as expounded in Williams (1999). Here is Williams' understanding of Davidson.9 The core of Davidson's view is his theory of interpretation. This theory of interpretation serves to set up a oneone correspondence between sentences of the home language and sentences of the target language. But how do we best give expression to such facts? If we allowed ourselves 'means that' then we could express this correspondence using sentences like "Le President de France est fou" means that the President of France is mad. But Davidson famously argued against the use of "means that", and wants instead just to use the material biconditionals. However, "Le President de France est fou" if and only if the President of France is mad. is not even grammatically well-formed. We need a proper sentence on the left hand side. The reason we append a truth predicate to the name of the target sentence is simply that we need to have a sentence on the left hand side, and a sentence that stands in the right sort of equivalence relation to the target language sentence. The overall point is that the truth predicate here is not necessarily constrained to be the ordinary truth predicate, or any predicate expressing a concept that the speakers of the language described need have any inkling of. All that the deflationist is looking for is a predicate that performs a certain expressive role. Maybe the ordinary truth predicate does that job. But it could be that a predicate different from the truth predicate is better suited to play this role. How is one way that it might be so. What the deflationist is looking for, ideally, is a predicate that obeys the standard rules for truth. We know that there cannot, in a classical setting, be such a predicate. So the deflationist 9 The discussion to follow in this paragraph follows Williams' discussion quite closely. 6 will have to settle for what best approximates this ideal. This can be a predicate different from the ordinary truth predicate. (As we will see later, Kevin Scharp's views on truth may illustrate this point.) 5. The cognitivist justification relates to the explanatory role of the concept of truth in a psychological explanation of our linguistic activity. Here is a different kind of theoretical project: giving a theoretical account of how our language represents the world. Even if truth and reference don't play the role in psychological explanation envisaged by the cognitivist justification, one can think that surely representational word-world relations do obtain, and we want truth and reference concepts to express these relations. Maybe a replacement concept can be an improvement over the ordinary concept when it comes to this theoretical purpose. But one problem here concerns making a case regarding what an improved replacement concept used in such a theoretical account ought to be like? One possible thought here might be that a representational concept of truth is to be explained by appeal to the notion, made famous by Kripke, of a grounded sentence. A sentence which doesn't assert anything about the truth-values of other sentences is grounded, and one which does assert something about truth-values of other sentences is grounded if the process of tracing through what sentences its truth-value depends on terminates at grounded sentences.10 One suggestion might be that if we use 'true' to serve a representational role, then we should say that only grounded sentences are true.11 One prominent theory with this consequence is the Kripkean minimal fixed point theory.12 The idea that only grounded sentences are true is known to have counterintuitive consequences, as discussed by commentators on Kripke.13 Take a sentence that says of itself that it isn't both true and untrue. Intuitively, such a sentence is true. But it isn't grounded. However, such worries about counterintuitiveness seem less germane if the minimal fixed point theory isn't supposed to capture the ordinary concept of truth but instead is supposed to characterize a new, technical concept. Our intuition that the sentence in question is true doesn't speak to whether the sentence is true in the relevant technical sense of 'true'. So one cannot straightforwardly argue against the Kripkean minimal fixed point theory – conceived of as a theory of what an improved concept of truth is like – based on this intuition. How, 10 See Kripke (1975), p. 693f. 11 Maudlin (2004), ch. 2, can be seen as arguing the point that focusing on representation has this upshot – although Maudlin does not present his discussion as concerning a special concept of truth designed to be used for certain theoretical purposes. 12 See Kripke (1975). 13 See Gupta (1982), pp. 33ff. 7 then, can one decide between that theory and possible rivals? One problem we run up against here has to do with the fact that the concept we are considering replacing is, in some way, a very basic concept. What we are considering is the possibility of some concept C of representing the world correctly such that C is distinct from the ordinary concept of truth and somehow better captures the idea of correct representation of the world than the concept of truth does. One may easily be skeptical of the project, wondering what independent grasp we have of correct representation such that correct representation can be held to come apart from truth.14 6. Let me turn now to a slightly different issue. As mentioned early on, some theorists, including myself, think that the proper lesson to draw from the semantic paradoxes is that the ordinary concept is in some way inconsistent. In this and the next section I will discuss the question of the replacement of truth from the perspective of inconsistency views on truth. Part of the reason is that I think such a view is correct and I want to explore its consequences. But the main reason is this. The claim that the concept of truth is inconsistent rather immediately invites questions of whether it ought to be replaced, and the question of replacement has already given rise to interesting discussion in this context. While the discussion to follow most immediately concerns the consequences of the inconsistency view, the issues raised are, as I will emphasize, broader. The literature abounds with different purported solutions to the liar paradox, but each of them in turn has radically counterintuitive consequences – and not just counterintuitive consequences but consequences that seem to be at odds with what we arrive at by reflection on the meanings of the key expressions involved. One may naturally suspect that the same will be true of any purported solution. Such suspicions provide motivation to adopt an inconsistency view on the semantic paradoxes. An inconsistency view says that when we go through the paradoxical reasoning we correctly follow the rules for the key expressions, the truth predicate and the logical expressions. Most straightforwardly, we may think of the rules for 'true' as being the standard truth rules, and the rules for the logical expressions as being the classical logical principles. Of course the real story may be more complicated than this. 14 There is a way that correct representation might come apart from truth. If one is a certain kind of "pluralist" about truth – see e.g. Lynch (2009) – then one can think that statements made in some discourses are apt for correspondence truth whereas statements made in other discourses are merely apt for deflationary truth or truth in the sense of a coherence theory. One can conjoin this with the idea that only correspondence truth is properly representational. But whatever the proper fate of this pluralism, this doesn't speak to whether a concept of truth designed to capture the idea of correct representation might obey different logical principles from those obeyed by the ordinary concept of truth. I ought perhaps to add that anyone who embraces an inconsistency view on truth of the kind I mentioned earlier, and will go on to discuss, will find it natural to equally embrace an inconsistency view on the concept of correct representation. 8 One possible virtue of an inconsistency view is that it explains the appearance that the liar paradox simply lacks a solution: that whatever purported solution we come up with has absolutely unacceptable consequences. The inconsistency view's explanation is that whatever we say, we end up in violation of some constitutive rules. (I wouldn't put any theoretical weight on the following way of describing the situation, but it is evocative: think of using a term with a particular meaning as taking on certain semantic obligations – obligations regarding how to use the term. When a language is inconsistent, the semantic obligations speakers take on are inconsistent. There will then be certain situations where whatever the speaker tries to say, she will end up violating some semantic obligation.15) A complication regarding inconsistency views is that the inconsistency should be seen as the joint inconsistency of the principles governing the concept of truth with other principles, for example those governing logical concepts: it is not the concept of truth taken individually that is inconsistent. Despite this real complication, I will continue to speak of inconsistency theories of truth. The reason is that truth still tends to be singled out for special treatment. Somehow truth is still seen as the main culprit. An immediate question about any inconsistency theory of the kind described concerns what the talk of 'rules' amounts to. Certainly I myself think of such talk as merely informal, and I think it is important that it be cashed out. There are different possible ways to cash out the talk of rules. One view on how to cash out the talk of rules is: a concept is inconsistent if and only if competence with it requires being disposed to accept inconsistent claims involving the concept. (Call the kind of view I have described the dispositions view.) Another possible view is that a concept is inconsistent if and only if competence with it requires actually having inconsistent beliefs involving the concept. (Call this the belief view.) A third type of view explains competence in normative terms. Scharp (2007) operates with a notion of entitlement. The rules governing a concept are what competence with the concept entitles a speaker to accept. An inconsistent concept is one such that the speaker's competence with the concept entitles her to accept inconsistent claims. The entitlement is, as Scharp stresses, defeasible. It can for example get defeated by the realization that the claims jointly lead to contradiction. (Call this the normative view.) Finally, Burgess and Burgess (2011) say that there can be no principled objection to talk of semantic rules given that "linguists have been freely positing them in syntax and phonology ever since the downfall of behaviorism".16 This is most 15 One virtue of this way of putting it (though again I wouldn't put any weight on it) is that it helps characterize what distinguishes the general kind of inconsistency view here discussed from dialetheism – the view that there are true contradictions – which also could be regarded as a kind of inconsistency view. Dialetheism doesn't immediately yield that there is no way that a speaker can satisfy her semantic obligations. It only yields that sometimes doing so involves accepting both a sentence and its negation as true. 16 Burgess and Burgess (2011), p. 133. 9 immediately relevant to the issue at hand if the semantic rules are held to be properly analogous to the rules linguists postulate in syntax and phonology. The suggestion then seems to be that the linguistic rules are the principles the mind uses in semantic processing. (To provide a label, let us call this the psychological view.)17 My own favored view is the dispositions view. An immediate objection to this kind of suggestion is that experts can lose any disposition to accept the assumptions that jointly lead to paradox – simply by being keenly aware that these assumptions jointly lead to paradox – and still the expert obviously doesn't lose competence.18 For future reference, call this the experts objection. This objection can be raised, in different form, also against the belief view and the psychological view. In response to this objection it can be said that an expert like that is still in a different situation from someone who just flatly refuses to accept one or more of the assumptions, without being able to, or inclined to, provide a reason – the assumption simply doesn't strike her as correct. The expert, by contrast, can provide reasons for refusing to accept the assumption. It is because of this difference that the expert is still competent, while the person who just flatly denies one of the assumptions lacks full competence.19 One can add this to the talk of dispositions (or the talk of beliefs or psychological processing, if one prefers one of those other views) to get this result.20 Another response is to appeal to the linguistic environment. One can respond to the experts objection by saying that if indeed the experts still employ the concept of truth with its ordinary content despite their dispositions having changed, they do so only by virtue of deference facts – or generally facts about the speaker's linguistic environment and the speaker's relations to her linguistic environment. The experts objection arises in a different way for the normative view: an expert loses her entitlement to the principles in question but still remains competent. Perhaps the quickest way for the friend of the normative view to deal with this objection is to identify competence with some sort of prima facie entitlement rather than entitlement simpliciter. Another immediate question regarding the viability of an inconsistency view concerns whether not an inconsistency view implies – seemingly absurdly – either that every sentence of our language is true (for they all follow from the rules) or that none is true (for 'true' is incoherent and nothing falls under an incoherent predicate). Now, saying that the rules governing the truth predicate are inconsistent is not by itself to say anything about the semantic value of the truth 17 Johnston (forthcoming) has a very different kind of view, one on which the rules are rules for the property of being true and are not primarily associated with the truth predicate or the concept of truth. 18 See especially ch. 4 of Williamson (2007) where this objection is developed the most fully. 19 About "full competence". The contrast is with someone who uses a word (concept) with its ordinary meaning (content), but not by virtue of her competence alone but by virtue of standing in deference relations to other speakers or thinkers. 20 I am not here primarily concerned to defend my preferred view. Obviously there is much more to be said in a full response to the objection. My main purpose here is just to indicate what type of view I prefer, and what types of considerations might be marshaled in its defense. 10 predicate, and inconsistency theorists can and do say very different things about this. Some inconsistency theorists – the radical ones – do hold that the inconsistency of the concept of truth has very radical consequences: that the truth predicate lacks a semantic value, or is empty, or that every sentence of our language is true. Some radical inconsistent theorists are Azzouni (2006, 2007) and Patterson (2007, 2008, 2009). These theorists try to explain away the seeming absurdity of the conclusion. I am myself more moderate, where to be moderate is to hold that even if the concept of truth is inconsistent, the semantic value of the truth predicate is not trivial or degenerate. Some other inconsistency theorists who take a moderate line are Johnston (forthcoming) and Scharp (2007, 2013a, 2013b). Here is my preferred way of defending the moderate line. Distinguish between the rules governing an expression (e.g. the introduction and elimination rules for 'and') and the semantic value of that expression (e.g. the truth function that 'and' expresses). It is standardly held that if some rules are meaning-constitutive for an expression, then the semantic value of an expression is such as to make the rules true and truth-preserving. For example, given that the standard rules for conjunction are the rules for 'and', the semantic value of 'and' is what makes these rules correct. This is the standard semantic value for 'and', which renders these rules truth-preserving. If we apply this picture wholesale then we shall have to say that 'true' fails to have a semantic value: for no semantic value can render the rules for 'true' correct. But there is a possible straightforward revision. Compare David Lewis's well-known view on the reference of theoretical terms.21 Lewis (following Carnap) held theoretical terms to be implicitly defined by the theories in which they occur. In the simplest case, the referent of a theoretical term is whatever makes true the sentences of the theory wherein the term occurs. But we certainly want to say that theoretical terms occurring in false theories can refer, so we can't always say exactly that. Lewis' solution is to allow that the term refers to what comes closest to making true those sentences of the theory. Closeness here is not just a matter of what, quantitatively, makes true the most sentences. Overall best fit is what is at issue; qualitative considerations enter in as well. And if it turned out that a given theory was inconsistent, the same would apply. We might still want to allow that theoretical terms introduced by the theory refer, and we can get to say this in the same way as in the case of an, as it were, merely false theory. It may be obvious where I am going with this: the relationship between the semantic value of 'true' (and of the logical expressions) and the rules which govern them is the same as that between the semantic value of a theoretical term introduced by an inconsistent theory and the sentences of that theory. The semantic values of the expressions employed in the liar reasoning are then not such as to make all premises in the reasoning true and all steps truth-preserving. While the rules, or meaning-constitutive principles, are inconsistent, the actual truth conditions are not. So somewhere in the liar reasoning there 21 See e.g. Lewis (1970), (1972) and (1997). 11 is an untrue premise or a non-truth-preserving step. One thing I would add, however, is that it is likely, on the picture sketched, that it will be indeterminate what the semantic value of the truth predicate is, and what the semantic values of the logical expressions are. This is because it is reasonable to speculate that there will be no unique assignment of semantic values that comes closest to being ideal.22 7. The above summarizes what, in general, an inconsistency view on the semantic paradoxes of the kind I want to focus on is, and also what my favored version of such a view is. Given an inconsistency view, the question naturally arises whether our actual concept of truth ought to be replaced. A first point to make is that there is no reason to think that an inconsistency theory has to entail that the concept of truth is not good enough for everyday purposes. First, most straightforwardly, it is plain that employment of the concept works well enough for everyday purposes. If any version of the inconsistency view contradicted this, that would be a good reason to abandon the view. Second, with the exception of the belief view, none of the versions of the inconsistency view that I have outlined positively says that competence with the concept of truth requires having inconsistent beliefs – so the inconsistency is rather more well-behaved. Third, the following reasoning bears considering. Compare a more standard view – a non-inconsistency view – on truth and logic in face of the liar with an inconsistency view. On the former kind of view the principles governing the truth predicate and the logical expressions will be rather more complicated than they are on the latter kind of view. The inconsistency theorist can say that that the principle governing the truth predicate is that it obey the standard truth rules and the principles governing the logical expressions are ordinary classical ones. Then ask: what is more convenient for practical purposes – the quick but dirty rules that in special situations lead to contradictions but in all normal situations are convenient, or rules guaranteed never to lead to contradictions but that tend to be more cumbersome? To properly make this argument one would of course need to compare simplicity of sets of rules in more detail. Moreover, how compelling the efficiency argument, as we can call the argument just sketched, is can certainly depend on the underlying conception of semantic rules. The argument works best when accompanying what I earlier called the psychological view. It appeals to efficiency in processing and only the psychological view immediately ties the rule talk to what is going on in actual processing. All I am doing here is to indicate how, when we are thinking of usefulness for practical purposes, there may be positive reasons to prefer an inconsistent concept of truth. 22 Again to stress, I am only concerned to lay out what my view is, not to provide a full defense of it. 12 The serious question concerns whether for certain theoretical or explanatory purposes, the concept of truth would need to be replaced. I have myself kept using the concept of truth in theorizing even while having deemed it inconsistent. By contrast, another inconsistency theorist, Scharp, has prominently argued that since the concept of truth is inconsistent it must be replaced, and he has devoted a good deal of attention to just what must replace it.23 There are further distinctions to be drawn. Are we considering whether the ordinary concept of truth ought not to be used at this stage of inquiry, or are we considering whether at the ideal limit the ordinary concept ought not to be used? One possible view is that the inconsistency of the concept of truth is not such a serious defect that one cannot go on employing it, but still it is some sort of defect and at the ideal limit, the concept ought not to be used. One can agree with Scharp insofar as one thinks that the ordinary concept of truth ought not to be used at the ideal limit, and think it is an interesting question what an improved concept of truth might be like, even while one happily keeps using the ordinary concept at this stage of the game. At any rate, I do not see what good argument there can be for thinking that a potentially viable inconsistency theory could have the consequence that the ordinary concept without question ought to be abandoned right away. The more reasonable question concerns whether the inconsistency theory implies that the concept of truth ought not to be used at the ideal limit, and the following remarks pertain primarily to that question. (One can think that the distinction just drawn trivializes the whole issue of replacement: if we are thinking about this stage of inquiry, it is obvious that a concept's inconsistency need not mean that it ought to be replaced, but it is clear that a concept's inconsistency means that it ought not to be used at the ideal limit.) I think it is clear that there is prima facie reason to suspect that a radical inconsistency theorist ought to favor replacing the concept of truth. But even moderate inconsistency theorists may feel the pressure to replace the concept – surely, it may be thought, we should not employ inconsistent concepts in our explanatory theories, even if these inconsistent concepts are relatively well behaved. However, there are complications. For example, take again the cognitivist justification for truth-theoretic semantics. I argued that given this justification, truth-theoretic semantics must employ a concept of truth already in use – if not the concept of truth expressed by a truth predicate of ordinary language then at least a concept of truth used by our minds in semantic processing. This puts pressure on any replacement idea, as noted. These considerations stand even given a radical version of the inconsistency view. In fact, in a number of papers Douglas Patterson has argued for the following combination of views: a speaker's semantic competence consists in her 'cognizing', in 23 See especially Scharp (2013a) and (2013b). 13 Chomsky's sense, the right truth theory, but an inconsistency view on truth is correct, so what she thereby cognizes is inconsistent.24 (In fact, Patterson's view is a radical inconsistency view.) Patterson's view highlights the fact that in presenting a theory given which competence consists in cognizing a truth theory, a theorist needn't assert the theorems of the truth theory at issue. He says, e.g., To explain how people reason and interact with the world around them we ascribe cognition of or belief in theories, but we don't think those theories have to be true. Why should it be any different when it comes to the semantics of the languages people speak?25 Generally, and apart from truth theories, if some speakers employ a somehow defective expression or concept, a full account of their language or thought will have to describe that fact, and it will have to use that concept at least in descriptions of what the speakers say and think – but this does not mean that the theorist giving the account will need to, so to speak, make any uses of this expression her own. She need only mention it or make use of it in attitude ascriptions. Moreover, while the label "inconsistency" invites the reaction that if the concept of truth is inconsistent then it definitely ought to be replaced, at least for purposes of serious theorizing, many different things might be meant by calling the concept of truth inconsistent. Calling it inconsistent in one way or other involves saying that it is governed by inconsistent rules. But as discussed above, this rule talk can be cashed out in different ways. One thing that can be meant involves that anyone employing the concept of truth must have inconsistent beliefs. This is the belief view, from above. If this is what is meant, one could see why the inconsistency of the concept of truth would be a reason to replace it for theoretical purposes. But no other inconsistency view entails that users of the concept of truth must have inconsistent beliefs. The other inconsistency views – the different dispositions view, the normative view, and the psychological view – only entail that a user would have to have dispositions to form inconsistent beliefs, or would be prima facie entitled to inconsistent beliefs, or have internalized rules that allow for contradictions to be derived. None of these things is an immediate calamity; none of these things is immediately such that a theorist who 24 "Cognize" is originally Chomsky's technical term, used by Chomsky to avoid what he saw as irrelevant complications pertaining to "know". As often used, "cognize" is presumed to be factive, just as "know" is. I here follow Patterson in allowing that one can cognize what is in fact not true. Patterson says, e.g., "Understanding or ''semantic competence'' with respect to a natural language is agreement with others in theory cognized, not truth of that upon which there is agreement" (2009, p. 413). 25 Patterson (2009), p. 412. Patterson goes on to say that all natural language sentences are meaningless, on the ground that the truth theory cognized by speakers doesn't confer meanings on these sentences. That is a radical view, and seems like an extra, optional step. 14 finds herself in this position with one of the concepts she uses in a theoretical setting unquestionably must change her ways. On moderate versions of the inconsistency view, the inconsistent concept of truth can in principle stand for a relatively well-behaved property. This brings up another distinction having to do with replacement. One question will concern whether we should abandon the current concept for a different concept; a different question will concern whether we should avoid using any concept that stands for the property our actual concept stands for. A possible view is that the current inconsistent truth concept is to be avoided, but our theory will still have use for a concept of truth standing for the same property that our actual concept of truth stands for.26 8. Scharp, who favors replacing the ordinary concept of truth given an inconsistency view, has argued against the way I have approached this matter and for replacing the concept of truth. He focuses on reference-determination: We also know that because  [the truth predicate of my theory] expresses an inconsistent concept, not all of its constitutive principles are true (or valid). Eklund does not tell us which of truth's constitutive principles fail...The question is: how can  function properly in Eklund's theory, which is supposed to provide a semantics for L, if some of its constitutive principles fail? Monoaletheism (i.e., no sentence is both true and false) is an essential principle for a nondialetheic semantics, and I do not see how a semantic theory could assign the right truth conditions to the sentences of L unless the truth predicate it employs obeys the ascending and descending truth rules...However, these are the very principles that give rise to the liar paradox. Thus, some of them have to fail...In sum, Eklund's theory casts truth in a crucial explanatory role, and it implies that some of truth's constitutive principles are untrue; however, it seems that if some of truth's constitutive principles fail, then it is unsuited to play this explanatory role.27 26 In section 3, I outlined some problems concerning the replacement idea, having to do with the nature of the standard, cognitivist justification for truth-theoretic semantics. It seems that this justification demands that the concept of truth employed in semantic theory must be the same as that employed by ordinary speakers in semantic processing. I noted one possible way around this argument: maybe the concept used in semantic processing differs from the concept we have a word for in natural language, and it could be held that a concept of truth used in semantics must be the one actually used by speakers in semantic processing. In the context of discussion of inconsistency views it bears noting that it may be natural for an inconsistency theorist to hold that the concept of truth used in semantic processing shares the features of the concept expressed by the ordinary "true" by virtue of which the latter is inconsistent. In particular, there can be as much reason to hold that the ordinary truth rules are rules governing the former concept just as there is reason to hold that these rules are rules governing the latter concept. For example, if the efficiency argument is a good argument it applies at least as convincingly to the concept of truth employed in semantic processing as to the lexicalized concept of truth. 27 Scharp (2007), p. 613. 15 In the last sentence, Scharp appears to be saying that because the ordinary concept of truth is inconsistent, a theorist cannot legitimately use it in her metalanguage: he appears to say that because my theory implies that some of the constitutive principles for 'true' are untrue, I cannot legitimately assign to 'true' an explanatory role. General worries along these lines were dealt with in the previous section. However, the most important part of Scharp's argument is independent of any general concerns about employing an inconsistent concept in a theoretical setting. It is that since the ordinary truth predicate cannot obey both the ascending and the descending truth rules, it is unsuitable to play the role in reference-determination that I assign to it. This point, whatever in the end is its fate, does not rely on the idea that inconsistent concepts cannot be cast in theoretical roles. One may worry that this point still cannot be correct since – in a classical setting28 – no predicate can obey these rules, and hence this cannot be a strike against the ordinary truth predicate. However, Scharp has a reply to this. His own preferred substitute for the ordinary concept of truth is a pair of predicates, one of which ("ascending true") obeys the ascending truth rule and the other of which ("descending true") obeys the descending truth rule: he thinks that in this roundabout way we can obey both truth rules. Still, the generality of the problem he raises must be emphasized: it arises for pretty much everyone. Scharp does not say exactly why it is supposed to be necessary to employ a predicate that obeys the truth rules (or employ predicates that jointly obey the truth rules, as in the case of Scharp's own theory). Burgess (ms) reconstructs Scharp's argument as follows: Mainstream semantics derives its sentential meaning specifications from T-sentences. But Eklund thinks that not all T-sentences are true. He's therefore faced with an embarrassing choice between inconsistent and "fragmentary" semantic theories. Take the T-sentence for the strengthened liar. If Eklund refrains from accepting this T-sentence (on pain of accepting its absurd classical consequences), then he's forced to sit mute on the semantics of the strengthened liar. The problem isn't so much that Eklund can't "assign the right truth-conditions" to paradoxical sentences, as that he can't consistently assign them truth conditions at all.29 A first point to note about the argument thus reconstructed – a point Burgess makes – is that nothing in the Lewisian account of reference-determination forces me to think of a T-sentence as the canonical way of stating what the semantics of the strengthened liar sentence is. All that I am committing myself to is the claim that the extension and antiextension of the truth predicate are 28 And recall that throughout I am setting aside the possibility of revising logic. 29 Burgess (ms), p. 11. 16 determined in the Lewisian way; there is no need for this to go via T-sentences.30 So even if I cannot accept the T-sentence for the strengthened liar, that does not force me to be silent about its semantics. However, Scharp's argument still raises an interesting issue. Suppose, e.g., that we are operating with a truth predicate that doesn't obey the descending truth rule. What the machinery of reference-determination churns out are things like that such-and-such a sentence S of the object language is true. But unless one can rely on the descending truth rule in full generality, one cannot always infer from this to S – and as far as language use is concerned, the basic question is whether or not to utter S. So A machinery of reference determination that churned out things of the form S is T would be more useful in this regard if T obeyed the descending truth rule, for otherwise S cannot be concluded. However, to the extent that the type of consideration just presented is taken as decisive when it comes to what truth predicate to employ, we are treating the truth predications instrumentally. We are thinking of 'S is T' judgments merely as means to the end of concluding S. This is the way of thinking associated with deflationism. Another way of thinking emphasizes the importance of whichever property 'T' stands for: e.g., we are concerned with whether S is true not just as a means to figuring out whether to judge or assert that S, but because it matters, for purposes of thinking about language, whether S is true. The distinction is easy to overlook, because we are so accustomed to moving freely between S and "S is true". But in contexts where it is salient that the truth predicate may fail to obey both truth rules, the distinction becomes important. I will not here attempt to decide between the two outlooks. But I do want to relate all this to Scharp, who as mentioned is the inconsistency theorist who has taken the question of the replacement of truth the most seriously. Scharp argues for employment of his pair of predicates, expressing ascending truth and descending truth, on the ground that it is these predicates together that do the best job, in a classical setting, of performing the tasks of endorsement and rejection associated with the truth predicate; and he argues that the costs of abandoning classical logic are too high. He thinks that because his pair of predicates has this virtue, this pair should play the role otherwise assigned to the concept of truth in semantics. But how does Scharp conceive of this role, such that the virtues of his pair of predicates are virtues as far as playing truth's theoretical role in semantics is concerned? Scharp does not actually say much about this. The closest he comes to having an extended discussion of the role of truth is in ch. 7 of his (2013b), where he presents a Davidson-inspired appeal to measurement theory. The discussion is however so abstract that it is not 30 Burgess' article is mainly devoted to dealing with another complication: when I appeal to Lewisian ideas regarding reference-determination I make essential use of the ordinary concept of truth when arguing for the legitimacy of this concept, and one might think there is a worrisome kind of circularity there. While taking this worry seriously, Burgess presents a reply to it. 17 clear what amounts to truth conceived of as correct measurement. But based on the foregoing, I can make some remarks. Scharp can hardly accept any version of the cognitivist justification for truththeoretic semantics. That would presuppose that what ordinary speakers have tacit knowledge of involves the concepts of ascending and descending truth, and this claim seems rather implausible, and besides, Scharp's reasoning in favor of his pair of predicates does not proceed by way of considering what ordinary speakers can be held to have tacit knowledge of. But for a deflationist, Scharp's proposal may well look attractive. All that the deflationist looks for in a truth predicate is the ability to perform an expressive role, and Scharp's team of predicates is designed to perform this role. Generally, it is natural to want a truth predicate to obey the standard truth rules. But it must be asked where the demand that it obey these rules comes from. One source of the demand is the conviction that the ordinary truth predicate obeys the truth rules. This is problematized by the liar reasoning. And at any rate, questions about what the ordinary truth predicate is like must be distinguished from questions about what we should want a truth predicate to be like for theoretical purposes. Another source of the demand is precisely the sense that it is important for theoretical purposes that a truth predicate obey these truth rules. And no doubt there are expressive benefits, of the kind prominently emphasized by deflationists, to having a truth predicate obeying these rules. An important question is what not merely expressive purposes there are for which a truth predicate needs to obey these rules. Maybe there are such purposes, but Scharp does not make clear which such purposes he might have in mind. When explicitly considering deflationism, in (2013b), Scharp is actually fairly negative. He insists that truth has an "explanatory role", something the deflationist denies, and that it is because truth has this explanatory role that deflationism is inadequate. But again, when one looks at the role Scharp himself allots to truth, it is as a device for endorsement and rejection; and the deflationist too emphasizes that truth has that role. I think it is misleading to call that role "explanatory", but that is another matter. 9. What I have been concerned with here is what the case might be for replacing the ordinary concept of truth by some other truth-like concept for the purposes of theoretical projects related to language. Before closing I ought also to mention, briefly, the question of whether there is a case for replacement when it comes to projects that do not immediately pertain to the study of natural language. Some such projects may be found in logic or metamathematics. Then there are questions about things like the aim of inquiry. Sometimes truth is thought of as the, or an, aim of inquiry – but maybe it is not the ordinary concept of truth but a replacement concept that stands for the proper 18 aim of inquiry? Let me just briefly remark on one difficulty for this idea. If we try to imagine a community whose members aim to judge that p not when p is true but when p is true* (where truth*truth), are we not really imagining a community that judges something with a different content, that p*, instead of that p? After all, somehow or other – with details to be filled in depending on which theory of content one prefers – the content of a judgment somehow depends on use and the judgment's relations to the world, and this community's judgments of the relevant kind are correlated with it being the case that p* and not with it being the case that p. (Let me illustrate this using an especially stark example. Suppose we want to say that they aim to judge that p when p is false. Then they will make the relevant judgments when we in the corresponding situation would judge that not-p. Do they not then judge that not-p instead of judging that p?) But if so, such a community seems not to be possible. And if a community operating with a different truth-like norm than a norm of ordinary truth is not possible, then it is not possible to have an aim of inquiry other than truth. Obviously there is much more to be said here. I am only very briefly indicating some of the difficulties for this other project of replacing truth.31 REFERENCES Azzouni, Jody: 2006, Tracking Reason: Proof, Consequence, and Truth, Oxford University Press, Oxford.. Azzouni, Jody: 2007, "The Inconsistency of Natural Languages: How We Live With It", Inquiry 50: 590-605. Beall, Jc (ed.): 2008, Revenge of the Liar, Oxford University Press, Oxford. Burgess, Alexis: ms, "Coping with Contradiction: A Case Study in Conceptual Ethics". Burgess, Alexis and John Burgess: 2011, Truth, Princeton University Press, Princeton. Chalmers, David: 2011, "Verbal Disputes", Philosophical Review 120: 515-66. Eklund, Matti: 2002, "Inconsistent Languages", Philosophy and Phenomenological Research 64: 251-75. Field, Hartry: 2008, Saving Truth from Paradox, Oxford University Press, Oxford. Gupta, Anil: 1982, "Truth and Paradox", Journal of Philosophical Logic 11: 1-60. Gupta, Anil and Nuel Belnap: 1993, The Revision Theory of Truth, MIT Press, Cambridge, Massachusetts. Johnston, Colin: 2014, "Conflicting Rules and Paradox", Philosophy and Phenomenological Research 88: 410-33. Kripke, Saul: 1975, "Outline of a Theory of Truth", Journal of Philosophy 72: 690-716. Larson, Richard and Gabriel Segal: 1995, Knowledge of Meaning, MIT Press, Cambridge, Massachusetts. Ludwig, Kirk: 2002, "What is the Role of a Truth Theory in a Meaning Theory?", in Joseph 31 Stich (1990, pp. 115-27) tries to compare different concepts of truth in precisely the way that seems problematic given the brief argument sketched. 19 Campbell, Michael O'Rourke and David Shier (eds.), Meaning and Truth: Investigations in Philosophical Semantics, Seven Bridges Press, New York. Lynch, Michael: 2009, Truth as One and Many, Clarendon Press, Oxford. Martin, Robert L. (ed): 1984, Recent Essays on Truth and the Liar Paradox, Oxford University Press, Oxford. Maudlin, Tim: 2004, Truth and Paradox: Solving the Riddles, Clarendon Press, Oxford. McGee, Vann: 1991, Truth, Vagueness and Paradox, Hackett, Indianapolis. Patterson, Douglas: 2007, "Inconsistency Theories: The Significance of Semantic Ascent", Inquiry 50: 575-89. Patterson, Douglas: 2008, "Understanding the Liar", in Beall (2008). Patterson, Douglas: 2009, "Inconsistency Theories of Semantic Paradox", Philosophy and Phenomenological Research 79: 387-422. Pietroski, Paul: 2000, "The Undeflated Domain of Semantics", Sats: The Nordic Journal of Philosophy 1: 161-76. Priest, Graham: 2006, In Contradiction, Oxford University Press, Oxford. (Second edition.) Scharp, Kevin: 2007, "Replacing Truth", Inquiry 50: 606-21. Scharp, Kevin: 2008, "Aletheic Vengeance", in Beall (2008). Scharp, Kevin: 2013a, "Truth, the Liar and Relativism", Philosophical Review 122: 427-510. Scharp, Kevin: 2013b, Replacing Truth, Oxford University Press, Oxford. Stanley, Jason: 2005, "Semantics in Context", in Gerhard Preyer and Georg Peter (eds.), Contextualism in Philosophy: Knowledge, Meaning, and Truth. Oxford University Press, Oxford. Stich, Stephen: 1990, The Fragmentation of Reason, MIT Press, Cambrudge, Massachusetts. Tarski, Alfred: 1935, "The Concept of Truth in Formalized Languages", in Logic, Semantics, Metamathematics, second edition, ed. by J. Corcoran. Indianapolis: Hackett. Williams, Michael: 1999, "Meaning and Deflationary Truth", Journal of Philosophy 96: 545-64. Williamson, Timothy: 2007, The Philosophy of Philosophy, Blackwell, Oxford.