Truth pluralism without domains

Truth pluralists say that truth-bearers in different “discourses”, “domains”, “domains of discourse”, or “domains of inquiry” are apt to be true in different ways – for instance, that mathematical discourse or ethical discourse is apt to be true in a different way to ordinary descriptive or scientific discourse. Moreover, the notion of a “domain” is often explicitly employed in formulating pluralist theories of truth. Consequently, the notion of a “domain” is attracting increasing attention, both critical and constructive. I argue that this is a red herring. First, I identify the theoretical role for which pluralists appeal to domains, which is to answer what I call the “Individuation Problem”: saying what determines the way in which a particular truth-bearer is apt to be true. Second, I argue that pluralists need not appeal to domains for this purpose. I thus conclude that, despite the usual way of glossing the view, there is no role for the notion of a “domain” to play in the pluralist’s theory of truth. I argue that this defuses the “Problem of Mixed Atomics” and allows the pluralist to sidestep potentially intractable disputes about the nature of domains.


Introduction
Truth pluralism, as we'll understand it here, is the view that different claims are apt to be true in different ways. 1 On the most prominent way of developing this idea, some claims are apt to be true in a "realist" way (e.g., in virtue of corresponding to reality), while others are apt to be true in an "anti-realist" way (e.g., in virtue of cohering with a relevant body of beliefs). In particular, while ordinary descriptive claims like (1) or scientific claims like (2) are apt to be true in a realist way, mathematical claims like (3) or ethical claims like (4) or social claims like (5) (or comic claims, or aesthetic claims, or modal claims, etc.) are apt to be true in an anti-realist way. 2 (1) Fido is furry.
This view is almost invariably glossed by saying that what it takes for a claim to be true varies between "discourses", "domains", "domains of discourse", or "domains of inquiry". 3 While truth may be realist in the ordinary descriptive or scientific domains, truth may be anti-realist in the mathematical or ethical or social (or comic or aesthetic or modal, etc.) domain. Not only that, but the notion of a "domain" is often explicitly employed in formulating pluralist theories of truth. 4 Consequently, the notion of a "domain of discourse" is attracting increasing amounts of attention in the literature, both critical and constructive. On the critical front, concerns have been raised concerning atomic claims that are intuitively part of more than one domain, 5 and some have expressed doubt concerning whether the intuitive notion of a "domain of discourse" can be rendered sufficiently precise to do serious theoretical work. David (2013: 50), for instance, suggests that "the notion of a domain of discourse may well be a serious liability for pluralism about truth". 6 On the constructive front, and partially in response to such worries, pluralists have started to develop competing accounts of domains. 7 In my view, the notion of a "domain of discourse" is a red herring. Such attention is only warranted if domains are needed to play some role in the pluralist's theory. 8 If, as I'll argue here, there is no theoretical role for domains to play, then questions about the nature of domains, what determines the domain a particular claim falls into, and what to say about claims that are in more than one domain fall by the wayside. We might still employ the intuitive notion of a "domain" when we want to give a rough-and-ready, impressionistic, intuitive gloss on the view; but when it comes down to theoretical brass tacks, pluralists have no need for it. Making this argument requires (i) identifying the theoretical role(s) for which pluralists deploy domains and (ii) arguing that such pluralists don't need to deploy the notion of a domain for these purposes.
For what purpose(s), then, do pluralists employ the notion of a "domain"? If different claims are apt to be true in different ways, then it is incumbent on the pluralist to say what determines the way in which a particular claim is apt to be true. Call this the Individuation Problem. Pluralists who appeal to domains do so to answer the Individuation Problem: the way in which a particular claim is apt to be true is determined by its domain. 9 Lynch (2009: 78-79), for example, maintains that "which further property manifests truth for a given proposition depends […] on the domain of inquiry to which it belongs." Indeed, Wyatt (2013: S231-S233) and Edwards (2018a: 85-86) argue that pluralists must appeal to domains for this purpose. Moreover, as far as I can see, this is the only role that domains play in pluralist theories of truth. 10 As such, if pluralists do not need to appeal to domains to answer the Individuation Problem, then there is no role for the notion of a "domain" to play in pluralist theories of truth.
In Sect. 2, I argue that such pluralists do not need to appeal to domains to solve the Individuation Problem. I start by developing two domain-free answers to the Individuation Problem on behalf of two of the most prominent pluralists in this tradition, Michael Lynch and Douglas Edwards (Sect. 2.1 and 2.2). These particular proposals exemplify a general strategy for solving the Individuation Problem without appealing to domains, which I articulate in Sect. 2.3. Given this strategy, pluralists need not 7 E.g., Edwards (2018a;2018b: ch.4), Kim & Pedersen (2018), Lynch (2009, Wyatt (2013), Yu (2017a). 8 The assumption is not that truth pluralism per se requires the notion of a "domain", but that pluralists in the prominent Wright-Lynch-Edwards tradition do so. Since this is the kind of pluralism of interest in this paper, I will often use the generic terms "pluralism" and "pluralist" to refer to this kind of pluralism in particular. 9 See, e.g., the work cited in n.4. This role is, of course, implicit in the familiar intuitive gloss too. 10 An anonymous reviewer suggests that while the Individuation Problem may be the main reason pluralists think they must appeal to domains, some pluralists appeal to domains for other purposes while acknowledging that they don't have to appeal to domains for such purposes. If so, my claim here is too strong, but also stronger than it needs to be: there are other purposes for which pluralists appeal to domains; but since such an appeal is purely optional, the claim that pluralists don't need to appeal to domains still stands. For my own part, I've not been able to identify any such "optional" role for domains either, so I stand by the stronger claim in the text. But those who share the reviewer's reservation are invited to weaken the claim appropriately: there is no role for which the notion of a "domain" is required in the pluralist's theory of truth.
appeal to domains to solve the Individuation Problem. Since I see no other theoretical role for domains to play, I conclude that pluralists have no need for such a notion. Section 3 responds to objections. 11

Individuation without domains
Let's start by introducing some terminology to frame the discussion and noting some desiderata on an answer to the Individuation Problem.
Suppose we've decided on what the primary truth-bearers are: propositions, sentences, beliefs, or what-have-you. We can then sort the primary truth-bearers into truth-classes: a truth-class, C T , is the class of primary truth-bearers for which truth consists in some property, T. Different views on the metaphysics of truth can thus be construed as views about which truth-classes are non-empty. 12 For instance, traditional truth monists agree that there is exactly one non-empty truth-class, containing all the (primary) truth-bearers. But they disagree about which truth-class this is: on the correspondence theory, it is the correspondence truth-class, C correspondence ; on the coherence theory, it is the coherence truth-class, C coherence .
According to truth pluralism, by contrast, there are at least two non-empty truthclasses: (1) and (2) might be in the correspondence truth-class, while (3)-(5) are in the coherence truth-class, for example. Pluralist theories can thus disagree along two orthogonal dimensions: (i) which truth-classes are non-empty; and (ii) which truth-bearers fall into which truth-class. For present purposes we abstract from such differences.
With the notion of a truth-class in hand, we can state the Individuation Problem like so: the Individuation Problem for a pluralist theory of truth is to say what determines which truth-class a truth-bearer falls into. (Note that the Individuation Problem introduces a third orthogonal dimension along which pluralists can disagree: two pluralists can, in principle, agree on which truth-bearers fall into which truth-classes, but disagree about why they fall into said truth-classes.) A note on the scope of the challenge. As is by now familiar, pluralists face difficulties when truth-bearers that are apt to be true in different ways are "mixed" together in, e.g., conjunctions, disjunctions, and so on. 13 There are several different responses 11 In more recent work, Lynch (2013b: 32-34) also argues that he does not need to appeal to domains. Unfortunately, Lynch's leaves his domain-free response to the Individuation Problem entirely schematic ("what makes a particular proposition true […] will depend on facts about that proposition. What is it about? What concepts does it employ and so on?"); and, as Wyatt (2013: S232) argues, seems to commit himself to an explanatorily unsatisfying strategy that treats propositions on a case-by-case basis, rather than offering explanatory generalisations (what Wyatt calls "bare" rather than "grounded" determination claims). In my view, Lynch ought to endorse the non-schematic, grounded determination claims that I call Lynchian Individuation (Sect. 2.1). (In Sect. 3.3 I argue against Wyatt's claim that such grounded determination claims must appeal to domains.) 12 I've chosen to frame this metaphysical dispute as concerning what truth consists in. For some theories, other formulations -in terms of, e.g., reduction, grounding, realisation, determination, manifestation, or identity -would be better. This does not matter for present purposes -read "consists in" as a placeholder. 13 See Williamson (1994), Tappolet (2000), Edwards (2008), Cotnoir (2009), Lynch (2009, Yu (2017aYu ( , 2017b, Kim & Pedersen (2018), and Gamester (2019). to this problem. We will stay neutral on the issue here, and instead focus on the prior question of what determines the truth-class that an atomic truth-bearer falls into. Throughout the rest of this paper, I'll leave the restriction to atomic truth-bearers implicit. 14 We want our answer to the Individuation Problem to be exhaustive: it should place every truth-bearer into a truth-class. A non-exhaustive answer to the Individuation Problem would render the pluralist's theory incomplete. (In the early stages of theory development, we may have to settle for incompleteness; but completeness is nonetheless a desideratum.) It should also arguably be exclusive: it should place every truth-bearer into exactly one truth-class. For suppose that a single truth-bearer, p, was in two truth-classes: C correspondence and C coherence . The immediate worry -raised by Wyatt (2013: S230), Lynch (2013b: 32-33), David (2013: 49 n.9), and Edwards (2018a: 85-86) -is that p might be both true and false in virtue of instantiating one property but not the other (e.g., cohering without corresponding). 15 Now, one might resist the demand for exclusivity by insisting that any truth-bearer that falls into more than one truth-class will instantiate one of the relevant truth properties iff it instantiates all of the others. (In the above example: that p coheres iff p corresponds.) However, it's far from clear how one would render this principle independently plausible 16 -so it would be better not to give away this hostage to fortune if possible. Moreover, if the principle is true, then this provides an alternative route to exclusivity: rather than saying that p is apt to be true in virtue of corresponding and also apt to be true in virtue of cohering, we could say that p is apt to be true in virtue of both corresponding and cohering. That is, instead of saying that p is in both C correspondence and C coherence , we could say that p is in a further, "conjunctive" truth-14 An anonymous reviewer worries that this restriction may be impermissible, since we may want to treat mixed compounds and mixed atomics in the same way. However, pluralists can (and often do) maintain that claims of different logical forms (like mixed compounds and mixed atomics) are true in different ways; and most if not all of the extant responses to the Problem of Mixed Compounds are compatible with, and many even require, treating mixed compounds in a different way to mixed atomics. E.g., Edwards (2009) proposes that any logically complex claim (including a mixed compound) is ipso facto in the logical domain; this reasoning would not carry across to an atomic claim. Lynch (2009: 90-91) proposes that for compounds (including mixed compounds), no property besides truth itself manifests truth; nothing commits him to saying the same thing about mixed atomics. Kim & Pedersen (2018) propose that compounds like negations, disjunctions, and conjunctions are apt to be true in a different way to any atomic claim. My own preferred approach is to say that all claims of different logical forms are apt to be true in different ways, a view I think is implicit in standard recursive analyses of truth anyway (Gamester 2019). The only potential exception is Yu (2017a), who maintains that both mixed compounds and mixed atomics fall into "impure" domains. However, (i) it is unclear how to interpret the impure truth properties Yu associates with these domains, let alone how to interpret them such that it is plausible that both mixed atomics and mixed compounds are apt to be true in this way; and (ii) while Yu's proposal is compatible with there being atomics that are true in the same way as mixed compounds, it does not require this. 15 Yu (2017b) explores a view which rejects exclusivity, but does not consider this worry. 16 The prospects for doing so turn on the details of the pluralism in question. For example, Kölbel (2008) proposes a kind of truth dualism in which one way of being true, trueS, is a species of the other, trueD: very roughly, to be trueS is to be trueD and objective. So, if any truth-bearer p that is in C truthS and C truthD is guaranteed to be trueD only if objective, then p is trueS iff p is trueD. While I doubt that this particular proposal would work, this illustrates how one could go about motivating the principle in question. Note, however, that most extant varieties of truth pluralism do not have this structure. class: C correspondence−and−coherence . So taking exclusivity to be a desideratum shouldn't beg any significant questions.
With this scene-setting in place, I'll now argue that those pluralists who appeal to domains can in fact solve the Individuation Problem without appealing to domains. I'll demonstrate this by first developing domain-free answers to the Individuation Problem on behalf of two of the leading proponents of the view: Lynch (Sect. 2.1) and Edwards (Sect. 2.2). For each pluralist, I'll outline their underlying motivation for pluralism, 17 and then show how each motivation leads naturally to an answer to the Individuation Problem. This will render salient a particular strategy for solving the Individuation Problem, which I will articulate in Sect. 2.3.

Lynchian Individuation
According to Lynch (2009), the correspondence theory of truth ought to be cashed out in causal terms. This comes in two steps. First, the correspondence of a truthbearer as a whole is analysed in terms of the denotation of its components: thus, supposing that (1) -'Fido is furry' -is a belief composed of concepts, 18 for (1) to correspond to reality is for the object that the concept FIDO denotes (i.e., Fido) to instantiate the property that IS FURRY denotes (i.e., the property of being furry). Second, the denotation of these components is cashed out in causal terms: for FIDO to denote Fido is for there to be a certain causal relation between the concept and the thing in the world, likewise for IS FURRY.
So, for a belief to correspond, according to Lynch, it is necessary that every component concept of the belief has its denotation in virtue of standing in a causal relation to what it denotes. Lynch's case for pluralism derives from the claim that, while this is plausible for some beliefs (like, say, (1)), it is not plausible for others. In particular, it is not plausible when the entities the components of the belief denote cannot enter into the appropriate causal relations. Lynch (2009: 33-35) suggests that this may be the case if the entity in question is abstract, non-natural, or mind-dependent. For such beliefs, Lynch suggests, truth must consist in something other than correspondence. Let's use 'coherence' as a placeholder for this alternative. 19 This suggests the following answer to the Individuation Problem: Lynchian Individuation.
17 For a more detailed overview, see Gamester (2020). 18 Lynch primarily talks in terms of beliefs or judgements, only sometimes propositions. He also suggests that the considerations apply mutatis mutandis to sentences (Lynch 2009: 23). 19 I here take a liberty with Lynch's account for ease of exposition: Lynch is not committed to all non-corresponding beliefs being true in the same way. Lynch (2009: ch.8) argues that moral judgements are true in virtue of possessing a property he calls concordance; but he may think that, say, mathematical beliefs are true in a different way. However, while he is not committed to moral and mathematical beliefs being true in the same way, he also does not offer a principled basis for thinking that they are true in different ways (in the terms of Sect. 2.3, we don't know what the underlying differences between mathematical and ethical beliefs would be). Given such a principled basis, we would be able to formulate a more refined version of Lynchian Individuation on Lynch's behalf. As things stand, the less refined version is the best we can do.
(a) A belief B is in C coherence iff there exists some component c of B such that c denotes an abstract, non-natural, or mind-dependent entity. (b) A belief B is in C correspondence iff (i) there exists some component c 1 of B such that c 1 denotes a concrete, natural, and mind-independent entity, and (ii) there does not exist a component c 2 of B such that c 2 denotes an abstract, non-natural, or mind-dependent entity.
Since (b)(ii) is the negation of the right-hand side of (a), Lynchian Individuation clearly renders C coherence and C correspondence exclusive. They are exhaustive iff: every belief has a component concept that denotes some entity; and every entity is either concrete, natural, and mind-independent, or else abstract, non-natural, or mind-dependent.

Edwardian individuation
Consider, now, Edwards's (2018b: 84-88) "strong" argument for pluralism. Edwards draws on a contrast between objective and projected properties: a property F is objec- 20 Edwards argues that, when 'is F' denotes an objective property, 'a is F' is true because a is F, and is thus true in a representational sense (we'll label this "correspondence"); whereas when 'is F' denotes a projected property, a is F because 'a is F' is true, meaning the latter is true in a non-representational sense (which we'll label "coherence"). Edwards, then, should answer the Individuation Problem like so: Edwardian Individuation.
Edwardian Individuation is exclusive on the plausible assumption that no property is both objective and projected. It's exhaustive given: (i) that every predicate denotes a property; and (ii) that every property is either objective or projected; and (iii) that all truth-apt, atomic sentences are of the form 'a is F'. (If any of (i)-(iii) are false, then Edwardian Individuation may be non-exhaustive; but the resulting incompleteness is inherited from Edwards's pluralism -we could not offer a more exhaustive answer to the Individuation Problem without taking on more commitments than Edwards.) Of the several respects in which Lynchian and Edwardian Individuation differ (including what they take the primary truth-bearers to be), two are worth highlighting. First: the metaphysical distinctions each appeals to. Lynchian Individuation appeals to the distinctions between abstract and concrete entities, non-natural and natural entities, and mind-dependent and mind-independent entities. Edwardian Indi- 20 Edwards aligns this distinction with that between "sparse" and "abundant" properties, and typically uses the latter terminology. It's far from obvious that the two distinctions do align, however, and it is the objective/projected distinction that matters for his argument. Accordingly, I use this terminology. viduation appeals to the distinction between objective and projected properties. This is unsurprising, given the different ways in which Lynch and Edwards motivate their views.
Second: for Edwardian Individuation, all that matters is what kind of property is denoted by the predicate in the target truth-bearer; it does not matter what kind of entity is denoted by the singular term. (This is despite the fact that Edwards (2018b: 77) maintains that the objective/projected distinction applies to objects as well as properties. So, for Edwards, 'a is F' is in C correspondence if 'is F' denotes an objective property, even if 'a' denotes a projected object.) 21 For Lynch, by contrast, if any part of the truth-bearer denotes an abstract, non-natural, or mind-dependent entity, then it falls outside the scope of his preferred version of the correspondence theory. Again, this difference is symptomatic of underlying differences in their arguments for pluralism.

The general strategy
Lynchian and Edwardian Individuation show that two of the leading proponents of pluralism do not need to appeal to domains to answer the Individuation Problem. This is already a significant conclusion. Moreover, these proposals exemplify a general strategy for answering the Individuation Problem without appealing to domains.
As philosophers, we often find ourselves needing to warm people up to a philosophical idea or theory -that is, with needing to offer a rough-and-ready, impressionistic, intuitive case in favour of the view, to get people to take it seriously as an option in theoretical space. When we want to warm people up to truth pluralism, it's natural to deploy the intuitive notion of a "domain of discourse". While the correspondence theory of truth may seem plausible enough for ordinary descriptive or scientific discourse, the intuitive motivation goes, it seems significantly less plausible when it comes to, say, mathematical, ethical, social, comic, aesthetic, or modal discourse. And, congruently, while some anti-realist conception of truth may seem plausible enough in the mathematical, ethical, social, comic, aesthetic, or modal domain, such conceptions seem significantly less plausible when it comes to ordinary descriptive or scientific discourse. The pluralist thus suggests that each of these conceptions of truth is correct only locally: while truth consists in correspondence in some domains, it consists in (say) coherence in other domains.
It is clear, however, that the pluralist ultimately owes us more than this intuitive case in favour of the view. For even if we were to grant that truth-bearers in different domains are apt to be true in different ways, we still need to be told why this is so: why it is that those truth-bearers we're intuitively inclined to classify as "mathematical" or "ethical" are apt to be true in a different way to those we are intuitively inclined to classify as "scientific". For this explanatory purpose, I submit, a brute appeal to the domains they are in -that one truth-bearer is apt to be true in one way because it is in, say, the mathematical domain, while another is apt to be true in a different way because it is in the scientific domain, end of story -would be unsatisfying. We need to be told what it is about the truth-bearers in the mathematical and scien-21 In personal communication, Edwards confirms that this is the correct interpretation of his view.
tific domains, what it is about being "mathematical" or "scientific", that explains the alethic variation. For example, elsewhere I have suggested two broad strategies for explaining such variation: one ontological, one teleological (Gamester 2020: 11,353). On the ontological approach, what explains why truth-bearers in different domains are apt to be true in different ways is the nature of the entities those truth-bearers are concerned with (e.g., whether they are abstract or concrete, natural or non-natural, mind-independent or mind-dependent, objective or projected). On the teleological approach, what explains the variation is the function of the relevant thought and talk (e.g., whether it serves a representational or expressive function). Call those factors that explain why truth-bearers in different domains are apt to be true in different ways the underlying differences.
This is just what we see in the literature. As discussed above, both Lynch (2009) and Edwards (2018b) appeal to ontological distinctions (although each appeal to different ontological distinctions). Pedersen (2014) likewise appeals to the distinction between mind-dependent and mind-independent entities. Cotnoir & Edwards (2015) appeal to ontological pluralism: that is, the thesis that different entities literally exist in different ways. In more recent work, Lynch (2013a) appeals to functional differences, arguing that moral expressivists should endorse a substantive but non-representational conception of moral truth; and I have been developing a similar proposal (Gamester, 2018;forthcoming). But if it is these ontological or teleological (or whatever other) differences that ultimately explain why these truth-bearers are apt to be true in different ways, then we can answer the Individuation Problem by appealing to these underlying differences, rather than appealing to domains.
One might worry that such a strategy will fail to vindicate the aforementioned intuitive motivation for the view, which is precisely that truth-bearers in different domains are apt to be true in different ways. But clearly an answer to the Individuation Problem need not appeal to the notion of a domain to vindicate this intuition. For instance, if most of those truth-bearers we intuitively classify as "mathematical" are concerned with abstract entities, while most of those we intuitively classify as "scientific" are concerned with concrete entities, then Lynchian Individuation will vindicate the intuition that truth-bearers in these different "domains" are apt to be true in different ways, despite not appealing to the truth-bearers' domains to explain why this is so.
So, truth pluralists can and should answer the Individuation Problem by appealing to the underlying differences that explain why truth-bearers that are intuitively in different "domains" are apt to be true in different ways, and thus need not appeal to the notion of a "domain" for this purpose. I cannot see any other purpose for which pluralists have appealed to the notion of a "domain". As such, I conclude that there is no role for the notion of a "domain" to play in the pluralist's theory of truth.

Pluralism without domains
In Sect. 2, I articulated a strategy for solving the Individuation Problem which makes no explicit appeal to the notion of a domain of discourse and concluded on this basis that there is no theoretical role for which the notion of a domain is needed in the plu-ralist's theory of truth. There are two possible responses to this argument. One is to identify some other theoretical role for which pluralists require domains. As I say, the literature affords no obvious candidates on this front. So, for present purposes I set this response aside. The other possible response is to argue that, while my strategy for solving the Individuation Problem makes no explicit appeal to domains, it nonetheless involves some kind of implicit appeal to domains, and thus does not constitute a genuine alternative. There seem to be three lines of reasoning to this conclusion, which I will use to frame the following discussion of the proposal's relative merits.

Objection 1
First, one may argue that what I call "truth-classes" are in fact domains. After all, truth-classes are classes of truth-bearers that are apt to be true in different ways. And truth pluralists hold that truth-bearers in different domains are apt to be true in different ways. So, "truth-class" is just another name for a domain. So, Lynchian and Edwardian Individuation are really accounts of domains.
This line of reasoning misconstrues the notion of a domain that truth pluralists usually appeal to. That there are multiple non-empty truth-classes is a distinctive commitment of truth pluralism as such. That there are multiple domains of discourse is not. On the contrary, pluralists are typically at pains to emphasise that they are not the only ones who are committed to there being multiple domains of discourse. For instance, Wyatt (2013: S228) writes that: The conviction that there is more than one discourse underpins many debates about realism, antirealism, and irrealism, error theory, expressivism, and fictionalism, and cognitivism and non-cognitivism. It is thus important for many philosophers, not only truth pluralists, to be clear about what, exactly, a discourse is supposed to be.
The mathematical error theorist is an error theorist about mathematical discourse; the ethical non-cognitivist is a non-cognitivist about ethical discourse; and so on. So others besides pluralists have a vested interest in being able to distinguish mathematical discourse and ethical discourse from other domains of discourse. Lynch (2009: 79;2013b: 33) and Edwards (2018a: 88;2018b: 61) express the same sentiment. The distinction between domains of discourse that pluralists appeal to is thus meant to be one that non-pluralists can appeal to too -Edwards (2018a: 94) is explicit that his "account of domains is intended to be available to theorists of various sorts, not just truth pluralists." So we cannot identify domains with truth-classes. 22 Indeed, further reflection shows that the identification of domains with truthclasses is a non-starter. For one thing, it would scupper any response to the Individuation Problem that appealed to domains. The claim that different truth-bearers are apt to be true in different ways because they are in different domains becomes the trivial 22 It should be noted, however, that the same confusion is sometimes implicit in the literature. Cook (2011: 627), for instance, suggests that there "seem to be no good reasons for thinking that there are only finitely many discourses" in a context where his argument requires that there infinitely many ways of being true. claim that they are apt to be true in different ways because they are apt to be true in different ways. For another, it would mean that different domains of discourse are by definition apt to be true in different ways -but the pluralist may well be happy that different domains of discourse (e.g., the moral and the aesthetic) are apt to be true in the same way. (Indeed, pluralists generally seem to assume that there are many different domains of discourse -mathematical, ethical, social, aesthetic, biological, chemical, modal, etc. -but only usually suggest that there might be two or three ways in which atomic truth-bearers are apt to be true.)

Objection 2
The second line of reasoning is that, while my strategy for answering the Individuation Problem does not appeal to domains, pluralists can use the very underlying differences I appeal to on Lynch's and Edwards's behalf -namely, ontological distinctions between abstract/concrete, non-natural/natural, mind-dependent/mind-independent, and projected/objective entities -to individuate domains.
For instance, Lynch (2009: 79-80) says that what distinguishes propositions 23 in different domains from each other are the kinds of concepts they are composed of; and that "[o]ne kind of concept differs from another by virtue of (a) its relation to, and (b) the character of, the properties that kind of concept is a concept of." Schematically, the idea is that the propositions in domain D1 are in D1 in virtue of being composed of concepts that stand in certain relations to properties of character C1; while propositions in domain D2 are in D2 in virtue of being composed of concepts that stand in certain relations to properties of character C2; and so on. See Wyatt (2013: S229-S230) for a clear presentation and refinement of Lynch's proposal. Unfortunately, neither Lynch nor Wyatt tells us how they intend to fill in this schema (that is: what kind of property is associated with what domain). But a natural thought is that they might use the ontological distinctions Lynchian Individuation appeals to. For instance, they may say that propositions are in the mathematical domain in virtue of being composed of concepts that stand in certain relations to abstract entities; or that propositions are in the social domain in virtue of being composed of concepts that stand in certain relations to mind-dependent entities; and so on. 24 Similarly, Edwards (2018b: 78-79) claims that the domain of an utterance of the form 'a is F' is determined by the kind of predicate it uses, and that "predicate kinds are distinguished by the kinds of functional roles that predicates have." In turn, "[t]he functional roles are understood in terms of the features of the properties that the predicates are purported to pick out." (Edwards 2018a: 89) 25 Again, one might think that Edwards could appeal to the kind of ontological distinctions Lynchian and Edwardian Individuation appeal to in fleshing out how the features of these properties differ from one another, and thus how different predicates' functional roles differ from one another, which in turn determines the domain of an utterance that uses the predicate. Now, I'm sceptical that any such strategy for giving an account of domains will be successful. But for present purposes, let's set such worries aside. Let's grant that pluralists like Lynch, Wyatt, and Edwards might be able to use the kind of underlying differences that Lynchian and Edwardian Individuation utilise (perhaps supplemented with further resources) to give an account of domains of discourse -of what distinguishes, say, scientific discourse from mathematical discourse, ethical discourse from social discourse, and so on. But this just draws attention to what is, in fact, the key advantage of my proposal: my strategy for solving the Individuation Problem renders such an account of domains of discourse unnecessary. If one intends to answer the Individuation Problem by appealing to intuitive distinctions between domains, then one needs to show that these intuitive distinctions can be rendered sufficiently precise to be able to do substantive theoretical work. My strategy has no such commitment.
Consider the "Problem of Mixed Atomics". 26 Schematically, truth pluralists say that truth-bearers of type 1 are apt to be true in one way, while truth-bearers of type 2 are apt to be true in another. The Problem of Mixed Atomics works by identifying atomic truth-bearers that are plausibly of both type 1 and type 2, and asking in what way these truth-bearers are apt to be true. This Problem is pressing when the "types" in question are taken to be domains, since there are plausibly atomic truthbearers that are in more than one domain. 27 Anecdotally, I've found that intuitions sometimes clash about whether some of these are really mixed atomics. This is grist to my mill: insofar as we do not share clear intuitions about cases, we should doubt whether the intuitive distinctions we draw between "discourses" or "domains" are fit to do the explanatory work pluralists assign to them. 28 (11) is "atomic in the sense that it does not break down via an application of the rules for truth-functional connectives into simpler propositions that are themselves apt for truth […]. That is not to deny that it is 'complex' in other equally valid senses of the term." (Stewart-Wallace, 2016: 364).
non-exclusive. 29 On (b), it becomes non-exhaustive. 30 The worry about (c) is that it is difficult to see what principled grounds there might be for insisting that every atomic truth-bearer falls into exactly one domain of discourse; e.g., for saying that (6) is a part of aesthetic discourse rather than mathematical discourse (or vice versa). Edwards (2018b: 78-79), for instance, opts for (c). He argues that, for sentences of the form 'a is F', the domain is determined by the predicate and not the singular term. His argument is that what "makes these kinds of sentences sentences in that they are bearers of content" is not the object denoted by 'a', but the attribution of a property to that object, which is done by the predicate 'is F'. 31 He "substantiates" this conclusion by observing that "many different kinds of thing can be said about the same object: a single chair can be blue, solid, beautiful, sad, dangerous, presidential, or singular". But this is hardly convincing. While it is true that 'snow is white' is only a sentence in virtue of attributing a property, it is also only a sentence because it attributes that property to something. That is: both the singular term and the predicate play a role in making 'a is F' a bearer of content. 32 And while it is true that many different kinds of thing can be said about the same object, it's also true that the same thing can be said of many different kinds of object: a chair, person, act of kindness, mathematical proof, sculpture, musical work, and touchdown can all be beautiful, for example. Why doesn't the latter observation give us just as much reason for privileging the singular term as the former observation gives us for privileging the predicate? (Meaning we overall have no reason to privilege either.) Now, I'm not pretending this short discussion is the final word on the matter: perhaps there is some way of settling all this in favour of one particular way of dividing up truth-bearers into domains. 33 But the point I want to stress is that, by avoiding 29 Wyatt (2013: S233) endorses (a), but secures exclusivity by suggesting that C correspondence acts as a "default" truth-class, such that a proposition falls into C correspondence unless it is composed of some concept such that it "cannot be true in virtue of representationally corresponding", in which case it falls into an epistemic truth-class, e.g., C coherence . But on this proposal, two propositions -one "mixed" and one "pure" -can be in the same domain, but different truth-classes; so a proposition's truth-class is not determined by its domain after all, or at least not solely by its domain. Indeed, Wyatt does not tell us what concepts he has in mind, but given his Lynchian inspiration a plausible suggestion is concepts that denote abstract, non-natural, or mind-dependent entities; but then Wyatt's proposal is equivalent to Lynchian Individuation, which (I'm arguing) does not appeal to domains at all. 30 Wyatt (2013: S231) and Stewart-Wallace (2016: 364) pose the Problem of Mixed Atomics as a nonexhaustiveness worry; David (2013: 49-50, n.9) as a dilemma between non-exclusiveness and nonexhaustiveness. 31 "A sentence is about its object […]. But what makes these things sentences is that there is something more: there is something that is said about the things that the sentences are about. […] This 'saying of' occurs due to the attribution of a property to the object." 32 The potential existence of sentences formed of a predicate but no singular term (e.g., 0-placed predicates or sentences like "it rains", where "it" is a bogus subject occurring merely for grammatical reasons) does not undermine the conclusion that in the relevant cases the singular term is just as important as the predicate. 33 Note that there are countless other candidate ways of doing so besides Edwards's privileging of the predicate. For instance, one could argue that certain domains "outrank" others, in the sense that they win out in mixed cases (e.g. if the mathematical outranks the aesthetic, then any putatively mixed mathematical and aesthetic examples count as mathematical). Hybrids are available too: perhaps the mathematical outranks all other domains, but in non-mathematical cases it's determined by the predicate. I have no idea how to decide between these proposals, but perhaps it can be done. any appeal to domains, my proposal sidesteps the whole debate -the issue of which domain(s) examples like (6)-(11) fall into is neither here nor there. And since Lynchian and Edwardian Individuation sort truth-bearers into exclusive classes, there is no corresponding "Problem of Mixed Atomics" to deal with.
Of course, both Lynchian and Edwardian Individuation take a stance on which truth-classes particular truth-bearers fall into. But each has a principled basis for doing so, which is obtained from the underlying argument for pluralism. As noted at the end of Sect. 2.2, the reason that Edwardian Individuation privileges the predicate rather than the singular term, while Lynchian Individuation does not, is because Edwards's (2018b: 84-88) argument for pluralism exclusively turns on what kind of property (objective or projected) is ascribed by the predicate and is insensitive to what kind of object is denoted by the singular term. Assuming that Edwards's argument for pluralism is in good standing, the response to the Individuation Problem is in good standing too. (If the underlying argument for pluralism is not in good standing -if, for instance, the singular term's denoting a projected object is also sufficient for 'a is F' to be true in a non-representational sense -then the response to the Individuation Problem can be modified accordingly.) If Edwards endorses Edwardian Individuation, then also finding a principled basis on which to sort truth-bearers into domains is simply unnecessary.

Objection 3
Finally, one may argue that my proposal does appeal to domains, just different domains to the ones pluralists normally appeal to. Instead of the scientific, mathematical, ethical, or social domain, one might argue, Lynchian Individuation appeals to the at-least-partially-abstract-non-natural-or-mind-dependent domain and the strictly-concrete-natural-and-mind-independent domain; while Edwardian Individuation appeals to the projected-property domain and the objective-property domain. Now, if we use 'domain' to pick out any class of truth-bearers that instance a certain kind, then since any response to the Individuation Problem will have some principled basis for sorting truth-bearers into different truth-classes, it plausibly follows that any response to the Individuation Problem will appeal to domains of some kind. This, for instance, seems to be the abundant conception of a "domain" that Wyatt and Edwards need when they argue that pluralists must appeal to domains to answer the Individuation Problem. Wyatt argues that any informative answer to the Individuation Problem "…will cite general facts about the kind(s) of concepts of which a certain proposition 〈p〉 is composed. This entails that 〈p〉 instances a certain proposition-kind. Domains are just classes of propositions that instance a common kind, so domains then enter straight away." (Wyatt 2013: S232-S233) Clearly domains only "enter straight away" from the claim that the proposition instances a common kind if we assume that any class of propositions that instances a common kind is a domain. Similarly, Edwards (2018a: 85-86) maintains that, if there are many ways in which sentences can be true, but sentences don't come divided into different domains, then each individual sentence will be apt to be true in more than one way -suggesting that without domains the pluralist cannot sort different truthbearers into different truth-classes at all. This is only plausible if we assume that, for any principled difference between truth-bearers we might appeal to, the existence of that principled difference implies that those truth-bearers are in different domains.
One problem with this is that, as discussed above, pluralists including Wyatt and Edwards are, at other times, clear that the division of truth-bearers into "domains" that they have in mind is not just any principled division of truth-bearers into different classes, but specifically the division into the, e.g., scientific, mathematical, ethical, and social domains of discourse that seems to underlie the usual debates about localised forms of realism, anti-realism, etc. More important, however, is that this abundant conception trivialises the notion of a "domain". The claim that the truthclass a truth-bearer falls into is determined by its domain becomes the claim that the truth-class a truth-bearer falls into is determined by the kind of truth-bearer it is. We know that. The Individuation Problem doesn't merely ask for an assurance that there is something in virtue of which a truth-bearer is apt to be true in one way rather than another, but asks what it is about the truth-bearer that determines the way in which it is apt to be true. The abundant conception of a domain thus renders this response to the Individuation Problem utterly uninformative. Moreover, on this conception the project of offering a general account or theory of domains looks wrong-headed: if any class of truth-bearers of a certain kind constitutes a domain, then the appropriate question is not "What are domains?" but "Which domains are relevant to my answer to the Individuation Problem?" That the relevant classes of truth-bearers constitute domains will be explanatorily uninteresting, precisely because the status is so easy to come by. The abundant conception of a "domain" that Wyatt and Edwards need for their arguments to go through thus renders the appeal to domains in answering the Individuation Problem uninformative and the project of developing an account of domains wrong-headed, as well as being in tension with the understanding of a "domain" they explicitly have in mind elsewhere.
To summarise: the distinctions between "domains of discourse" that pluralists appeal to and offer accounts of are the intuitive distinctions between, e.g., mathematical, scientific, ethical, and social domains of discourse. Domains are therefore not to be identified with truth-classes, nor can we let just any class of truth-bearers of a certain kind constitute a domain, lest we render the response to the Individuation Problem uninformative. My strategy for solving the Individuation Problem therefore cannot be said to appeal to domains, in the relevant sense. It may be possible to give an account of domains using the resources that I appeal to on Lynch's and Edwards's behalf. But it may also not be possible. The key advantage of my proposal is that we sidestep the entire issue: we do not need to give an account of domains to solve the Individuation Problem.

Conclusion
Truth pluralism is usually glossed as the view that truth-bearers in different "discourses", "domains", "domains of discourse", or "domains of inquiry" are apt to be true in different ways. The notion of a "domain of discourse" is consequently attracting increasing amounts of attention in the literature, both constructive and critical. I've argued that this is a red herring. In particular, I've argued that the pluralist can and should solve the Individuation Problem -saying what determines the way in which a particular truth-bearer is apt to be true -without appealing to domains. Since there doesn't seem to be any other theoretical role for the notion of a "domain" to play, there is no role for the notion of a "domain" to play in the pluralist's theory of truth. As such, pluralists do not owe us an account of what, exactly, a "domain of discourse" is, despite the usual gloss on the view.
As mentioned in Sect. 1, I'm not sure anything I've said here is an objection to glossing the view in terms of domains of discourse. Perhaps this is a good way of getting a rough-and-ready, impressionistic, intuitive handle on the view before we try and pin down the details. My objection is to taking this gloss too seriously and inferring that the intuitive distinctions between "scientific discourse", "mathematical discourse", "ethical discourse", "social discourse", and the rest are an important part of the pluralist's theory of truth. While it is important that the pluralist has an answer to the Individuation Problem, the pluralist's answer need not and should not appeal to this intuitive distinction between domains of discourse, but should instead appeal to the relevant underlying differences, such as ontological or teleological differences, between truth-bearers that by her lights explain why truth-bearers in different "domains" are apt to be true in different ways.