Diaphonic pluralism: from truth pluralism to disagreement pluralism

In this paper, I offer a pluralistic framework for disagreement and I develop a strategy to account for the varieties of disagreement on the basis of the varieties of the truth across different domains of discourse. Truth-pluralism is thus sufficient for delivering pluralism about disagreement—that is, diaphonic pluralism.


Introduction
In recent years, a considerable body of literature has been published that investigates the connections between truth pluralism and other forms of pluralism. More specifically, the thesis that logical pluralism is entailed by truth pluralism (Lynch, 2008(Lynch, , 2009Pedersen, 2014;Cook, 2018;Shapiro & Lynch, 2019) and that metaphysical or ontological pluralism entails truth-pluralism (Cotnoir & Edwards, 2015;Pedersen, 2014) has been discussed. These investigations are driven by an idea that motivates this paper: truth is very central and intimately connected to other central notions, such as validity and being. However, while considerable work has been done on the potential connections between alethic, logical and ontological pluralism, this paper offers an argument that adds something new to the literature. In fact, no case has been made to connect truth pluralism to pluralism about disagreement. I argue that such a case can be made.
Special thanks to the Bologna Cogito Research Seminar of the University of Bologna, the research group of the Pluralism Research Project of the Veritas Research Center at the University of Yonsei, the Research Seminar in Theoretical Philosophy of the University of Bielefeld, and the DFG Research Group on Disagreement in Philosophy of the University of Bonn. This paper has greatly benefited of comments from Filippo Ferrari, Marcel Kertels, Christian Nimtz, Nikolaj Jang Lee Linding Pedersen, Crispin Wright and Luca Zanetti. In the following, I will draft a pluralist proposal about disagreement that is based on alethic pluralism. I call this form of pluralism diaphonic pluralism. 1 The rest of this paper is structured as follows. I start by specifying the conception of pluralism that is employed in this paper (Sects. 2 and 3). I will then briefly introduce alethic pluralism (Sect. 4) and its the core principles (Sect. 5), which will be then employed to characterise diaphonic pluralism. In Sect. 6, I state the core principles of diaphonic pluralism and I show their conceptual dependence on the alethic core principles. Next, (Sects. 8, 9 and 10) I provide a partial vindication of the claim that the metaphysics of disagreement can be based on the metaphysics of truth. After addressing some objections (Sect. 11), I summarise the main points of this paper (Sect. 12), which support the thesis that alethic pluralism provides the resources for articulating pluralism about disagreement.

Pluralism
The word "pluralism" is used in a variety of different ways in the philosophical and political literature. In this work, I deal with one specific conception of pluralism, which is illustrated by the following four tenets.
First, pluralism is about a topic and is not a stance (e.g., a stance of being tolerant): Topic aboutness: Pluralism is always about a topic X.
Second, to be pluralist involves a mild realism in the sense that it requires the distinction between those "entities that things are said to bear, possess or exemplify" (Orilia & Swoyer, 2017) (i.e., properties) and mental representations. 2 Concept/property distinction: Pluralism requires the distinction between our own ways of representing a feature's reality (concepts) and what these concepts are about (properties).
Third, pluralism involves one concept and many properties: One concept, many properties: Pluralism about topic X requires the existence of one concept of X and many X-properties (related to different domains of inquiry).
Pluralism is not the (sort of Putnamian) claim that reality is multifaceted because we can represent reality in different ways. On the contrary, to be pluralist about X is to claim that from our own way of representing reality we cannot infer the features of what they represent. Our concept X underdetermines the features of reality because it tracks different features related to different domains of inquiry 3 . Instead of having 1 The name comes from the ancient Greek "διαφωνια", meaning discord and disagreement. 2 I have characterised concepts using the most popular approach (i.e., the mental representation view, prominently represented by Fodor) just to give the sense of concept/property distinction. However, the project of this paper does not rely on on taking sides in the debate on concepts. Those unsympathetic to the mental representation view, can understand the present conception of concepts either along the abstractionist view or the ability view (Margolis & Laurence, 2019). 3 I will not take issue here on whether or not it is best to relativise to domains or subject matters (see Wyatt (2013)). many X-concepts, we have just one X-concept but many X-properties that are tracked by this concept in different domains.
Fourth, pluralism adopts network analysis for concepts and is committed to a multirealisability thesis: Network analysis & Multiple realisability: Pluralism requires that the content of concept X is fixed by a set of core principles and that such a concept is realised by a plurality of properties (i.e., the X properties), each of which realises the concept in relation to a domain of inquiry.
A pluralist analyses concept X by stating core principles (which are sometimes called "platitudes") about X that illustrate the connections between X and other concepts that bear central relations to it. In this way, the concept is implicitly defined by placing it in a network of conceptual relations with other concepts. This network identifies the role played by the concept when employed to represent reality. This role can then be fulfilled by different features of reality (different properties realise the concept) in different domains of inquiry.
These four tenets fix the understanding of pluralism that I employ. 4

Scope problems
The motivations for adopting pluralism in relation to a certain topic lie in the putative fact that topic X gives rise to scope problems. In the following, I will present two types of scope problems that constitute prima facie motivations for being pluralist: the Alethic Scope Problem for pluralism about truth, and the Normative Scope Problems for pluralism about disagreement.

Alethic scope problem
According to the Alethic Scope Problem, there is an apparent variability in the way in which propositions are true in different propositional domains. The following argument presents this scope problem: 1. Consider correspondence and coherence as two candidate truth-properties. 2. Correspondence might plausibly be applied to discourse about medium-sized dry goods; 3. Correspondence seems much less plausible in relation to (for example) legal discourse or basic arithmetic; 4. Coherence with the body of law might seem plausible in relation to legal discourse and coherence with axioms might seem plausible in relation to basic arithmetic; 5. Coherence seems to be much less plausible for discourse about medium-sized dry goods; 6. This pattern can be repeated for other candidate truth-properties; 7. Hence, no single truth theory is plausibly correct right across the board.
The pluralist can make sense of this situation by allowing a variety of truth properties by letting a number of truth theories work together. No single monistic truth theory is thus right across the board. However, once it is restricted to a specific domain of discourse, it can accommodate the characteristic features of the domain. Jointly, all of these monistic truth theories have a scope that is wide enough to accommodate the different features exhibited by the diverse domains of discourse. 5

Normative scope problems
Normative scope problems are based on the insight that the normative function that truth exerts varies. This idea, which was first articulated in Ferrari (2018), is based on the observation that there seems to be a notable variation in the normative significance of enquiry-related phenomena, such as disagreement as it occurs. Following and building on the work of Ferrari, we can say that this normative significance has at least two axes of variability. The first axis is topic variability: There seems to be variability in the way in which we disagree in relation to different topics. The second axis of variability is vagueness variability: For each topic of disagreement, there seems to be variability in the way in which we disagree when clear and borderline cases are concerned. I will briefly address each of these axes because they are central for motivating a pluralist analysis of disagreement.

Topic variability
Topic variability is the phenomenon for which the relation of disagreement varies in relation to what the disagreement is about (e.g., matters of taste, refined aesthetic matters, moral issues, scientific matters, etc.). The presence of disagreements concerning matters of taste are perceived to be less intrusive and have a much weaker normative significance than the presence of other kinds of disagreement (e.g., paradigmatically, disagreements about moral issues where the subjects involved seem to take a stance on the debated issue, but only with hesitation and uncertainty).

Vagueness variability
The normative significance of disagreement also varies depending on whether the disagreement concerns determinate or indeterminate cases. The normative profile of indeterminacy is related to cases such as vagueness where (in relation to borderline cases) none of the attitudes of acceptance, rejection or suspension of judgement are inconsistent with conceptual competence. The presence of vague concepts seems to leave open the question of what to think when borderline cases are concerned. 6 5 See Wright (1992a), Sher (1998), Lynch (2004b). This argument is effective against nondeflationary monistic truth-theories. A (monistic) deflationist could deflect the argument by the classical double counting counter-objection: the features highlighted of the different domains pertain to the metaphysics of the domain, but not to the metaphysics of truth. For a treatment of the double-counting objection, see Lynch (2018). 6 The standard semantic view of vagueness (e.g., that borderline cases are cases of truth-value gaps due to the incompleteness of meaning of vague expressions, a classic example is supervaluationism Fine (1975)] and I will not elaborate further on these scope problems. Some have criticised the cogency of these considerations. 7 However the question of this paper is not whether or not the scope problems are genuine. The question that I want to consider is the following: Assuming that scope problems are genuine, has alethic pluralism the resources to account for both the scope problems for truth and disagreement? This paper offers a tentative positive answer to this question because it argues that diaphonic pluralism is rooted in alethic pluralism. Before introducing diaphonic pluralism, I thus need to introduce alethic pluralism.

Alethic pluralism
According to alethic pluralism, the truth-concept is realised by different properties with respect to different domains of inquiry. Alethic pluralism employs the so-called two-stage analysis for analysing truth: First stage: A set of core principles for truth is identified. Second stage: A case is made for the thesis that the truth-concept determines different realiser(s) in different domains (i.e., the truth properties).
As for the first stage of the analysis (i.e., the conceptual analysis), there is controversy on which core principles to employ to provide a network analysis of the truth concept. 8 In the following, (Sect. 5) I will choose a set of core principles for truth. Each of these principles has been included by most of the truth-pluralists. However, I will not offer arguments for this choice. The only positive consideration that I can offer is that they seem to be central for the concept of truth, they nicely fit together and (crucially) they are capable of providing a unified pluralist framework for truth and disagreement.
As for the second stage (i.e., the metaphysical analysis), there is controversy on whether or not to include a generic truth property along with properties realising truth in different domains. In fact, truth pluralism comes in at least two general brands: strong and moderate pluralism. According to strong pluralism, there is no generic truth property but just local truth properties (i.e., properties realising truth with respect to specific domains). 9 According to moderate pluralism, the local truth properties cohabit with a generic truth property that is always exemplified along with the local ones. 10 In Footnote 6 continued the standard epistemic view of vagueness [e.g., that borderline cases are cases of ignorance of the location of boundary of vague predicates, see Williamson (1994)) are inconsistent with the earlier characterisation of borderline cases because such theories plausibly imply that a judgment on borderline cases must be suspended. I take this to be a central problem of these views. For more details, see Moruzzi (2005), Wright (2016). 7 For a criticism on the alethic scope problem, see Dodd (2002Dodd ( , 2013, Sainsbury (1996), Horwich (1996. this paper, I will not take issue on the moderate/strong controversy. 11 The main point of this paper with respect the metaphysics of truth is that each property realising truth in a domain is sufficient to construct a relation realising disagreement in that domain. This point is independent of the question of whether or not there is a generic truth property (and a generic disagreement property).

Core principles for truth
In this section, I will formulate the four core principles for truth. These principles will be central to the core principles for disagreement that I will present in the next section.
The first two principles are normative principles for the attitudes of acceptance and rejection. Acceptance and rejection are not here understood as interdefinable (vs Frege-Geach conception Frege (1960), Geach (1965) but each has its own normative profile-i.e., its correctness conditions.
As for acceptance, the basic idea is that accepting a proposition <p> is, roughly, endorsing the truth of <p>: (Acceptance) Accepting <p> is correct if and only if <p> is true.
As for rejection, the basic idea is that rejecting <p> means, roughly, endorsing the untruth of <p>: (Rejection) Rejecting <p> is correct if and only if <p> is untrue. 12 The norms of acceptance and rejection involve two different concepts: the truth concept and the untruth concept. Once alethic pluralism is in place, because the property realising the truth concept is variable, it is variable also the property realising the untruth concept. This distinction allows for the possibility of logical pluralism: depending on the logic of the domain, the set of false propositions and the set of untrue propositions (i.e., the extensions of 'false' and of 'untrue') might coincide or diverge. 13 Acceptance and rejection are mutually exclusive but they do not necessarily exhaust the set of cognitive attitudes. There are also other cognitive attitudes, such as imagining, conjecturing, assuming, and, perhaps, 14 suspending judgement. In this paper, I will Footnote 10 continued (2000, 2001, 2004a, 2004b, 2006), determination pluralism (Edwards, 2011(Edwards, , 2013(Edwards, , 2018 and manifestation functionalism (Lynch, 2009) 11 Though my sympathies lie in the strong camp, see . 12 I ignore Lynch's the view that "prima facie" qualification for these principles (see Lynch's Norm of Belief (2009, p. 17)) is needed because I do not see which other considerations other than truth (untruth) might make it (correct) wrong to accept a proposition. Of course, extra-considerations might impact on whether or not one ought to accept a true proposition (consistency considerations might trump what is good to accept in a theory) or whether it is good to accept a proposition (a proposition so complex that to understand it you would waste all of your life and compromise your well-being). 13 In some domains, the untruth property will be identical to the property realising the falsity concept (e.g., domains where classical logic or intuitionistic logic hold), but in other domains the two properties might differ (e.g., if a para-complete logic is the correct logic; see Coliva and Moruzzi (2019)). 14 See Ferrari and Incurvati (2022). only deal with acceptance and rejection. If other cognitive attitudes have a role for disagreement, then the present framework will need some extension.
Acceptance and rejection are also involved in two other core principles, which are known in the literature under the label "transparency". According to transparency, to accept a proposition is to accept its truth and to reject it is to reject its truth: (Transparency) If a subject S possesses the concept of truth, then for S to accept (reject) <p> is to accept (reject) that <p> is true Lastly, the fourth core principle is the (in)famous equivalence schema: (Equivalence schema) p if and only if <p> is true Of course, a deflationist could object that the first three principles are not really basic principles for truth because they can be derived from the the equivalence schema together with minimal principles that make no use of the truth notion. 15 It is not the aim of this paper to argue against deflationism. For the sake of argument, we will assume truth-pluralism together with its package of core principles. 16

Diaphonic pluralism
In this section, I will introduce the pluralistic framework for disagreement.
Disagreement is here understood as a relationship between cognitive attitudes with certain contents. To be more precise, I will stipulate that disagreement as a relationship between cognitive mental attitudes of acceptance and rejection. I put forward this stipulation in a Carnapian spirit: as an explication of the ordinary notion of disagreement. I will thus ignore possible refinements of the notion of disagreement that involve non-cognitive attitudes. Whether or not it is possible to give a unified framework for the disagreement involving cognitive and non-cognitive attitudes is a question that lies outside the scope of this project. 17 Much of the literature in meta-ethics has dealt 15 They are: (Acceptance*) Accepting <p> is correct if and only if p.

(Rejection*)
Rejecting <p> is correct if and only if not-p.
If a non-classical setting is needed, then Rejection* must be modified (e.g., with a weak negation operator).
The equivalence schema provides the means to get the related norms. As for Transparency, it is a direct consequence of plugging in the equivalence schema into every attitude attribution (even if they are hyperintensional contexts, the idea is, plausibly, that the equivalence can be applied because it is a conceptual necessity). 16 For truth-pluralists' arguments against deflationism, see Wright (1992a), Lynch (2009). For a deflationist critique that the norm of acceptance is a core principle for truth, see Dodd (2013). 17 See Zeman (2020) for a minimal definition of disagreement that is intended to capture also non-cognitive attitudes. Zeman addresses the literature on disagreement in the philosophy of language, trying to build a minimal definition that is compatible with the different theories of disagreement that are offered in the recent philosophy of language. Let me spend a few words on Zeman's project. First, Zeman addresses a potentially different topic than the present project. In fact, Zeman intends to provide a definition that is compatible with all of the definitions of disagreement that have been developed in the recent literature that deals with (putative) linguistic data on disagreement. These theories try to provide, by means of semantic and pragmatic tools, a definition of disagreement that can account for these data. In contrast, my project with the question of whether the ethical discourse can be analysed as only involving cognitive attitudes. It is fair to say that if it turns out that a non-cognitive analysis is needed for the ethical discourse (or for other domains), then the present proposal will be severely limited in its scope. The present project assumes the maxim of methodological conservatism: it can thus be seen as tool for testing how far cognitivism can go in analysing different areas of discourse. 18 Following the two-stage analysis, we can split the question about the nature of disagreement into two questions: (Concept of Disagreement) What is the concept of disagreement? (Metaphysics of Disagreement) What is the relation of disagreement?
As in the case of truth, we answer these questions accordingly: First stage A set of core principles for the concept of disagreement (Diaphonic Principles) is identified such that it provides a network analysis of the disagreement concept; Second stage A case is made for the thesis that the disagreement-concept determines different realisers in different domains (i.e., the disagreement relations).
In the following sections, I will address both stages in that order.

Diaphonic principles
To address the first stage, I will offer a network analysis of disagreement by stating three core principles for the concept of cognitive disagreement (diaphonic principles). My claim is that these principles implicitly define the concept of disagreement by relating it to other notions. The first diaphonic principle intends to capture the central thought that disagreement involves incompatibility between the correctness of attitudes. In other words, when disagreement occurs, it is excluded that the attitudes involved can be jointly correct: 19 Incompatibility If the relation of disagreement obtains between two cognitive attitudes (of acceptance or rejection), then the attitudes cannot be jointly correct.
The second diaphonic principle connects disagreement to error-attribution. The basic idea is that when we disagree, we ought to think that some error is involved. In this sense, disagreement involves a dimension of objectivity. However, this dimension finds its motivations in the scope problems. It is unclear whether these scope problems amount just to linguistic data. I am sceptical about this latter idea because I think that linguistic data about speech acts are much more coarse grained than intuitions about attitudes (i.e., the question of whether it is correct to accept that something involves less complications than the question of whether it is correct to assert that something). Second, the problem with Zeman's interesting proposal is that it seems to be too schematic to have some substantial content. However, whether or not Zeman's proposal is defensible is independent from the present proposal. If it turned out that Zeman's proposal succeeds, then diaphonic pluralism could be seen as a specification of Zeman's schema in relation to cognitive attitudes. 18 In the same spirit of Wright (1992b).
is minimal because we are here liberal with respect to the kind of error that is involved in disagreements-the dimension of error could in principle vary. 20 Error If the cognitive attitudes of two subjects are in disagreement, then it is correct for the subjects to accept that there is some error involved.
The third diaphonic principle connects disagreement to the attitude of taking an adversarial stance towards the subject that we disagree with. More precisely, the principle states that we are justified to attribute error to those that we justifiably think are in disagreement with us: Opposition If subject A has a justification for having a cognitive attitude towards <p> and she has a justification for accepting that she is in disagreement with subject B in relation to B's cognitive attitude towards <q>, then, ceteris absentibus, A has a justification for accepting that B's cognitive attitude towards <q> is incorrect.
Notice that the qualification "ceteris absentibus" is meant to ensure that disturbing factors are absent. These disturbing factors include cases such as A has justification for thinking that they are an expert or that A and B are peers. 21 I put forward the claim that Incompatibility, Error, and Opposition together provide a network analysis for a minimal concept of (cognitive) disagreement.

Conceptual dependence
In this section, I argue that disagreement conceptually depends on truth:

Conceptual Dependence
The concept of disagreement conceptually depends on the concept of truth.
The notion of conceptual dependence is articulated by means of the mechanism of network analysis: each diaphonic principle conceptually depends on some core principles for truth. In general terms, a core principle C P 1 conceptually depends on another C P 2 just in case: 2. or there is a deductive argument for C P 2 such that (a) the argument employs C P 1 as a principle; (b) this deductive argument constitutes the canonical justification for accepting the former core principle.
The notion of canonical justification is roughly that of an argument that follows the logical form of the claim to be justified (see Dummett's notion of normal Dummett (1975)).
If a core principle is either presupposed or it occurs in a canonical justification for another core principle, then I say that the former core principle constitutes the canonical grounds for the latter.
My claim is thus that the canonical grounds for accepting the diaphonic core principles involve alethic core principles. Once these dependence relations are in place, we can distinguish between primary and secondary core principles: the diaphonic principles (Incompatibility, Error and Opposition) are secondary core principles because they conceptually presuppose the primary core alethic principles, which in turn functionally define the truth concept.
In the following, I will thus offer the arguments that are meant to show that the canonical grounds for each diaphonic principle involve alethic core principles.

Incompatibility's dependence
As for the first diaphonic principle (i.e., Incompatibility), the argument is quite trivial. Incompatibility invokes the notion of correctness of acceptance and of rejection. By Acceptance, accepting <p> is correct if and only if <p> is true. By rejection, rejecting <p> is correct if and only if <p> is untrue. Incompatibility presupposes thus the concepts of truth and untruth, and thus Rejection and Acceptance are the canonical grounds for Incompatibility.

Error's dependence
As for the second diaphonic principle (i.e., Error), the canonical grounds are shown by the following argument: 22 23 The argument for Error is thus based on two primary core principles for truth (Equivalence Schema and Acceptance), a secondary core principle for disagreement (Incompatibility) and an analytic principle on error. 1 (1) A's cognitive attitude towards <p> and B's cognitive attitude towards <q> are in disagreement.
(Assumption) 1 (2) The correctness of A's cognitive attitude towards <p> precludes the correctness of B's cognitive attitude towards <q>.
(Core principle connecting correctness to error) 1,3 (6) It is correct to accept that either A is in error or B is in error.
1,3 (7) If A's cognitive attitude towards <p> and B's cognitive attitude towards <q> are in disagreement, then it is correct to accept that either A or B is in error.

Opposition's dependence
The third secondary core principle for disagreement (i.e., Opposition) has the most complicated argument for showing its canonical grounds.

(1)
A has a justification for accepting <p>.
2 (2) A has justification for accepting <A's cognitive attitude towards <p> and B's cognitive attitude towards <q> are in disagreement>. (Assumption)

(3)
A has justification for accepting <A's attitude towards <p> and B's attitude towards <q> cannot be both correct >.

(5)
A has a justification for accepting that accepting <p> is correct.
(Acceptance and closure of justification under conceptual entailment: 4) 1 (5*) A has a justification for the truth of <accepting <p> is correct>. (PDJA:5) The step from (5) to (5*) relies on the following principle: Propositional/Doxastic Justification for Acceptance (PDJA) If subject A has a justification for accepting that accepting <p> is correct, then A has justification for the truth of <accepting that <p> is correct>.
The motivation for PDJA lies in the link between propositional and doxastic justification. 24 A doxastic justification for having a cognitive attitude for <p> involves 24 Following Volpe (2017), we can define propositional and doxastic justification in the following way: Propositional justification The sort of justification that proposition enjoys for an agent when the agent is epistemically justified to believe it; a propositional justification for the proposition that <p> has the truth-value that is required by the satisfaction of the correctness conditions of the cognitive attitude. 25 Once PDJA is in place, the argument can continue: A has a justification for <accepting <p> is correct>. (Equivalence Schema: 5*) Now, absent any further consideration concerning B, from the mere fact that A has a justification for the correctness of accepting <p> (i.e., (6)) and from the fact that A has a justification for thinking that A and B cannot be both correct (i.e., (3)), it follows that: An analogous conclusion can be reached with an analogous reasoning for the attitude of rejection: A has a justification for rejecting <p>.
(Assumption) 1+, 2 (10) If A has justification for rejecting <p> and A has justification for accepting <A's cognitive attitude towards <p> and B's cognitive attitude towards <q> are in disagreement>, then, ceteris absentibus, A has a justification for accepting <B's cognitive attitude towards <q> is incorrect>.
(Conjunction introduction and Conditional introduction: 9, 2, 7) Doxastic justification An agent's cognitive attitude is doxastically justified just in case (i) it is a cognitive attitude in a proposition that is propositionally justified for the agent and (ii) it is held on the basis of that which propositionally justifies its content. 25 The doxastic/propositional link with respect to acceptance and rejection is expressed by the following principles: PDJA Acceptance: A doxastic justification for accepting <p> amounts to a propositional justification for the truth of <p> because truth is required for the correctness of acceptance. PDJA Rejection: A doxastic justification for rejecting <p> amounts to a propositional justification for the untruth of <p> because untruth is required for correctness of rejection.
Assuming that acceptance and rejection are the only cognitive attitudes involved, then from 8 and 10 we can conclude Opposition: 1,2,1+ (11) If A has a justification for having a cognitive attitude towards <p> and A has a justification for the proposition that she is in disagreement with B in relation to B's cognitive attitude towards <q>, then, ceteris absentibus, A has a justification for accepting <B's cognitive attitude towards <q> is incorrect>. (8,10) The upshot of the argument is that Opposition is a secondary core principle because it conceptually depends on two core principles for truth: Equivalence Schema and Incompatibility (where Incompatibility in turn conceptually depends on Acceptance, Rejection and Equivalence Schema). 26

Metaphysical encapsulation
I now turn to the second stage of the analysis of disagreement, which is its metaphysics. In analogy to the claim of conceptual dependence, I want to put forward a claim about the relation between the metaphysics of truth and the metaphysics of disagreement. The basic idea is that once a property realises truth in a given domain, then this property is sufficient to construct the relationship that realises disagreement in that domain.
Let us say that a property P is encapsulated in another property Q just in case the property P is a component of the (complex) property Q. Standard examples of metaphysical encapsulation can be found (for example) in disjunctive properties (e.g., the property of being a man is encapsulated in the property of being either a man or a cheese). But we also have encapsulation without recurring to logical properties (e.g., the property of being a man is encapsulated in the property of being a married man).
My thesis is than then that truth is encapsulated in disagreement. More precisely: if T is a property playing the truth-role in a domain and R is a property playing the disagreement role in that domain, then T is encapsulated in R.
How then should we argue for metaphysical encapsulation in a pluralist framework? My take is that a justification for metaphysical encapsulation lies in the structure of the two-stage analysis: conceptual dependence is sufficient for having metaphysical encapsulation. This idea is expressed by the following general conjecture about the relationship between conceptual dependence and metaphysical encapsulation: Cascade Dependence When two sets of core principles S1 and S2, respectively, define two concepts C1 and C2 by means of a network analysis, then if C1 conceptually depends on C2 and they both refer, then a property realising C2 is metaphysically encapsulated in the property/relation realising C1.
Several remarks are in order to clarify Cascade Dependence. First, the principle is limited to those concepts admitting a network analysis. On the supposition that some concepts escape this analysis, then their metaphysics would not be subject to this principle. Such a case would be provided by several explanatory primitive concepts; that is, concepts that cannot be explained or elucidated because their grasp is required by any other concepts, but not vice versa. Second, the principle covers only those concepts that both refer. We exclude cases here such as the concepts of witch and of magic (which plausibly fail both to refer) and such as the concepts of phlogiston and combustion (where the former does not refer).
If we apply Cascade Dependence to the network analysis for disagreement and truth, then we get the relevant cascade dependence principle for these notions:

Disagreement-Truth Cascade Dependence
If the concept of disagreement conceptually depends on the concept of truth and they both refer, then a property realising truth in domain D is metaphysically encapsulated in a relation realising disagreement in D.
Given that we have established that the concept of disagreement depends on the concept of truth, then we can detach 27 the consequent of Disagreement-Truth Cascade Dependence and thus obtain the following conjecture of truth-disagreement metaphysical encapsulation:

Disagreement-Truth Metaphysical Encapsulation A property realising truth in
domain D is metaphysically encapsulated in a relation realising disagreement in D.
Disagreement-Truth Metaphysical Encapsulation says that any truth realiser is an ingredient of the disagreement realiser.
Can the Disagreement-Truth Metaphysical Encapsulation be vindicated? I must confess, I do not have any clue for finding a general argument that is capable of vindicating this principle in its full generality. I will therefore confine the justification of Disagreement-Truth Metaphysical Encapsulation by means of a piecemeal strategy: I will offer two examples related to two domains (mathematics and basic taste) in which I argue that the truth-potent property which plays the truth role in each domain is an ingredient of a relation that realises the diaphonic principles in that domain. Moreover, these examples show that there is somehow a common pattern in the argument. Such common pattern provides indirect evidence that the general conjecture is true.
Before moving on, a clarification is in order. Should I not vindicate Disagreement-Truth Cascade Dependence to vindicate Truth-Disagreement Metaphysical Encapsulation? After all, given that a justification for the antecedent of Disagreement-Truth Cascade Dependence has been acquired, providing a justification for Disagreement-Truth Cascade Dependence would make available, via closure, a justification for Truth-Disagreement Metaphysical Encapsulation. So why not proceed along this deductive line instead of concentrating on particular domains? Of course, this deductive strategy is perfectly acceptable, but it is a strategy that is hard to implement because Disagreement-Truth Cascade Dependence is a very complicated conjecture 27 The detachment is allowed on the further condition that concepts of truth and disagreement refer. An alethic nihilist Liggins (2019) would thus be untouched by this principle because she holds that truth is empty. By the same token, someone holding that the disagreement concept fails to refer (a diaphonic nihilist) would be equally unmoved by the cascade principle. to prove. I will thus adopt a sort of inductive strategy: by providing evidence for the truth of instances of Disagreement-Truth Metaphysical Encapsulation, I will (abductively) corroborate the Disagreement-Truth Cascade Dependence conjecture and thus, retrospectively, also the Disagreement-Truth Cascade Dependence conjecture. Of course, the evidence thus offered will be insufficient to prove Disagreement-Truth Metaphysical Encapsulation (and to a even lesser extent Disagreement-Truth Cascade Dependence!), but because we are all reasonable fallibilists, I hope that we are happy to accept these epistemic limitations.

Disagreement in basic arithmetic
The first case involves the domain of basic arithmetic: namely, the arithmetical truths encompassed by Peano axioms. Which property realises truth in such a domain? Of course, there has been and there is still ample debate on which understanding of arithmetical truth is correct. It is not the aim of this paper to embark on an argument in the philosophy of mathematics. However, assuming that the arithmetical domain is truth-apt, then there must be a property that realises truth in this domain. We need arguments from the philosophy of mathematics to discover which the property is. Let us then bracket this controversy and let us assume, for the sake of the argument, that truth in basic arithmetic is realised by a coherence property. I will now employ this assumption to illustrate how Disagreement-Truth Metaphysical Encapsulation can be vindicated in a domain where such a truth-property operates. Whether or not there are reasons to think that coherence is the right truth property for arithmetic is immaterial for this point.
I will understand here coherence as syntactic derivability from the Peano axioms. The assumption is thus that this property is the truth realiser in the domain of basic arithmetic. Crispin Wright effectively illustrates how this assumption can be understood: How is coherence here to be understood? Intuitively all the significant statements of first-order number theory fall into one of two classes: a simple-arithmetical base class whose members draw on no expressive resources save the numerals, the expressions for addition, multiplication and identity, and expressions for other operations which may be (recursively) defined in terms of those notions; and a remainder, each of which can be formed by (iterated) introductions of the logical constants into sentences of the base class in accordance with the standard first-order formation rules. From a classical point of view, it is quite intuitive that the truth value of every first-order pure arithmetical sentence supervenes upon the truth values of sentences in the base class: specifically, determine the truth value of each of the latter and you have implicitly settled the truth value of every pure arithmetical thought which may be expressed at first-order. (The crucial point, of course, is that simple arithmetic has the resources to name every element in the domain of quantification of full first-order arithmetic.) A natural version of truth as coherence, which should be attractive to those of broadly formalist disposition, simply follows through on this intuition, characterising the coherence of simple-arithmetical sentences in terms of their syntactic derivability from ingredients in B, and that of the remainder in accordance with the sort of recursive clauses familiar from standard truth theories (Wright, 1998, p.69).
We can express this assumption with the following principle:

Arithmetical Truth
The truth of an arithmetical proposition is realised by the syntactic derivability from the set of basic arithmetical truths B given by the Peano Axioms.
The thesis that I want to argue now is that Arithmetical Truth suffices to construct a disagreement-realiser relation in the domain of basic arithmetic.
Which relation can be the realiser for disagreement in arithmetic? To answer this question, I put forward an example of disagreement that could arise in this area of thought.
Suppose that Greta is in disagreement with Saul in relation to the proposition that 68 + 57 = 125 (let us call this latter proposition K). Greta thinks that K is true and, hence, she accepts K. Meanwhile, Saul thinks that K is untrue and, hence, he rejects K. If Greta and Saul disagree, then the first diaphonic principle (i.e., Incompatibility) entails that the correctness of Greta's acceptance of K is incompatible with the correctness of Saul's rejection of K. Hence, the truth of K is incompatible with the untruth of K. Given that the truth of K amounts to its syntactic derivability of 'K' from B and the untruth of K amounts to the lack of syntactic derivability of 'K' from B, then Greta's disagreement with Saul about K involves the (obvious) incompatibility of the requirements of the syntactic derivability of 'K' and the lack of the syntactic derivability of 'K' from B. This is for a disagreement involved by the attitudes of acceptance and rejection.
Let us slightly change the example to consider a case of a disagreement between two attitudes of acceptance: not only does Saul reject K but he also accepts that it not the case that 68 + 57 = 125 (let us call this latter proposition not-K). Greta thinks that K is true and, hence, she accepts K. Meanwhile, Saul thinks that K is false and, hence, he accepts not-K. If Greta and Saul disagree, then the first diaphonic principle (i.e., Incompatibility) entails that the correctness of Greta's acceptance of K is incompatible with the correctness of Saul's acceptance of not-K. Hence, the truth of K is incompatible with the falsity of K. Given that the truth of K amounts to its syntactic derivability of 'K' from B and the falsity of K amounts to the syntactic derivability of 'not-K' from B, then Greta's disagreement with Saul about K involves the incompatibility of the requirements of the syntactic derivability of 'K' and the the syntactic derivability of 'not-K' from B.
An analogous example could be constructed for a case disagreement involving two attitudes of rejection (e.g., Greta rejecting not-K and Saul rejecting K), and a case disagreement involving one attitude of rejection and one of acceptance (e.g., Greta accepting K and Saul rejecting K).
Given that there are arithmetical statements which are unprovable in a formal system from B, these different cases of disagreement require conditions of incompatibility that impose sensibly different conditions. It is an interesting project to explore these differences. For example, does rejecting and accepting a statement S that is unprovable in a formal system involve disagreement if truth is coherence? I will here simplify the issue for the sake of the argument: I will identify untruth with falsity and rejection with acceptance of a negated proposition. An important further step of my project is to also cover these cases. Once these simplifying assumptions are in play, we can generalise from the second example by putting forward the thesis that the disagreement relation in Arithmetical Disagreement is realised by the relation of not being mutually derivable from B: 28 Arithmetical Disagreement A has a cognitive attitude towards <p> and B has a cognitive attitude towards <q>, and 'p' and 'q' are not both syntactically derivable from B (where 'p' expresses <p> and 'q' expresses <q>).
Before moving on, I need to make a important remark. 29 Notice that the relation expressed by Arithmetical Disagreement can be claimed to be the realiser of the disagreement relation only if we make the simplifying assumptions mentioned before. Without those assumptions, we have to cover three cases instead of one: 1. disagreement with two acceptances, in this case the relation would be: Arithmetical Disagreement* A accepts <p> and B accepts <q>, and it is not both the case that 'p' is syntactically derivable from B and that 'q' is. (where 'p' expresses <p> and 'q' expresses <q>) 2. disagreement with one acceptance and one rejection, in this case the relation would be: Arithmetical Disagreement** A accepts <p> and B rejects <q>, and it is not both the case that 'p' is syntactically derivable from B and that 'q' is not. (where 'p' expresses <p> and 'q' expresses <q>) 3. disagreement with two rejections, in this case the relation would be: Arithmetical Disagreement*** A rejects <p> and B rejects <q>, and it is not both the case that 'p' is not syntactically derivable from B and that 'q' is not. (where 'p' expresses <p> and 'q' expresses <q>) The claim is thus that, in the most general case, these three relations jointly realise disagreement in the domain of basic arithmetic given Arithmetical Truth. However, it is fair to anticipate that my following arguments do not cover the general case because they are only meant to vindicate Arithmetical Disagreement*. For ease of exposition, I will limit to this case, although I think that extra arguments for the general case can be given. If the reader is deeply unsatisfied by this limitation, then I invite them to think of my framework as non-bilateralist and thus having only the acceptance norm as a fundamental.
Let us move now to the claim that Arithmetical Disagreement is the right relation realising disagreement in the domain of basic arithmetic. For the relation expressed by Arithmetical Disagreement to count as a disagreement relation, it must satisfy the three diaphonic principles (i.e., Incompatibility, Error and Opposition). I think that it can be shown that Arithmetical Disagreement satisfies these principles. In the following, 28 Assuming that basic arithmetic is consistent. 29 My thanks go to Julia Nennstiel for having pointed my attention to this issue. I argue that this is the case for the first two diaphonic principles. I leave the longer argument for the third diaphonic principle in the appendix (Sect. A).
As for Incompatibility, Arithmetical Disagreement trivially satisfies Incompatibility because the relation playing the disagreement-role in the arithmetical domain has been crafted out from that principle.
Let us now turn to Error. If Greta is in disagreement with Saul regarding K, then does Arithmetical Disagreement account for the normative requirement that it is correct to accept that one is in error?
Suppose that Greta is in disagreement with Saul because Greta accepts K, whereas Saul accepts not-K (the antecedent of Error). By Arithmetical Disagreement, it follows that "K" and "not-K" are not both syntactically derivable from B. "K" and "not-K" are not both syntactically derivable from B (Consistency of Arithmetic). So <"K" and "not-K" are not both syntactically derivable from B> is true, by Equivalence Schema. It is then correct to accept that "not-K" and "K" are not both syntactically derivable from B (Acceptance). By applying a minimal notion of error, we can say that a subject is in error when they have an incorrect cognitive attitude. Thus, accepting that one is in error amounts to accepting that either Greta's acceptance of K or Saul's acceptance of not-K is incorrect. But accepting that either Greta's acceptance of K or Saul's acceptance of not-K is incorrect involves accepting that "not-K" and "K" are not both syntactically derivable from B (otherwise they would be both correct!). Now note that accepting that "not-K" and "K" are not both syntactically derivable from B is correct (by the consistency of arithmetic). Thus, it is correct to accept that some error is involved (the consequent of Error).
In summary, we have inferred the consequent of Incompatibility by assuming its antecedent and by implementing the Arithmetical Disagreement relation. This shows that the Arithmetical Disagreement relation satisfies Error.
The conclusion of this section is thus that once we have a truth-property that realises truth in the domain of basic arithmetic (consistency), then we can construct a relation (Arithmetical Disagreement) that validates the disagreement principles and hence is a good candidate for realising the disagreement relation in this domain. 30 30 It could be objected that Arithmetical Disagreement cannot be the relation realising disagreement in basic arithmetic because it qualifies the following situation as a case of disagreement. Greta accepts that 2+2=4 and Saul that 0+0=1. Since these propositions cannot be both syntactically derivable from B, they satisfy the putative disagreement relation. But of course they are not in disagreement! Or so the objector claims (thanks to Christian Nimtz for this objection). My simple reply is that they are in disagreement. The reason is simple: they make incompatible requests on (mathematical) reality, hence their doxastic states represent the world in incompatible ways. This is is sufficient for me to count as disagreement. Maybe they do not realise this fact and they do not behave as if they were involved in a controversy, but this is Footnote 30 continued perfectly fine: it is not always easy to know when we disagree! To make the point clearer, it might worth remembering the distinction between disagreement as a state and disagreement as an activity (Cappelen & Hawthorne, 2009, pp. 60-61). Note that I only address the notion of disagreement as a state. Moreover, the disagreement as an activity is plausibly dependent on the notion of disagreement as a state (MacFarlane, 2014, pp. 119-120).

Disagreement in basic taste
Let us now consider a very different case from the domain of basic arithmetic: the domain of basic taste. Which property realises truth in such a domain? Of course, there has been and there is still ample debate on which understanding of truth for basic taste is correct. 31 It is not the aim of this paper to embark in an argument of the philosophy of basic taste, but again assuming that this domain is truth-apt, then there must be a property that realises truth in this domain. We need arguments from the philosophy of basic taste to discover which the property is. However, let us bracket this controversy and let us assume, for the sake of the argument, that truth in basic arithmetic is realised by a deflationary property. 32 As in the previous section, I will now employ this assumption to illustrate how Disagreement-Truth Metaphysical Encapsulation can be vindicated in a domain where such truth-property operates. Again, the question of whether or not there are reasons to think that the deflationary truth property is the right truth property for arithmetic is immaterial for this point.
If the truth property is deflationary, then to be true for a basic taste the proposition is instantiating an insubstantial property. 33 I take that for a truth property to be insubstantial, then it means that at least that truth has no nature (no constitution theory is available) and that truth plays no explanatory role in relation to basic taste. 34 Let us then assume that the property playing the truth-role in the domain of basic taste is the deflationary property understood in the aforementioned sense. We can then express the truth-property in the domain of basic taste as follows: Basic Taste Truth The truth of a basic taste propositions is realised by the insubstantial property of just satisfying the equivalence schema (where insubstantiality requires no constitution theory and no explanatory role).
In analogy with the previous section, the thesis that I want to argue here is that Basic Taste Truth suffices for constructing a disagreement-realiser relation in the domain of basic taste. Which relation can be the realiser for disagreement for basic taste? I find it also useful in this case to put forward an example of disagreement that could arise in this area of thought.
Suppose that Greta is in disagreement with what Saul in relation to a simple basic taste statement, such as "Sushi is delicious" (let us assume that this statement expresses the proposition that sushi is delicious, call it S). According to Greta, S is true whereas 31 See the recent surge of relativism exemplified in its most sophisticated form by the work of John MacFarlane (2014). 32 The view is defended in , 2020. See Wright (2006) for a proposal using the property of superassertibility. See also Wright (2021). 33   argue that truth in the basic taste domain is normatively inert. To get full deflationism, all the deflationary challenges must be blocked. 34 See Wyatt (2016). A proper characterisation of alethic deflationism is by no means easy. In fact, alethic deflationism is the sum of specific theses independent of each other. See Eklund (2017) for a critical assessment of this point. Although this characterisation problem is difficult, I think that by following principles it is possible capture to a decent level of precision monistic alethic deflationism. First, alethic deflationism includes an minimal alethic theory that is given by the propositions expressing the non-paradoxical instances of the equivalence schema: Saul rejects S as false (and thus he accepts that not-S is true). 35 Given Incompatibility, the correctness of Greta's acceptance of S precludes the correctness Saul's acceptance of not-S. By Acceptance, the correctness of Greta's acceptance of S is incompatible with the truth of not-S. Now, given that the truth of S is insubstantial, Greta's disagreement with Saul about S involves the incompatibility of S'truth with the truth of not-S, and the latter condition amounts, by basic logic and Equivalence Schema, to the fact that it is not the case that S and not-S. To disagree as to whether or not S is true or false involves the untruth of the <S and not-S>.
More generally, deflationism seems to involve a form of simple propositional account of disagreement: the realiser for disagreement for deflationary truth amounts simply to an incompatibility between the contents of the attitudes of the agents: Basic Taste Disagreement Subject A has a cognitive attitude towards <p> and B has a cognitive attitude towards <q> and <p> and <q> cannot be both true.
According to Basic Taste Disagreement, the deflationist realisation of disagreement is just having cognitive attitudes whose contents cannot jointly have a certain truth-value. Given a deflationary understanding of fact (p iff it is a fact that p, ( (Horwich, 2010), p. 282)), disagreement is just having conflicting cognitive attitudes towards propositions that cannot jointly represent facts.
Again, for the relation expressed by Basic Taste Disagreement to count as a disagreement relation, it must satisfy the three diaphonic principles (i.e., Incompatibility, Error and Opposition). It can be shown that Basic Taste Disagreement satisfies these principles. In the following, I argue that this is the case for the first two diaphonic principles, and I leave the longer argument for the third diaphonic principle in the appendix (Sect. B).
Equivalence Schema <p> is true if and only if p Now, crucially, the minimalist alethic theory is coupled with a minimalist alethic conception (Horwich, 1998) that can be expressed by the following principles (this reconstruction is a joint work with Filippo Ferrari): Function Truth has an important expressive function for generalisations and so on. Exhaustion A full grasp of the ordinary concept of truth requires nothing more than our ordinary disposition to accept all non-pathological instances of the Equivalence Schema. Truth-aptness Every domain of (assertoric) discourse is truth-apt. Existence There is a genuine truth property that applies to propositions. Uniqueness There is only one truth property. Translucency For any truth property t, t's nature is fully revealed by a grasp of the ordinary concept of truth.
The latter five principles taken together entail what is generally conceived as the core metaphysical tenet of alethic deflationism: Insubstantiality Truth's nature is metaphysically insubstantial.
The integration of a deflationary theory in a pluralistic framework requires substantial revision. First, Exhaustion must be revised because the Equivalence Schema is not the only core alethic principle. Second, Uniqueness must be abandoned because there is more than one truth property. Third, Translucency must also be rejected because it cannot read off from the truth-concept alone which property plays the truth role in a given domain of enquiry. Which alethic pluralist frameworks allow the integration of deflationary truth property is an interesting question that cannot be dealt with in this paper, see . 35 I here operate with the same simplifying assumptions that were stated in the previous section (i.e., untruth is equated to falsity and rejection is equated to acceptance of a negated proposition).
As for Incompatibility, Basic Taste Disagreement trivially satisfies Incompatibility because the Basic Taste Disagreement-relation has been crafted out from that principle.
Let us now turn to Error. If Greta is in disagreement with Saul on S, then does Basic Taste Disagreement account for the normative requirement that it is correct to believe that one is in error? Let us employ again a minimal notion of error according to which a subject is error when she has an incorrect cognitive attitude. Given that Greta accepts S, Acceptance requires that her attitude is correct only if S is true. Whereas given Saul accepts not-S, Acceptance requires that his attitude is correct only if not-S is true. By hypothesis, the truth-property in the domain of S is the insubstantial property satisfying no more than the equivalence schema Equivalence Schema (i.e., Basic Taste Truth). Thus, accepting that one is in error amounts to accepting that S and not-S are not both true, which in turns amounts to the accepting the falsity of <S and not-S>. By Basic Taste Disagreement, the disagreement between Greta and Saul on S entails that S and not-S are not both true. Assuming that no contradiction is true in the basic taste domain, 36 we have that disagreement logically entails that one is error, and so Error is vindicated.
Summing up, as in the previous section, we have inferred the consequent of Incompatibility by assuming its antecedent and by implementing the local relation of disagreement (i.e., Basic Taste Disagreement). This shows that the Basic Taste Disagreement relation satisfies Error.
The conclusion of this section is thus that once we have a truth-property that realises truth in the domain of basic taste (deflationary truth), then we can construct a relation (Basic Taste Disagreement) that validates the disagreement principles and hence is a good candidate for realising the disagreement relation in this domain.
Let us take stock. I have argued that in two domains, once a local truth property is identified, we can construct the local realisers of the disagreement relation. My conjecture is that this work can be done in all other domains. Thus, once we fix the property playing the truth-role, we thereby also fix the relation playing the disagreement role.

Objections
In this section, I consider two objections that identify, I believe, two critical points for this project. I hope that my answers to each of the objections can shed light on the prospects for diaphonic pluralism.

The normative significance objection
It could objected that Diaphonic Pluralism does not address the Normative Scope problem. Even granting Conceptual Dependence and Disagreement-Truth Metaphysical Encapsulation, why would this architecture shed light on the normative differences of disagreement that we witness in the different domains of enquiry?
Let us call this objection the Normative Significance Objection. The gist of this objection comes, I believe, from the following considerations. The error involved in a disagreement on whether <68+57=125> is true involves a fault that is hardly present in the case of a disagreement on the truth that <sushi is delicious> (some philosophers hold that here we have a faultless disagreement!). So, what difference could make the different realisers of the truth property for the normative differences in the kind of disagreement mentioned above?

Reply to the normative significance objection
To answer the Normative Significance Objection, I think that it is useful to expand on the deflationary story that I have sketched previously in relation to a disagreement about basic taste. The story goes as follows. When two subjects disagree that <sushi is tasty>, then one accepts <sushi is tasty> and the other one accepts that <sushi is not tasty>. If it is not the case that sushi is both tasty and not-tasty, then what does the error amount to here? The deflationary answer is simple: the error is just the fact that, granting that contradictions are not true, the two attitudes make, taken together, contradictory demands on the world. Notice that no feature of the truthproperty contributes to the explanation of this fact (i.e., truth is explanatory inert).
Provided that contradictory demands on the world cannot be met, 37 the joint correctness of the attitudes is thus excluded. Hence, one attitude must be incorrect. By employing a minimal notion of error, a subject is error when they have an incorrect cognitive attitude. Hence, one is in error. Notice again that truth plays no explanatory role here: just logical facts plus correctness conditions explain why an error is involved.
The shallow fact, say, that sushi is tasty does not make the error of accepting the contrary a substantial error. The existence of an error is just based on the (thin) logical fact that <p> and <not-p> cannot be both true (provided that dialetheism is ruled out) and on the nature of the attitudes (what counts for them to be correct). 38 Compare the latter point with the well-known deflationary point on truth: the shallow fact that sushi is tasty does not make the truth of <sushi is tasty> substantial (as if there were a correspondence relation satisfied).
So what about the putative difference in the nature of an error between the domain of basic arithmetic and the domain of basic taste? Crispin Wright (Wright, 2001(Wright, , 1992a has famously formulated the principle of Cognitive Command to account for two types of error: representational error and non-representational error: Cognitive Command it is a priori that differences of opinion on one and the same state of affairs are explainable only in terms of (i.) different information of the disputants, (ii.) unsuitable conditions, or (iii.) malfunction in reasoning (Wright, 1992a, pp. 92-93). 37 A deflationist approach to basic taste is therefore incompatible with a dialetheist approach. For the the prospects of the dialetheist approach to subjective matters see Coliva and Moruzzi (2019), where it is argued that a dialetheist has troubles with the normativity of disagreement that cannot be easily avoided unless strong concessions (logical pluralism plus local trivialism). 38 For this train of thought, see Wright (2021b).
Cognitive Command is a criterion for deciding whether or not a domain is representational. 39 If Cognitive Command fails, then an error is not representational. Now the thought is that differences in the kind of error involve differences in the normative profile of the proposition, thus giving rise to a pluralism about the normative profile of propositions: Normative Alethic Pluralism (Ferrari, 2016(Ferrari, , 2018(Ferrari, , 2021: taking truth to function as the main norm governing enquiry, the normative strength with which truth constrains enquiry varies. A subject can make an error in many different ways. Making an error can vary from a robust function "fraught with ought" to a rather weak function of "mere correctness", depending on which normative dimensions of truth are operative with respect to a given proposition. 40 The doctrine of Normative Alethic Pluralism is in principle independent from alethic pluralism. However, an alethic pluralist naturally understands the normative variability as rooted in metaphysical and epistemological features of a domain-the same features that select which truth-potent property is operative are those that ground the differences in normativity. It remains, of course, an open question as to whether and how it can be shown that Normative Alethic Pluralism is rooted in the metaphysical and epistemological features of domains.

The normative inflation objection
This is a more local objection given that it applies to the example that I have provided for the domain of basic taste. In Sect. 10, I conjectured that the domain of basic taste requires a deflated truth-property. Among the conditions for being deflated, it must be the case that the truth-property is normatively inert. 41 However, two out of four of the alethic core principles have normative significance (Acceptance and Rejection). Hence, the truth property for the basic taste domain, provided that it satisfies the core principles, cannot be normatively inert.

Reply to the normative inflation objection
The ground for the normative inertia of a local deflationary property for basic taste has to be found in the failure of the potential different in extensionality between truth and justification for basic taste [for further details, see ]. The normative principles that belong to the set core alethic principles do not exert any normative force for a truth-realiser in the domain of basic taste because they are very thin platitudes compatible with deflationism (Wright, 2021). 39 For a discourse to be representational, it has to have assertions aiming "to produce mirrors, in thought or language, of the state of affairs with which the discourse distinctively deals" (Wright, 1992a, p. 92.) 40 Ferrari states three basic different normative forces (Ferrari, 2016(Ferrari, , 2018: deontic (a subject ought to judge that p (if and) only if p is true), axiological (it is valuable (good) to judge that p (if and) only if p is true) and criterial (it is correct (fitting) to judge that p (if and) only if p is true). 41 Wright's inflationary argument (Wright, 1992a) was meant to jeopardise deflationism exactly on this point.

Conclusion
In this paper, I have articulated a pluralistic framework for disagreement: diaphonic pluralism. More specifically, I first provided an argument for the dependence of the concept of disagreement on the concept of truth. Second, I formulated the conjecture (i.e., Disagreement-Truth Metaphysical Encapsulation) that a property realising truth in a domain suffices to construct a relationship realising disagreement in that domain. Third, I provided two examples relative to the domain arithmetic and of basic taste as evidence for this conjecture. Fourth, I addressed two objections: the first related to the question of how to account for different kinds of error, and the second related to the question of how to integrate a local deflationary truth property in a pluralist framework.
Diaphonic pluralism offers a unified framework to account for the differences in variety of (cognitive) disagreements that we witness in relation to the different areas of discourse. Moreover, this framework is built on the basis on alethic pluralism, thus offering an integrated and compact framework to address questions about the nature of truth and disagreement.
Let me conclude with two general points on what this paper has shown in relation to the debate on pluralism.
First, a corollary of this paper is that it shows something that I believe is significant about the commitments of truth pluralists: if my line of argument is sound, then truth pluralists are committed to pluralism about disagreement. Just like pluralism about truth, pluralism about disagreement is a substantial thesis. Consequently, the moral is that pluralism is, at least, a package of theses including truth and disagreement.
Second, whether or not we can stabilise the dependence arguments offered in the literature to also include logical consequence and existence in the pluralist package remains an open question. In this regards, let me conclude with a note on the kind of dependence argument that I have provided for the thesis that truth pluralism entails diaphonic pluralism. I have developed an argument template to establish connections between different forms of pluralism. The first step of the argument is to establish conceptual dependence. The second step is to use cascade dependence (including metaphysical encapsulation) together with 'witness concepts' and several 'witness properties' to connect two forms of pluralism. This argument template is theoretically significant because its range of application potentially extends beyond the case discussed in the present paper. The conjecture is thus that many of the arguments for connecting between different forms of pluralism in the literature can be reconstructed more rigorously by using the template argument that has been developed in this paper for the case of truth and disagreement.
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A Appendix 1: Arithmetical disagreement satisfies opposition
Opposition: If Greta has a justification for having a cognitive attitude towards K and she has a justification for accepting that she is in disagreement with Saul in relation to Saul's cognitive attitude towards not-K, then does Greta have a ceteris absentibus justification for accepting that Saul's cognitive attitude towards not-K is incorrect?
• Suppose that Greta has a justification for accepting K.
• Thus, Greta has a justification for accepting the truth of K (Transparency).
• This amounts to a justification for accepting the syntactic derivability of 'K' from B (Arithmetical Truth). • Suppose further that Greta has a justification for accepting that her acceptance of K and Saul's acceptance of not-K disagree. • Greta has a justification for accepting that 'K' and 'not-K' are not both syntactically derivable from B. • By Transparency, Greta has a justification for accepting that <'K' and 'not-K' are not both syntactically derivable from B> is true. • By acceptance, Greta has a justification for the correctness of accepting that 'K' and 'not-K' are not both syntactically derivable from B • Now, absent any further consideration concerning Saul, from the mere fact that Greta has a justification for the correctness of accepting that the syntactic derivability of 'K' from B is correct and from the fact that she has a justification for the correctness of accepting that 'K' and 'not-K' are not both syntactically derivable from B, it follows that: • Ceteris absentibus, Greta has a justification for accepting that accepting 'not-K' is syntactically derivable from B is incorrect. • By PDJA, Greta has a justification for the truth of <accepting that the syntactic derivability of 'not-K' from B is incorrect>. • By Equivalence Schema Greta has a justification for accepting that the syntactic derivability of 'not-K' from B is incorrect. • Hence, Greta has a justification for accepting that Saul's acceptance of not-K is incorrect.

B Appendix 2: Basic taste disagreement satisfies opposition
Opposition: If Greta has a justification for having a cognitive attitude towards S and she has a justification for accepting that she is in disagreement with Saul in relation to Saul's cognitive attitude towards not-S, then does Greta have a ceteris absentibus justification for accepting that Saul's cognitive attitude towards not-S is incorrect?
• Suppose that Greta has a justification for accepting S.
• Thus, Greta has a justification for accepting the truth of S (Transparency).
• By acceptance, Greta has a justification for the correctness of accepting S.
• Suppose further that Greta has a justification for accepting that her acceptance of S and Saul's acceptance of not-S disagree. • By Basic Taste Disagreement, Greta has a justification for accepting that S and not-S are not both true. • By Transparency, Greta has a justification for accepting that <S and not-S are not both true> is true. • By Acceptance, Greta has a justification for the correctness of accepting that S and not-S are not both true. • Now, absent any further consideration concerning Saul, from the mere fact that Greta has a justification for the correctness of accepting S and from the fact that she has a justification for the correctness of accepting that S and not-S are not both true it follows that: • Ceteris absentibus, Greta has a justification for accepting that accepting not-S is incorrect. • By PDJA, Greta has a justification for the truth of < accepting that not-S is incorrect>. • By Equivalence Schema Greta has a justification for accepting that not-S is incorrect.
• Hence, Greta has a justification for accepting that Saul's acceptance of not-S is incorrect.