Disagreement for Dialetheists

ABSTRACT

Dialetheists believe some sentences are both true and false. Objectors have argued that this makes it unclear how people can disagree with each other because, given the dialetheist’s commitments, if I make a claim and you tell me my claim is false, we might both be correct. Graham Priest (2006a) thinks that people disagree by rejecting or denying what is said rather than ascribing falsehood to it. We build on the work of Julien Murzi and Massimiliano Carrara (2015) and show that Priest’s approach cannot succeed: given the same dialetheist’s commitments you may be correct to reject a claim that I correctly believe. We argue further that any attempt to solve the problem by identifying a new attitude of disagreement will also fail. The culprit, we claim, is the attempt to find a pair of attitudes that satisfy ‘exclusivity’—that is, attitudes such that both cannot be simultaneously correct. Instead of identifying disagreement by the kinds of attitudes involved, we propose dialetheists focus on the normative landscape and identify it in part by whether parties have reasons to change their attitudes. We offer our own normative theory of disagreement to help dialetheists with this challenge.

KEYWORDS:

• dialetheism
• disagreement
• logic
• normativity

1. Introduction: Disagreement and Exclusivity

In this paper we attempt to solve the disagreement problem for dialetheists. Dialetheism is the view that there are dialetheia: sentences or propositions which are simultaneously both true and false. This leads to a problem accounting for disagreements, but the problem rests on an often-unstated assumption that ‘exclusivity’ is necessary for disagreement. In the current section we explain what this assumption means. In §2 and §3 we argue that ordinary linguistic and logical tools such as negation and denial won’t help dialetheists solve the problem of disagreement. In §4 we argue that, in any case, the assumption of exclusivity must be rejected, and in §5 we show that our own normative theory of disagreement allows dialetheists to successfully identify when people disagree with one another. In §6 we consider and diagnose a complication and we conclude in §7 by summarising the benefits of our approach.

Traditionally, philosophers have understood disagreement as a particular kind of clash of cognitive attitudes, usually of beliefs. According to that common understanding, disagreement occurs when one person believes that $p$, and another person believes the negation of $p$ or that $p$ is false. In the background of this view lies the crucial assumption that disagreement involves attitudes that are exclusive with one another. One mental state is not exclusive with another just when it is impossible for a single person to have both states at the same time (although that may also be true), but rather when both attitudes cannot be simultaneously correct. We will justify this interpretation in §3. Exclusivity is thus a normative notion. The assumption of exclusivity explains both why the traditional analysis of disagreement focuses on cognitive attitudes and why it understands the relevant kind of clash as one of negation or falsehood. Cognitive attitudes, because it seems easiest with this type of attitude to tell which one excludes another, and negation or falsehood of a proposition, because they prima facie exclude the truth of the original proposition.

Interestingly, the assumption of exclusivity has not been relaxed by philosophers who explored alternative accounts of disagreement, even when on the face of it giving up on exclusivity would have made sense. Consider expressivists and other non-cognitivists who see our moral judgements as expressions of non-cognitive attitudes, such as desires or plans, and who nevertheless want to allow for disagreement about moral claims. One might have thought that, in an attempt to understand disagreement between non-cognitive attitudes, those philosophers would abandon exclusivity. After all, it seems plausible that your desire or plan to do one thing need not exclude my desire or plan to do another. But this has not been the path of most non-cognitivists. Rather they have tried, in different ways, to capture the idea that non-cognitive attitudes could be exclusive and to tie disagreement to these forms of exclusion. For example, some non-cognitivists have suggested that two people disagree if their desires cannot be simultaneously satisfied (Stevenson 1944: 3; Blackburn 1998: 69). While what is being excluded according to this analysis is not the truth of the other attitude, nevertheless a certain sort of exclusivity is being captured, namely, that if one of the attitudes is being satisfied then the satisfaction of the other is being excluded. For reasons we won’t go into here, this particular attempt to account for disagreement between non-cognitive attitudes has proven to be problematic (Ridge 2014: 171).

Another group of theorists who might have considered relaxing the assumption of exclusivity are relativists about truth. Consider early truth relativists (now sometimes called ‘contextualists’). According to these philosophers, statements of the form $A$’s are $F$s are a shorthand for statements of the form $A$’s are $F$’s relative to my standards. Different relativists held different views about the nature of the relevant standard, but all the same, it followed from this view that the truth-value of a statement is relativised to the standards of the group to which the speaker belongs. ‘Witches exist’ may have been true for certain villagers in medieval Europe but is not true for us. Now consider the question of disagreement. It is natural to maintain that the medieval villagers disagree with us about the existence of witches. But truth relativists, claim their critics, cannot accommodate this natural position. On the relativist view, the villagers believe that witches exist relative to medieval standards and we believe that witches don’t exist relative to 21^st century standards, and the content of one belief is not a negation of the content of the other. Relativists have often rejected the critics’ argument. However, whether or not their replies are satisfying, the debate could have been avoided by relaxing the demands of exclusivity. Adherence to the view that disagreement must be exclusive prevented relativists from exploring a whole range of alternative replies to the objection.

Our interest in this paper is with another group of philosophers who struggle to account for the notion of disagreement, namely dialetheists. Dialetheists believe some contradictions are true.¹ They insist that some claims are such that it is correct to believe them and it is correct to believe their negation as well. They thus must reject the traditional account of disagreement, and search for a novel way of characterizing this idea.² As we shall see, dialetheists—like non-cognitivists and relativists before them—have accepted the constraint of exclusivity in their search for a novel account. In the following sections we explore their attempts to offer such an account. Our first, weaker conclusion will be that, so far, dialetheists have failed to satisfy the constraint of exclusivity. Our second, stronger conclusion will be that dialetheists are bound to fail to satisfy this constraint. Accordingly, we will argue that the only way to offer a successful dialetheist theory of disagreement is to give up on the exclusivity constraint. However, we will insist that giving up on this constraint is not detrimental as long as one can satisfy the initial motivation for seeking exclusivity in disagreement. We will explain what that motivation is and then offer an alternative theory of disagreement for dialetheists—a theory which satisfies this motivation and which identifies disagreement where and only where dialetheists have otherwise recognised it.

Our theory of disagreement is normative. We believe that two people disagree if and only if the divergence between their attitudes implies that at least one of them has a reason to change their attitude. We will explain the details of our theory in §5 and show how it not only captures clear cases of disagreement, but also how its normative nature allows it to easily account for unclear cases in which people have different intuitions about whether a particular divergence of attitudes does or does not constitute disagreement. Our theory traces these differences in intuitions to different views about the normative standards that govern the acquisition and maintenance of beliefs. We have presented that theory elsewhere (Bex-Priestley and Shemmer 2017; Shemmer and Bex-Priestley 2021) as an attempt to explain disagreement among non-cognitive attitudes. However, we believe that it is a general-purpose theory and its success in resolving the problem of disagreement for dialetheists is further evidence that it can serve as a universal account of disagreement. This paper therefore serves the dual purpose of aiding the dialetheist as well as supporting our own theory by showing it has uses in unexpected areas.

2. What’s Wrong with Negation?

Here are two questions dialetheists struggle with: what is it to disagree with someone, and how can we express our disagreement? Common sense seems to tell us that if $A$ believes $p$ and $B$believes not $p$³ they disagree, and disagreement is expressed by asserting the negation of someone’s claim. Call this the Negation View. Yet if dialetheism is true there are cases where $p$ and not $p$ are both true, which drains the Negation View of its appeal. Consider the Liar:

$\mathit{L}$ $\mathit{L}$ is false.⁴

According to dialetheists, $L$ and not $L$ are both true—$L$ is a glut, both true and false—so the fact that$A$ believes $L$ is not sufficient to put her in disagreement with $B$ who believes not $L$. Why? Because of the underlying assumption described in §1 that disagreement can only arise from ‘exclusive’ attitudes (Priest 2006a: 103; Murzi and Carrara 2015: 111). We will define this notion as follows.

Exclusivity Two attitudes are exclusive if and only if they cannot both be correct.

Since a belief in $p$ and a belief in not $p$ are not necessarily exclusive, dialetheists like Graham Priest abandon the Negation View and search for exclusivity elsewhere.

3. What’s Wrong with Denial?

Priest believes that we express disagreement by denying what was said, where this is distinct from asserting its negation. He posits the mental state of rejection as that which is expressed by the speech-act of denial: ‘To reject something is to refuse to believe it: if it is in one’s belief box one takes it out, but whether or not it was in there before, one resolves to keep it out’ (Priest 2006a: 103). According to Priest, even though $L$ is false it is incorrect to reject $L$because $L$ is also true; belief is the correct attitude to take towards all truths, not rejection.⁵ Let us make this link between belief and truth explicit.

Link For all true propositions (including gluts) the correct attitude to take is belief, and for all other propositions the correct attitude is rejection.⁶

Given that Priest thinks belief and rejection ‘certainly seem to be exclusive’ (Priest 2006a: 103) he arrives at what we’ll call the Denial View: if $A$ believes $p$ and $B$ rejects $p$ they disagree, and disagreement is expressed by denying someone’s claim. This view of disagreement is explicitly espoused by Priest (2006a: 107). We’ve been assuming that Priest understands exclusivity in the way we have defined it as a normative notion. However, we should consider an alternative non-normative understanding of exclusivity before we proceed and show why it is inadequate for the purpose of theorising about disagreement.⁷

Call our favoured definition, stated in §2, ‘correctness-exclusivity’. When Priest says belief and rejection are exclusive, rather than meaning it cannot be correct to believe and reject the same proposition, we could instead interpret him to mean that it is impossible (for a single agent at any given time) to believe and reject the same proposition. Call this notion possibility-exclusivity. We will run through three reasons why Priest must not accept possibility-exclusivity to be relevant to motivating his account of disagreement. First, it’s prima facie counterintuitive that it’s a necessary condition for disagreement that the disagreeing mental states are impossible to co-instantiate. Those who accept the Negation View, for example, may also accept it’s possible to believe $p$ and not $p$. Many people want to account for disagreement in non-cognitive states too—such as disagreement in tastes, likes and dislikes, plans, or conflicting desires—and it doesn’t seem impossible for a single agent to have these discordant mental states. Priest of course might move from the Denial View to the view that disagreeing states are necessarily impossible to co-instantiate (because belief and rejection do seem possibility-exclusive), but he should not move in the other direction because it’s unclear why anyone would pre-theoretically accept that possibility-exclusivity is necessary.

Second, possibility-exclusivity is clearly insufficient for disagreement. It is impossible to both have a belief and lack that same belief, but if $A$ believes $p$ and $B$ does not, $A$ and $B$ need not disagree, since $B$ may not have considered the matter—Priest would accept this. There are many other impossibilities for individuals, such as sitting and standing or having a headache and not having a headache, that wouldn’t count as disagreements in interpersonal cases. Since there are many features that individual people could not have but would fail to count as disagreement if two different people had them, the reason Priest identifies belief and rejection as the disagreeing attitudes must be something other than impossibility of co-instantiation. Third, it is natural to speak of people disagreeing with themselves, especially if they are irrational, but this is ruled out by requiring possibility-exclusivity. For these reasons, we (along with Murzi and Carrara 2015) explicitly use correctness-exclusivity as the notion that has relevance to disagreement. If dialetheism is true, the Negation View loses its appeal because believing $p$ and believing not $p$ is sometimes correct, not simply because it is sometimes possible.

Unfortunately, the Denial View fails too. The following sentence is based on Julien Murzi and Massimiliano Carrara’s ‘Paradox of Deniability’ (Murzi and Carrara 2015, p.112).

$\mathit{D}$ It is correct to reject $D$.⁸

If $D$ is true (whether or not it is also false) then, by Link, it is correct to believe $D$. But if what $D$ says is true then it is correct to reject $D$ too and so, assuming $D$’s truth, belief and rejection are not exclusive. What if $D$ is neither true nor a glut of truth and falsehood? That is, what if it’s only false, or a truth-value gap where it is neither true nor false? In this case, in light of Link, it is correct to reject $D$. But this is exactly what $D$ says, which means $D$ is true and therefore correct to believe. Once again, both belief and rejection are correct attitudes to take towards $D$.

What does this show? It shows that belief and rejection are not exclusive attitudes after all. Sometimes believing $p$ is correct and rejecting $p$ is correct, which casts doubt on the Denial View. If $A$ believes $D$ and $B$ rejects $D$, why say they disagree when both of them are correct to do so and, if both are rational, they will fully admit the other’s attitude is correct? The reason dialetheists reject the Negation View is because it is sometimes correct to believe $p$ and correct to believe not $p$. If the search for exclusivity is their reason, they should reject the Denial View too.⁹ But in any case, the search for exclusivity seems to us to be in vain.

4. What’s Wrong with Exclusivity?

We have relied above on the following definition of exclusivity:

Exclusivity Two attitudes are exclusive if and only if they cannot both be correct.

And on a principle of correctness for beliefs:

Link For all true propositions (including gluts) the correct attitude to take is belief, and for all other propositions the correct attitude is rejection.

Before we proceed let us add a natural extension of Link:

Link + If it is correct to believe $p$, $p$ is (also) true. If $p$ is only false, it is incorrect to believe $p$.

We have considered rejection (and its expression ‘denial’) and found that it cannot function as an exclusive attitude of disagreement. The next question to ask is whether there could be any attitude of disagreement that is exclusive with the belief that $p$. Call such an attitude ‘$X$’. What we want to know is whether there could be an attitude $X$ towards (a function of)¹⁰ $p$ such that it cannot be the case that both $X$ and the belief that $p$ are correct. If the answer is ‘yes’, perhaps we could identify $X$ as the attitude of disagreement. However, given the dialetheist’s commitments, we believe that the answer is ‘no’. Suppose we think we’ve found such an attitude $X$, and consider the following paradox of disagreement.

$\mathit{O}$ It is correct to disagree with $O$.

If $O$ is true (whether or not it is also false), then in virtue of its content it is correct to disagree with it, which—we are assuming—is to have attitude $X$ towards $O$. But since $O$ is true then, by Link, it is correct to believe $O$ too. Therefore, $O$ cannot be true on the assumption that $X$ is exclusive with belief. So, let’s suppose $O$ is only false or a truth-value gap. What is the correct attitude to take towards $O$? Given Link + and since we’ve shown that $O$ cannot be true, the answer cannot be belief.¹¹ Nor can it be $X$, because that would mean that what $O$ says is true. Perhaps it’s some other attitude, or perhaps no attitude is correct to take towards $O$. Call this the immune position. $O$ is in no way true, so it is neither correct to agree with it (believe it) nor correct to disagree with it (have attitude $X$ towards it).

The trouble with the immune position appears when considering what to do with someone who believes $O$. Call her Sheryl. Sheryl asserts ‘$O$ is true. It is correct to disagree with $O$.’ Defenders of the immune position (‘immunists’) think she’s wrong to believe $O$. $O$ is not true and it’s not correct to disagree with $O$. They tell her ‘Your attitude is incorrect, Sheryl. You’re mistaken.’ Hang on, doesn’t this sound like a disagreement? Thinking that somebody else’s belief is wrong, incorrect, or mistaken, seems prima facie to count as disagreeing with them. Assuming for now that immunists do in fact disagree with Sheryl, the situation is the following: on the assumption that $O$ is either only false or is a truth-value gap, and that the only way to accommodate this fact is to adopt the immune position, it turns out that it is correct to think that Sheryl is incorrect in believing $O$, or in other words, that it is correct to disagree with $O$—and given the content of $O$, this means that $O$ is true and so it is also correct to believe $O$. So again, exclusivity must be rejected.¹²

Perhaps immunists will dig in their heels and insist that even though they believe Sheryl cannot be correct, despite appearances they do not disagree with her. What are their options? They could claim that while the correctness of the judgement that the other person’s belief is incorrect does entail that it is correct to disagree with her, it does not in itself constitute disagreement. For disagreement, immunists would insist, one needs additionally to adopt attitude $X$. But this position would not help immunists save the exclusivity of disagreement since it would commit them, on the one hand, to the claim that it is incorrect to believe $O$, and therefore that it is correct to disagree with $O$ (have attitude $X$ towards $O$); and on the other hand, given that this is exactly what $O$ says, to the claim that it is correct to believe $O$. Exclusivity is lost. Immunists could instead adopt a more radical position. They could claim that the fact that it is correct to judge that believing $p$ is incorrect, not only fails to constitute disagreement with the person who believes $p$, but does not even entail the correctness of disagreeing with the person who believes $p$. But this more radical position makes a mystery out of the attitude of disagreement. A dialetheist who adopts this radical position now rejects the claim that one should disagree with false statements and rejects the claim that one should disagree with ‘only false’ statements, and rejects the claim that one should disagree with statements that it is incorrect to believe. To protect exclusivity, this dialetheist would give up on any plausible standards of correctness for the attitude of disagreement.

In any case, we are yet to see a good candidate for $X$. We therefore suggest dialetheists abandon the search for a single mental state which is exclusive with belief. But a plurality of mental states won’t help either. Consider a slight variation:

${\mathit{O}}^{\ast }$ There is a correct attitude which disagrees with $O^{\ast }$.

If $O^{\ast }$ is true (whether or not it is also false), then in virtue of its content it is correct to disagree with it. If a plurality of disagreement-attitudes are candidates, disagreement needn’t be a matter of adopting $X$. But there is a correct attitude in disagreement with $O^{\ast }$; call it ‘$Y$’. $Y$ constitutes disagreement with $O^{\ast }$ and it is correct. Yet $O^{\ast }$ is true and so, by Link, it is correct to believe it. Once again, disagreement is flouting exclusivity: it is correct to believe $O^{\ast }$ and it is correct to hold the disagreeing attitude $Y$ towards $O^{\ast }$.

Let’s suppose instead that $O^{\ast }$ is only false. From here there are two routes to take and neither of them are acceptable. First, we might say that $O^{\ast }$ is false because, while it is indeed possible to disagree with $O^{\ast }$, it is incorrect to do so. This ‘possiblist’ position is identical to the immunists’ position discussed above and we saw how the choice points from there took us to an unacceptable position. Instead, then, we might say that $O^{\ast }$ is false because it is impossible to disagree with $O^{\ast }$. Unfortunately, this is an even more radical position than the one the immunists might have taken. Thinking it is incorrect to disagree with an only-false claim is bad enough, but thinking that there is a belief in an only-falsehood which is impossible to disagree with, leaves us scratching our heads in wonder. What prevents the disagreement? It now seems that the only motivation for this position is the desire to protect exclusivity.

We conclude that dialetheists’ search for exclusivity is doomed. Given dialetheism, there are bound to be some sentences, such as $O^{\ast }$, that are both correct to agree with and correct to disagree with. Dialetheists should stop looking for exclusive attitudes and adopt our normative theory of disagreement instead, a theory we developed independently of this debate in order to solve the disagreement problem for expressivism.

5. A Normative Theory of Disagreement

Our search for a new solution to the dialetheist’s disagreement problem is driven by two desiderata. First, to give a unifying analysis for all cases of disagreement; an analysis that will guarantee disagreement when its conditions are satisfied and at the same time will not predict disagreement where dialetheists see none. Second, to vindicate a deep intuition about the close connection between disagreement and exclusivity. The treatment of that connection is, however, a subtle matter. The Liar, the paradox of deniability and the paradox of disagreement suggest that dialetheists won’t be able to identify any general pair of attitudes such that, when taken towards any arbitrary statement, necessarily they cannot both be correct. The second desideratum thus requires a different sort of explanation of the connection between exclusivity and disagreement.

Our own normative theory of disagreement promises to provide such a solution. We argue that $A$ and $B$ disagree if and only if:

1. $A$ has attitude $a$, $B$ has attitude $b$, and $a$ and $b$ are different.

2. $A$ and $B$ share a common project with certain standards for the formation and retention of attitudes (this may or may not be a normative judgement; we take no stand on this issue).

3. Given the standards imposed by their common project, the divergence¹³ of $a$ and $b$ implies that at least one of A and $B$ has reason to change their attitude.

In short, in our view, disagreement exists when the diverging attitudes of two people indicate that at least one of them has reason to change their attitude. If Ariana thinks the cookie jar is full and Ilya thinks it is empty, the divergence between their beliefs indicates that one of them has reason to change his/her belief because it is physically impossible for the cookie jar to be both empty and full.

A few clarifications are in place. First, the view is normative since the satisfaction of the third condition depends on the obtainment of normative facts: facts about reasons for having attitudes. It is, however, neutral on normative and metanormative matters since our view takes no stand on the nature of reasons and when they obtain. Second, the view offers a general analysis of disagreement, one that applies to beliefs but also to other attitudes, such as desires or plans. Third, the project we speak of in condition (2) may be a practical project but need not be. In the case of beliefs, it is most natural to understand this project as the project of getting at the truth.¹⁴ Fourth, the divergence between attitudes need not be the reason for $A$ or $B$ to change their attitude; the divergence is merely an indication that one of them has a reason to change their attitude.

We cannot go through all the common objections to our theory here but it’s worth mentioning the one that comes up most often.¹⁵ Sometimes all parties to a disagreement are rational. Perhaps $A$ and $B$ have different bodies of evidence, or—if subjective Bayesianism is true—even the exact same body of evidence but different prior probabilities, leading $A$ to correctly reason to a belief that $p$ and $B$ to correctly reason to a belief that not $p$ (and let’s say all know that $p$ is not a glut). In such cases, why think there is any reason for either $A$ or $B$ to change their attitude? Our answer draws upon the distinction between subjective and objective reasons. If Mary’s drink is poisoned and there’s no way she could know this, does she have a reason to avoid drinking it? Subjectively no, but objectively yes—the reason is that it will kill her. Similarly, neither $A$ nor $B$ has a subjective reason to change their attitude, but one of them—whoever is misrepresenting reality—has an objective reason to do so. This is congruent with the notion of correctness we’ve been using, according to which a rational belief may be incorrect and an irrational belief may be correct. Thorough defences of our normative theory of disagreement can be found in our earlier papers (2017; 2021), including a more detailed discussion of this particular objection (2017: 204-5; see also 2017: 199 and 2021: 505). Our purpose in this paper, however, is to show how our theory helps dialetheists to analyse the notion of disagreement when they have previously struggled to do so.

Consider then the application of our analysis to the Liar. Aaron believes that the Liar is true and Betty believes that its negation is true. We might think they share a common project with the following standard: for all true propositions (including gluts) the correct attitude to take is belief; for all other propositions the correct attitude is rejection (Link). The Liar, on the dialetheist view, is both true and false, and therefore Aaron and Betty’s common project does not imply that at least one of them has reason to change their attitude. In fact, they should retain their attitudes and, if they haven’t done so already, adopt each other’s attitude too. Our theory correctly predicts, given dialetheism, that Aaron and Betty do not disagree about the Liar.

Our theory achieves the two desiderata. It achieves the first desideratum because it predicts disagreement where and only where the dialetheist sees disagreement. It achieves the second desideratum because it can explain why people connect disagreement with exclusivity. The potential for disagreement exists where, given the standards imposed by a common project and the structure of the world, there is normative pressure to exclude at least one of two held attitudes, which is often explained by a guarantee that one of the attitudes is incorrect. However, our view is not committed to the claim that pressures to exclude only exist when the attitudes are exclusive—there may be normative pressure to switch between two attitudes that are both correct, for instance. (To exclude is not to reject, then, since rejection involves a resolution to keep a proposition out of one’s belief box, and we want to allow for oscillation.) As we explain in the next section, whether the pressure to exclude in a given instance is grounded in strict exclusivity is a normative question, and different dialetheists may have different normative commitments.

Our theory dispenses with the idea that there exist unique attitudes of disagreement. That is, we reject the thought that there exists a pair of attitudes that in all cases constitutes disagreement when taken towards the same proposition. Since we give up on the existence of unique attitudes of disagreement, we also give up on the idea that there are unique linguistic markers for disagreement. So how does one express disagreement on our view? If $A$ expresses attitude $a$, $B$ can express disagreement by expressing attitude $b$ such that $a$ and $b$ satisfy the conditions we outlined above. The type of attitude—belief, rejection or anything else—and the mode of expression are not universal, and the search for a single general kind is a wild goose chase.

6. What the Paradoxes Can Tell Us

Since our view does not rely on the attitude of rejection to explain disagreement it might seem that it avoids the worries generated by the paradox of deniability. Likewise, since it does not rely on any special attitudes of disagreement (of the type designated by ‘$X$’ and ‘$Y$’ in §4) it also looks like it avoids the worries generated by the paradox of disagreement. Yet an opponent may say that the paradoxes of deniability and disagreement, while causing particular trouble for views that seek unique attitudes of disagreement, also pose an obstacle to any account of disagreement suitable for dialetheism. How then should a proponent of our view deal with these paradoxes?

Let us focus on the paradox of deniability.¹⁶ We showed in §3 that it is correct to believe $D$ and it is correct to reject $D$. Now ask yourself what we should think of two people, Sarah and Novenka, the first who believes $D$ and the second who rejects $D$. Do they disagree? On the one hand they are both correct in adopting their respective attitudes, and on the other hand it seems that their attitudes in some sense clash. Before we meet this challenge, we remind the reader that in our view, whether a duo is considered to be in disagreement depends on one’s account of the reasons that exist in a particular type of situation and with respect to particular attitudes. Thus, our position with regards to disagreement, in itself, takes no stand on the question of whether $D$ may be disagreed with by rejecting it.¹⁷ In order to answer that question one would have to combine our account with a substantive normative view about reasons for attitudes—in this case, for the attitudes of belief and rejection.

So, what would a dialetheist say about Sarah and Novenka? We see no reason to think that all dialetheists would answer this question in the same way; dialetheism in itself underdetermines the answer. Let us nevertheless consider two possible approaches to this conundrum. According to the first approach there is nothing wrong in principle with two people who believe and reject the same statement, even if they share the same epistemic goal of believing only what is true.¹⁸ On this approach there is no universal standard that requires a person not to believe a statement that is correctly rejected nor vice versa. Thus, the fact that Sarah correctly believes $D$ does not show there is any reason for Novenka not to reject it. A dialetheist who adopts this approach will conclude that Sarah and Novenka do not disagree. One believes $D$ and the other rejects it, but both are correct to do so.

Alternatively, consider a second approach according to which there are always reasons not to believe a statement that can be correctly rejected and there are always reasons not to reject a statement that can be correctly believed. This would mean that Sarah and Novenka disagree with each other because the combination of their attitudes indicates that at least one of them (in fact both) has reason to change their mind (despite the correctness of their current attitudes). On our account, that is the mark of disagreement. This second approach provides us with an example of a (type of) situation where the necessary tie between disagreement and exclusivity is severed, since the disagreement here arises from attitudes that are both correct. The fact that our account of disagreement can accommodate this second normative approach does not undermine our ability to capture the intuition that there is a tight connection between exclusion and disagreement. As we explained towards the end of §5, the connection is due to the fact that disagreement always indicates a normative pressure to exclude a certain attitude whether or not that pressure comes from the attitude’s incorrectness. On the second normative approach to belief and rejection, reasons to change one’s mind (that is, pressures to exclude) come from the correctness of the alternative attitude rather than the incorrectness of the current attitude.¹⁹

The reader might be frustrated. Which approach is right? Do Sarah and Novenka disagree or not? Our answer is that, at least from a dialetheist perspective, it is unclear, and the unclarity is due to the normative uncertainty in this case. Frustrating as it may be, we believe this supports our theory of disagreement. Intuitions about whether Sarah and Novenka disagree about $D$ are murky to begin with, so if a theory explains this murkiness, this counts in its favour. Furthermore, when cases are normatively straightforward for dialetheists—who think, for instance, that believing the Liar and believing its negation is obviously no disagreement—our view explains this obviousness. Given the truth and falsity of the Liar, the fact that $A$ believes $L$ and $B$ believes not $L$ does not imply there is any reason for $A$ or $B$ to change their mind. This is why it is clear that dialetheists should see no disagreement between $A$ and $B$ about $L$. In short, our view predicts and explains intuitions about disagreement better than other views do, both in clear and in unclear cases.

7. Conclusion

Dialetheists wish to find an exclusive set of attitudes as constituents of disagreement. In light of the Liar and other allegedly true contradictions, the set cannot be a belief in a proposition and a belief in its negation. Priest opts for belief and rejection. But in light of the paradoxes of deniability and disagreement he must give up on exclusivity after all. This leaves him and other dialetheists with a view of disagreement that is unmotivated, because if exclusivity isn’t necessary for disagreement according to the Denial View, then it’s unclear what advantage this view has over the initial Negation View.

Our normative theory of disagreement allows dialetheists to have it all. They get:

• An independently motivated view of disagreement.

• An explanation of why negating the Liar does not express disagreement.

• A vindication of the intuition that a pressure to exclude is central to disagreement—a vindication which is compatible with:

• A rejection of the view that exclusivity is necessary for disagreement.

Acknowledgements

We would like to thank the members of the LANCOG working group at the University of Lisbon for first suggesting that our theory of disagreement might help dialetheists.

We would like to thank Thomas Brouwer, Matt Cull, Carl Fox, Will Gamester, Dominic Gregory, Julien Murzi, and Graham Priest for reading and discussing with us some of the ideas contained in this paper.

We would like to thank Rosanna Keef for reading and commenting on earlier versions of this paper, and for her extremely helpful suggestions and ideas.

We would like to extend a special thanks to Ilya Shemmer for his extensive comments, for suggesting to us the generalized paradox of disagreement ($O^{\ast }$) and for pointing out that given this generalized paradox it would be impossible to find exclusive attitudes of disagreement even if one relaxed the requirement that these would be the same attitudes on every occasion.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 Modern dialetheism appeared in the mid-70s in the works of Asenjo and Tamburino (1975), Routley and Meyer (1976), and Priest (1979). A good introduction to dialetheism, as well as a selection of defences of, and attacks on, the position, can be found in Priest, Beall, and Armour-Garb (2004). Since the foremost objection to dialetheism is that it entails trivialism (the truth of every statement), its adoption, at least in the modern setting, has been accompanied by the acceptance of paraconsistent logic, which crucially, blocks the entailment from contradiction to any arbitrary conclusion. A good survey of the relation between truth and logic which consider both classical as well as non-classical approaches (including paraconsistent approaches) can be found in Beall, Glanzberg, and Ripley 2018.

2 The objection that dialetheists cannot express disagreement is presented by, among others, Parsons (1990), Shapiro (2004), and Littman and Simmons (2004). An alternative to Priest’s solution is offered by Beall (2013). Worries about this approach, or the underlying move that enables it, are found in Field 2008, Berto 2014, and Murzi and Carrara 2015.

3 From this point on, we assume ‘not $p$’ and ‘$p$ is false’ are equivalent. This isn’t an assumption everyone shares, but it makes for easier reading. We don’t believe anything important hangs on it here.

4 The Liar has been discussed since antiquity. An early modern presentation and solution appears in Tarski 1935. A good short overview of the paradox and the general approaches to solving it is found in the SEP article ‘Liar Paradox’ (Beall, Glanzberg and Ripley 2016). Dialetheism and its accompanying paraconsistent logic is but one branch in one of the families of solutions to the paradox. There exist solutions within classical logic (e.g. Tarski 1935, McGee 1991), contextualist solutions (e.g. Burge 1979, Barwise and Etchemendy 1987) as well as other solutions within non-classical logic (e.g. Kripke 1975 and Petersen 2000). There is a recurring theme in replies to these various solutions. Responders point out that on the one hand, the solution involves an unacceptable loss of expressive power in the language used to express the paradox, and on the other hand the paradox can be recreated in other languages or in other areas of the language that are needed to capture the complexity of natural language. The claim that dialetheists cannot express disagreement and the formulation of new Liar paradoxes in response to Priest’s attempt to capture disagreement in terms of acceptance and rejection fits this pattern. Parallel objections were presented to paracomplete solutions of the paradox. For two recent considerations of and replies to such objections, see Richard 2008 and Schroeder 2010.

It should be noted that while the Liar is a central motivation for the development of dialetheism it is not the only one. Accordingly, the accompanying problem of finding a way of expressing disagreement within a dialetheist context is a general problem for dialetheism.

5 ‘For belief, correctness is truth. Correct belief is true belief’ (Gibbard 2005: 338). Velleman (2000: 15) also writes ‘truth serves as the standard of correctness for belief’ and Priest himself (2006b: 61) advocates a teleological theory of truth whereby correct assertion just is true assertion. It is important to distinguish between this sense of ‘correct’ and another sense whereby ‘correct’ means justified or rational or some variant thereof. In our intended sense, many of our justified beliefs could turn out to be incorrect.

6 Note that Link does not mandate the inference from $p$’s falsehood to it being correct to reject$p$, but from $p$ being neither true nor a glut to the correctness of rejecting $p$. Again, it’s worth reiterating that correctness is not about rationality. For any proposition (with a determinate truth-value) it will be correct to believe it or correct to reject it, but in practice there are many things we should rationally suspend judgement about: perhaps it is neither rational to believe nor rational to reject string theory until we get more evidence.

7 Thanks to a helpful reviewer for pressing us on this issue.

8 Murzi and Carrara (2015: 112) acknowledge that one way out of the paradox is to stipulate that we cannot describe the norms of rejection. They dismiss this option because it is highly counterintuitive for natural languages where normative discussion about any mental state seems possible. We believe this is fair and that dialetheists would agree, since they are typically hesitant to restrict the expressive power of a language. As mentioned in footnote 4, non-dialetheist solutions to the liar paradox result in a loss of expressive power, so if dialetheists wish to boast an advantage in this respect, they are under dialectical pressure to allow expression of norms of rejection.

9 Some non-dialetheists subscribe to the Denial View. Should they also reject it? Not necessarily. Proponents of gappy views, for example, may find a resolution to the paradox of denial that is amenable to the Denial View of disagreement. (Thanks to a helpful reviewer for suggesting gappy theorists may not have to believe or reject $D$ or take any stand on the correctness of these attitudes, or they may reject $D$ while rejecting all statements about whether it is correct to do so (they may reject ‘all the way down’ as they do with revenge liars), or they may believe it’s correct to reject $D$ without rejecting it.) We’re not sure if they can find such a resolution, but if they can, then anyone wedded to the Denial View should prefer gappy views over dialetheist views. We do not explore possible non-dialetheist solutions to the paradoxes in this paper. Our focus is on whether those wedded to dialetheism have any prospect of accounting for disagreement.

10 In the Negation View, we have belief in the negation of $p$. In the Denial View we have rejection of $p$ itself.

11 Perhaps a dialetheist could say it is both correct and incorrect to believe $O$, but then they’re giving up on exclusivity (as a necessary condition of disagreement) right away, so they are no opponent of ours.

12 What if they say they do not disagree with Sheryl about $O$, but they disagree with her about the correct attitude to take towards $O$? They think belief (and $X$) is incorrect whereas Sheryl presumably thinks belief (and $X$, flouting exclusivity) is correct. While this may indeed be a disagreement, it is a red herring. Sheryl might have no opinion on the correctness of belief in $O$. It seems to us that defenders of the immune position, who do not think $O$ is true, disagree with Sheryl, who thinks $O$ is true, about the statement $O$ itself.

13 Attitudes are divergent if they are directed towards different objects or if they are different kinds of attitude.

14 Our theory leaves open the nature of the project that would license disagreement for each pair of attitudes and it accommodates the possibility of the existence of multiple simultaneous projects. We will, however, for the remainder of this paper, assume truth to be the aim of the common project.

15 Thanks to the associate editor for raising this worry.

16 The paradox of disagreement shares some of the features of the paradox of deniability but also introduces some additional complexities. A full discussion of the paradox of disagreement is beyond the scope of this paper. The relevant lesson from our discussion of the paradox of deniability below is that such paradoxes can at most help us reject some simple views of disagreement. Beyond that, one’s approach to these paradoxes will depend on one’s prior epistemic commitments.

17 In our view, strictly speaking, a disagreement is not with a statement but with a person. So while we accommodate talk of disagreement with a statement, we mean such an expression to be elliptical for disagreement with a person who believes the statement.

18 Something wrong may be indicated by different people’s belief and rejection of the same statement in particular cases (e.g. ‘grass is green’) but the case of the paradox of deniability is not one of them.

19 The idea is that if your correct attitude $Y$ isn’t possible to hold in conjunction with a correct attitude $Z$ (or if it’s possible but there is nevertheless some reason not to do so), then you’ll be normatively ‘pulled’ towards switching from $Y$ to $Z$, even if you aren’t ‘pushed’ away from your current attitude $Y$ due to any incorrectness. Since the situation is symmetrical, if you do switch you will then be normatively pulled towards switching from $Z$ back to $Y$ again.