Disagreement, Points of View, and Truth-Relativism

Truth-relativism is the claim that the truth of statements is dependent on the context in which they are made. In this article, truth-relativism is considered as a way to explain disagreements. Viewpoint relativism, a recent version of truth-relativism, is introduced as a useful framework to analyse how truth-relativism approaches disagreements. Viewpoint relativism is based on contextual semantics and the logic of viewpoint, which is a two-dimensional modal logic. In viewpoint relativism, the central concept is a point of view in relation to which truth claims are evaluated. Viewpoint relativism is compared to the truth-relativism of Peter Lasersohn and John MacFarlane. Finally, truth-relativism is defended against the critique of Paul Boghossian that it represents untenable ‘replacement relativism’.


Introduction
Truth-relativism (alethic relativism) is defined as the claim that the truth or falsity of statements is dependent on the context or background in which statements are made (Baghramian, 2004, p. 128). In this article, truth-relativism will be analysed in terms of contextual semantics. In this framework, truth-relativism is a claim that the truth of statements is dependent on an extra parameter given by context and referring to some background factor like taste, aesthetical standard, perspective or even culture and a conceptual system. I call this extra parameter relatum. In truth-relativism, a truth predicate is the two-place predicate of the form 'p is true in relation to r', where p is a statement and r is a relatum. By using these terms, truth-absolutism could be defined as the claim that truth-value is constant (invariant) relative to all relata; therefore, a truth predicate can be presented as a one-place predicate: 'p is true'. 1 .
We can approach truth-relativism by considering how it explains propositional disagreements. There are many approaches to define and argue what disagreement is. They share, however, one common issue: Disagreement is related to logical contradictions. Following this insight, I take disagreement to mean a situation where two (or more) parties A and B explicitly disagree over the truth of a certain statement p: For example, A asserts that p and B asserts that not-p. If p is true, then it is accurate for A to believe it. The issue is, can A and B both accurately believe contradictory statements?
In the analysis of disagreement there are two major alternatives: (1) The statement p expresses different propositions for A and B.
(2) The statement p expresses the same proposition for A and B.
If (1) holds, we can say that disagreement is apparent (or not genuine disagreement) because different propositions are not in conflict. If (2) holds, there are two possibilities: (2.1) Either p or not-p must be false.
(2.2) Both p and not-p can be true.
In the case of (2.1), we can say that the disagreement is absolute, and in the case (2.2), we can say that the disagreement is relative. That (2.1) is absolute means that A and B cannot both be right. In the case of (2.1), the principle of non-contradiction is applicable: Contradictory propositions cannot both be true in the same sense at the same time. 2 According to truth-absolutism, (2.1) is the right analysis of the disagreement of type (2).
On the other hand, truth-relativism tries to give an account of how a proposition and its negation could be both true (2.2). Clearly, (2.1) implies the negation of (2.2). To escape the principle of non-contradiction one has to show that in the case (2.2), contradictory propositions p and not-p are not true 'in the same sense at the same time'. For that, truth-relativism introduces different kinds of relata to which truth claims are relativised. This makes the disagreement relative: There is no contradiction that a proposition is true relative to one relatum and false relative to another relatum. A challenge of truth-relativism is to give an account for (2.2) without falling back to case (1). This strategy presupposes that relata could be detached from propositions and distributed to truth-conditions. Discussion about truth-relativism is very much concentrated to just the analysis of disagreement (Cappelen & Huvenes,2 Contradictions are allowed in some deviant logics (cf. Rescher & Brandom, 1980). 1 To be more exact, these predicates attribute truth in relation to a world w (in absolute conception) and in relation to a world and a relatum (in relative truth). Meiland (1977) has proposed that there is a one-place truth predicate for relative truth, say '…true-in-relation-to-relatum-r'. I do not follow this lead because it means that there will be as many truth predicates as there are relata. It is better to have just one two-place predicate that is applicable to different relata.
One special issue related to disagreement is the possibility of faultless disagreement, which means that the two parties A and B disagree about the truth of p while neither A nor B has made a mistake (Kölbel, 2003). Note that if a person believes a proposition that is not true, she has made a mistake. If the disagreement is of the type (2.1), then either A or B has made a mistake. Absolutism denies faultless disagreements, but some relativists are also against them. 3 Faultless disagreement is mainly an epistemic concept, however, but we can interpret it in terms of semantics so that a disagreement is faultless if the beliefs of both parties are accurate. Defined in this way, faultless disagreement is a relative disagreement.
In a very general way, we can say that in a disagreement, disputants have different points of view over the same issue. The aim of this article is to present an approach to truth-relativism that is based on the concept of points of view. To further develop truth-relativism, a formal framework for defining the basic concepts is needed. Modal logic and contextual semantics seem to offer proper tools for this (see Hautamäki, 1983b;Kaplan, 1989;Lasersohn, 2017;Lewis, 1980;MacFarlane, 2014). In the sequel, I will first introduce my concept of points of view and then define viewpoint relativism based on it. After that, I will compare my approach to some recent forms of truth-relativism. Finally, I will defend relativism against some criticism.

Points of View
The concept of points of view has been under intensive research in recent years (Hautamäki 1986(Hautamäki , 2016(Hautamäki , 2020Colomina-Almiñana, 2018;Lehtonen, 2011;Vázquez & Liz, 2015a). The structure of points of view can be analysed in two ways: either in terms of propositional attitudes or in terms of location and access (Vázquez & Liz, 2015b). In the first approach, a point of view is some kind of propositional attitude of a subject towards some contents (believing, experiencing). In the definition of points of view by Liz and Vazquez, there are a bearer B of a point of view, set of relations of B to conceptual or non-conceptual contents and a set of possession conditions for having the point of view. Intuitively, a point of view is a relational system connecting a bearer to contents in various ways. In the second approach, points of view are ways of having access to the world (cf. Colomina-Almiñana, 2018). A point of view is constituted by a location offering a certain perspective (e.g. scientific observations). Lehtonen (2011) has proposed a definition of the concept of the epistemological point of view close to that of Liz and Vázquez. By points of view, he means mental seeing or rational examination. According to Lehtonen (2011, p. 250), there are three kinds of variables in points of view: observer-related variables (subject, observer, interest, etc.), tools-related variables (conceptual apparatus, method, data, etc.) and object-related variables (object, focus, observables, etc.). A point of view contains a subject, an object and the methods of approach that connect them. These factors receive different values and emphases in different situations.
In a point of view, a subject selects some aspect of an object to consider. Subject is a person, group or culture who owns a point of view (a bearer of a point of view). Object is any target or focus of points of view, like entity, episode, class and issue. In general, the object might be the 'world'. Aspects are facets, features, parts or qualities of objects. Say, weight is an aspect of physical objects and profit is an aspect of investments. It is plausible to suppose that things are complex and multifaceted and therefore objects have indefinitely many aspects. The idea of an aspect is that objects might have different properties in relation to different aspects. When a subject has selected an aspect, he sees or conceives the object in relation to that aspect. With this in mind, I define point of view as follows: (  Hales, 2006;Vázquez & Liz, 2015b). 4 Condition 'A represents O to S' can be interpreted in two ways. First, we can emphasise the active role of the subject, where the subject chooses an aspect A to represent or describe O. For example, a person can use gender to represent a person. This means that the subject S focuses on a certain aspect A of the object O, for example, the aforementioned gender. What the subject S thinks about O and how she interacts with it is dependent on precisely A. On the other hand, the condition allows for a more objective interpretation of points of view. For example, for the subject, a certain observation can represent a physical object. In this case, we can say that the aspect opens access to an object.
Typical expressions of points of view are as follows: These examples are quite different in order to show that the scope of the concept of points of view is large and provides a general starting point to develop truth-relativism.

Viewpoint Relativism
Viewpoint relativism is a form of recent truth-relativism. The major objective of truth-relativism is to explain how the same proposition could be both true and false. Its idea is to introduce a special variable contextual element in relation to which truth is evaluated. In viewpoint relativism, this is done by applying it to contextual semantics, 5 taking points of view as parts of context (see Hautamäki, 2020). In contextual semantics, contents and truth-conditions of sentences in a context are separated. 6 According to the truth definition presented by Kaplan (1989, p. 522), a sentence φ is true in context c if the content expressed by φ in c is true at the circumstance of c. He calls character the function from contexts to contents and content the function from circumstances (indices) to truth values. In the definition of truth presented by Lewis (1980), truth is defined in relation to the pair <c,i>, where c is a context and i is a relevant index containing the elements of the context needed to evaluate the truth of a sentence. A sentence φ is true in context c at index i if the content expressed by φ in c is true at i. The idea of this truth definition is presented in Fig. 1 (cf. Lewis, 1980, p. 93). This construction guarantees that the content is dependent on a context but not on the index of context.
The above well-known concepts of Kaplan and Lewis are presented here because various forms of truth-relativism are sensitive to the interpretation of contextual semantics. Later, I will consider truth-relativism presented by Lasersohn (2005Lasersohn ( , 2017 and MacFarlane (2014). Contextual semantics help to avoid contextualism, which means that a sentence expresses different propositions in different contexts (DeRose, 1999;Kölbel, 2004). One implication of contextualism is that in disagreements, the opponents believe different propositions and therefore there are no genuine disagreements (cf. with case (1) above).
I am applying viewpoint logic to develop viewpoint relativism in line with Kaplan/Lewis (see Hautamäki, 1983b). 7 In this logic, the truth of sentences is defined in relation to possible worlds 8 and aspects (points of view or perspectives) 9 . A possible world is a technical term used to refer to different possible situations in the world (or states of the world), and similarly, aspects are used to denote different features of worlds. In addition to normal modal operators 5 By contextual semantics, I refer to semantic systems developed by David Kaplan (1989) and Davis Lewis (1980). 6 For this separation, look at Recanati (2008). 7 Hales (1997Hales ( , 2006 has independently developed a similar logic in his studies of relativism. Author's version from year 1983 is propositional, whereas Hales' version contains quantification, but in terms of operators, these logics are the same. I am presenting propositional logic here because the idea of viewpoint logic can be seen clearly from it. 8 'Time' acts as an element of models in addition to possible worlds in standard contextual semantics (cf. Kaplan, 1989). I omit it in this presentation, but one can consider possible 'worlds' to be multidimensional, containing situations, time, speaker, audience etc. But it is not difficult to include time as an element of contexts. 9 I use the term 'aspect' here because it is in agreement with the definition (3) of point of view.
(possibility and necessity), two new operators are introduced: 'A' for absoluteness and 'R' for relativity. 10 The formal definition of the model for propositional viewpoint logic is the following: Let P be a set of propositional symbols and L, a set of sentential operators plus P.
The model for L is the structure: where W is a non-empty set of possible worlds; V is a non-empty set of aspects; F assigns a subset of W×V to each p ∈ P: F(p) ⊆ W×V.
The interpretation of language is made in relation to couples <w,v>, where w is a possible world and v is an aspect of w. 11 The truth-values of sentence of L are defined by the truth-function T(φ,w,v), which gives a truth-value 1 (true) or 0 (false) to all sentences. If T(φ,w,v) = 1, I would say that φ is true at w from the aspect v. Supposing that a model M is given, T is defined as follows: The dependence of the truth-value of a sentence on context and index 10 In the viewpoint logic of Hautamäki (1983b) there are two two-dimensional accessibility relations, S1 and S2, in the set WxV, where W is a set of possible worlds and V is a set of aspects. Relation S1 is an accessibility relation for modal operators and S2 is an accessibility relation for operators 'A' and 'R.' Modal operators are omitted from this presentation. 11 It is possible to use, beside worlds and points of view, time and location as semantic elements like in Kaplan (1989).
When establishing truth-relativism on the basis of viewpoint logic, we must specify how to include points of view in contexts of utterance. Note first that the subject S can select different aspects in different worlds. For a lucid treatment, let P S be a function that assigns an aspect to each world: P S (w) ∈ V. P S (w) is called the point of view of S at w. By c[s,w,v] we denote to the context c, where s is the speaker (an evaluator) of c, w is the world of c and v is an aspect of w. The definition of viewpoint-relative truth is (4).
If v = P S (w), then the triple [s,w,v] is a point of view according to the definition (3). When φ is true in c[s,w,v], I would say that φ is true of w from the point of view of s or simply that φ is true for s at w. It is better to keep 'context' quite open to different interpretations: Sometimes, it is the context of utterance or use and sometimes, say, the context of evaluation. Similarly, the subject s of context might be a speaker, an assessor, an evaluator or a judge, you name it.
The context c[s,w,v] unambiguously fixes the point <w,v>, in relation to which the truth-value of the sentence φ is determined. The semantic rules of viewpoint logic guarantee that all sentences of interpreted language <L,M> have an unambiguous truth-value. All sentences are true or untrue from the point of view of s, and this is determined by whether the sentences are true or untrue in the point <w,P s (w)>. One consequence of viewpoint-relative truth is that a sentence can be true and false from different points of view but not from the same point of view.
One interesting consequence of this logic is that everything true is relatively true. Formally, (5) is a valid formula.
It is not a very strong principle, but it is, however, an important feature of truthrelativism, as Steven Hales has emphasised. (Hales, 2006, p. 102-3.) It can be interpreted as saying that behind all truths there is point of view from which it is true.
It is interesting to note that viewpoint logic can be extended to cover other logics than standard two-valued logic. In Hautamäki (1983b), modal operators for necessity and possibility are included, beside operators A and R. It is also shown that tense logic is easy to define by taking the set V of aspects to be time instances (cf. also Hautamäki, 2015). Then A means 'always' and R 'sometimes'. One promising line to extend viewpoint logic to allow three truth-values are the following: 1 for true, 0 for false and a third value, say ½, for the case of undefined (cf. Grandy, 2006). To do that, let the interpretation F be a function that assigns to every propositional letter p a function F(p) from the set W×V to the set {0, ½, 1} of truth-values. The truth-function T is defined for atomic formulas as follows: could be interpreted so that the truth-value of p at w from the viewpoint v is undefined or even that v is not applicable. The truth-value for other formulas can be defined in lines of any three-valued logic (see Grandy, 2006).
In viewpoint relativism, it is not supposed that points of view are represented explicitly in sentences. 12 When Anne says (6), the content is not that Mona Lisa is beautiful according to Anne's aesthetic standard; it is just the proposition that Mona Lisa is beautiful.
And this proposition is evaluated in relation to Anne's point of view, which belongs to the circumstance of evaluation. Anne's point of view can be seen in this case to be the aesthetic standard she uses to evaluate beauty. The key word is 'beautiful'. In some other cases, the connection between an expression and points of view is not so obvious. Say, (7) Pulsars are rotating neuron stars.
To evaluate the truth-value of (7), we must know in which discussion it is stated or used. In this case, the context might be that of modern astrophysics. In a very general way, we can interpret this situation so that the subject is the science community and the point of view is astrophysics. 13 This approach also works in analysing moral statements. Peter says, (8) Killing is forbidden.
In viewpoint analysis, the truth conditions contain a reference to Peter's moral code (say the Bible, or the Christian religion). The moral statement (8) is true from Peter's point of view (e.g. the Bible).
Alethic relativism could be defined in terms of viewpoint-relative truth. The concepts of 'absolute' and 'relative' are defined as follows: • A statement is absolute at w if it is true (or false) at w from all aspects. • A statement is relative at w if it is true at w from one aspect and false from another aspect. Now we can define basic alternatives to truth-theories in this context. According to absolutism, all sentences are absolute at all wolds. This means that if a sentence is true, it is true absolutely: φ → Aφ. Points of view have no effect to truth-values of absolute sentences: The truth-values are invariant under changes of points of view.
Basically, absolutism means that the truth-values of all statements are independent of points of view, and this is not a feasible option. There are convicting examples of statements whose truth is dependent on points of view. Almost all adjectives like 'big,' 'beautiful,' 'hot' etc. are somehow dependent on points of view.
According to strong relativism, all statements are relative, i.e. relative at all worlds. With a sophisticated argument, Hales (1997Hales ( , 2006 proves that this position is untenable. 14 A short argument against strong relativism is that all logical truths are absolute, not relative. When absolutism and strong relativism are untenable, the only reasonable form of truth-theory in the framework of viewpoint logic is moderate relativism according to which there are relative statements. In Hautamäki (2020) viewpoint relativism is defined as the hypothesis that language contains statements whose truth value is dependent on points of view. This amounts to mean that according to viewpoint relativism, there are relative statements.

Disagreements
The crucial test for truth-relativism is its ability to explain disagreement: How can the same proposition be true and false? For that we need to define what are the contents (propositions) of statements in viewpoint logic. In intensional semantics, the content or the meaning of a sentence is defined to be a function from possible worlds to truth-values (cf. Hautamäki, 1983b;Kaplan, 1989). In viewpoint logic, a truth-value is dependent on possible worlds and aspects; therefore, the content must be a function of worlds and aspects. Formally, the content of a sentence φ at w is the function Cφ w that maps aspects to the set {0,1} of truth-values as follows: (9) Cφ w (v) = T(φ,w,v).
Viewpoint relativism offers an elegant way to treat disagreements. Suppose that A and B disagree about the truth of a statement φ. Let their contexts of evaluations be c1[A,w1,v1] and c2 [B,w2,v2], respectively. The basic types of disagreement can be defined as follows: • Disagreement is apparent if Cφ w1 ≠ Cφ w2 . • Disagreement is genuine if Cφ w1 = Cφ w2 (as a special case w1=w2). • Disagreement is absolute if it is genuine and v1 = v2. • Disagreement is relative if it s genuine and v1 ≠ v2.
In apparent disagreement, A and B are talking about different things, say, about sweet and sour apples, and it is plausible to suppose that the content of φ is different in A's and B's contexts. In genuine disagreements, the content of φ is the same in both contexts c1 and c2. In absolute disagreement, it is impossible that both A and B are right because if v1 = v2=v then Cφ w1 (v)≠Cφ w2 (v). In relative disagreement, both A and B might be right because they have different points of view.
As an example, I will analyse a disagreement about 'taste.' 15 Suppose that Joe asserts (believes) (10) and Nora asserts (believes) (11). (10) and (11) are contradictory statements and the disagreement seems to be of the type (2.1).
In order to apply viewpoint relativism to this case, we have to decide how to treat 'tasty' in terms of points of view. Note that I have introduced propositional logic, where we could not treat predicates (adjectives) and their interpretations. One obvious interpretation is that person's taste is an aspect to look at the world. The truthcondition for this case can be presented as follows by the definition of viewpointrelative truth: (12) The sentence 'Apples are tasty' is true in the context c [S,w,v] if and only if 'Apples are tasty' is true at <w, v> where v is S's taste, v = P S (w).
This definition means that the sentence 'Apples are tasty' is true in context c if it is true of w according to S's taste in w. Thus, we have the following analysis of the relative disagreement between Joe and Nora: (13) T('Apples are tasty', w1, Joe's taste) = 1 and T('Apples are not tasty', w2, Nora's taste) = 1.
Thus, the sentence (10) is true relative to Joe's taste and its negation (11) is true relative to Nora's taste. The truth-value of this taste sentence is 'subjective' in the sense of being dependent on the subject's taste (Joe's or Nora's taste). The sentence 'Apples are tasty' has no truth-value without specification of relatum, because its 15 'Taste' has been a favourite example in discussion about disagreement; e.g. Belleri (2010); Cappelen and Huvenes (2018); Egan (2010); Hirvonen (2014); Lasersohn (2005); MacFarlane (2014); Stojanovic (2007). On the other hand, Hales argues that 'taste predicates do not adequately motivate relativism over the other possible solutions'; instead, he proposes to consider disputes involving 'irreconcilable differences'. However, I prefer to consider taste predicates because they uncover essential challenges related to truth-relativism, but compare Hautamäki (2020), Chapter 3.8 Defending Relativism. The analysis of 'taste' is applicable to other similar attributes like 'cool,' 'fun' or 'stylish.' My approach also works in disagreements related to different kinds of 'standards of evaluation', like disagreements about moral statements ('Stealing is wrong'), aesthetical statements ('Mona Lisa is beautiful') or epistemic statements (justification). Then aspects are just these standards. For epistemic standards, see Hautamäki (2020), Chapter 5. truth-value is viewpoint-dependent. But when a subject is fixed by the context, the sentence 'Apples are tasty' has a definite truth-value determined by objective facts of the context. I would like to call contextual objectivity the claim that the proper context of use should contain all relevant elements including a variable relatum needed to determine objectively the truth-value of a sentence uttered in the context. 16 It is important to note that contextual objectivity does not imply that the truth in a context of use is absolute. The presence of viewpoint or taste in the context of use means that the truth-value of a sentence is relative, not absolute. Contextual objectivity does not presuppose that the content of statements is determined by the context of use as contextualism states; it is not excluded that the same proposition has different truth-values in different contexts. We will see that Lasersohn and Mac-Farlane have a different stance on this issue.
But is this kind of analysis of disagreement satisfactory? Let us suppose that the disagreement is of the type (2.2): Against contextualism, the same proposition is taken to be true and false. There is no contradiction, however, because truth is determined in relation to different relata; so, the disagreement is relative, not absolute.
The crucial test for the analysis of disagreement is how the disputants see the disagreement. This depends on the semantic competence of speakers. According to the assumption of semantic competence, 'speakers of English are semantically competent with predicates of taste: they master their meaning and truth conditions' (Stojanovic, 2007). 17 If speakers are semantically competent, then they know that the truth-value of taste statements like (10) is dependent on the taste of speakers. They understand that both (10) and (11) can be true, but in relation to different tastes (Joe's and Nora's). This means that they know that the disagreement is relative. On the other hand, if speakers are not semantically competent, the disagreement seems to be absolute, of the type (2.1) and then (14) Either (10) or (11) must be false.
Then Joe believes that (10) is true and (11) is false and Nora believes inversely. If Joe and Nora would like to settle their disagreement, the other must change taste. 18 So far, I have argued that • If speakers are semantically competent, disagreement is relative for them. • If speakers are not semantically competent, disagreement is absolute for them.
What this result shows is that disagreement seems to be quite different from the point of view of truth-theory (semantics) and from the point of view of speakers (pragmatics). If speakers are not semantically competent, a relative disagreement seems to be absolute for them.

Lasersohn's and MacFarlane's Stance on Truth-Relativism
Viewpoint relativism is a variation of truth-relativism based on contextual semantics. Contextual semantics has been a starting point for several recent forms of truthrelativism, sometimes called 'New Relativism.' 19 The scope of new relativism is a quite large and there are several researchers working in this field (cf. Baghramian & Carter, 2020). Technically, we can add many kinds of coordinates to index, thus leading to different kinds of relativism. In general, a crucial question for truth-relativism is which relatum is relevant when evaluating the truth of statements in a context. Representatives of relativism disagree on the answer. Many relativists, but not all, agree that typically, the relevant relatum is the speaker's. 20 This view is in accordance with contextual semantics according to which the context of utterance fixes all relevant parameters. I have called this feature contextual objectivity. Some relativists like Peter Lasersohn and John MacFarlane disagree over this practice, arguing that it makes relative truth 'absolute'.
As a first example, I will consider Lasersohn's form of relativism (Lasersohn, 2005 andLasersohn, 2017). Its aim is to give a sound account of disagreements containing reference to speakers' or persons' subjective attitudes or standards of evaluation. A typical example is taste, say the statement 'Apples are tasty'. The issue is how to analyse the situation where apples are tasty for Joe (10) but not for Nora (11). Lasersohn proposes that the truth-value of taste-sentences is dependent on individuals, or 'judges' as he calls them. Using the formalism of viewpoint logic, one can take aspects to be judges: (15) Either (10) or (11) must be false.φ is true in context c iff T(φ,w,j) = 1, where w is the world of c and j is a judge.
The intuition here is that the judge's perspective decides whether the statement said by the speaker is true. 21 The judge is not necessarily the speaker of the context. '[W]e must allow that the objective facts of the situation of utterance do not uniquely determine a judge'. (Lasersohn, 2005, p. 669) It follows that the truth-value of sentences containing predicates of personal taste is not objectively assigned by contexts of use and varies from judge to judge. Later Lasersohn (2017) explicitly introduced contexts of assessment to provide a judge (or a perspective). Then the truth-value of a sentence is evaluated in relation to two contexts, the context of use and a context of assessment.
The major reason to introduce judge and context of assessment to semantic theory is the need to make a distinction between 'matters of fact' and 'matters of opinion'. According to Lasersohn, if the judge is given by the context of use, then the truth-value of a sentence is factual and absolute, not relative. Only letting judge vary according to contexts of assessment, we could express the subjectivity of tastylike sentences. To have this effect, the value of a relative parameter must be indeterminate by the context in which the sentence is used. Lasersohn's theory, especially in Lasersohn (2017), is similar to the assessment relativism of MacFarlane.
According to MacFarlane, relativism that relativized propositional truth to nonstandard parameters is not as such relativism 'in the most philosophically interesting sense' (MacFarlane, 2014, p. vi). 22 He claims that if all relevant parameters (relata) are determined by the context of use, then truth-values are absolute, not relative (p. 67). More is needed to have genuine truth-relativism. For that, he introduces assessment relativism. His basic proposal is that the truth-value of an utterance is not determined by the context of use; it can only be assigned relative to a context of assessment. 23 According to truth-value relativism, there is no absolute fact of the matter about whether a proposition, as used at a particular context, is true; it can be true as assessed from one context and false as assessed from another. (MacFarlane, 2014, p. 73) The starting point of assessment relativism is that in language, there are assessment-sensitive expressions E (like 'tasty') whose extensions e vary according to contexts c[i]. The index i has a crucial role here, it contains at least a world w and a value of E in c. The novelty of assessment relativism is to define the truth-value in relation to a context of use and a context of assessment. The definition of assessment-sensitive truth is as follows (cf. MacFarlane, 2014, p. 67): (16) The sentence φ is true as used at a context c1[w1, e1] and assessed from a context c2[w2,e2] iff φ is true at c1[w1, e2]. 24 The context c1[w1, e2] is a hybrid built by replacing e1 in the index of c1 with e2 from the context of assessment. The role of the context of assessment is just to provide a value to assessment-sensitive expression. The hybrid context contains a new circumstance of evaluation, where the value of E is that of the assessor, e2. It 24 The condition 'φ is true at c1[w1, e2]'can be presented as 'T(φ,w1,e2) = 1' in viewpoint logic. 22 MacFarlane call this kind of relativism 'nonindexical contextualism'. According to him, it does not benefit from the possibility to replace or change an element of index in a context (elements like taste or aesthetic standard). Cf. the concepts of use-sensitive and use-indexical in MacFarlane (2014, pp. 79 and 89). 23 Cf. Chapter 3.2 in MacFarlane (2014). follows from the definition (16) that the truth-value of the sentence φ as used at a context c1 varies according to contexts of assessment.
MacFarlane criticises 'nonindexical contextualism', which considers only the context of an utterance in determining truth-values, for commitment to absolute truth. This can be seen clearly from the following quote (MacFarlane, 2016).
And on the other hand, there are ways of relativizing propositional truth to subjective factors like tastes that should not count as truth-relativist, since they retain the idea that whether an assertion of is made truly-whether it is objectively correct-is an absolute matter.
Here, MacFarlane clearly refers to truth-relativism, which accepts contextual objectivity. But I am afraid that he misinterprets contextual objectivity, because it doesn't imply absoluteness. According to the very concept of relative truth, if a sentence φ is true in a context c containing a relatum r, φ is true relative to r, not absolutely true. If it were absolutely true, contradictory statements like (10) and (11) would both be absolutely true. This misinterpretation can be interpreted in terms of viewpoint logic as acceptance of the invalid formula 'Rφ → φ'.
Because the relatum is dependent on the subject, relative truth in a context also expresses the subjectivity of 'opinions' well. I can't agree with the claim of MacFarlane and Lasersohn that to make justice to the subjectivity of taste-like sentences, a new contextual element (like judge or taste) must be introduced outside the context of use. The cost of this manoeuvre is the delusion of the very concept of context. Contextual objectivity doesn't exclude relative subjectivity but it is incompatible with absolutism. Note that assessment relativism also accepts contextual objectivity in the hybrid context, like Lasersohn (2017) writes: To say that Elderberries are tasty is true relative to a context of assessment with John as the judge is to say that it is objectively true that elderberries are tasty for John.
A major argument of MacFarlane for assessment relativism is the treatment of disagreements. 25 According to assessment relativism, in disagreement a speaker and an assessor are not in a neutral position because it is the assessor's context that matters. Behind assessment relativism there seems to be a special internal view of disagreement, according to which parties of disagreement are deeply involved and take their own beliefs to be true simplicité. For them it is 'a mistake to believe a content that is not true from one's own perspective' (Kölbel, 2004). Consider the statements (10) and (11) and suppose that Nora is an assessor. What Joe said is false from the point of view of Nora, and Nora is right because she is an assessor. Assessment relativism takes this disagreement to be of the type (2.1), which is also the interpretation of disagreement given by absolutism: Either (10) or (11) must be false. But then assessment relativism loses the core of relativism, i.e. the claim that the same proposition could be true and false, but of course in different contexts (case 2.2).
Assessment relativism puts speakers and assessors into an asymmetrical position: If a speaker and an assessor disagree, it is the assessor who is right. In viewpoint relativism, all disputants are in a symmetrical position and there is no need to decide "who is right." Both might be right from their own points of view, like in the disagreement between Joe and Nora: Apples are tasty for Joe but not tasty for Nora. This disagreement seems to be a logical contradiction because Nora denies what Joe says, but semantically taken, it is not a logical contradiction because both statements could be true relative to the disputants' taste. 26 Of course, if Joe and Nora are not semantically competent, they might feel that there is a real contradiction between them (this could be called pragmatic controversy).
Behind assessment relativism, there seems to be a presupposition that disputes are crises to be resolved (MacFarlane, 2007, p. 30). But why must Joe change his mind about the taste of apples although Nora disagrees with him? This also applies to retraction: Why must I retract my earlier opinion when I have changed my mind? According to viewpoint relativism, genuine disagreements are not something to solve, but something to understand, to be aware of different points of view. 27

'Replacement Relativism'
The practice of relativism to introduce a new parameter to solve disagreements is, of course, prone to criticism. 28 From this large discussion, I will point out only some examples, and after that I will concentrate on Boghossian's critics of so-called 'replacement relativism'. Soames (2011) defends the monadic concept of truth over the relative (dyadic) concept of truth used in relativism. He claims that if such relativizations are to make sense, they must be explained in terms of the monadic notion of truth. Be referring to possible world semantics, he states that for a proposition p to be true at w is just for it to be the case that if w were instantiated, then p would be true. So in the last analysis, a proposition p is true only if the universe is the way p says it to be. Soames excludes, without arguments, the possibility that the the world could be viewed in many ways, and this is what pluralism and relativism want 26 When a statement is true in relation to a relatum r, its negation is false in the same relation. 27 In this connection, it is worth mentioning that MacFarlane (2020) has recently presented a new analysis of vagueness ('Richard is tall') where expressions are evaluated in relation to world/delineation pars <w,d> where the threshold d is determined by the speaker's 'hyperplan'. In terms of viewpoint logic, d can be seen to be an aspect. 28 The idea to define relativism in terms of hidden variables originated from Harman (1975). For general criticism of relativism, see e.g. Cappelen and Huvenes (2018), García-Carpintero and Kölbel (2008), Hales (2011), Lynch (2011), Niiniluoto (2014, and Soames (2011). to capture (cf. Colomina-Almiñana, 2018). The reduction of relativistic truth to the monadic notion of truth is not always possible. Lynch (2011) argues that truth-relativism cannot be global. Therefore, relativists must accept truth pluralism, according to which there is more than one property that makes judgements true. If that property is the correspondence with reality, then the monadic concept of truth, true simplicter, is working well. But if the property is to be true relative to a perspective, then the monadic notion of truth is not applicable. According to Lynch, the truth-relativist should be truth pluralist. Although I accept this conclusion in principle, I consider contextual semantics and especially the principle of contextual objectivity to provide a unified concept of truth.
Relativism and realism often seem to be in strong opposition (Baghramian, 2004). Niiniluoto, a well-known representative of realism, interprets relative truth in terms of belief: Personal truths are simply identified with personal beliefs. 29 It follows that relative truth leads to a conflict with the fundamental laws of logic. But this conflict follows only if the truth predicate is interpreted as truth simplicité. This is an example of criticism based on truth monism. A serious challenge for truthrelativism is the claim of Cappelen and Hawthorne (2009) that the context of an utterance determines a proposition, which is absolutely true or false (cf. also Mac-Farlane, 2014). Truth-relativism rejects this kind of contextualism, as we have seen. If the context of utterance c contains a variable element r, a relatum, and the same proposition p is true in c[r1] and false in c[r2], then it is untenable to claim that p is absolutely true and absolutely false.
According to Boghossian (2006b) 'the relativist about a given domain, D, purports to have discovered that the truths of D involve an unexpected relation to a parameter'. I interpret the criticism of relativism by Boghossian so that relativism is committed to the replacement simple of statements by statements referring to these extra parameters. 30 The problem with relativism is that speakers do not necessarily know that there are such parameters. So, relativism does not respect people's intentions in communication and even attributes error to them. Take an example. When Peter utters the sentence (17): (17) Anchovy is delicious.
he does not express the proposition that anchovy is delicious, but rather the relational proposition (18).
(18) Anchovy is delicious according to my (Peter's standard of) taste.
According to Boghossian (2006b) 'it would be wrong to construe the discovery of relativism about a given domain as the discovery that the characteristic sentences of that domain express unexpectedly relational propositions'. Of course, if Peter really intended (18), the content of (17) would change. (17) is an expression of taste but (18) is a description of Peter's taste towards anchovy.
This criticism, however, does not meet truth-relativism that separates contents and circumstances of evaluation of sentences. Truth-relativism is not content-relativism and is not committing to the replacement of (17) by (18). So, in this sense Boghossian's criticism is not adequate. But still there is the question what Peter intends to say by uttering (17).
Let us consider two cases: (19) Peter is semantically competent (aware of points of view).
(20) Peter is not semantically competent (not aware of points of view).
If (20) is the case, it is easy to understand why he has not intended anything like (18). Peter wants to say that (17) is simply true, not that it is true relative to his point of view. Also, the audience might interpret Peter's intention to be to just state that (17) is true. 31 But in the case of (19), the situation is more complicated. His intention might be to communicate to an audience that (17) is an absolute fact, not a subjective statement, or he just likes to stress his opinion, or perhaps he wants to manipulate the audience to believe in the same way as he. But it is also possible that Peter is supposing that he and the audience share the same point of view (taste); and then, mentioning the point of view explicitly is not necessary. In any case, I do not see a reason to suppose that by uttering (17) Peter intends to utter (18). Boghossian (2006b) also has a comment against the relativization of truth-conditions. He states that the truth-conditions of simple sentences, like (17), are expressed in relativism by relational conditions, like (18). Therefore, truth-relativism attributes a truth-condition error to speakers. One answer to Boghossian is that truth-relativism is a theory of truth. Ordinary speakers do not have to know the truth-theory in order to be able to communicate. But when evaluating the truth, one has to use a theory of truth. Truth-relativism is the claim that truth is dependent on points of view (or perspectives, tastes, etc.). Truth attribution is made in metalanguage, where the contents of statements are related to circumstances of evaluation and at this metalevel, points of view are introduced like in (21): (21) The sentence (17) is true iff anchovy is delicious relative to the speaker's taste.
This expresses the truth-condition for (17), not its content. The content of (17) is that anchovy is delicious and, therefore, the sentence (18) expresses it wrongly and is in no way replacing the sentence (17).
The basic issue here is why the truth-condition for (17) is relativistic like in (21) and not absolutist in the sense of Tarskian T-sentences 32 like in (22). 31 Hirvonen (2014) argues that the Folk theory of taste is objectivist; people are taking taste-assertions to be objective. 32 Tarski (1999). Semantic theory of truth is intended to capture the absolute concept of truth; T-sentences are not valid as such for the relativistic theory of truth. In viewpoint logic, the absolute concept of truth could be defined by the formula 'φ is true iff Aφ is true'.
The burden of relativism is to argue why some sentences like 'Water is liquid' are interpreted to be absolute and others like 'Anchovy is delicious' to be relative.
One can call a sentence viewpoint-dependent if its truth-condition contains a speaker's point of view like in (21). We can distinguish two forms of relativism: According to strong relativism, all sentences are viewpoint-dependent, and according to moderate relativism, there are viewpoint-dependent sentences. It is difficult to defend strong relativism, but a moderate relativism like viewpoint relativism is an interesting hypothesis. One way to confirm moderate relativism is to present linguistic and semantic data containing viewpoint-dependent expressions (cf. Hautamäki, 2020, p. 98). One class of such is e.g. assessment-sensitive expressions. The systematic theory to explain viewpoint-dependence is still lacking, however.

Conclusions
In this article, I introduced viewpoint relativism as a general framework to analyse truth-relativism and disagreements. It is shown that viewpoint relativism gives a comprehensive account of disagreements. In this framework, the concept of viewpoint-relative truth is defined. According to it, relative truth is objective and depending on the point of view given by the context of use; this is the claim of contextual objectivity. This approach is compared to truth-relativisms presented by Lasersohn and MacFarlane. According to them, the truth-value of sentences containing predicates of personal taste is determinable relative to a context of assessment beside the context of use. They argue that if the context of use fixes the truth-value, then truth is absolute, not relative. I disagree, because the fact that a proposition p is true in one context does not exclude its being false in another context. The use of two contexts in a truth definition makes things complicated and turns contexts incomplete. Finally, I defended the concept of relative truth against the criticism of Boghossian. What he missed is that relativisation concerns truth-conditions, not sentences or their contents. are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.