Towards a Unified Notion of Disagreement

Delia Belleri, Michele Palmira

The definitive version of this article is to be published in the Grazer Philosophische Studien, 88, 2013. Please refer to the published version.

AbstractIncreasing attention has been devoted to disagreement in recentyears. In particular, the topic of disagreement has been revivedby arguments purported to discredit certain forms ofContextualism, and to defend new forms of Relativism in thesemantics of knowledge attributions, epistemic modals, tastepredicates, aesthetic judgements and so on.In this paper, we pursue two aims: first of all, we wish tooutline a unified notion of disagreement which can act as a common“schema” of which various, more specific notions of disagreementcan be said to be particular instances. Secondly, in view of sucha unified notion of disagreement, we draw some methodologicalconsiderations regarding the argumentative strategies usedespecially by proponents of Relativism in order to defend theirtheory, which heavily draw on the idea that these theories areparticularly fit to capture certain intuitions of disagreement.

Introduction

Increasing attention has been devoted to disagreement in recentyears. In particular, the topic of disagreement has been revivedby arguments purported to discredit certain forms ofContextualism, and to defend new forms of Relativism in thesemantics of knowledge attributions, epistemic modals, tastepredicates, aesthetic judgements and so on.In this paper, we pursue two aims: first of all, we wish tooutline a unified notion of disagreement which can act as a common“schema” of which various, more specific notions of disagreementcan be said to be particular instances. Secondly, in view of sucha unified notion of disagreement, we draw some methodologicalconsiderations regarding the argumentative strategies usedespecially by proponents of Relativism in order to defend theirtheory, which heavily draw on the idea that these theories areparticularly fit to capture certain intuitions of disagreement.

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The paper is thus organised: In section 1, we will put forth aschematic definition of disagreement. In section 2, we will arguethat some definitions of disagreement, which are based on a notionof propositional truth as relative to circumstances of evaluation,are instances of the proposed schema. In section 3, we will arguethat also definitions of disagreements which rely on a stronglyrelativised notion of propositional truth (such as, to put it inJohn MacFarlane’s lingo, truth at “contexts of assessment”) areinstances of the schema. In section 4, we draw some methodologicaland conceptual considerations with respect to the strategy ofusing arguments from disagreement in order to defend one'ssemantics. In particular, we will emphasise that, if the proposedschema is correct, then certain arguments based on disagreementget significantly weakened.

1. Disagreement

In this section, our aim is to propose a definition ofdisagreement. To forestall misunderstanding, we claim from theoutset that we will be interested in doxastic disagreement, whichis a relation between individuals capable of having propositionalattitudes, as opposed to practical disagreement, which concernscoordination in action. Moreover, we will be interested indisagreement as a contrast between non-gradable propositionalattitudes. In general, we regard disagreement as obtaining betweentwo parties who make full acceptances, which in turn bear a specialrelationship to each other. In order to describe thisrelationship, we need to introduce some terminology. First of all, we will characterise disagreement in terms ofacceptance and rejection of semantic bearers. This expression refersto entities that are the primary bearers of truth and modalproperties, and that can be the object of our attitudes. It isworth noticing that the expression semantic bearer may stand forboth standard propositions as sets of possible worlds and non-standardpropositions as sets of more complex circumstances of evaluation,such as time-location-world triples1. Quite interestingly, the term

1 Though we explicitly employ a notion of propositions as sets of truth-conditions, we acknowledge that the notion of semantic bearer doesn't pose anyconstraints on the ontology of these entities. Thus, semantic bearers could alsobe structured propositions. Use of a notion of propositions as sets of truth-conditions simply ensures a continuity with the most recent literature ondisagreement, which employs this kind of conception.

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“semantic bearer” may also be employed to talk about sentences.2 Inother words, the term “semantic bearer” is designed to be suchthat it will allow the theorist to remain uncommittal as to thestructural and ontological features of the entities involved.Secondly, let us define the notions of acceptance and rejection.One accepts a semantic bearer φ if one asserts or believes φ.Conversely, one rejects a semantic bearer φ if one denies, ordisbelieves φ.Thirdly, we will say that the acceptance of a semantic bearergives rise to certain conditions of accuracy for that acceptance. Wedefine accuracy as truth of the accepted semantic bearer φ at therelevant “point of evaluation”. Here again we wish to remainuncommittal about what a point of evaluation may consist of. Apoint of evaluation may be a circumstance of evaluation whichcomprises the world of acceptance, but also the world-location-time of acceptance. Let us provide some examples.Suppose that I accept the sentence “It's sunny in Paris now” at 12pm; we can regard this sentence as expressing a standardproposition, corresponding to the set of possible worlds in whichit is sunny in Paris at 12 pm. The relevant “point of evaluation”will be a circumstance consisting of a possible world w. Myacceptance of this sentence will be accurate if and only if, atthe world of acceptance @, it is sunny in Paris at 12 pm. Supposenow that I accept the sentence “It is raining” as talking aboutSeattle, at 12 pm; this sentence may be regarded as expressing anon-standard proposition, being the set of world-time-locationtriples at which it's raining. The point of evaluation willtherefore be a complex circumstance of evaluation consisting of a<w, t, l> triple. My acceptance of this sentence will be accurate ifand only if it’s raining at the w, t, l relevant to my acceptance—namely the actual world @, 12 pm and Seattle. As one may have noticed, there are two main aspects on which we2 Of course, this implies that one has to define truth and falsity,necessity and possibility as properties of sentences and provide an account ofpropositional attitude reports which avoids the idea that an attitude verb thattakes that-clause complements expresses a two-place relation between subjectsand propositions. Several strategies have been attempted in this direction, fromtraditional sententialism to paratactic solutions and theories based on arelation with interpreted logical forms. A recently revived alternative (seeMoltmann 2003) is the multiple theory of judgment put forth by Bertrand Russellto the effect that an attitude verb specifies a multiple relation which relatesthe subject to the propositional constituents, e.g. in the case of atomicsentences to properties and their arguments.

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wish to remain neutral: (i) the nature and structure of theentities accepted and rejected by the parties to a disagreement(which we call semantic bearers) and (ii) the structure of thepoint of evaluation for their acceptances and rejections.Maintaining a neutral approach on these aspects enables thetheorist to see some interesting implications. One implication is,for instance, that acceptance of a sentence e that expresses a non-standard proposition p in circumstances c may have the same(broadly construed) conditions of accuracy as an acceptance of asentence e′ that expresses a standard proposition q. In the way ofillustration, consider the following pair of acceptances, andtheir related conditions of accuracy.

an acceptance of “It is raining” as concerning Seattle at 12pm, is accurate iff it is raining in Seattle, at 12pm, in w;

an acceptance of “It is raining in Seattle now” at 12 pm isaccurate iff it is raining in Seattle, at 12pm, in w;

Although the former acceptance may be regarded as taking as itsobject a non-standard proposition, while the latter acceptancetakes as its object a standard proposition, both are accurate(i.e. true) in the same (broadly conceived) circumstance—namelythe circumstance in which it's raining in Seattle at 12 pm, at w.Talk of “semantic bearers” here allows to erase the structuraldifference between the accepted entities, and to concentrate onthe fact that the acceptances are true in the same (broadlyconceived) circumstances of evaluation. Admittedly, in order tofully appreciate the import of this result, it's important thatone remains open-minded about the notion of circumstance ofevaluation.Fourthly, let us move to the relation in which two attitudes (likean acceptance of φ and a rejection of φ, or an acceptance of φ andan acceptance of not-φ) should stand in order for a disagreementto arise. For a start, it seems that for a disagreement to obtain,two parties should “talk about the same thing”. Clearly, if Aasserts “I am hungry” and B asserts “I am not hungry”, A and Bcannot be in disagreement, for they are expressing differentpropositions, even though superficially the sentence asserted by Bis the negation of the sentence asserted by A. To give but anidea, in the typical and simplest case of disagreement, A and Bare “talking about the same thing” to the extent that arerespectively accepting and rejecting the same proposition p, though

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this need not hold for all disagreement cases.3 In a Kaplanian semantic framework (Kaplan 1989), there is alsoanother sense in which the two parties should talk about the same thing:both parties should have attitudes that concern (i.e. are true orfalse at) the same circumstances of evaluation, for instance the sameworld, the same time, the same location, the same standards ofprecision, etc. If this condition is not satisfied, disagreementfalls apart. To illustrate. Suppose A asserts “It's raining” whiletalking about Paris and B asserts “It's not raining” while talkingabout London. Since each assertion concerns (i.e. is accurate orinaccurate at) a different place, the two speakers do not count asdisagreeing. In order for there to be disagreement, the parties'assertions should concern (i.e. be accurate or inaccurate at) thesame aspects of the circumstances of evaluation. This requirementis explicitly acknowledged by Michael Rieppel, who writes:

An account of [...] disagreement ought to take thecharacter of the CE that is relevant to the accuracy ofthe acceptance and rejection directly intoconsideration. Most straightforwardly, we could try thefollowing: A’s acceptance of a proposition [φ] and B’srejection of a proposition [ψ] are in disagreement justin case [...] the acceptance and rejection concern the same things.(The things an acceptance (rejection) concerns are [...]simply the values of the parameters of the CE that isdetermined by the context of acceptance (rejection).

[Rieppel 2011: 248, ouremphasis]

In a similar fashion, Ragnar Francén urges that:

If [two people] do not disagree over the truth-value ofthe proposition in question at a given circumstance ofevaluation, then there is no truth-value they disagreeabout at all. For (in [a Kaplanian] semantic framework)propositions have no truth-value independently ofcircumstances.

3 See MacFarlane (2007): 24. Consider the following scenario: At 4 pm Maryaccepts “Mick is drinking beer”, while at 5 pm Sylvia accepts “Nobody wasdrinking beer one hour ago”. Mary and Sylvia disagree, although they areaccepting different propositions. We will thoroughly discuss cases like thisbelow.

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[Francén 2010:29]

The final issue is that of stating what kind of relationshipshould occur between two attitudes which are about the same thingfor them to give rise to disagreement. We believe that the desiredrelation is a kind of “coordination” between the accuracyconditions of the two attitudes (be they two acceptances, or anacceptance and a rejection). Rieppel proposes to regard theattitudes as “coordinated” in such a way that:

The fulfilment of the accuracy condition of A’sacceptance guarantees the fulfilment of the inaccuracycondition of B’s rejection, or vice versa.

[Rieppel 2011: 251, ouremphasis]

We deem Rieppel's idea valuable, and we wish to endorse the spiritof his proposal. Our contribution goes in the direction ofclarifying and fully spelling out the notion of guarantee which,as Rieppel himself admits, is a little obscure.We propose to regard the idea of guarantee as encapsulating acounterfactual notion. Consider an acceptance of “It's raining” whichconcerns Seattle, countered by a rejection of “It's raining”concerning Seattle as well. We may say that the accuracyconditions of the first acceptance are such that, if they werefulfilled, this would ipso facto make the rejection inaccurate. Thisseems a fairly accurate description of what it means for thefulfilment of the accuracy conditions of the acceptance toguarantee the fulfilment of the inaccuracy conditions of therejection. Moreover, this may provide grounds for abandoning theguarantee metaphor in favour of a non-metaphorical, clearerstatement of the semantic relation between the acceptances andrejections involved in disagreements. We admit that this kind ofrelation seems not to be further explicable; indeed, it seems toregister a brute fact, as it were, about how the accuracy of oneattitude is “coordinated” to the inaccuracy of another attitude ina situation of disagreement.Having introduced the main terminological and conceptual aspectspresupposed by our view, let us state the definition of

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disagreement we will use in the present paper:

[Disagreement] A and B are in disagreement iff, for twosemantic bearers φ and ψ, the accuracy conditions of A’sattitude towards φ are such that, if they were fulfilled,this would ipso facto make B’s attitude towards ψ inaccurate,or vice-versa.

To exemplify the definition, consider A, who accepts “It’sraining” of Seattle, at 12 pm. In Chicago, at 12 pm, B accepts“It’s not raining in Seattle now”. According to definition juststated, A and B are in disagreement to the extent that A’sacceptance of “It’s raining”, concerning Seattle at 12 pm hasaccuracy conditions which, if fulfilled, would ipso facto make B’sacceptance inaccurate.This characterisation may seem at first glance to overgeneratedisagreements.4 Suppose A utters “Cicero was an orator” and Breplies “I agree”. Shortly after, B asserts “Tully was not anorator” and A replies: “I agree”. Provided they are both sincere(that is, they speak on what they believe), A and B seemreasonably to agree with each other. However, their situation fitswith our characterisation of disagreement, because, provided“Cicero” and “Tully” both refer to the same individual X, then theaccuracy conditions of A’s attitude towards <X was an orator> aresuch that, if they were fulfilled, this would ipso facto make B’sattitude towards <X was not an orator> inaccurate, or vice versa.So the two subjects would turn out as disagreeing, even thoughthey seem to be reasonably agreeing.We believe that, contrary to what it may seem at first glance,this is not a case of overgeneration. A and B are disagreeing aboutwhether or not X was an orator—they are just not aware of that,because they inadvertently use different names that, as a matterof fact, are co-referential. Thus, although A and B reasonablytake themselves to agree (after all, since they are ignorant ofthe coreferentiality of “Cicero” and “Tully” it is reasonable forthem to think that they agree), they are really disagreeing. Thatcases like this obtain implies that, in order to instantiate thedisagreement relation, subjects need not be aware of theirinstantiating it. This is in line with some independent, veryintuitive insights, which tell us that some disagreements are states(cf. Cappelen and Hawthorne 2009), in which presumably two

4 Thanks to an anonymous referee for pressing us on this issue.

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subjects may find themselves whether or not they are aware ofthat. Thus, two scientists who lived in remote ages and placescould count as in disagreement (from a bird's eye point of view,as it were) if, were the accuracy conditions of the firstscientist's acceptance to be fulfilled, the second scientist'sacceptance would ipso facto be inaccurate or vice-versa. There seemsto be no problem with saying that Ptolemy and Galileo were indisagreement (or at least that their views were), even though theycertainly weren't both aware of that at the time. So, at least incases similar to the one at issue, there is no threat ofovergeneration, because one would really expect there to be adisagreement.In the subsequent sections, we will show that [Disagreement] cansubsume at least three other kinds of disagreement definitionsthat have been proposed so far. If this is the case, then[Disagreement] provides a template or schema which describes thegeneral structure of each of these specific kinds of disagreement.

2. Parametric Accuracy Views of Disagreement

According to John MacFarlane (MacFarlane 2007: 23) acceptance of aproposition p is accurate just in case p is true at the circumstancethat is relevant to the evaluation of the acceptance in itscontext. It's easy to see that the notion of accuracy is, at leastat this stage, analogous to the notion of accuracy as stated inthe previous section—the only difference being that the notion ofaccuracy is formulated in terms of semantic bearers rather thanpropositions, and it presupposes a neutral notion of point ofevaluation rather than the Kaplanian notion of circumstance ofevaluation of the context. In a Kaplanian framework, the circumstances of evaluation arecomposed by one or more parameters of evaluation—such as a parameterfor possible worlds w, times t, locations l and so on. Accuracy ofan acceptance of p depends on the truth of p at one or more ofthese parameters. Let us call such a notion Parametric Accuracy.Depending on which parameters one is ready to admit into thecircumstances of evaluation, different kinds of ParametricAccuracy can be obtained. If one only admits for possible worlds,the resulting notion of Parametric Accuracy will be one in whichthe accuracy of any acceptance is fixed once and for all at w, so tospeak, for the truth of the accepted proposition p in turn isfixed once and for all at w. Let us call the resulting notion Eternal

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Parametric Accuracy. Eternal Parametric Accuracy will be favoured bythose theorists who, following Frege, are keen on the idea thatpropositions are specific with respect to certain features, such astime, and hence are true eternally. Mark Richard, Nathan Salmonand, more recently, Jeffrey C. King are among these authors (seeRichard 1981, Salmon 1986, King 2003).By contrast, if one is willing to admit worlds plus times, orworlds plus times and locations—in the footsteps of Kaplan (1989)and David Lewis (Lewis 1980)—one will get yet another notion ofaccuracy, namely one according to which the accuracy of differentacceptances of p will vary with the truth-value of p, which in turnmay change as the acceptance's time (or time-and-location)changes. So for instance, if we suppose that “Socrates is sitting”expresses the temporal proposition that Socrates is sitting, this impliesthat an acceptance of this sentence at t1 may turn out as accurate,if Socrates is sitting at t1, while an acceptance of the samesentence at t2 may turn out as inaccurate, if Socrates is notsitting at t2. Since the truth-value of p will not be fixed onceand for all, but it will be sensitive to how the values acquiredby the acceptance's time-parameter (or time-space parameter) vary,the resulting notion will be a Non-eternal Parametric Accuracy.5

Consideration of these two different kinds of Parametric Accuracyhas reverberations on the notion of disagreement one wants toconstrue. In general (and drawing partly on MacFarlane 2007), wemay say that a disagreement obtains just in case A's acceptanceand B's rejection are “coordinated” in such a way that they cannotboth be accurate with respect to the same circumstance ofevaluation. Depending on which parameters one admits into thecircumstances of evaluation, one can get two different types ofdefinitions of disagreement. The first definition describes asituation in which two parties accept and reject contents that aretrue at possible worlds only, hence a situation in which theaccuracy of one's attitude can only be eternal. The definitionwould be as follows:5 A qualification is in order. The notion of non-eternal accuracy at usehere isn't meant to be compatible with the idea that the same acceptance of pmay be accurate at time t1 and inaccurate at time t2. The acceptance's accuracy is“eternal”, so to speak, once it's established at a time t; what's not eternal isthe truth of the proposition, which could vary according to whom and whenaccepts it. If the acceptance's accuracy were non-eternal as well, one would bealready endorsing a radical form of Relativism (on which we will expound insection 3), which would imply, in the spirit of Evans (1985), abandoning theidea that an acceptance (like for instance an assertion) can be absolutely accuraterelative to a certain time t.

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[Eternal Parametric Disagreement] Disagreement obtains just incase A's acceptance and B's rejection are “coordinated”in such a way that they cannot both be accurate withrespect to the same possible world w.

By contrast, if one is ready to countenance more parameters in thecircumstances of evaluation than simply a possible worldsparameter—for instance, a time parameter—, then a non-eternalnotion of disagreement becomes available:

[Non-Eternal Parametric Disagreement] Disagreement obtains justin case A's acceptance and B's rejection are“coordinated” in such a way that they cannot both beaccurate with respect to the same world-time pair.

We wish to argue that Eternal and Non-eternal ParametricDisagreements are just two instances of the more general[Disagreement] schema we outlined above.Let us start with [Eternal Parametric Disagreement]. Consider A, whoaccepts “It's raining in Paris now” and B, who rejects thatsentence. An acceptance (rejection) of “It is raining in Parisnow” is accurate iff it is true (false) that it is raining inParis at the time of the utterance at w. The relevant point ofevaluation for the accuracy of the acceptance is the world of theutterance. We may redescribe the situation in terms of [Disagreement]in the following way: the accuracy conditions of A’s acceptance of“It's raining in Paris now” are such that, if they were fulfilled,this would ipso facto make B’s rejection of “It's raining in Parisnow” inaccurate, or vice-versa. This seems definitely to be thecase: if it were to rain in Paris at the world and time ofacceptance, then A would be right (her acceptance would beaccurate with respect to the relevant parameter) and B would beipso facto wrong (her acceptance would be or inaccurate with respectto the relevant parameter).Now we may move to an instance of [Non-Eternal Parametric Disagreement].Consider A, who accepts “It's raining” while speaking about Parisat 12pm, and B, who rejects that same sentence while speakingabout the same circumstances. A non-eternalist may say that anacceptance (rejection) of “It is raining” is accurate iff it istrue (false) that it is raining in Paris at 12 pm at w. Therelevant point of evaluation for the accuracy of the acceptance

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may be regarded as being a triple <w, t, l> of world-time-location,where the values of the parameters are given by the context ofacceptance. With this in mind, we may redescribe the situation interms of [Disagreement] in the following way: the accuracy conditionsof A’s acceptance of “It's raining” are such that, if they werefulfilled, this would ipso facto make B’s rejection of “It's raining”inaccurate, or vice-versa. Once again, this seems to be the case:if it were to rain in Paris at 12 pm at w, then A would be right,in the sense that her acceptance would be accurate with respect tothe relevant parameters, and B would be ipso facto wrong, in thesense that her acceptance would be inaccurate with respect to therelevant parameters. The definition provided by [Disagreement] is general enough to covercases in which one party accepts a standard proposition, which haseternal accuracy conditions, while the other party accepts (orrejects) a non-standard proposition, which has non-eternalaccuracy conditions. Suppose that A accepts the sentence “It'sraining in Paris now” at 12 pm; B, who is in London, accepts “It'snot raining” while talking about Paris at 12 pm. In this case, adisagreement obtains between two acceptances of sentences thathave different degrees of specificity, and which may be regardedas expressing structurally different contents. The contentexpressed by “It's raining in Paris now” is specific as to timeand location, and may be regarded as expressing a standard,eternal proposition; by contrast the content expressed by “It'snot raining” is non-specific as to time and location, and may beregarded as expressing a non-standard, non-eternal proposition.This difference doesn't prevent the application of the [Disagreement]template. As we observed in the previous section, talk of semanticbearers enables the theorist to bypass the distinction betweenstandard and non-standard propositions; also the neutral notion ofpoint of evaluation provides a way of erasing the differencebetween various ways of cashing out the circumstances ofevaluation of an accepted content. So for example, an acceptanceof “It's raining in Paris now” at 12 pm and an acceptance of “It'sraining” concerning Paris at 12 pm have the same (broadlyconstrued) accuracy conditions, in that they are both accurate iffit's raining in Paris at 12 pm at w. In order for the [Disagreement] template to apply, all that needs tobe acknowledged is that, regardless of the differences in thecontents accepted, A's acceptance and B's rejection haveincompatible (broadly construed) accuracy conditions. This is,

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once again, easy to see. A's acceptance of “It's raining in Parisnow” at 12 pm is accurate iff it's raining in Paris at 12 pm at w,while B's rejection of “It's raining” of Paris at 12 pm isaccurate iff it's not raining in Paris at 12 pm at w. This iscompatible with the idea, stated in [Disagreement], that the accuracyconditions of A's acceptance are such that, if they werefulfilled, B's rejection would ipso facto be inaccurate, or vice-versa. Thus, the [Disagreement] template applies in those cases inwhich the contents accepted and rejected by the parties havedifferent structural features—for instance, one is a standard,eternal proposition, while the other is a non-standard, non-eternal one. To sum up: In this section, we have drawn attention on twoavailable definitions of disagreement, one in terms of EternalParametric Accuracy, the other in terms of Non-Eternal ParametricAccuracy. We have shown that both definitions can be regarded asinstances of the more general template provided by [Disagreement].Moreover, we have shown how [Disagreement] can adequately capturecases in which two speakers disagree by accepting a standard,eternal proposition and a non-standard, non-eternal propositionrespectively.

3. Perspectival Accuracy View of Disagreement

So far we have been concerned with a view of accuracy which takesit for granted that a certain acceptance is accurate iff theaccepted proposition is true at the circumstances of evaluation ofthe context of acceptance. In other words, it has been a tacit assumptionthat the default context which fixes the values of the parametersof the circumstances of evaluation is the context in which theacceptance is performed. This, however, need not be so in general.There could be areas of discourse in which—a semanticist couldobserve—the context in which the acceptance is performed plays no“default” role as opposed to other contexts, as far as judging theaccuracy of the acceptance is concerned. This seems to obtain inthe taste area of discourse: when A accepts a sentence like “Icecream is tasty”, it seems that B is entitled to evaluating A'sacceptance as inaccurate (false), to the extent that B finds icecream awful. Even A could, in a later moment, judge her previousacceptance of “Ice cream is tasty” as inaccurate (false), if herviews on tastiness had changed in the meantime. Different points ofview on the matter may determine different evaluations of the same

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acceptance—thus making it the case that an acceptance is accuratein some points of view, and inaccurate in others.Semantic Relativists have given a formal and conceptual spell-outof the informal notion of point of view just illustrated. Forthem, in order to give an adequate semantics for a range ofexpressions, such as “tasty”, we have to countenance a differentspecies of contexts, which may be entirely independent of thecontext of acceptance, and in which the accuracy of an acceptancemay be simply evaluated: MacFarlane calls them contexts of assessment;Max Kölbel calls them perspectives, while Richard calls them judges(see MacFarlane 2005, 2007, Kölbel 2003, 2004, and Richard 2008.We ignore differences between these views, for present purposes).If we adopt MacFarlane's terminology, the notion of accuracymentioned in section 2 becomes relative to contexts of assessment.The resulting notion differs from the Parametric Accuracy outlinedin the previous section, in that the values of (at least some)parameters in the circumstances of evaluation are not always fixedby default at the context of acceptance, but are settled at thecontext of assessment, which may be completely independent of thecontext of acceptance and is typically thought of as a point ofview or perspective on the world. Accuracy then becomes Perspectival,as in MacFarlane (MacFarlane 2007: 26):

[Perspectival Accuracy] An acceptance (rejection) of aproposition p at a context c is accurate (as assessed froma context of assessment ca) iff p is true (false) at thecircumstance <wc ; sca>, where wc = the world of c and sca = thestandard [...] of the assessor at ca.

Adopting a perspectival notion of accuracy has consequences on howone conceives of disagreement. As we argued in section 1, forthere to be disagreement two acceptances should be about the samething: for example, the same world, time, location. In a Kaplaniansemantics, which regards propositions as true at circumstances ofevaluation, disagreement obtains just in case two attitudesconcern (e.g. the accepted propositions are true or false at) thesame circumstances of evaluation. Relativism differs from aKaplanian semantics in that it countenances contexts of assessmentin addition to contexts of acceptance (or utterance). A reasonablemove on the part of the Relativist will therefore be that ofrequiring that, for a disagreement to obtain between perspectivalacceptances, there be at least one perspective (or context of

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assessment) relative to which they can't both be accurate.Perspectival disagreement may be thus characterised:

[Perspectival Disagreement] Disagreement obtains just in case A'sacceptance and B's rejection are “coordinated” in such away that they cannot both be accurate with respect to thesame context of assessment ca.

We would like to argue that the notion of [Perspectival Disagreement] isbut a specific instance of the more general schema provided by[Disagreement].An acceptance of “Ice cream is tasty” is accurate iff it is truethat ice cream is tasty at the world w of acceptance and at the taste-standard s of the assessor. More specifically, we may say that suchan acceptance is accurate just in case the accepted proposition istrue at a certain point of evaluation, where the point ofevaluation could be spelled out as a couple <w, s>, where w is theworld of acceptance and s is the taste standard of assessment. Withthis in mind, we may consider the situation in which A accepts“Ice cream is tasty” while B rejects “Ice cream is tasty”, and re-describe it in terms of [Disagreement] in the following way: A and Bare in disagreement to the extent that the accuracy conditions ofA’s acceptance of “Ice cream is tasty” are such that, if theywere fulfilled, this would ipso facto make B’s rejection of “Icecream is tasty” inaccurate, or vice-versa. This seems to portrayhow things stand with respect to A's and B's situation. Suppose byhypothesis that, with respect to a certain context of assessment k,ice cream was tasty. This would make the proposition that ice cream istasty true at k, and hence A's acceptance would be accurate at kwhile B's acceptance would be ipso facto inaccurate at k.Note that saying that [Perspectival Disagreement] is but an instance ofthe more general [Disagreement] template doesn't imply reducingdisagreement on perspectival matters (taste, aesthetics, ethics)to disagreement on objective matters, as if semantic bearers like“Ice cream is tasty” were to be absolutely true or false.In fact, we think we don't need be bothered by this worry at all:the reason is that the way itself in which [Disagreement] isformulated is completely neutral as to the semantics underlying acertain discourse. Whatever the nature of the semantics of taste-assertions, [Disagreement] applies to a situation in which A asserts“X is tasty” and B rejects it just in case, relative to the relevant point ofevaluation, the accuracy conditions of A's assertion are such that,

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were they to be fulfilled, this would make B's assertioninaccurate. The schema provided by [Disagreement] leaves enough spacefor the theorist to maintain her favourite notion of accuracy at apoint of evaluation, where this point of evaluation may beidentified with the world, the world-time of the context ofacceptance, or even the world of acceptance and the standard oftaste of the context of assessment. This freedom allows thetheorist to take as little commitments as possible on thesemantics of the relevant area of discourse, while at the sametime capturing intuitions of disagreement.To sum up, in this section we have covered the notion ofPerspectival Accuracy, which gives rise to yet a further varietyof disagreement, called [Perspectival Disagreement]. We have argued thatthis variety of disagreement is yet a further instance of thegeneral schema provided by [Disagreement] in section 1.

4. Some Implications

Where do all these considerations leave us? Arguing for the thesisthat the varieties of disagreement just surveyed are but instancesof the more general [Disagreement] schema has some methodologicalimplications which are worth of consideration.First of all, regarding the Eternalism vs. Non-Eternalism debate,focus on the [Disagreement] schema makes it apparent that argumentsfor Non-Eternalism which draw on the point that the theory managesto capture certain specific intuitions of disagreement do notfavour Non-Eternalism as against Eternalism. For, as long asEternalists can comply with [Disagreement], they can capture the sameintuitions.As an example of Non-Eternalism, take a Temporalist semantics. Ifthere are temporal propositions, i.e. propositions that are trueor false at a time, then it is possible to account for thefollowing disagreement:

(Beer) At 4 pm Mary accepts “Mick is drinking beer”,while at 5 pm Sylvia accepts “Nobody was drinkingbeer one hour ago”.

Temporalists therefore endorse a conception of disagreement interms of incompatibility between the accuracy of acceptances at acircumstance of evaluation (like for instance [Non-Eternal ParametricDisagreement]). According to this move, Mary and Sylvia are

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disagreeing to the extent that Mary's acceptance of the temporalpropositions that Mick is drinking beer and Sylvia's acceptance of thetemporal proposition that nobody was drinking beer one hour ago concern thesame circumstance of evaluation (4 pm, w), with respect to whichthey cannot be both accurate. See MacFarlane (2007: 22-24).What we wish to argue is that one doesn't need either temporalpropositions or a specifically Temporalist notion of disagreementin order to account for the disagreement displayed in (BEER). Infact, one can be an Eternalist and capture the disagreementbetween Mary and Sylvia equally well, as long as one's accountcomplies with the [Disagreement] schema. As an example of Eternalist semantics, let us consider the accountput forward by Jeffrey C. King, in his influential paper “Tense,Modality, and Semantic Values” (2003). In the paper, King suggeststhat we take the contents expressed by sentences such as “Mick isdrinking beer” and “Nobody was drinking beer one hour ago” tosimply be functions from possible worlds to truth-values, and notfunctions from time-worlds pairs to truth-values. Morespecifically, King argues that the logical form of tensedsentences contains an extra-argument place for times, to berepresented as a phonetically silent pronoun. This pronoun can bebound by first-order language quantifiers which quantify overmoments of time, such as “in the past”, “in the future”, “one hourago”, “in three days”. Alternatively, the pronoun can get a valuesuch as “July 15, 1967, 12 pm” from contextual variableassignment. In each case, the result is that sentences are viewedas expressing time-specific, eternal propositions.Let us now apply King's account to the sentences accepted by Maryand Sylvia in (BEER). Suppose that Mary manifests her acceptanceby uttering “Mick is drinking beer”. First of all, note that theproposition expressed by Mary’s utterance at 4 pm of “Mick isdrinking a beer” contains the present tense; in King's terms, thismeans that Mary's utterance is equivalent to an utterance of “Mickis drinking beer now”. Since the time of utterance is 4 pm, Mary'sutterance shall express the time-specific content that Mick isdrinking a beer at 4 pm. Suppose that Sylvia, too, manifests heracceptance by uttering “Nobody was drinking beer one hour ago”.What's the content of Sylvia’s utterance? In a King-styleanalysis, the following two facts are key: first, the utterance isperformed at 5 pm; second, the sentence uttered contains theexpression “one hour ago”, which is to be treated as an objectlanguage quantifier. These factors make Sylvia's utterance

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equivalent to an utterance of “Nobody was drinking beer one hourearlier than now”; since the time of utterance is 5 pm, the utteranceshall express the content that nobody was drinking beer one hourearlier than 5 pm. Let us now see how having adopted an Eternalist account affects adescription of the disagreement situation. We wish to point outthat, as long as the Eternalist succeeds in describing thesituation in terms of [Disagreement], then she is on a par with theTemporalist as to this issue, in the sense that she is in aposition to account for (BEER) and therefore offer a bettercharacterisation of disagreement than the naïve view. In theEternalist's framework, Mary's acceptance of the time-specificcontent that Mick is drinking a beer at 4 pm is accurate iff Mick isdrinking a beer at 4 PM at w, while Sylvia's acceptance of thetime-specific content that nobody was drinking beer one hour earlier than 5 pmis accurate iff nobody is drinking beer at 4 pm at w. As one cansee, the acceptances' accuracy conditions make Mary's acceptanceincompatible with Sylvia's. We may safely say that, if theaccuracy conditions of Mary's acceptance were fulfilled, thenSylvia's acceptance would ipso facto be inaccurate, accordingly with[Disagreement]. If this is so, then Eternalism can account for (BEER)just as adequately as Temporalism, and both theories provide theresources to go beyond a naïve view of disagreement.Similar, and perhaps more interesting considerations apply toRelativism. As we saw in the previous section, Relativists arguethat a notion like [Perspectival Disagreement] is particularly fit tocapture the structure of taste-disputes. But is [PerspectivalDisagreement] the only definition available? With regard to this, wewish to argue that disagreement on matters of taste may becaptured by the [Disagreement] template quite independently ofRelativism. We will show that one may adopt a Communitarian varietyof Indexical Contextualism and still be able to explaindisagreement on taste, as long as one is able to comply with the[Disagreement] schema. What follows from this is that Relativismdoesn't provide a special vantage point on disagreement on mattersof inclination, contrary to what its proponents have argued.To forestall misunderstandings, however, we wish to clarify thatit is not the aim of the present discussion to argue in favour ofa Relativist or a Contextualist account of taste discourse. As iswell-known, a number of objections have been raised against bothapproaches and it is an open question to what extent, if any,Relativism and Contextualism can satisfactorily account for

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predicates of personal taste. In this paper, however, we are notinterested in establishing whether Relativism or Contextualismscore as rough equals on overall theory assessment; rather we wishto evaluate whether these two theoretically sophisticatedrenditions of taste discourse are both compatible with the[Disagreement] schema we’ve been recommending.Having clarified this, consider the following example of tastedisagreement.

(GUACAMOLE) Bob accepts “Guacamole is tasty”; Margaretaccepts “Guacamole is not tasty”.

As we have seen in section 3, proponents of Relativism contendthat their theory is particularly fit to capture the special kindof disagreement that obtains between Bob and Margaret (seeMacFarlane 2005, 2007). A brand of Relativist semantics that seemsto succeed in this task is, for instance, MacFarlane's AssessmentSensitivity view. In this view, Bob's acceptance takes as objectthe taste-neutral content that Guacamole is tasty while Margaret'sacceptance takes as object the taste-neutral content that Guacamole isnot tasty. Disagreement arises insofar as acceptances of thesecontents cannot both be accurate if evaluated at the same contextof assessment ca.What we will show in the following paragraphs is that disagreementon matters of taste may be adequately captured also by a Non-Relativist semantics, provided the [Disagreement] schema is met.An example of Non-Relativist semantics is Indexical Contextualism,i.e. the view that some expressions contain hidden free-slots tobe saturated in context; in this specific case, IndexicalContextualism will be identified with the view that the predicatetasty(x) contains some hidden argument place for a taste-standard sthat gets filled by a syntactically realized but phoneticallysilent pronoun. Thus, “tasty” is really a two-place predicatetasty(x, s). In the Indexical Contextualist framework, an utteranceof “Guacamole is tasty” in context c1 shall express the “taste-specific” content that Guacamole is tasty for sc1. In order for IndexicalContextualism to get it right about the disagreement in(GUACAMOLE), the view must be combined with the assumption thatthe value of s is the same for both the parties of the dispute. Inorder to meet this requirement, the Indexical Contextualist mightposit that the value of s is fixed by the gustatory standardadopted by the group formed by the participants to the

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conversation. Hence, the content of Bob's acceptance (manifestedthrough assertion) may be cashed out as being that Guacamole is tasty forsc1 while Margaret's acceptance (manifested through assertion) willbe equivalent to the content that Guacamole is not tasty for sc1, where sc1 isthe standard relevant to the group formed by Bob and Margaret.6 Letus call a proposal along these lines a Communitarian version ofIndexical Contextualism (see e.g. Glanzberg 2007 and Sundell2011).Following the Communitarian Indexical Contextualism outlinedabove, we might say that the conditions for the accuracy of Bob'sacceptance are that guacamole is tasty relative to sc1 at w, whilethe conditions of accuracy of Margaret's acceptance are thatguacamole is not tasty relative sc1 at w. With these considerationsin mind, we may safely say that, if the accuracy conditions ofMargaret's acceptance were fulfilled, then Bob's acceptance wouldipso facto be inaccurate. This seems to be an adequate description ofthe disagreement between Bob and Margaret, which complies with[Disagreement].7 (Note that such a description is completely neutralas to the metaphysics of taste—the existence of taste properties,for instance—as well as to the semantics of taste assertions—whether “tasty” is a two-place predicate.) The conclusion to be drawn from these considerations is thefollowing: once [Disagreement] has been spelled out, Relativism turnsout as not being the only semantic theory which is in a position6 Note that the standard “adopted by” or “relevant for” the group need notbe the standard of the group. This entails that, for instance, Bob's assertionof “Ice cream is tasty” needs not be equivalent to an assertion of “Ice cream istasty for us”, but only needs be equivalent to an assertion of “Ice cream is tastyaccording to the currently relevant standard”. 7 It is worth noticing that this point is different from the point made byKölbel (2007) and López de Sa (2008) to the effect that Indexical Contextualismcan predict disagreement if we accept the idea that the sentences involved indisagreements on personal taste carry a presupposition to the effect that thespeaker’s gustatory standards agree with the audience’s gustatory standards. Onthis view, although the disagreement is not captured at the level of semanticbearers, disagreement among individuals is nevertheless predicted, for thespeakers take themselves to disagree because both of them presuppose that theirstandards of taste are alike. By contrast, Communitarian Indexical Contextualismbrings the communitarian standard directly into the circumstances of evaluation;communitarian aspects therefore affect the semantic evaluation of each party'sacceptance, rather than their beliefs as to whether disagreement does or doesn'thold. In light of these considerations, what we argue is that IndexicalContextualism, in the Communitarian version we are considering, capturesdisagreement at the level of semantic bearers without bringing into the picture anypresupposition of commonality.

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to account for situations like the one obtaining in (GUACAMOLE).The methodological consequence is that arguments that purport todefend Relativism on the account that it is the only theory ableto explain taste disagreements appear as considerably weakened,for if the template provided by [Disagreement] is adequate, thenRelativism has at least one competitor on this level—namely,“Communitarian” Indexical Contextualism.

Conclusion

In this paper, we have worked out a notion of disagreement whichcan act as a schema or template, of which other, more specificnotions can be regarded as instances. Such a template subsumesnotions of disagreement based on propositional truth as relativeto circumstances of evaluation (called “Parametric” views) as wellas notions of disagreement which rely on propositional truth asrelative to contexts of assessment (“Perspectival” views).Consideration of such a template helps gain a deeper understandingof the notion itself of disagreement, in that it points at acommon structural feature which different, specific notions ofdisagreement share. At the same time, consideration of thetemplate has some methodological repercussions. In particular, itturns out that, in view of this common template, arguments whichaim at defending one particular semantic view on the account thatit captures certain intuitions of disagreement appear assignificantly weakened. For, if various types of disagreement allrespond to a common, general template, alternative views may arisein opposition to the defended theory, which may enable one toaccount for the same intuitions while making different—and perhapsless controversial—semantic commitments.

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