How to Be an Ethical Expressivist

Philosophy and Phenomenological ResearchVol. XCI No. 1, July 2015doi: 10.1111/phpr.12138 2014 Philosophy and Phenomenological Research, LLC

How to Be an Ethical Expressivist

ALEX SILK

University of Birmingham

Expressivism promises an illuminating account of the nature of normative judgment. Butworries about the details of expressivist semantics have led many to doubt whether ex-pressivisms putative advantages can be secured. Drawing on insights from linguisticsemantics and decision theory, I develop a novel framework for implementing an express-ivist semantics that I call ordering expressivism. I argue that by systematically interpretingthe orderings that gure in analyses of normative terms in terms of the basic practical atti-tude of conditional weak preference, the expressivist can explain the semantic propertiesof normative sentences in terms of the logical properties of that attitude. Expressivismsproblems with capturing the logical relations among normative sentences can be reducedto the familiar, more tractable problem of explaining certain coherence constraints on pref-erences. Particular attention is given to the interpretation of wide-scope negation. The pro-posed solution is also extended to other types of embedded contextsmost notably,disjunctions.

1. The Expressivist Program

Expressivism is something of a four-letter word in some circles. (Is thatnot triply a lie?) And yet there is something persistently alluring about itsresearch program. Though expressivism was originally developed as a meta-ethical position about normative language and judgment, its appeal hasextended across philosophical disciplines. Expressivist semantics have beengiven for a diverse class of expressionsnot just for normative terms likeought, wrong, and rational, but also for epistemic terms like mightand probably, for attitude verbs like knows and believes, and even formeans itself.1 Expressivism promises an illuminating account of themeanings of such expressions, the nature of judgments involving them, andthe connection between such judgments and motivation or action. But

1 See, e.g., Hare 1952, 1981; Price 1983; Blackburn 1984, 1998; Gibbard 1990, 2001,2003, 2012; Field 2000; Horgan & Timmons 2006; Yalcin 2007, 2012; Schroeder2008a; Swanson 2012; Moss 2012. I will treat expressivism as a thesis primarily aboutnatural language expressions rather than concepts.

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foundational worries about the details of expressivist semantics have ledmany to doubt whether these advantages can be secured.

On a standard truth-conditional semantics the semantic properties of sen-tences (e.g., inconsistencies, entailments) are, in the rst instance, explainedin terms of properties of the contents of those sentences: To a very roughrst approximation, the sentences Grass is green and Grass is not greenare inconsistent because they have incompatible truth-conditions. The pri-mary explanatory weight is placed on an assignment of contents to sen-tences and on relations among those items of content. Expressivists take adifferent tack. Though it is somewhat contentious how best to understandexpressivism, I take as my starting point the following familiar characteriza-tion. At the explanatory outset, the expressivist attempts to account for thesemantic properties of sentences in terms of properties of the attitudes orstates of mind that utterances of those sentences conventionally express.2

Contents or truth-conditions, even if or when they are assigned to sentences,do no work in fundamental explanations of the semantic properties of thosesentences. Expressivists can be understood as accepting the followingrequirement on fundamental semantic explanation:

THE EXPRESSIVIST PROGRAM

The semantic properties of sentences are to be explained, fundamentally, interms of properties of the attitudes conventionally expressed by utterances ofthose sentences.

In the case of ordinary factual sentences, this requirement might not seemoverly difcult to satisfy. For example, the meaning of Grass is greenwould be explained in terms of the belief that grass is green, or what it isto bear the belief relation toward a certain representational content. And theinconsistency between Grass is green and Grass is not green would beexplained in terms of the incoherence in both believing that grass is greenand believing that grass is not green. There is of course something to beexplained here, but this, as they say, is everyones problem.

Fortunately for us who like a good philosophical puzzle, expressivistsstandardly deny that all declarative sentences express ordinary factualbeliefs. (Probably why expressivist treatments of Grass is green tend notto get a lot of press.) It is with these other sentences that expressivism getsits teeth. An expressivist about some linguistic expression E claims (perhapsinter alia) that E-sentences dont conventionally represent how the world,

2 See, e.g., Rosen 1998: 391392; Unwin 2001: 62, 72; Schroeder 2008b: 576, 580, 586;Dreier 2009: 97. There may be good reasons to think there are positions deserving to becalled expressivist that dont proceed in this way (see Charlow 2013b, Silk 2013). Butsince this is a standard way of understanding expressivism, I accept it here for the sakeof argument.

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narrowly construed, might be, or even where or when one might be locatedin the world. E-sentences dont conventionally determine ordinary possibleworlds propositions; they dont have truth-conditions in the canonical sense.Insofar as E-expressions can gure in valid reasoning and be embedded incomplex linguistic environments, the expressivist must give an alternativeaccount of what their meanings are, and how these meanings composition-ally interact with the meanings of other expressions to determine the mean-ings of expressions of arbitrary complexity. This is a technical challenge,but, given THE EXPRESSIVIST PROGRAM, it isnt merely technical. Whatever for-mal solution is given, the expressivist must provide a systematic way ofinterpreting the formalism, and of characterizing what states of mind corre-spond to what formal objects in such a way that explains the semantic prop-erties of the sentences that express those states of mind.

This is the root of the so-called Frege-Geach problem.3 Many haveregarded it as fatal to expressivism. But I am more optimistic. In this paperI develop a novel framework for implementing an expressivist semanticsthat I call ordering expressivism. Drawing on developments in linguisticsemantics and decision theory, I argue that ordering expressivism provides aformally and interpretively adequate solution to the Frege-Geach problem.For concreteness I focus on expressivist treatments of normative terms, butthe points can be applied to expressivist treatments of other expressions.Following work by Jamie Dreier, I treat the semantic properties of sentencesas explained, fundamentally, in terms of coherence constraints on attitudes.I then show how to implement this idea in an existing, general composi-tional semantic framework. The resulting view addresses complications con-cerning indecision, indifference, and incomparability, and generalizes tocover normative, non-normative, and mixed sentences. This avoids limita-tions in previous accounts. Ordering expressivism constitutes a more securesemantic basis for a broader expressivist theory of language and judgment.

The structure of the paper is as follows. I focus primarily on one promi-nent instance of the Frege-Geach problem: the interpretation of wide-scopenegation (the negation problem). 2 characterizes the problem. 3 consid-ers three prominent accountsthose by Allan Gibbard, Mark Schroeder,and Jamie Dreierin terms of which I will situate my proposed solution.4 motivates and develops the ordering expressivist framework and showshow it can solve the negation problem. 5 extends the proposed treatmentof negation to the case of other types of embedded contexts, with particularattention to Mark Schroeders recent problem of mixed disjunctions.Ordering expressivism combines the advantages of Gibbards and Dreiersaccounts while avoiding their limitations.

3So-called because it was prominently raised by Geach (1960, 1965), who attributed itto Freges distinction between content and assertoric force. See also Searle 1962.


2. The Negation Problem

The negation problem is the problem of saying in general what attitude cor-responds to wide-scope negationwhat attitude is expressed by sentencesof the form :/and of doing so in such a way that captures how a nor-mative sentence and its negation are logically contradictory, as per THE EX-PRESSIVIST PROGRAM.

Lets ll this in. Consider the following normative sentence.

MUST Alice has to help the poor.

For the expressivist, the meaning of MUST is, in the rst instance, to begiven, not in terms of its content or truth-conditions, but in terms of the atti-tude or state of mind it conventionally expresses. For concreteness, sayMUST expresses the attitude of requiring Alice to help the poor. Now con-sider MUST NOT.

MUST NOT Alice has to not help the poor.

Since the deontic modal have to is the primary operator in MUST NOT as itis in MUST, MUST NOT, the expressivist tells us, expresses the same sort ofattitude as MUST. No fancy footwork necessary: MUST NOT expresses the atti-tude of requiring Alice not to help the poor. The internal negationthenegation within the scope of have toposes no new challenges.

We have accounts of what attitudes are expressed by MUST and MUSTNOT. But what about NOT MUST?

NOT MUST Alice doesnt have to help the poor. (/Its not the case that Alicehas to help the poor.)

In NOT MUST we have an external negation, a negation that takes scope overhave to. What attitude should we say that NOT MUST expresses? Because ofTHE EXPRESSIVIST PROGRAM, not just any answer will do. Since NOT MUST isthe contradictory of MUST, the attitude expressed by NOT MUST must berelated in the right sort of way to the attitude of requiring Alice to help thepoor to reect the logical inconsistency between MUST and NOT MUST.

First, does NOT MUST express the requiring attitude toward Alice not help-ing the poor? No. Both requiring / and requiring :/ might be incompatiblein such a way as to capture the inconsistency between a sentence and itsnegation. But as we just saw, the attitude of requiring Alice not to help thepoor is the attitude expressed by the internally negated sentence MUST NOT.And MUST NOT and NOT MUST dont have the same meaning or express thesame attitude.

Second, does NOT MUST express the lack of the requiring attitude, the atti-tude of failing to require Alice to help the poor? No. Both requiring / andfailing to require / might be incompatible in such a way as to capture the

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inconsistency between a sentence and its negation. But the attitude of failingto require Alice to help the poor is the attitude ascribed in NOT BELIEVEwith, say, Bert as subjectbut the attitude we need to explain is the attitudeascribed in BELIEVE NOT.

NOT BELIEVE Bert doesnt believe that Alice has to help the poor.

BELIEVE NOT Bert believes that Alice doesnt have to help the poor.

NOT BELIEVE, but not BELIEVE NOT, is true if Bert has no views on whetherAlice has to help the poor.

Third, does NOT MUST express the attitude of permitting Alice not to helpthe poor. Yes! But because of THE EXPRESSIVIST PROGRAM we arent off thehook just yet. What we need to explain is how MUST and NOT MUST are logi-cally inconsistent. But if we take the attitudes of permitting and requiring asbasic, we must stipulate how they are logically related, i.e., that requiring /is inconsistent with permitting :/. But this is precisely what we need toexplain. Sure enough, NOT MUST expresses an attitude of permitting. But theproblem is to say how this attitude is logically related to the attitude ofrequiring, and to do so in such a way that doesnt presuppose an interpreta-tion of external negation.

In sum, we started by saying that the unembedded sentence MUSTexpresses an attitude of requiring. We then asked what attitude its negationNOT MUST expresses that captures the logical inconsistency between the twosentences. Neither way of inserting a negation into the requiring attitudefailing to require / and requiring :/captures the attitude expressed byNOT MUST. So we might posit a distinct attitude, an attitude of permitting,and say that it corresponds to the external negation of have to. ThoughNOT MUST does express an attitude of permitting, we cannot stop here lestwe leave opaque the logical relations between the distinct attitudes ofrequiring and permitting and thus, given THE EXPRESSIVIST PROGRAM, betweenthe sentences that express them. So, either we capture the inconsistencybetween MUST and NOT MUST but get the attitudes expressed wrong, or weget the attitudes expressed right but fail to capture the inconsistency. This isthe negation problem.4

3. A Stylized History

A brief recapor at least a stylized historyof the current state of playwill be instructive. For purposes of situating my positive account, I willfocus on developments stemming from work by Allan Gibbard and JamieDreier, understood in part in the context of work by Mark Schroeder. In this

4 See especially Unwin 1999, 2001, Gibbard 2003, Dreier 2006, 2009, Schroeder 2008a,b, c, Horgan & Timmons 2009.


section I will highlight what I take to be the crucial advances in theiraccounts, and will raise several problems and potential limitations. In 45I will develop a framework for implementing an expressivist semantics thatcombines the virtues of Gibbards and Dreiers accounts while avoidingtheir costs.5

3.1. Enter Gibbard

In his response to the Frege-Geach problem, Allan Gibbard (1990, 2003)introduces an extension of ordinary possible worlds semantics. Rather thantreating the contents of sentences as (determining) sets of possible worlds,Gibbard (2003) treats the contents of sentences as (determining) sets ofpairs of possible worlds and hyperplans.6 A hyperplan is a maximal contin-gency plan, a plan that, for any occasion for choice one might conceivablybe in and for any action open on that occasion, either forbids or permitseither rejects or rejects rejectingthat action on that occasion (2003: 56); itrepresents the plan of someone who is maximally decided. The content ofan attitude or judgment is given in terms of the world-hyperplan pairsthepossible ways things might be factually and normativelythat it rules out.

On rst glance it might seem that the model theory itself sufces for aresponse to the negation problem. One might say the following. The contentof MUST is a certain set of hyperplans, those that require Alice to help thepoor. Since negation means set complementation, the content of NOT MUSTis the complement set of hyperplans. Since these two sets of hyperplans aredisjoint, we have incompatibility of content. So we predict the inconsistencyof the sentences. Were home free.

Or not. As Gibbard himself recognizesalong with many interpretersafter himthe formal semantics isnt sufcient for an expressivist responseto the negation problem. As per THE EXPRESSIVIST PROGRAM, the expressivistcannot help herself to content or truth-conditions, even of a more ne-grained sort, to explain the semantic properties of sentences. Rather, thefundamental explanation of the inconsistency of MUST and NOT MUST mustbe in terms of the nature of the attitudes expressed. The expressivist mustsystematically interpret the formal objects in question by mapping themonto psychological attitudes whose individual natures and interrelations dothe explaining of the semantic properties in question.7

Then what is Gibbard up to? The crucial contribution of Gibbardsaccount, on my view, is that it starts with an existing framework for doingformal semanticspossible worlds semanticsand then systematically

5 Thanks to Jamie Dreier and an anonymous referee for helpful discussion about how bestto situate my positive account.

6 The theory in Gibbard 1990 is couched in terms of systems of norms.7 Cf. Unwin 2001: 72; Dreier 2006: 221, 2009: 95, 97; Schroeder 2008b: 586.

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provides that framework with an expressivist interpretation. The composi-tional semantics proceeds roughly as usual; the abstract objects that Gibbarduses as semantic valuessets of world-hyperplan pairsfunction like setsof possible worlds. What makes Gibbards use of the framework distinc-tively expressivist is the interpretation he gives for it. Gibbards expressi-vist extension of possible worlds semantics thus provides a crucial piece ofapparatus for what Simon Blackburn (1988) once called a fast track solu-tion to the general Frege-Geach problem. By systematically interpreting ele-ments of a familiar formal apparatus in terms of states of mind, Gibbardoffers a general strategy for implementing an overall expressivist semantictheory.

The prospects for Gibbards account turn on the details of the expressi-vist interpretations he gives for the various elements of the formalism. Forthe particular case of negation, one way of interpreting Gibbard is asattempting to solve the negation problem through the completeness ofhyperplans (see esp. 2003: 5359, 7175). A hyperplan represents the plansof an agent who is fully decided about what to do. For any relevant circum-stance and available action, a hyperplan either rejects the action or permitsitthat is, either disagrees with performing it or disagrees with disagreeingwith performing it. A hyperplan that fails to require :/ (fails to disagreewith /) ipso facto permits /. We can thus interdene the attitudes of requir-ing and permitting without external negation: permitting / is dened as dis-agreeing with requiring :/. Negation corresponds to a basic attitude ofdisagreeing. Roughly, MUST expresses an attitude of requiring Alice to helpthe poor, and NOT MUST expresses an attitude of disagreeing with requiringAlice to help the poor. These attitudes are plausibly related in the right sortof way as to explain the logical inconsistency between the sentences thatexpress them. Permitting is interdened with requiring so as to illuminatethe logical relations among sentences that express those attitudes.8

In 2 we noted that we must distinguish thinking that one doesnthave to do somethingthinking its contradictory is permittedfrom notthinking that one has to do somethingnot thinking it is required. I have

8 Dreier (2006: 222224), Schroeder (2008b: 585586), and Charlow (2011: 241, 265266) interpret Gibbards completeness constraint on hyperplans as requiring hyperplansto either require or forbid every available action. I view this interpretation as incorrect.Gibbard is clear that a hyperplan can merely permit an action (permit but not require it);contrary actions can be tied for best according to a hyperplan (see Gibbard 1990: 88n.3;2003: 56). Schroeder (2008b: 598n.7) claims that Gibbards argument that normativeterms pick out natural properties relies on the claim that hyperplanners cannot be indif-ferent. I disagree. The argument relies on there being a natural property that describeswhat is permitted by the hyperplan in a situation; but I dont see why this propertycouldnt be a disjunctive property. In any case, it isnt my aim to be doing Gibbard exe-gesis. What will be important is that the view described in the main text (which I amattributing to Gibbard) is insufcient.


two worries with Gibbards account of negation, which stem from twoways in which these attitudes can come apart: indecision and decidedagnosticism.

First, human agents arent hyperplanners. We can be undecided. So, theexpressivist must be able to represent a state of indecision, and distinguishit from states of permitting or indifference. The challenge is to do so in amanner amenable to expressivism, i.e., not in terms of agents beliefs. Onemust be able to say more than that, fundamentally, indifference betweenalternatives is believing them to be equally good (in the relevant sense), andindecision about alternatives is having no belief about which is better (inthe relevant sense). The worry isnt that Gibbards formal frameworkdoesnt have enough structure to represent the distinction between unde-cided and indifferent states of mind. It does. But we need some story aboutwhat it is about an agents state of mind such that the one type of abstractobject rather than the other represents that state of mind. Absent such astory, the worry is that any adequate one will be incompatible with expres-sivism (cf. Dreier 2006: 227228).

Second, even restricting our attention to decided states of mind, Gib-bards way of interdening permitting and requiring mischaracterizes theseattitudes and hence the attitudes intuitively expressed by MUST and NOTMUST. Even if one is fully decided, one can disagree with requiring /because one rejects taking any attitude toward /. One might take neutralityto be the stance to take; one might be decidedly agnostic. Disagreeing withrequiring / isnt equivalent to permitting :/, even in the context of ahyperplan. One might reply that the relevant attitude of disagreement is adecided state of mind that is incompatible with agnosticism. But this raisesthe worry that we may no longer be trading in a familiar general notion ofdisagreement in attitude. We may be assuming precisely what needs to beexplained, namely, that there is such an attitude and that it neednt beunderstood in terms of belief.9

3.2. Enter Dreier

In response to the problem of distinguishing indifference from indecision,Jamie Dreier (2006; cf. 2009: 105107) proposes to take the attitude ofstrict preference as basic and then dene the attitude of indifference interms of preference. On Dreiers denition, someone is indifferent(dened indifferent) between two options / and w iff (a) she doesntprefer / to w and doesnt prefer w to /, and (b) for any option v, sheprefers / to v iff she prefers w to v and prefers v to w iff she prefers v to/ (2006: 228; cf. Broome 2004: 21). That is, one is indifferent between

9 Cf. Unwin 2001: 6567; Hawthorne 2002: 176; Gibbard 2003: 7175.

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two alternatives iff one prefers each of them to exactly the same things,and one prefers exactly the same things to each of them. One is undecidedbetween two alternatives iff one isnt indifferent between them and onefails to prefer either alternative to the other. According to these denitions,whereas indifference is a transitive relation, indecision is not. (I might beundecided between eating ten jellybeans and eating a donut, and undecidedbetween eating a donut and eating eleven jellybeans, though I prefer eatingeleven jellybeans to eating ten.) So, says Dreier, we can cash out the atti-tude of indifference, and distinguish it from indecision, in terms of themore basic practical attitude of strict preference.

The crucial advance in Dreiers account, in my view, is its move to inter-dene various relevant attitudes in terms of a more basic practical atti-tudein Dreiers case, strict preferencethe logic of which is used toexplain the semantic properties of normative sentences. To see the impor-tance of this move, it can be helpful to situate Dreiers account in the con-text of Mark Schroeders (2008a,b) way of framing the negation problem.10

Schroeder distinguishes two types of ways that states of mind can be incon-sistent. States of mind are A-type inconsistent iff they are the same attitudetoward inconsistent contents. Believing that / and believing that :/ is anexample of A-type inconsistency. States of mind are B-type inconsistent iffthey are distinct and apparently logically unrelated attitudes toward thesame content (2008b: 581; emphasis in original). Requiring / and permit-ting / is (allegedly) an example of B-type inconsistency. According to Sch-roeder, expressivists can help themselves to A-type inconsistency but not toB-type inconsistency; helping themselves to B-type inconsistency would behelping themselves to everything they need to explain, namely, how certainattitudes can be inconsistent in a way that doesnt ultimately reduce to theirbeing inconsistent beliefs.

What Dreiers account highlights is that A-type inconsistency isnt theonly promising model of inconsistency in attitude. Not all logical relationsamong attitudes need be explained in terms of logical relations among theobjects of those attitudes. If we can interdene requiring and permitting interms of preference, then the inconsistency between sentences like MUST andNOT MUST neednt be explained either in terms of distinct fundamental atti-tudes or a single attitude toward inconsistent contents. The inconsistencycould be explained in terms of familiar coherence constraints on preferences(more on which in 4). Like belief, preference has a logic; combinations ofpreferences can be incoherent. Suppose you prefer to go back to sleep, butalso prefer not to lose your job. If you realize that the only way to keepyour job is to get up, then something in your attitudes has to change, as

10 Thanks to an anonymous referee for encouraging me to frame the importance of Dreiersaccount in this way.


Dreier (2009: 106) puts it, like how something would have to change ifyou believed that all ravens are black and that Tweety is a raven but seethat Tweety isnt black. If normative sentences express preferences, thenMUST and NOT MUST would be inconsistent, the thought goes, because theyexpress an incoherent body of preferences. Dreier himself only sketcheshow to apply this model, and only for simple cases. I wont ultimately betaking up his apparent suggestions about how to do so. What is importanthere is that Dreiers proposal brings into a relief a strategy for respondingto the negation problem that may avoid the putative problems detailed inSchroeder 2008a for expressivist accounts framed in terms of A-type incon-sistency.

Despite these contributions, I would like to raise three worries for Dre-iers account. The rst two arent intended to be decisive. I raise them sim-ply to highlight potential limitations in Dreiers account. It would bepreferable if we could develop an expressivist theory that avoided them.The third limitation is more serious.

Call indifference according to Dreiers denition D-indifference. SupposeChip has the following preference structure. He prefers eating vanilla icecream to being stabbed, he prefers chocolate ice cream to being stabbed, heprefers winning the lottery to eating vanilla ice cream, and he prefers win-ning the lottery to eating chocolate ice cream. However, he has neverconsidered the question of how to compare vanilla and chocolate ice cream.So, he fails to prefer chocolate to vanilla and fails to prefer vanilla to choc-olate. Chip is D-indifferent between eating chocolate and eating vanilla.Both are ranked below the same alternativeswinning the lotteryandboth are ranked above the same alternativesgetting stabbed. But Chipisnt indifferent between vanilla and chocolate; he is undecided betweenthem. So being D-indifferent isnt sufcient for being indifferent. One canbe D-indifferent while still being intuitively undecided.

Dreier recognizes that cases like Chips pose a problem for his denition(2006: 230). He notes that his denition relies on there being a sufcientlyrich eld of preference to exclude treating cases like Chips with incom-plete preferences from representing indifference. But cases like Chips can-not be regarded as dont cares by the theory. They are precisely the sortsof preference structures that distinguish indifference from indecision. (Or, aswe will see shortly, they are at least one such sort of preference structure.)Two alternatives can be D-indifferent either by being ranked the same, orby failing to be ranked relative to one another but bearing the same rela-tions to every other alternative. Only the former case represents indiffer-ence. Unless we assume that the preference relation is completeandthereby rule out indecision from the startsatisfying D-indifference isntsufcient for indifference.

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There is certainly more to be said in reply. I wont press the worry fur-ther here.11 Sufce it to say that Dreiers account requires that agents havea suitably rich eld of preferences in order to distinguish indifference andindecision. At minimum, it is worth investigating whether we can developan expressivist theory that avoids this requirement.

A second limitation in Dreiers account stems from a second way inwhich ones preferences can be incomplete. Lacking preference and notbeing (D-)indifferent isnt sufcient for being undecided. Suppose you areforced to make a choice about which of your children, A or B, to save andwhich to let die. You fail to prefer either alternative to the other. But youarent indifferent. You treat the lives of each of your children as uniquelyprecious. Being told, for example, that you could get a free box of tissuesif, but only if, you saved A, wouldnt settle for you what to choose. Youprefer saving A and getting the tissues to just saving A without gettingthem, but its not the case that you prefer saving A and getting the issues tojust saving B. Your attitude is insensitive to mild sweetening, as they say(Hare 2010; De Sousa 1974). And yet, intuitively, you arent undecidedabout what to prefer. You have considered the question, and, we can sup-pose, no further reection would lead you to change your attitude. Youdecidedly treat alternatives where you save A as incomparable to alterna-tives where you save B. If this is right, the expressivist now has three atti-tudes to distinguish: indifference, indecision, and what we might calldecidedly treating as incomparable.12

Even if there are in fact no genuine incomparabilities in values, it isntimpossible to think otherwise. Whether it is rational is more contentious.13

This may affect whether an attitude of decidedly treating as incomparable isthe sort of attitude that needs to be characterized in giving an expressivistsemantics. Nevertheless, it would be preferable if the viability ofexpressivism wasnt held hostage to these debates.

11 Dreier invokes preferences among lotteriesobjects engineered to enrich the eld ofpreference in just the way we need (2006: 231)to motivate that cases like Chipsmay be rare enough that conating indifference and indecision in these cases wont besuch a serious bullet to bite. The problem is that lotteries can do precisely what Dreiersays: they can enrich agents preferences. Delineating an enhanced prospect, and forcingchoices that involve it, can articially rene an agents (incomplete) preference structure.It can function precisely to remove the basis for ones indecision. Hypothetical choicecan explain actual preference only insofar as the agent is already sensitive to anddecided among the relevant options.

12 Ruth Chang (2002) claims that, in addition to incomparability, understood negatively asthe lack of any comparative relation, there is also a fourth positive value relation ofparity (the other three being better than, worse than, and equally good). I willput aside any purported differences between incomparability and parity in what follows.

13 For survey discussion, see Hsieh 2008.


Third, and most importantly, Dreiers account is only directly applied tosentences that express pure practical states of mind. No attempt is made toimplement the account of normative language and preference in a generalcompositional semantic theory. Doing so is non-negotiable. Some havethought that complex sentences combining normative and non-normativeclauses raise unique problems. An adequate expressivist treatment of thepurely normative fragment of the language must generalize to cover non-normative sentences and mixed sentences as well.

The lesson from this section is this: We need an account that combinesthe virtues of Gibbard and Dreier. We need a way of integrating a Dreier-style account of inconsistency in attitude into a general, independentlymotivated formal semantic framework. We need a Gibbard-style fast-trackapparatus with a Dreier-style expressivist interpretation. In the remainder ofthe paper I will develop a positive expressivist account that providesprecisely this. This account avoids the potential limitations in Gibbards andDreiers accounts described in this section.

4. The Negation Problem: A Solution

4.1. Ordering Expressivism

Given THE EXPRESSIVIST PROGRAM (1), merely offering a formalism thatassigns contents to sentences wont sufce for an expressivist explanationof the semantic properties of normative sentences. Nevertheless I want totake a step back from THE EXPRESSIVIST PROGRAM for a moment and simplyexamine how we might formally distinguish the various attitudes in ques-tion. Perhaps the resulting formalism will suggest new possibilities for ex-pressivists to explore.

Forget the framework of Gibbardian hyperplans for a moment. Norma-tive terms are semantically modal. They concern not what happens in theactual worldor not merely what happens in the actual worldbut whathappens in certain alternative possibilities. On the consensus best theoryin linguistic semantics, modal expressions are analyzed in terms of anordering semantics.14 Modals are interpreted as quantiers over possibleworlds. The domain of quantication is set by two parameters: a set ofrelevant (accessible) worlds and a preorder . (a reexive and transitive

14 Equivalently, a premise semantics (Lewis 1981a). See especially Lewis 1973, van Fraas-sen 1973, Veltman 1976, Kratzer 1977, 1981, 1991. For simplicity I will make the limitassumption (Lewis 1973: 1920) to ensure that there is a set of most highly rankedworlds. I will sometimes follow common usage among philosophers and use order andordering to refer to preorders (Lewis 1973: 48), though mathematicians typicallyreserve order for specically antisymmetric preorders, i.e. preorders that dont permitties. Familiar examples of preorders are the relations of being at least as tall as, at leastas clever as, etc.

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relation), where this preorder ranks worlds along a relevant dimension.Different choices of accessibility relations and preorders correspond todifferent readings of modalse.g., epistemic, deontic, goal-based. Amodal quanties over the accessible worlds that rank (among the) highestin the preorder, i.e., over the accessible worlds that arent .-bettered byany other accessible world. Call these worlds the .-best worlds. To arst approximation, necessity modals like have to and must univer-sally quantify over the set of .-best worlds, and possibility modals likemay existentially quantify over the set of .-best worlds. For example,According to the law, you have to pay your taxes is true iff you payyour taxes in all the relevant worlds that best approximate the legalideal. Since our concern here is with normative language, hereafter I willassume that . is a practical normative ranking of possibilities; . can beunderstood as reecting the content of a practical normative view.15

Before getting all in a huff about how the expressivist cant appeal to suchtruth-conditions to do fundamental explanatory work, notice that this frame-work appears to make many of the distinctions we need. We could say that .requires / iff all the .-best worlds are /-worlds (worlds in which / is true);that . forbids / iff none of the .-best worlds are /-worlds; that . merelypermits / iff some but not all of the .-best worlds are /-worlds; that . isindifferent between alternatives u and v iff u . v ^ v . u; and that . treatsalternatives u and v as incomparable iff u 6. v ^ v 6. u. (We will return toindecision below.)

This formal apparatus suggests the following strategy for the expressivist,given a normative term N and preorder . that gures in the interpretationof N-sentences:

How to solve the Frege-Geach problem:

1. Interpret . as some suitable practical attitude.

2. Use of the logic of this basic attitude to capture the semanticproperties of N-sentences.

3. Dene any other attitudes intuitively expressed by N-sentencesin terms of the basic attitude corresponding to ..

This, schematically, is my proposal for how expressivists can solve theFrege-Geach problem. Call an expressivist theory that makes use of this

15 I use expressions like .-best to emphasize that best is being used neutrally to referto the maximal elements of the preorder, regardless of the dimension along which thoseelements are being ranked. The preorders in question neednt rank worlds along a specif-ically evaluative dimension. Making use of orderings thus doesnt prejudge the questionof whether to go in for a teleological normative theory, or even a maximizing theory.


strategy ordering expressivism. Ordering expressivism is a framework fordeveloping an expressivist theory. It can be implemented in various waysdepending on a range of broader linguistic and metaethical issues. Whatis most important for present purposes is the structure of the solutiondisclosed by ordering expressivism. For concreteness it will help to llin some of the details. But I make no claim that the particular theory tofollow is the only adequate way of implementing ordering expressiv-ismor even that the general ordering expressivist framework constitutesthe only way of solving the Frege-Geach problem. I welcome thedevelopment of alternatives with which the present account may becompared.

What attitude should we say is represented by . in the formal seman-tics? Not just any choice of attitude will do. Here are three constraints.First, the attitude must be a practical attitude. If we are to capture thepractical character of normative language and judgment, the attitude wechoose to explain the meanings of normative terms must itself be practi-cal in nature. It must be action-guiding and motivating; it must regulatechoice and behavior. Relatedly, second, the attitude must be expressivist-friendly. It mustnt require being understood in terms of belief. Third,the attitude must have a logic. Given that normative sentences have logi-cal properties, can stand in logical relations, and can gure in valid rea-soning, the attitude expressed by normative sentences must imposecertain logical constraints.

For concreteness I will follow Dreier in starting with an attitude ofpreference. But since . is a preorder, I suggest, naturally enough, thatwe interpret it as the attitude of weak preference, or preferring at leastas much. This choice of attitude has several advantages. First, weakpreference is a practical attitude. Its connection with action is well stud-ied in decision theory. Second, weak preference is plausibly expressivist-friendly. The majority view is that it neednt be construed as a beliefthat one alternative is at least as good as another.16 Third, there are richliteratures in preference logic and decision theory describing and justify-ing the logical properties of and coherence constraints on preferences(3.2).17 Fourth, there is a tradition in preference logic of treating weakpreference as the primitive relation. This independent research provides apromising basis for an expressivist account of the meaning of normativelanguage.

16 For relevant discussion, see, e.g., Smith 1987, Lewis 1988, Broome 1991, 1993, Byrne& Hajek 1997.

17 Classic references include Ramsey 1928, Davidson et al. 1955, Davidson 1976. For sur-vey discussion, see, e.g., Hansson 2001, Hansson & Grune-Yanoff 2012.

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(Some theorists who mark a fundamental distinction between evalua-tive vocabulary (good, bad, beautiful, desirable, base) and deonticvocabulary (must, may, right, wrong, permissible, obligatory,forbidden) may wish to say that the former, but not the latter,express weak preferences. Such theorists may recast the ensuing discus-sion in terms of capturing the logical inconsistency between, say, sen-tences about what is evaluatively best and their negations. Since thisisnt the place to take up issues concerning the relation between deonticand evaluative language and attitudes, for expository purposes I willassume that our example deontic modal sentences express weak prefer-ences. Theorists with different commitments about specically deonticlanguage may feel free to recast our discussion in terms of their pre-ferred choice of attitude, assuming it meets the constraints describedabove.)

An agents weak preferences inherit the logic of the preorder. Just as wesay that ordinary belief states are inconsistent if they arent representable interms of a non-empty set of worlds, so the expressivist may say that statesof weak preference are inconsistent if they arent representable in terms of anon-empty preorder. Of course at the end of the day she will need someexplanation for why having preferences that arent representable in this wayis incoherentjust like how everyone, expressivists and non-expressivistsalike, needs an analogous story in the case of belief. And she must showhow the relevant sort of incoherence is of the right kind to explain the logi-cal inconsistency of normative sentencesjust like how an expressivist, likeSchroeder, who appeals to A-type inconsistency (2) must explain why agiven type of attitude (belief, being for) is inconsistency transmitting, i.e.why the attitude is such that bearing it toward inconsistent contents is inco-herent in a way that explains the logical inconsistency of sentences (or,more generally, why logical relations among the objects of the attitude placeconstraints on the logic of the attitude itself). Accounts of preferentialincoherence are well-known, and the literatures on them vast (nn. 1617).I wont attempt to offer such an account here. Sufce it to say that it isindependently plausible that there are coherence constraints on preferences,and that these constraints are of the right sort to underwrite fundamentalsemantic explanations. At minimum we have made progress if we canreduce expressivisms problem with negation to the familiar, more tractableproblem in decision theory of explaining why preferences that dont satisfycertain constraints are incoherent.

The expressivist can then use the logical properties of preferences tocapture the logical properties of certain normative sentences. Consider thefollowing ordering expressivist interpretations of the familiar truth-conditionsfor MUST and NOT MUST:


(1) a. MUST is true at w, according to ., iff Alice gives to the poor in allthe .-best worlds

b. MUST expresses an attitude of having all of ones most weaklypreferred alternatives be ones where Alice gives to the poor

(2) a. NOT MUST is true at w, according to ., iff Alice doesnt give to thepoor in some of the .-best worlds

b. NOT MUST expresses an attitude of having some of ones most weaklypreferred alternatives be ones where Alice doesnt give to the poor

In response to the negation problem, we can say that MUST and NOT MUSTare inconsistent because their conjunction expresses an incoherent set ofweak preferences. It is incoherent to have all of ones most weakly pre-ferred alternatives be ones where Alice helps the poor and some of onesmost weakly preferred alternatives be ones where Alice doesnt help thepoor. There is no (non-empty) preorder that represents such a body of pref-erences. Preferential incoherence appears to be the right kind of inconsis-tency in attitude to explain the inconsistency between normative sentences/ and :/.

Taking the weak preference attitude as basic, we can dene in terms of itvarious other attitudes intuitively expressed by normative sentencese.g.,requiring, permitting, merely permitting, and forbidding. To a rst approxi-mation: A requires / iff all of As most weakly preferred alternatives are /-worlds; A permits / iff some of As most weakly preferred alternatives are/-worlds; A merely permits / iff some but not all of As most weakly pre-ferred alternatives are /-worlds; and A forbids / iff all of As most weaklypreferred alternatives are :/-worlds. By dening requiring and permittingin terms of the single basic attitude of weak preference, we can avoid theworries discussed in 2 with taking, say, the attitude of requiring as basicand then dening permitting in terms of failing to require or disagreeingwith requiring. The inconsistency between requiring / and permitting :/the attitudes intuitively expressed by MUST and NOT MUST, respectivelyisexplained in terms of the incoherence of the preferences in terms of whichthey are dened.

In this way, the expressivist can import developments in truth-condi-tional semantics for modals, though with some interpretive tweaks. Ihave shown how she can do so in terms of a standard ordering seman-tics because of its familiarity. But adopting this kind of ordering seman-tics, or any ordering semantics for that matter, isnt essential to theunderlying expressivist maneuver. Even if an alternative way of analyzingmodals proves to be superior, the expressivist will be able to implementour general strategy as long as there is some particular element in theanalysis corresponding to the normative reading of the expression (e.g.,

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the preorder in an ordering semantics), where the structure of this ele-ment captures any logical relations among sentences containing normativeterms. Given requirements of compositionality and empirically adequacy,it is hard to see how a successful semantics could fail to have this prop-erty. Despite its name, ordering expressivism neednt be held hostage toan ordering semantics for modals.

This point may become relevant depending on ones broader viewsabout the semantics of modals and the nature of preference (or whateverpractical attitude is chosen)e.g., concerning quanticational vs. scalarsemantics for modals; relations among comparative and quantitativenotions of possibility and probability; information-sensitivity in normativemodals; the objects of preference; the relation between exclusionary andcombinative preferences; and the justication of coherence constraintson preference. A plurality of implementations of ordering expressivismwill be possible depending on ones commitments on these sorts ofissues.18 How the semantics, metasemantics, philosophy of mind, psy-chology, and decision theory interact and mutually constrain theorizinglikely wont be straightforward. Moreover, for all I have said, theprospects of ordering expressivism may vary for different normativeexpressions and practical attitudes. It isnt trivial that the best philosophi-cal interpretation of the best semantics for a given expression will beconsistent with expressivism.

Such complications neednt detain us here. For present purposes, Iwill continue to assume a standard ordering semantics for modalscoupled with an interpretation of the preorder in terms of weakpreference. The preorder on worlds in the semantics can be understoodas reecting preferences among maximally specic possibilities. Thiscoheres nicely with the standard use of maximal states of affairs (pointpropositions, or maximally consistent sets of sentences, in the limitingcase) as the objects of preference in decision theory and preference logic.However, there may be large equivalence classes in the preorderdepending on which features of the world are relevant to onespreferences in the given context. Preference relations on non-maximal

18 To take just one example: Many authors in the literature on information-sensitivity haveargued that a deontic modals domain of quantication can reect what alternatives arebest given a relevant body of information (e.g., Kolodny & MacFarlane 2010, Carianiet al. 2011, Charlow 2013a, Dowell 2013, Silk 2014). If this is right, then certain deon-tic modal claims may be understood as expressing ones derived preferences given onesinformation (beliefs, credences). (More on this in 5.) How one implements this woulddepend on ones views about the details of the semantics and how much decision-theo-retic apparatus, if any, is explicitly encoded (e.g., whether there is an explicit representa-tion of information-independent desires/utilities/values). Thanks to an anonymous refereefor raising this issue.


possibilities may be relevant in the interpretation of other kinds of nor-mative expressions.19

4.2. Indecision

In 2 we raised the challenge of capturing in an expressivist-friendly man-ner the difference between indifference and indecision. In 3.2 we consid-ered Dreiers response and noted two limitations. First, it fails to distinguishindifference and indecision in certain agents with impoverished preferences.Second, it fails to distinguish two ways in which ones preferences can beincomplete. Indecision is distinct from having incomparabilities in onespreferences. Given the coherence of thinking that one might nd oneself ina practical dilemma, there is a third attitude to be explained: the attitude ofdecidedly treating as incomparable. In this section I will argue that the ex-pressivist can distinguish these attitudes by showing how they encode dif-ferent practical dispositionsspecically, different dispositions in choicesituations. (To be clear, the aim isnt to reduce these attitudes to patterns ofchoice behavior. Choice behavior is treated as revealing attitudes, not asconstituting them.)

Start with distinguishing indifference from decidedly treating as incom-parable. Much work in revealed preference theory has concerned how toderive a preference order among alternatives by treating choice asbasic.20 Agents are modeled by choice functions which select elementsfrom (nite) sets of options. An agents choices are treated as revealingher psychological state of mind, her preferences. Traditionally, choosingboth alternatives u and v from an option set has been interpreted asrevealing indifference between u and v. But an alternative is to interpretsuch a choice as revealing that no other element in the option set isstrictly preferred to u or v.21 This might be because one is indifferent

19 The literature on comparative modal notions may be relevant here (e.g., Portner 2009,Lassiter 2011, Katz et al. 2012; for related discussion on generating orderings on propo-sitions from orderings on worlds, see Lewis 1973, Halpern 1997). Note that the appealto preferences on maximally specic possibilities is neutral on whether preferences onmaximal vs. non-maximal possibilities are more fundamental. What is important forpresent purposes is simply that there are preferences on maximal alternatives. Thoughdecision theorists standardly treat preference as a relation on (mutually exclusive, possi-bly singleton) sets of worlds, this neednt hinder the expressivist from utilizing a classicordering semantics for modals, given the systematic availability of reductions of preor-ders to partial orders (i.e., antisymmetric preorders, preorders without ties): for any pre-order . on worlds, there is a corresponding partial order on the set of equivalenceclasses of worlds with respect to .. Thanks to an anonymous referee for pressing me onthese issues.

20 For classic discussions, see Samuelson 1938, Arrow 1959, Richter 1966, Hansson 1968,Sen 1970.

21 See, e.g., Nehring 1997, Sen 1997, Eliaz & Ok 2006.

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between u and v, but it also might be because one treats them as incom-parable. Nevertheless we can distinguish these two types of attitudes onthe basis of further choice behavior. Results in Eliaz & Ok 2006 attestto the fruitfulness of the following approach. The technical details wouldtake us too far aeld, but the rough intuitive idea is this: We check if,for all choice situations, the agent chooses u whenever she chooses vand vice versa; we check if u and v are treated identically in all occa-sions for choice that involve them. If they are, this reveals that the agentis indifferent between u and v. If they are not, she is better regarded astreating u and v as incomparable.22

For example, suppose Alice must choose what beer to buy out of x, y,and z. The relevant factors guiding her choice are taste and smell. As fortaste, she strictly prefers x to y and y to z. As for smell, she strictly prefersy to z and z to x. Since she strictly prefers y to z with regard to both tasteand smell, she will not choose z when y is an option. But suppose thatwhile Alice is still contemplating her choice Bert swoops in and takes thelast of beer y. Left with a choice between x and z, Alice seems to have noway of choosing merely in light of her preferences; after all, x is preferredto z with regard to taste but z is preferred to x with regard to smell, and(lets suppose) she has no further preferences. Her choice set for {x, z}might thus be {x, z} (in the sense that she might subjectively randomizechoice between x and z). However, we can determine that Alice treats x andz as incomparable and isnt indifferent between them in light of her furtherchoice behavior. For there is some other choice situation that doesnt con-tain (say) znamely, where the option set is {x, y}with respect to which

22 More precisely (cf. Eliaz & Ok 2006: 6667): An agent treats u and v as incomparable ifboth u and v are choosable from fu; vg i:e:; cfu; vg fu; vg, for choice functioncand there exists a (nite, non-empty) set S of alternatives that contains u but not v, suchthat at least one of the following holds, where S*:= (S [ {v})n{u}, i.e., the option set thatresults from swapping u with v:

a. u 2 cS ^ v 62 cSb. u 62 cS ^ v 2 cSc. c(S)n{u} 6 c(S)n{v}

Eliaz & Ok 2006 prove that choice behavior that satises a weakened version of the WeakAxiom of Revealed Preference can be used to derive a unique, possibly incomplete prefer-ence relation (whose strict part is suitably rich). The pairs which the agent treats as incom-parable in the above sense can be proven to be precisely those pairs which areincomparable relative to this preference relation. Eliaz & Ok 2006, as well as others in thetradition in theory of choice stemming from Aumann 1962, treat themselves as characteriz-ing indecision (via incomparabilities), but, for reasons discussed in 3.2, I prefer to inter-pret their results as characterizing the attitude of decidedly treating as incomparable.


x and z arent treated symmetrically: whereas x is choosable out of {x, y}, zisnt choosable out of {z, y}, the set that results from swapping x with z, aswe have seen. (In terms of the denition in note 22, it is the (a)-conditionthat is satised.)

Now turn to indecision. In theory of choice, there is a requirementthat an agent must, when given a set of options, select a subset of thatset. Dropping this requirement, by allowing as a possible response theaction of positively refraining from choosing, seems to provide onenatural way of characterizing indecision. Indecision between u and vwould be revealed by (perhaps inter alia) deferring choice between uand v. It isnt counterintuitive that if I am genuinely undecided betweenu and ve.g., because I have never considered the question of how tocompare u and vI may, if presented with a choice between them,refuse to make a choice, at least for the time being. After all, I haventworked out my preferences, and so any choice, even choosing both uand v, would give a false impression of my state of mind. Indecisionbetween alternatives, as revealed in this way, amounts to a kind ofunwillingness even to pick, or a preference to defer choosing amongthem.

I see two general ways in which this kind of indecision-revealing choicebehavior could be used to generate representations of agents states of mind:one introduces more structure into the representation of normative beliefs;the other introduces more structure into the representation of bodies of pref-erences themselves. For space purposes I describe only the former option inthe main text; I leave discussion of the latter option for an extended note(n. 25). Before proceeding I want to reiterate that the question of how torepresent indecision is subordinate for the expressivist to the question ofhow to characterize indecision. What is primary is our characterization ofindecision as a preference to defer choice, as revealed by a refusal tochoose. This is what undergirds our expressivist explanation for why a cer-tain agent should count as being in a state of mind represented by the rele-vant type of formal object. Nevertheless, although questions of how torepresent indecision may be of secondary importance, they are importantjust the same.

Our indecision-revealing choice behavior can be used to characterize aset of preference preorders, representing ways in which the agent couldcoherently resolve her indecision (complete her preferences) given the restof her choice behavior. For example, simplifying by only considering twoalternatives u and v, the state of mind of an agent who defers choosingbetween them could be modeled in terms of the set {.1, .2, .3}, where.1, .2, and .3 are characterized as follows, representing strictly preferring

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u to v, strictly preferring v to u, and being indifferent between u and v,respectively:23

.1: u

(4) A doesnt believe that / is required iff for some weak preference preorderin As practical alternatives, some of the most weakly preferredalternatives are :/-worlds (i.e., iff some of the weak preference preordersin As practical alternatives permit :/).

(5) A believes that :/ is permitted iff for all weak preference preorders inAs practical alternatives, some of the most weakly preferred alternativesare :/-worlds (i.e., iff all of the weak preference preorders in Aspractical alternatives permit :/).

This reects how failing to believe that / is required is weaker than believ-ing that :/ is permitted. The former holds only if some weak preferencepreorders consistent with ones preferences are a certain way, whereas thelatter holds only if all the weak preference preorders consistent with onespreference are that way. Similarly, one decidedly treats two alternatives asincomparable only if they are incomparable in all the weak preference pre-orders in ones practical alternatives.25

25 An alternative way of representing indecision is by enriching our representation ofbodies of preferences. Suppose we represent a body of weak preferences with a set ofpreorders rather than a single preorder. Intuitively, we might think of each preorder inthe set as representing a partial strategy that the agent accepts, and the set of preordersas representing the agents overall plan for action. A strategy, in the decision-theoreticsense, assigns a single act to every possible occasion for choice. It represents what theagent takes to be a permissible course of action given her preferences. One could thensay that / is required according to a overall planthe set of preordersiff for all preor-ders in the set, all the most weakly preferred alternatives are /-worlds; and that / is per-mitted according to the overall plan iff for some preorder in the set, all the most weaklypreferred alternatives are /-worlds. This choice of representation entails that an overallplan can fail to require / without thereby permitting :/; required and permittedwont be duals: Its not the case that / is required iff for some preorder in the set, someof the .-best worlds are :/-worlds; but :/ is permitted iff for some preorder in theset, all the .-best worlds are :/-worlds. And an overall plan can be undecided about asingle proposition without merely permitting it: / is merely permitted iff for some butnot all of the preorders in the set, all the .-best worlds are /-worlds; but the overallplan is undecided about / if, e.g., for none of the preorders in the set, all the .-bestworlds are /-worlds. On this representation, a subjects practical state of mind has thesame structure as a body of preferences. Indecision is encoded in the representation ofpreference itself.

A brief example may be helpful. Suppose my overall plan consists of the followingpartial strategies, represented as sets of propositions: = {{I eat a cookie, I give to thepoor},{I eat a brownie, I give to the poor}}. (These sets of propositions can determinepreorders in the usual way: given a set of propositions P, for any worlds u and v,u .P v iff all propositions in P that are true in v are also true in u.) On this overall plan,my eating a cookie and my eating a brownie are both merely permitted, since some butnot all of my partial strategies entail that I take the action in question; my giving to thepoor is required since all of my partial strategies entail that I give to the poor; and I amundecided about all other actions (not entailed by these), since they arent entailed byany of my partial strategies. So, unlike hyperplans, overall plans in this sense neednt becomplete (or consistent: incomparabilities may be represented by all of ones partialstrategies entailing contrary propositions).

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In sum, I have suggested that the expressivist can distinguish the atti-tudes of indecision, indifference, and decidedly treating as incomparablein terms of differences in choice behavior. Indifference among alterna-tives is revealed by treating them identically in all relevant occasions forchoice. Treating them as incomparable is revealed by not treating themidentically in this way but still choosing all of them when presented withall and only them. Indecision is revealed by deferring choice. It remainsto be seen how best to develop these ideas more comprehensively. Nev-ertheless I take them to constitute a promising expressivist strategy. Thisstrategy avoids problems and limitations of previous approaches, likeDreiers, as discussed in 3.2. It is also independently interesting andattractive.

5. Beyond Negation: The Disjunction Problem

Lets recap. Ordering expressivism combines the virtues of Gibbards andDreiers accounts (3). Following Dreier, semantic properties of sentences,like inconsistency, are explained, fundamentally, in terms of (non-A-type)coherence constraints on attitudes. Given the counterintuitive consequencesof expressivist accounts framed in terms of A-type inconsistency canvassedin Schroeder 2008a, it would be promising if an alternative way of solvingthe Frege-Geach problem was available. Ordering expressivism is one suchalternative. Ordering expressivism takes a single practical attitude to beexplanatorily basice.g., weak preferenceand denes the attitudes intui-tively expressed by various kinds of normative sentences in terms of it. Thelogical relations between the apparently logically unrelated attitudes of,e.g., permitting and requiring are illuminated by dening both attitudes interms of weak preference (Schroeder 2008b: 581; emphases altered). Evenif positing brute inconsistency relations between distinct attitudes isproblematic, explaining inconsistency relationships between attitudes interms of the logic of a more fundamental attitude is not. A-typeinconsistency isnt the only legitimate kind of inconsistency in town.

Like Gibbard in his extension of possible worlds semantics, orderingexpressivism co-opts independently motivated apparatus from formalsemantics on modals, but gives it a systematic expressivist interpretation.A concern some have with expressivism is that it seems to require us torebuild compositional semantics from the ground up. It would beunfortunate, to put it mildly, if we had to reexplain everything that con-temporary truth-conditional semantics has taught us. An advantage of thegeneral ordering expressivist strategy in 4.1 is that it allowsexpressivists to import developments in truth-conditional semantics formodals in giving their semantics for normative terms. It provides a rec-ipe for giving an expressivist account of complex normative sentences,


and recovering the state of mind expressed by a sentence from its com-positional semantics: interpret all occurrences of . in the semantics interms of the practical attitude associated with .. To a rst approxima-tion, some examples with conjunction, quantiers, and conditionals are asfollows. The (a)-examples give the ordinary truth-conditions; the (b)-examples give the attitude expressed. (In (7) I give the reading wheremost takes wide scope.)26

(6) a. Alice has to give to the poor, and Bert has to give to the poor istrue at w, according to ., iff Alice gives to the poor in all the.-best worlds and Bert gives to the poor in all the .-best worlds.

b. Alice has to give to the poor, and Bert has to give to the poor expressesthe attitude of having all of ones most weakly preferred alternativesbe ones where Alice gives to the poor, and having all of ones mostweakly preferred alternatives be ones where Bert gives to the poor.

(7) a. Most people have to give to the poor is true at w, according to .,iff for most people x in w, x gives to the poor in all the.-best worlds.

b. Most people have to give to the poor expresses the attitude of havingall of ones most weakly preferred alternatives be ones where, for most(actual) people x, x gives to the poor.

(8) a. If Alice has a job, she has to give to the poor is true at w, accordingto ., iff Alice gives to the poor in all the .-best worlds where Alicehas a job.

b. If Alice has a job, she has to give to the poor expresses the attitudeof having all of ones most weakly preferred alternatives where Alicehas a job be alternatives where Alice gives to the poor.

Perhaps there are other types of normative sentences whose semantic proper-ties the expressivist cannot capture in this way. The devil will be in the details.But these examples should give the expressivist a license for optimism.

Perhaps not for long. Mark Schroeder has objected that expressivistscannot directly apply the tools of truth-conditional semantics (2011: 9).Schroeders Exhibit A: disjunction. In the remainder of this paper I willfocus on Schroeders objection concerning mixed disjunctions, disjunctivesentences where one disjunct expresses a pure belief state and the other dis-junct expresses a pure practical state.

26 How one develops an expressivist treatment of deontic conditionals will depend on onesbroader views on the syntax and semantics of different types of implicitly and explicitlymodalized conditionals. These issues, notoriously complex as they are, are complicatedfurther by the fact that conditionals are themselves constructions that have been subjectto expressivist treatments. I offer the interpretation in (8) simply for illustrative purposes.

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(Since Schroeders objection is partly technical in nature, some parts ofthis section are, of necessity, a bit more formal than the others. To keep thediscussion generally accessible, I only mention those technical points thatare directly relevant to the philosophical issues. The important philosophicalpoints should be clear enough, I hope, even for readers less interested in thetechnical details.)

As noted in 3.1, expressivists can implement their compositional seman-tics with an extension of possible worlds semantics, treating the contents ofsentences as sets of pairs of worlds w and (say) weak preference preorders ..But because of THE EXPRESSIVIST PROGRAM, she must provide a systematic wayof interpreting the formalism and characterizing what states of mind corre-spond to what formal objects in such a way that explains the semantic proper-ties of the sentences that express those states of mind. In the special cases ofpreference-independent and world-independent contentssets of pairssuch that if one pair is in the set, so is every pair with the same w or . coordi-nate, respectivelythe expressivist has a story: The former characterize ordin-ary factual beliefs, like the belief that grass is green, and the latter characterizepreferences, like the belief that murder is wrong. But what should we sayabout contents that are neither preference-independent nor world-indepen-dent? Schroeder objects that the expressivist cannot give an adequate generalanswer to this question, and that, as a result, the expressivist interpretation ofmixed disjunctions is empirically incorrect.

Schroeder argues that, on certain natural assumptions, expressivism pre-dicts that if / is a non-normative sentence and w is a normative sen-tence, then it is impossible to believe / _ w without either believing / orbelieving w:

[I]f / is normative and w is non-normative, there is no state of puredescriptive belief that someone who believes that / _ w is guaranteed tobe in, and there is no [pure preference state] that she is guaranteed to bein. So ipso facto there is no combination of a descriptive belief state and[pure preference state] that she is guaranteed to be in. . .

But since were assuming that the only states of mind there are are ordin-ary descriptive beliefs, ordinary [preference states], and their combina-tions. . . on this view there is no room for such a state. (2011: 14, 12,variables adapted; cf. p. 31, 2008a: 124127)

A bit more slowly: Giving or its usual interpretation as set union, thecontent of the state of mind expressed by the mixed disjunctionAlice doesnt have a job or Alice has to help the poor is as follows.

(9) {hw, .i: Alice doesnt have a job in w, or Alice helps the poor in allthe .-best worlds}


Call this set S. Bert believes that Alice doesnt have a job or she has tohelp the poor iff Berts total belief statehis doxastic-practical alternatives(4.2; cf. n. 25)is a subset of S. But assuming that the only states of mindare ordinary factual beliefs and pure preference states and their combina-tions, then since S is the union of a world-independent content (a contentthat only constrains .) and a preference-independent content (a content thatonly constrains w), Bert can have this disjunctive belief only if either Bertsdoxastic alternatives is a subset of S or Berts practical alternatives is a sub-set of S. So Bert believes that Alice doesnt have a job or she has to helpthe poor only if either Bert believes that Alice doesnt have a job or Bertbelieves that Alice has to help the poor. But this is incorrect. Bert canbelieve that Alice doesnt have a job or she should help the poor but beuncertain about which. One can believe a disjunction without believingeither disjunct. So, Schroeder concludes, the expressivist conates believing/ _ w with either believing / or believing w.

Like the case of the negation problem, this objection is partly technicaland partly interpretive. It is technical because we need a way of blockingthe entailment in question. It is interpretive because whatever story we tellabout how to block this entailment, we need to be able to interpret theresulting apparatus so as to explain what states of mind are expressed bydisjunctive sentences and how these states of mind are logically related toother states of mind.

As Schroeder notes, an intuitive way of thinking of the attitude expressedby a disjunctive sentence is in terms of Blackburns (1988) notion of beingtied to a tree. A disjunction / _ w can be understood as expressing a con-ditional commitment to take on the attitude expressed by / upon rejectingthe attitude expressed by w, and vice versa. But saying this raises a nowfamiliar problem: another attitude has been introducedthe attitude of beingtied to a treeand it must be explained how this attitude is logically relatedto the other attitudes in the expressivists repertoire so as to capture the logi-cal relations among disjunctive and non-disjunctive sentences. For example,we need to capture how / _ w, :/, and :w are logically inconsistent.But the situation isnt hopeless. The attitude expressed by disjunctive sen-tences neednt be construed as an attitude that is logically unrelated to theattitudes of requiring, permitting, etc. Taking up our strategy in response tothe negation problem, if we can derive these attitudes from a common corewe can capture their logical relations sans stipulation.

Before turning to questions of interpretation, observe that Schroedersobjection fails if we drop the assumption that total belief states must becharacterized into a purely descriptive component and a purely practicalcomponent, or that the only states of mind there are are ordinary

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descriptive beliefs, ordinary [preference states], and their combinations.27

The reason for Schroeders assumption, of course, is a worry that the ex-pressivist lacks a systematic way of interpreting sets of world-preferencepairs that are neither world-independent nor preference-independent. Butour solution to the negation problem suggests a natural response. I suggestthat we characterize these states in terms of ordinary belief and conditional(weak) preference. One might worry about introducing a new attitude, butthe attitude of conditional preference, its logic, and its connection withbelief and action are already well studied in decision theory and preferencelogic. Preferenceslike norms, values, goals, etc.typically dont come inthe form of blunt categorical injunctions. They arent usually of the formNo matter what, /!. Rather they often come with conditions under whichthey apply. For instance, if I want to go for a run, my preference neednt bethat I go for a run, come what may. More plausibly it is that I go for a rungiven that its sunny, that Im not injured, that I didnt just eat a burrito,and so on. Our preferences are often conditional, preferences for certain cir-cumstances. (Categorical preferences can be treated as preferences that holdconditional on any possibility.)

Thus far I have been treating modals as interpreted with respect to preor-ders. But since modals can themselves occur in intensional contexts, it isstandard in ordering semantics to index preorders to a world of evaluation(written .w). Which preorder is relevant for the interpretation of a givenmodal sentence can depend on how things are in the actual world, or onhow things could be but arent or could have been but werent. What con-text supplies for the interpretation of the modal is a function from worlds topreorders. Call such a function a preorder function. Preorder functions pro-vide a natural way of representing conditional preferences. Intuitively, a pre-

27 For a simple example, suppose our model contains only the following world-preferencepairs: hw1;.1i; hw2;.1i; hw1;.2i; hw2;.2i. Suppose we have a non-normative sentence/ and a normative sentence w such that s/t fhw1;.1i; hw1;.2ig andswt fhw1;.1i; hw2;.1ig, so that s/t [ swt fhw1;.1i;hw1;.2i; hw2;.1ig. (sat isthe set of world-preference pairs that verify a.) Suppose that Alice believes / _ w. ThenBelA s/t [ swt, where BelA is the set of hw, .i pairs that characterize Alices totalbelief state. If, as Schroeder suggests, BelA must be a subset of the intersection of onlyworld-independent and preference-independent sets of hw, .i pairsthat is, if Alicesbelief state must be characterizable only in terms of purely descriptive beliefs and purelypractical beliefsthen it indeed follows that BelA s/t _ BelA swt, that is, that Alicebelieves / or Alice believes w. (Given that BelA s/t [ swt, the only total belief statesthat are the intersection of world- and preference-independent sets of world-preferencepairs are s/t; swt; fhw1;.1ig, fhw1;.2ig, and fhw2;.1ig, and each of these is either a(possibly improper) subset of s/t or a (possibly improper) subset of swt. So ifBelA s/t _ swt, then BelA s/t or BelA swt.) But dropping Schroeders assump-tion blocks the entailment, for the following total belief states that are (possibly impro-per) subsets of s/t [ swt neither entail / nor entail w: s/t [ swt itself, andfhw1;.2i; hw2;.1ig.


order function kw ..w encodes ones preferences for the situation of wbeing actual; an indexed preorder .w represents ones preferences given therelevant circumstances in w. (Hereafter I use the unindexed . as short forkw ..w to denote preorder functions.) Suppose I prefer to go for a rungiven that its sunny, and I prefer not to run given that it isnt sunny. Let-ting S and S be representatives of relevant equivalence classes of worldswhere its sunny and not sunny, respectively, we can represent these condi-tional preferences with a preorder function . that is such that worlds whereI run are, other things equal, .S-better than worlds where I dont run, andis such that worlds where I dont run are, other things equal, .S-better thanworlds where I do (n. 19).

In this way, preorder functions can be interpreted as preferences condi-tional on maximally specic possibilities. As in 4.1, this isnt to deny thatagents have preferences conditional on non-maximal possibilities, and it isneutral on the relation between preferences conditional on maximal vs. non-maximal possibilities. Since not all circumstances in a world may be rele-vant to ones preferences, just as the preorders themselves may permit ties(they neednt be antisymmetric), so too preorder functions may map differ-ent worlds to the same preorder (they neednt be injective). Representingbodies of conditional preference with preorder functions has the advantageof utilizing existing apparatus from contemporary ordering semantics formodals. However, like in 4.1, alternative implementations will be possibledepending on ones broader views about the sorts of issues mentionedthere.

A world-preference pair now consists of a possible world w and a body ofpreferences conditional on w being actual. The singleton {hw, .wi} representsa fully opinionated and decided state of mind; it represents a state of mind thatis settled on w being the actual world, and decided on a body of conditionalpreferences ., which together determine the preferences .w. Generalizing, anarbitrary set of world-preference pairs fhi;.ii; h j;.ji; . . .; hu;.ui;hv;.vi; . . .g represents a belief state that is compatible with i, j, u, v, . . ., anda preference state compatible with . conditional on i, j, . . ., .* conditional onu, v, . . ., and so on; it represents a state of uncertainty and indecision. Forexample, the set fhw1;.1w1i; hw1;.2w1i; hw2;.1w2ig represents a state of mindthat is uncertain about whether w1 or w2 is actual, and is undecided aboutwhether to have the preferences .1w1 , .

2w1 , or .

1w2 . There are two important

things to notice about this: First, indecision in ones preferences can be theresult of uncertainty, but it doesnt have to be. Second, ones preferencesneednt be independent of ones beliefs.

Lets consider a concrete example to illustrate how appealing to condi-tional preferences, and representing them in terms of preorder functions, canhelp solve the disjunction problem. Let J, J, G, and G be (representativesof equivalence classes of) relevant worlds in which Alice has or doesnt

74 ALEX SILK

have a Job, and Gives or doesnt give to the poor. And let .1, . . . , .4 bepreorder functions with the following properties:

.1: G\1J G;G\1J G

.2: G\2J G; G\2J G

.3: G\3J G;G\3J G

.4: G\4J G; G\4J G

Intuitively, .1 represents a preference that Alice give to the poor regardlessof whether she has a job; .2 represents a preference that Alice give to thepoor iff she has a job; .3 represents a preference that Alice give to the pooriff she doesnt have a job; and .4 represents a preference that Alice notgive to the poor regardless of whether she has a job. The contents of Alicedoesnt have a job (:job) and Alice has to give to the poor (M(give)),respectively, are as follows:

s:jobt fhw;.wi : Alice doesn't have a job in wg fh J;.1Ji; h J;.2Ji; h J;.3Ji; h J;.4Jig

sMgivet fhw;.wi : Alice gives to the poor in all the .w-best worldsg fhJ;.1Ji; h J;.1Ji; hJ;.2Ji; hJ;.3Jig

The content of the mixed disjunction Alice doesnt have a job or she hasto give to the poor is the union of these sets:

s:job _Mgivet s:jobt [ sMgivet fhJ;.1Ji; hJ;.1Ji; hJ;.2Ji; hJ;.2Ji; hJ;.3Ji; hJ;.4Jig

For concreteness, consider the following subset of this set, T fhJ;.2Ji;hJ;.2Jig. The crucial question is this: What state of mind is represented byT? Intuitively, it is the state of mind of being uncertain about whether Alicehas a job, and of preferring that she give to the poor conditional on her hav-ing a job and preferring that she not give to the poor conditional on her nothaving a job. It is a state of uncertainty and indecision (in this case, wherethe indecision derives from the uncertainty). Since T is a subset of the con-tent of the mixed disjunction but not of the content of either disjunct, ifT represents Berts total state of mind, then Bert counts as believing thatAlice doesnt have a job or has to give to the poor, without believing that


Alice doesnt have a job or believing that she has to give to the poor. Theinference from believing / _ w to believing / or believing w is blocked.

To be clear, the proposal is not that utterances of mixed disjunctionsconventionally express simple conditional preferencese.g., preferencesthat hold conditional on the negation of a factual antecedent. Saying thiswould fail to provide a general interpretation of disjunction. For instance, itwont apply to disjunctions in which each disjunct is normative. It also nat-urally raises a worry that disjunctions in which one disjunct is itself amixed disjunction will require us to iterate the go conditional strategypast the point where we have an independent grasp on the posited attitude(what would conditional conditional preference be?). An agent might countas believing that Alice doesnt have a job or has to give to the poor in vir-tue of having a standing conditional preference for Alice to give to the poorgiven that she a job. But having this conditional preference isnt necessaryfor believing the mixed disjunction. It isnt the state of mind conventionallyexpressed by an utterance of :job _ M(give). The attitude conventionallyexpressed by an utterance of a sentence / is the least committal way ofthinking that /.

Rather, the strategy is to give a general recipe for interpreting arbitrarysets of world-preference pairs in terms of ordinary beliefs about ways theworld might be and preferences that hold given that the world is certain ofthose ways (see above). This recipe is to apply to any disjunction, whethermixed or non-mixed, simple or complex. Indeed, it is to apply to any sen-tence (or at least any sentence whose content is a set of world-preferencepairs).28 The strategy is this:

How to solve the disjunction problem:

1. Give disjunction the formal semantics we would normally give it.(E.g., treat the content of / _ w as the union of the content of/ and the content of w.)

2. Drop the assumption that total belief states must be factorable intopurely descriptive and purely practical components.

28 Treating disjunctions with normative disjuncts as conventionally expressing attitudes ofindecision (perhaps among other things) is compatible with granting that one can acceptsuch disjunctions without being undecided. This is no different from the ordinary factualcase. Disjunctions with ordinary factual sentences conventionally express attitudes ofuncertainty, though one can accept them while being certain about which disjunct istrue.There may ultimately be reasons for further complicating the proposed representationsof semantic contents and states of mind in light of independent issues concerning episte-mic vocabulary (might, probably, etc.). See note 1; for specic discussion of disjunc-tion in epistemic expressivist theories, see Rothschild 2012, Swanson 2012.

76 ALEX SILK

3. Give a general way of interpreting (i.e., characterizing what statesof mind correspond to) arbitrary sets of world-preference pairs.

4. Apply this general strategy to the case of the contents of disjunc-tive sentences.

5. Note that Schroeders problematic entailment is blocked.

Ordering expressivism offers a general way of characterizing what states ofmind are represented by arbitrary sets of world-preference pairs that lets usdrop Schroeders assumption in Step 2 above. This interpretation explainsthe logical relations among mixed states of mind and their pure counter-parts, and, thus, among disjunctive and non-disjunctive sentences. It cor-rectly blocks problematic entailments in cases with mixed disjunctions, anddistinguishes believing / _ w from believing / or believing w. Moregenerally, in providing such a recipe for interpreting arbitrary sets of world-preference pairs, we can give a systematic expressivist interpretation ofnormative, descriptive, and mixed language. It is in this way that orderingexpressivism makes progress toward a fast track solution to the Frege-Geach problem (3).

6. Conclusion

Despite its checkered past, expressivism has found robust support in a vari-ety of domains. In the case of normative language and judgment, expressi-vism promises a substantive account of its distinctive practical character, afeature which alternative theories that assimilate the normative case to thenon-normative case often struggle to capture. But it is often thought thatexpressivism has intractable problems with capturing the meanings andlogical properties of complex sentences and so cannot make good on thispromise.

I have argued that we can make progress in eliminating expressivismssemantic stumbling block by developing what I call ordering expressivism.By interdening the attitudes intuitively expressed by normative sentencesin terms of a single basic practical attitude, the expressivist can capture thelogical relations among these attitudes and thus among the sentences thatexpress them. Though I have focused on the particular cases of negationand disjunction, the structure of our solution suggests a more general strat-egy for implementing an expressivist semantics. Ordering expressivism co-opts developments from linguistic semantics for modals by systematicallyinterpreting the orderings in these analyses in terms of a suitable practicalattitude. Though expressivism does make novel claims about semanticexplanation and the nature of normative language and judgment, it neednt


reinvent the compositional semantic wheel. This, I hope, will promptrenewed interest in other distinctive aspects of expressivism, as in philoso-phy of mind and psychology.29

References

Arrow, Kenneth J. 1959. Rational choice functions and orderings.Economica 26, 121127.

Aumann, Robert J. 1962. Utility theory without the completeness axiom.Econometrica 30, 445462.

Blackburn, Simon. 1984. Spreading the word. Oxford: Clarendon Press.1988. Attitudes and contents. In Essays in quasi-realism, pp. 182197.

New York: Oxford University Press.1998. Ruling passions. Oxford: Clarendon Press.

Broome, John. 1991. Desire, belief, and expectation. Mind 100, 265267.1993. Can a Humean be moderate? In R.G. Frey & Christopher

Morris (Eds.), Value, welfare, and morality, pp. 5173. Cambridge:Cambridge University Press.2004. Weighing lives. Oxford: Oxford University Press.

Byrne, Alex & Alan Hajek. 1997. David Hume, David Lewis, and decisiontheory. Mind 106, 411428.

Cariani, Fabrizio, Magdalena Kaufmann, & Stefan Kaufmann. 2013.Deliberative modality under epistemic uncertainty. Linguistics andPhilosophy 36, 225259.

Chang, Ruth. 2002. The possibility of parity. Ethics 112, 659688.Charlow, Nate. 2011. Practical language: Its meaning and use. Ph.D.

thesis, University of Michigan.2013a. What we know and what to do. Synthese 190, 22912323.2013b. The problem with the Frege-Geach Problem. Philosophical

Studies.Davidson, Donald. 1976. Hempel on explaining action. In Essays on

actions and events, pp. 261276. 2001. New York: Clarendon Press,2nd edn.

Davidson, Donald, John McKinsey, & Patrick Suppes. 1955. Outlines of aformal theory of value. Philosophy of Science 22, 140160.

De Sousa, Ronald. 1974. The good and the true. Mind 83, 534551.Dowell, J. L. 2013. Flexible contextualism about deontic modals: A puzzle

about information-sensitivity. Inquiry 56, 149178.

29 Thanks to Jamie Dreier, Kit Fine, Allan Gibbard, Sarah Moss, Peter Railton, Ian Rumtt,Mark Schroeder, Scott Sturgeon, Eric Swanson, audiences at the 2014 Central APA,MIT, the University of Birmingham

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