11.0 Questions and Answers

Questions about the logical properties of vague languages are often the primary focus of work on vagueness in philosophy. These questions have traditionally divided into two groups. The first concerns issues to do with the indeterminacy of vague expressions: questions about the correct logic of higher-order vagueness (e.g. Sainsbury Reference Sainsbury1991; Wright Reference Wright1992, Reference Wright, Moruzzi and Dietz2009; Williamson Reference Williamson1994, Reference Williamson1999; Soames Reference Soames and Beall2003; Bobzien Reference Bobzien2011, Reference Bobzien, Ierodiakonou and Morison2012, Reference Bobzien2013, Reference Bobzien2015; Dorr Reference Dorr, Moruzzi and Dietz2009, Reference Dorr2015) or the bivalence of vague utterances (e.g. Horwich Reference Horwich1990; McGee Reference McGee1991; Williamson Reference Williamson1994: §7; Keefe Reference Keefe2000b: §8; Raffman Reference Raffman2005a). The second concerns issues to do with the tolerance of vague expressions: questions about the correct resolution of the sorites paradox or the existence of sharp cutoffs (e.g. Cargile Reference Cargile1969; Fine Reference Fine1975; Wright Reference Wright1975, Reference Wright1987; Sainsbury Reference Sainsbury1988, Reference Sainsbury, Keefe and Smith1996; Edgington Reference Edgington1992, Reference Edgington, Keefe and Smith1997; Fara Reference Fara2000; Shapiro Reference Shapiro2006; Gaifman Reference Gaifman2010;Cobreros et al. Reference Cobreros, Égré, Ripley and van Rooij2012; Ripley Reference Ripley, Berto, Mares and Tanaka2013).

Independently, the last 40 years has seen a large growth in work on the systematic features of conversation by linguists, logicians, and philosophers. Much of this work has focused on categories of expression which exhibit two kinds of interaction with context. First, features of the use of the expressions are sensitive to discourse context; and, second, features of discourse context are sensitive to the use of the expressions. For want of a label, we can refer to this kind of two-way interaction between utterances and context as discourse dynamics. Formal and informal frameworks for theorizing about discourse dynamics have been developed for, amongst other kinds of expressions, anaphoric pronouns, modals and presupposition triggers.

As a range of authors have noticed, two-way interactions also appear between utterances of vague sentences and context (e.g. Lewis Reference Lewis1979; Kamp Reference Kamp and Mönnich1981a; Pinkal Reference Pinkal, Ballmer and Pinkal1983; Eikmeyer & Rieser Reference Eikmeyer, Rieser, Ballmer and Pinkal1983; Bosch Reference Bosch, Ballmer and Pinkal1983; Barker Reference Barker2002). This has given rise to a large, if frequently fragmented, literature on the discourse dynamics of vague language. Underlying this trend is the prospect that traditional problems of vagueness might be amenable to tools developed to model other discourse-level phenomena.

A noteworthy recent trend has been a surge in experimental work on a range phenomena related to the discourse dynamics of vagueness. Égré et al. (Reference Égré, de Gardelle and Ripley2013) report positive evidence of order effects in ‘dynamic’ or ‘forced march’ sorites sequences – though of a kind which conflict, to a greater or lesser extent with the predictions of e.g. Kamp (Reference Kamp and Mönnich1981a), Raffman (Reference Raffman1994, Reference Raffman1996). Syrett et al. (Reference Syrett, Kennedy and Lidz2010) provide empirical research into the use of definites with vague complements – including the discourse-level effects discussed in Section 11.2.1. Finally, there has been a substantial investigation of judgments about sentences, both atomic and complex, in the borderline region of a vague predicate (Bonini et al. Reference Bonini, Osherson, Viale and Williamson1999; Alxatib & Pelletier Reference Alxatib and Pelletier2011; Ripley Reference Ripley, Nouwen, van Rooij, Sauerland and Schmitz2011; Serchuk et al. Reference Serchuk, Hargreaves and Zach2011).

First, any minimally adequate theory of the discourse dynamics of vagueness should provide: (i) an explanation of the mechanism by which the use of vague expressions is sensitive to discourse context; and (ii) an explanation of the mechanism by which discourse context is sensitive to the use of vague expressions. Various responses to these two questions are possible, and can be combined in a number of different ways. I discuss and assess a range of these alternatives in the course of this chapter.

There are a number of issues which remain unresolved, even amongst those authors who take discourse-level phenomena to be of central interest in the study of vagueness. One prominent question concerns the extent to which the discourse dynamics of vague expressions can or should be assimilated to analogous behavior by other expressions (such as anaphoric pronouns, modals, and presupposition triggers).

A second question concerns the connection between discourse dynamics and traditional questions of vagueness. Discourse-level phenomena can be treated as an important object of study, without being taken to provide a solution to puzzles such as the sorites paradox. Accordingly, it is an open issue whether the interaction of vague language and context is worthy of investigation in virtue of its connection to the traditional questions discussed above, or merely as an independent phenomenon alongside them. I’ll make some brief proposals bearing on these questions in the concluding section of this chapter.

11.1 Preliminaries: Indeterminacy and Tolerance

Imagine a series of one hundred bottles of wine, where for $1\le n\le 100$, the nth bottle in the series costs n dollars. Over objects in this series, predicative and attributive uses of the adjective ‘expensive’ exemplify a range of phenomena associated with vagueness. Of these, work in philosophy especially has tended to focus on two: indeterminacy and tolerance.

Indeterminacy

In response to the question ‘Is bottle #50 expensive?’, what a competent speaker knows about her language may fail to require that she answer affirmatively, and, likewise, fail to require that she answer negatively. Furthermore, there appears to be no additional (nontrivial) information which she could acquire about the series of bottles which would change her situation. This phenomenon is frequently described in terms of indeterminacy – that is, bottle #50 is neither determinately expensive nor determinately not expensive.

Under these conditions, we say that #50 is a borderline case. The knowledge speakers must possess to be competent fails to settle how borderline are to be classified. This goes observation beyond the previous one regarding what is required of speakers.

We can also make a stronger observation. The fact that a competent speaker is neither required to classify bottle _#50 as expensive nor required to classify it as inexpensive does not by itself not settle how she is permitted to classify it. She might, after all, be required to make no classification. Yet indeterminacy appears to be also accompanied by permissiveness in use (for discussion, see e.g. Wright Reference Wright1987: 244; Tappenden Reference Tappenden1993: 553–561; Sainsbury Reference Sainsbury, Keefe and Smith1996: §9; Fara Reference Fara2000: 56; Shapiro Reference Shapiro2006; Égré & Klinedinst Reference Égré, Klinedinst, Égré and Klinedinst2010: 1; Gaifman Reference Gaifman2010: 7, among others). Where #50 is borderline, in responding to the question ‘Is bottle #50 expensive?’ a competent speaker is permitted to answer affirmatively, permitted to answer negatively and permitted to decline to answer one way or the other. That is, speakers are at liberty to decide how borderline cases are to be classified if at all.

Tolerance

For every n: $1⩽n⩽100$, the corresponding instance of the schema in (1) appears hard to reject:

The appeal of instances of (1) is attributable to the fact that ‘expensive’ is seemingly tolerant to minimal variation in price (Wright Reference Wright1975: 333). That is, it seems that any bottle which differs only marginally in price from an expensive bottle will be expensive itself.

However, while the instances of (1) are compelling, they are each classically inconsistent with the seemingly equally compelling (2)–(3):

From (2) – which says that a $100 bottle of wine is expensive – and the instantiation of (1) with 100, we can obtain the claim that bottle #99 is expensive via modus ponens. Repeated applications of this procedure, along with the transitivity of entailment and double negation introduction, will yield the denial of (3). Yet, since (3) says that a $1 bottle of wine is expensive, accepting its denial appears impermissible in any context.

Tolerance does not only manifest in judgments about conditionals like (1). Another product of tolerance is the apparent absence of sharp cutoffs. Instances of negated conjunctions, like (4), and disjunctions, like (5), also appear hard to reject:

As above, the set of claims comprising the instantiations of (4) and the instantiations of (5) are each classically inconsistent with (2) and (3). That is, from the claim that bottle #100 is expensive and each of the instances of either (4) or (5), it is possible to classically derive the conclusion that bottle #1 is expensive, also.

The possibility of deriving a contradiction using classical resources makes unrestricted acceptance of the instances of (1), (4) and (5) controversial. Many theorists either claim that some instance involving borderline cases is false (e.g. Sorensen Reference Sorensen1988, Reference Sorensen2001; Williamson Reference Williamson1994; Fara Reference Fara2000), or deny that any instance involving borderline cases is true (e.g. Fine Reference Fine1975; Kamp Reference Kamp1975; Keefe Reference Keefe2000a, Reference Keefe2000b).

In contrast, it is uncontroversial that the instances of the converse schema should be accepted:

The appeal of instances of (6) is attributable to what Fine (Reference Fine1975: 270) terms penumbral connections. Such connections correspond to constraints on the ways in which indeterminacy can be resolved. They manifest (in part) in the existence of determinate complex expressions with indeterminate constituents.Footnote ¹ For example, it may be indeterminate whether a 17-year-old is a child, but determinate that they are not both a child and an adult. It may be indeterminate whether a shade of chartreuse is green, but determinate that it is either green or yellow. In the present case, while it is indeterminate which bottles in the series are expensive, it is determinate that any bottle which costs more than an expensive bottle will be expensive itself.

The majority of work on vagueness in philosophy has concentrated on issues related to tolerance and indeterminacy (either separately or, less frequently, simultaneously). In contrast, work in linguistics has frequently focused on vagueness within particular lexical categories, including, e.g., gradable adjectives (Klein Reference Klein1980; Kamp Reference Kamp1975, Reference Kamp, Groenendijk, Janssen and Stokhof1981b; Barker Reference Barker2002, Reference Barker2003, Reference Barker2013; Kennedy Reference Kennedy2001, Reference Kennedy2007, Reference Kennedy, Égré and Klinedinst2010; Kennedy & McNally Reference Kennedy and McNally2004; Sassoon Reference Sassoon2013), nominals (Sassoon Reference Sassoon2013; van Deemter Reference van Deemter2010), hedges (Pinkal Reference Pinkal, Ballmer and Pinkal1983; Lasersohn Reference Lasersohn1999; Barker Reference Barker2002, Reference Barker2003), and quantifiers (Ballweg Reference Ballweg, Ballmer and Pinkal1983; Solt Reference Solt2016). The topic of this chapter marks one area in which the two fields have converged, with fruitful results.

11.2 Discourse Dynamics and Vagueness

As discussed above, permissiveness accompanies indeterminacy. In most discourse contexts in which it is indeterminate whether bottle #50 is expensive, a speaker may classify it as expensive, may classify it as not expensive, or may decline to classify it one way or the other.Footnote ^2, Footnote ³ However, the range of permissible uses of a vague expression is susceptible to change over the course of discourse. Using an expression can impose constraints on the way the same expression (or others related to it) can be employed in later, ‘downstream’ utterances.

This is most clearly revealed in the existence of discourses whose unacceptability cannot be attributed to the prior impermissibility of any particular constituent utterance. That is, we can identify sequences of utterances which are impermissible in context, despite the fact that each of their constituent utterances occurs in some sequence which would be permissible in the same context.

Recall that bottle #n in the sequence costs n dollars. There are many naturally occurring contexts in which a speaker could permissibly perform the sequence of utterances in (7) or, alternatively, permissibly perform the sequence of utterances in (8):

However, in any such context, it would be impermissible for the speaker to perform the sequence of utterances in (9):

Note that there is, at least initially, a permissible sequence (namely, (7)) in which #50 is classified as expensive, and a permissible sequence (namely, (8)) in which #51 is classified as not expensive. However, after #50 has been classified as expensive, it is no longer permissible for the speaker (or any other participant in a conversation in which the utterance has been mutually accepted) to classify #51 as not expensive.

Indeed we can, also, make a stronger observation: after #50 has been classified as expensive (and the utterance has been mutually accepted), participants in the conversation are required to classify #51 as expensive, should the question arise. That is, they are no longer permitted to decline to classify #51 one way or the other.

The impermissibility of (9) appears attributable to precisely the same source as the determinacy of the instances of (6). Classifying a bottle as expensive involves a (partial) resolution of indeterminacy. The penumbral connections associated with the expression require that any bottle which costs more than a bottle classified as expensive also be classified as expensive. Using the expression imposes constraints on future use, constraints which may preclude uses which were previously permissible.

Discourse-level effects do not only arise in virtue of penumbral connections, however. It also appears unacceptable for a speaker to perform the sequence of utterances in (10) in any context:

Again, note that there is, at least initially, a permissible sequence containing each constituent utterance as a sequence. However, after #51 has been classified as expensive, it seems no longer permissible to classify its predecessor as not expensive.

The impermissibility of the second utterance is attributable to the same source as the impermissibility of rejecting instances of (5). Since ‘expensive’ seems tolerant to minimal variation in price, it seems impermissible to classify as expensive any bottle which differs only marginally from a bottle classified as not expensive. To do so would be to commit to a sharp cutoff between the bottles which are expensive and the bottles which are not expensive – a cutoff of precisely the kind incompatible with tolerance.

Note, however, that the present case differs from it’s predecessor in at least one respect. It is far from obvious that, after #51 has been classified as expensive, it would be impermissible to decline to classify #50 one way or the other. Instead, it appears coherent for an individual to answer the question of whether #51 is expensive positively, but nevertheless be incapable of coming to a decision regarding #50. Indeed this would seem to be precisely the situation of subjects in a so-called ‘forced march’ sorites series (Horgan Reference Horgan1994; Raffman Reference Raffman1994). After classifying a bottle as expensive, it remains indeterminate, it seems, whether bottles only marginally less expensive are not expensive – a positive answer is not required, despite a negative answer being prohibited.Footnote ⁴

These observations combine to form a picture of the discourse dynamics of vague expressions. First, they suggest that features of the use of vague expressions are sensitive to context. The fact that there are contexts at which (7) would be permissible to utter but (9) would not (since it is unacceptable in every context) indicates that the permissibility of uttering a vague sentence can vary depending on the discourse context. In this case, the permissibility of classifying bottle #n as not expensive varies depending on the context resulting from the speaker’s first utterance (i.e. whether #n − 1 was classified as expensive or as not expensive). Second, they suggest that features of the context are sensitive to the use of vague expression. In particular, the fact that (10) is impermissible to utter in any context suggest that classifying bottle #n as expensive changes the discourse context so that for any n′ ≥ n−k, classifying bottle #n′ as not expensive is impermissible (where k is positive and, presumably, vague itself) and for any $n^{″}\ge n$, classifying bottle #n″ as expensive is required. Putting this together, use of vague expressions exhibits the two-way interaction between utterance and context constitutive of discourse dynamics.

11.3 Explaining Discourse Dynamics

A minimally adequate account of the discourse dynamics of vagueness will be required to answer two questions: how is the use of vague expressions dependent upon discourse context? and how is discourse context-dependent use of vague expressions? As we’ll see in this section, philosophers and linguists have provided a range of answers, which can be combined in a number of different ways.

11.4 Local Contexts and Vagueness

Discourse dynamics involve the two-way interaction between contexts and the expressions used in them. However, the context at which a constituent of a sentence is evaluated need not always coincide with the context at which the sentence itself is used. It is standard to distinguish between global context (the context at which the sentence containing an expression is evaluated) and local context (the context at which the expression itself is evaluated) (Karttunen Reference Karttunen1974; Heim Reference Heim1982, Reference Heim, Portner and Partee1983, Reference Heim and van der Sandt1990).

1. (15)

   a.	John stopped smoking.
   b.	If John used to smoke, he stopped.

Presuppositions triggers, such as ‘stop’, are sensitive to context. For an expression containing a trigger to be licit, the trigger’s presupposition must be satisfied in the context at which it is evaluated (Stalnaker Reference Stalnaker1973, Reference Stalnaker and Stalnaker1974; Karttunen Reference Karttunen1974; see also Abrusán, this volume). However, a discourse context which fails to license (15a) may nevertheless license (15b). This suggests that the local context at which expressions in the consequent of a conditional are evaluated is not the same as the global context at which the conditional is evaluated itself.

1. (16)

   a.	Iti is a spaniel.
   b.	Mary owns a dogi and iti is a spaniel.

Pronouns are also sensitive to context. For an expression containing a pronoun to be licit, the pronoun must be associated with an appropriate discourse referent in the context at which it is evaluated (Karttunen Reference Karttunen and McCawley1976; Kamp Reference Kamp, Groenendijk, Janssen and Stokhof1981b; Heim Reference Heim1982). However, a discourse context which fails to license (16a) may nevertheless license (16b). As with presupposition, this suggests that the local context at which expressions in the right-hand conjunct of a conjunction are evaluated is not the same as the global context at which the conjunction is evaluated itself.

Much work in linguistics and philosophy has focused on identifying how the local context of an expression is to be calculated from the global context along with its own syntactic environment. Such theories have two components. They must specify: (i) which constituents of an expression’s syntactic environment are relevant to calculating its local context; and (ii) what the contribution of those constituents to the local context is.

Theories which build dynamic behavior into the semantics of the language have often been taken to be well-placed to offer a theory of local context (Heim Reference Heim1982, Reference Heim1992; Beaver Reference Beaver1992, Reference Beaver2001; Zeevat Reference Zeevat1992; van Eijck Reference van Eijck1993, Reference van Eijck1994; for criticism of dynamic approaches, see Soames Reference Soames1982; Schlenker Reference Schlenker2008; Lewis Reference Lewis, Burgess and Sherman2014). While they must (arguably) give a stipulative response regarding the first issue (though see Rothschild Reference Rothschild2011), dynamic approaches are able to offer an appealingly simple response to the second. The effects of clausal expressions on local context and on global context are calculated in exactly the same way. That is, on a dynamic approach, an expression’s contribution in determining local context is simply its content: a function from one context to another.

The preceding discussion outlined a general picture of the discourse dynamics of vague expressions. According to this picture, classifying bottle #n as expensive resulted in a new discourse context in which, for any n′ ≥ n − k, classifying bottle #n′ as not expensive is impermissible (and for any n″ ≥ n, classifying bottle #n″ as expensive is required). It turns out that, when combined with an orthodox account of local context for logical connectives, we can use this picture to develop an appealing explanation of certain key tolerance phenomena (Section 11.1).

As first observed by van der Sandt (Reference van der Sandt, Bartsch, van Benthem and van Emde Boas1989, Reference van der Sandt1992), local contexts for presupposition triggers and anaphoric pronouns appear to be calculated in the same way. Accordingly, we will consider both when giving examples of orthodoxy regarding local contexts for connectives and quantifiers.

1. (17)

   a.	If John used to smoke, he stopped.
   b.	If Mary owns a dogi, iti is a spaniel.

As we saw above, in (17a)(=15b), the presupposition of ‘stop’ is satisfied in its local context, even if it remains unsatisfied in the global context. Similarly, in (17b), the indefinite in the antecedent can introduce a discourse referent on which the pronoun in the consequent is anaphoric. On this basis, the local context of the consequent of a conditional is generally assumed to be the local context of the conditional updated with the antecedent (Langendoen & Savin Reference Langendoen, Savin, Fillmore and Langendoen1971; Karttunen Reference Karttunen1973, Reference Karttunen1974; Gazdar Reference Gazdar1979).Footnote ⁷

Turning to the case of vague expressions, the local context of the consequent of (18) (=(1)), is the global context updated with the claim that bottle #n is expensive.

In the context resulting from the claim that bottle #n is expensive, it is impermissible to classify bottle #n − 1 as not expensive. So, at least on the assumption that we judge it impermissible to reject a conditional as long as it is impermissible to reject its consequent in its local context, this will explain why individuals are reluctant to reject any instance of (18).

Similar remarks extend to conjunction and disjunction:

1. (19)

   a.	John used to smoke and he stopped.
   b.	Mary owns a dogi and iti is a spaniel.

1. (20)

   a.	Either John never smoked or he stopped.
   b.	Either Mary doesn’t own a dogi or iti is a spaniel.

On the basis examples like (19a)–(19b), the local context of a right-hand conjunct is generally assumed to be the local context of the conjunction updated with its left-hand conjunct.Footnote ⁸ Similarly, on the basis examples like (20a)–(20b), the local context of a right-hand disjunct is generally assumed to be the local context of the disjunction updated with the negation of its left-hand disjunct. (NB: the case of anaphoric expressions in disjunction, first discussed by Partee, is a bit more complex. See, in particular Simons Reference Simons, Galloway and Spence1996 and Dekker Reference Dekker1999 for discussion.)

1. (21)

   a.	It’s not the case that: bottle #n is expensive but bottle #n − 1 is not.
   b.	Either bottle #n is not expensive or bottle #n − 1 is.

Accordingly, the local context of the right-hand conjunct of (21a) (=(4)), will be the global context updated with the claim that bottle #n is expensive. Given standard assumptions about negation, the same holds for the right-hand disjunct of (21b) (=5). Assuming a negated conjunction is judged permissible to reject only if it is permissible to accept each conjunct in its local context, we can explain our judgments about (21a). And, assuming a disjunction is judged permissible to reject only if it is permissible to reject each disjunct in its local context, we can equally explain our judgments about (21b).

By considering the local context of vague expressions, observations about tolerance at the level of discourse (exemplified in, e.g., (10)) can be extended to explain judgments at the sentential level, in cases involving conditionals, conjunction, and disjunction. This clearly falls far short of a complete theory of tolerance-related phenomena. In particular, absent an account of how discourse dynamics and local context should be reflected in the logic of a vague language, we still lack a solution to the sorites (and sorites-adjacent) puzzles. Nevertheless, we may hope that these kinds of issues can help to guide our choices developing in such an account. Authors such as Kamp (Reference Kamp and Mönnich1981a), Bosch (Reference Bosch, Ballmer and Pinkal1983), Ballweg (Reference Ballweg, Ballmer and Pinkal1983), Kyburg and Morreau (Reference Kyburg and Morreau2000), Barker (Reference Barker2002), Shapiro (Reference Shapiro2006), and Gaifman (Reference Gaifman2010) serve as examples of the potential fruitfulness of this approach.

11.5 Conclusion

The discourse-level phenomena associated with vagueness raise a range of new questions. As I’ve aimed to show in this chapter, the process of answering these questions may bring with it the potential to address ostensibly independent, traditional questions about vagueness. Having introduced the key phenomenon in Section 11.2, in Section 11.3 we looked at various approaches which could, in combination, account for the two-way interaction of vague utterances and context. Finally, in Section 11.4, I proposed one way to extend these considerations to the intersentential case, by appealing to features of local context.

12.0 Questions and Answers

The ability to conceive of alternatives – alternative situations, actions, places, times, even universes – is sometimes listed among the core cognitive/linguistic abilities that appear to set us apart from most nonhuman animals (e.g. ‘displacement’ in Hockett & Hockett Reference Hockett and Hockett1960).Footnote * Moreover, alternatives surface in accounts of a wide array of topics in philosophy and linguistics. This may reflect their centrality in language and cognition, or perhaps the fact that alternatives seem to make for a powerful ‘Maslow’s hammer’.

One exciting development is the notion that introducing alternatives to a discourse is a type of communicative intention in its own right, and, crucially, one which is expressed not just by interrogative sentences – declarative sentences too can serve to introduce certain alternatives, alongside the primary assertion they express (e.g. Alonso-Ovalle Reference Alonso-Ovalle2006; Ciardelli et al. Reference Ciardelli, Groenendijk and Roelofsen2013; Westera Reference Westera2017b). Another exciting development is the adoption of more data-driven, quantitative methods in the study of alternatives, for instance the probabilistic approach to alternatives of Rohde and Kurumada Reference Rohde, Kurumada, Federmeier and Watson2018, and the dataset of questions naturally evoked by text fragments of Westera et al. Reference Westera, Mayol and Rohde2020.

One key ingredient will be to discern and disentangle the various senses/roles in which ‘alternative’ is employed in linguistics, some of which are covered in this chapter. In addition, I think it is crucial that we try to ground the various notions of alternative in broader theories of cognition, as well as in quantitative empirical data.

I think that many basic questions concerning the various notions of alternative – what exactly they signify, how they are supposed to interact – have not been sufficiently considered. This chapter will consider such basic questions concerning several types of alternatives, namely focus alternatives, the alternatives introduced by disjunction, alternatives in the characterization of discourse goals (questions under discussion) and alternatives in the semantics of interrogatives.

12.1 Introduction

Research in formal semantics and pragmatics often invokes a notion of alternatives. Consider the following example, picked for the wide range of notions of alternatives it involves (uppercase represents a focus accent):

Common analyses of similar examples in the literature reveal at least the following notions of alternative.

• The numerals “two” and “three” have other numerals as their lexical alternatives, forming what is commonly called a Horn scale (after Horn Reference Horn1972): 〈“one,” “two,” “three,” “four,” …〉 – similar scales would exist for, e.g., quantifiers such as 〈“some,” “many,” “all”〉 and for adjectives such as 〈“warm,” “hot”〉.

• The strong focus accents on “two” and “three” lets each disjunct introduce focus alternatives into the semantics of the form “N of your friends were at the protest,” again in a separate dimension of semantics (Rooth Reference Rooth1992).

• The focus alternatives result in a presupposition that the utterance addresses a Question Under Discussion (QUD) paraphrasable as “How many of your friends were at the protest?” (Roberts Reference Roberts, Yoon and Kathol1996; Beaver & Clark Reference Beaver and Clark2009), which can again be modeled as a set of alternatives, i.e. a set of propositions of the form “N of your friends were at the protest.”

• The disjunction introduces its disjuncts into the semantics as alternatives, in a dimension of semantics separate from the ordinary, informational content (Alonso-Ovalle, Reference Alonso-Ovalle2006; Ciardelli et al., Reference Ciardelli, Groenendijk and Roelofsen2013).

• Because the sentence is an interrogative, its main semantic content would itself be a set of alternatives, containing (depending on one’s analysis) at least the two disjuncts, in some analyses also their joint negation (“neither”; Ciardelli et al. Reference Ciardelli, Groenendijk and Roelofsen2015).

• Besides the prior QUD addressed by the utterance, there is also the QUD which it sets up for the next speaker, which contains the two disjuncts along with, in some analyses, their joint negation (“neither”; Ciardelli et al. Reference Ciardelli, Groenendijk and Roelofsen2015) or, more correctly, some other alternative from the prior QUD, e.g. that three or perhaps even four of your friends were at the protest (Biezma & Rawlins Reference Biezma and Rawlins2012; Westera Reference Westera2017b).

Are these various notions of alternative all the same? If not, can they at least be assumed to interact in direct, formally characterizable ways?

Work in formal semantics suggests an affirmative answer to the second question, and a somewhat opportunistic, pragmatic stance with regard to the first. For instance, Questions Under Discussion are often treated as, essentially, implicit interrogatives, suggesting that alternatives from either the prior or the posterior QUD of an interrogative could be conflated with the alternatives in its semantic content. Some work on the semantics of interrogatives assumes that focus alternatives can be picked up by a question operator Q, which would promote the focus alternatives to constitute the main semantic content of the interrogative. For an account of disjunctive interrogatives it has been proposed that the alternatives introduced by a disjunction undergo a similar treatment: a question operator Q would keep the alternatives introduced by disjunction as alternatives in the interrogative’s semantic content, whereas in declaratives the disjunction-introduced alternatives would have no role to play. Moreover, it is tempting to use the same set of alternatives for genuine interrogatives and for embedded interrogative-like constructions (e.g. “John knows who was there.”).

This somewhat opportunistic stance towards the interactions of various notions of alternative may reflect a lack of conceptual clarity about what the different notions are supposed to represent; and this may be in part to blame on formal semantics’ tendency to rely on formalism for formalism’s sake, without necessarily asking how our formally defined notions may be independently grounded, e.g. in a broader theory of cognition. Something along these lines has been pointed out before at least with regard to lexical alternatives (or Horn scales), for instance by Russell (Reference Russell2006) who notes that Horn scales don’t really explain anything unless one explains why scales are the way they are; and by Geurts (Reference Geurts2011) who notes that there is only very little explicit reflection on what scales are supposed to be, and ultimately dismisses them as unnecessarily indirect and somewhat misleading representations of something like QUDs instead. The conceptual relations and differences between QUD alternatives, focus alternatives, alternatives introduced by disjunction and question alternatives have likewise not received the level of attention that the frequency of theoretical appeals to these notions demands.

I hope that this short chapter will encourage some deeper reflection on what the various notions of alternatives really signify and how they can be assumed to interact. I will discuss focus alternatives, alternatives introduced by disjunction, alternatives as used in the specification of QUDs, and alternatives in the semantics of interrogatives. More precisely, I will criticize the conflation of the set of focus alternatives with the meaning of an interrogative, discuss two conceptions of the alternatives introduced by disjunction (algebraic and attention-based), and argue against the predominant view of QUDs as, essentially, linguistic questions that represent discourse goals. I will outline a subtly different understanding of QUDs, according to which they are not goals in and of themselves, but are mere ways of organizing more elementary goals. This invites a view on QUDs as being more fluid and dynamic, and encourages us to think not just about alternative responses to a given QUD, but also about alternative QUDs.

12.2 Focus Alternatives

An influential role of alternatives in semantics and pragmatics is in characterizations of the focus of an utterance, as marked for instance in English and many other languages by means of pitch accents, or by specific particles or syntactic positions. In this section, after a quick introduction to the notion of focus alternatives, I discuss two cases where a direct formal interaction between focus alternatives and compositional semantics have been assumed: focus-sensitive operators such as “only” (e.g. Rooth Reference Rooth1985) and the relation between focus alternatives and the semantics of questions (e.g. Beck Reference Beck2006). I will argue (and review arguments from the literature) that assuming such an interaction may not be necessary or appropriate, and comes with certain risks.

The focus of an utterance is, intuitively, the part that matters most for advancing the conversation; for instance, it is the part that provides an answer to a preceding question:

1. (2)

   How many of your friends went to the protest?

   TWO of them went to the protest.

The numeral “two” caries the most prominent prosodic accent in the sentence, because it is the crucial part of the sentence given the question; indeed, the rest of the answer could have been omitted: “Two.” on its own would have communicated the same. Compare (ignoring the unnatural verbosity of the answer):

1. (3)

   Where did two of your friends go?

   Two of them went to the PROTEST.

In each case, the focus is the part of the utterance that would have been different had the speaker believed a different answer to the same question. This characterization naturally leads to defining focus formally in terms of the ways in which the utterance could have been different, i.e. a set of focus alternatives. For (2) this could be the set containing the proposition that one of them went, the proposition that two of them went, that three of them went, and so on. For (3) this could be the set containing the proposition that two of them went to the park, that two of them went to the protest, to the pool, home, to school, and so on.

Examples (2) and (3) illustrate the role of focus in determining question–answer congruence. This role can be explained, in outline, by assuming that the focus represents the pragmatically important part of an utterance, and noting that pragmatic importance depends crucially on what constitutes an answer to a contextual question. Under this view, focus alternatives would be merely a convenient way of formalizing ‘pragmatic importance’. However, a more common view on focus alternatives affords them a kind of semantic reality, where other expressions are assumed to be able to qualify and quantify over the set of focus alternatives. This could in some cases illustrate the somewhat opportunistic reuse of formal notions of alternatives which I mentioned in the introduction. I will discuss two examples of this.

The Focus-Sensitivity of “Only”

One phenomenon where focus alternatives have been assumed to directly influence the main semantics is the class of apparently focus-sensitive words such as “only.” The primary meaning of a sentence containing “only” changes with the placement of focus in its scope:

1. (4)

   a.	Two of my friends only went to the PROTEST together.
   b.	Two of my friends only went TO the protest together.

Example (4a) implies that the two friends didn’t go anywhere else together (the protest is the only place), whereas (4b) implies that the two friends were together on the way there but not on the way back. In the work of Rooth Reference Rooth1985, “only” is assumed to be directly sensitive to the focus alternatives: the set of focus alternatives is passed to the ordinary semantics of “only,” allowing it to state that only one of those alternatives is the case. Focus alternatives would thus be accessible as semantic objects to the ordinary meaning composition channel.

A slightly different perspective is offered by Rooth (Reference Rooth1992) and built upon by Beaver and Clark (Reference Beaver and Clark2009), who argue that there is no such direct interaction between ordinary meaning and focus alternatives. Rather, focus alternatives reflect the structure of the QUD, and it is the QUD to which words such as “only” are directly sensitive: “only” means that only one proposition in the QUD is the case. For instance, in (4a) the QUD, constrained by focus on the location “the protest,” might be phrased as “Where did two of my friends go?”; and in (4b) the QUD, constrained by focus on “to,” might be phrased as “Did two of your friends go to the protest together, and did they return together?” In both cases, “only” conveys that the answer given (i.e. that they went to the protest) is the only answer that is true, i.e. that they went nowhere else in (4a), and that they did not return together in (4b). This view on focus (for an accessible introduction see Beaver et al. Reference Beaver, Roberts, Simons and Tonhauser2017) makes it possible to conceive of focus alternatives as but a linguist’s convenient tool for formally describing what it means for a constituent to be pragmatically important, i.e. to be the focus of the sentence, rather than as being semantically ‘real’ in the sense of allowing other parts of the semantics to operate on them.

Focus and Question Semantics

Another direct interaction between focus alternatives and ordinary meaning is assumed in the influential approach to question semantics of Beck Reference Beck2006: the focus alternatives of an interrogative would be promoted to its ordinary meaning. For instance, for a “wh”-question, assuming focus on the “wh”-word, this amounts to the following:

1. (5)

   WHO went to the protest?

   Focus alternatives: {John went there, Mary went, Sue went, Bob went, … }

   $\downarrow$

   Ordinary meaning: {John went there, Mary went, Sue went, Bob went, … }

This approach has also been applied to disjunctive questions with focus on the disjuncts (so-called “alternative questions,” but see below), where a crucial assumption is that the focus alternatives of a disjunction are restricted to the disjuncts:

1. (6)

   Did JOHN go to the protest, or MARY?

   Focus alternatives: {John went there, Mary went there }

   $\downarrow$

   Ordinary meaning: {John went there, Mary went there }

(Example (7) below will show that this restriction of the focus alternatives and QUD to only the disjuncts is not adequate; the QUD must be able to contain other alternatives too; but for now I will set this criticism aside.) If Rooth’s (Reference Rooth1985) analysis of “only” is assumed, which provides the ordinary meaning with direct access to focus alternatives, then the idea that interrogativity (or a supposed interrogative operator) takes the focus alternatives and promotes them to the main meaning does not represent a big leap; instead of quantifying over the focus alternatives (like, supposedly, “only”), interrogativity would simply adopt them unchanged. By contrast, under Beaver and Clark’s view interrogativity would not be directly sensitive to focus alternatives, but only indirectly, via the QUD, which would be a more cautious approach to the possible interactions of different notions of alternative.

Now, let us explore this perspective on question semantics a bit further. This perspective just outlined would imply that the meaning of an interrogative is equivalent to its QUD, which may seem like an attractive outcome: QUDs are often treated as, essentially, implicit interrogatives. However, in fact the meaning expressed by an interrogative utterance is not in general equivalent to its QUD. Just as declarative utterances may offer either a complete or a partial answer, so too may interrogative utterances specify the QUD either completely or only partially. To illustrate, consider again the example with which this chapter started, but now comparing a final rise to a final fall:

1. (7)

   a.	Were TWO of your friends at the protest, or THREE? [final rise]
   b.	Were TWO of your friends at the protest, or THREE? [final fall]

The rise in (7a) conveys that there may be other relevant possibilities (e.g. that there were even four or five, or perhaps none), whereas the fall in (7b) conveys the opposite: it’s either two or three, nothing else. A straightforward analysis of this contrast treats the final intonation as indicating (non)exhaustiveness with regard to the QUD, i.e. whether the propositions mentioned in the interrogative (the disjuncts) are the only possible propositions in the QUD (e.g. Biezma & Rawlins Reference Biezma and Rawlins2012; Westera Reference Westera2017b). Crucially, for this sort of analysis to be possible, to even come to mind, it is crucial that we do not conflate the meanings of interrogatives with the QUDs they serve to address.

Summary

Summing up, in two cases where a direct formal interaction between focus alternatives and compositional semantics has been assumed, namely focus-sensitive operators such as “only” (e.g. Rooth Reference Rooth1985) and the relation between focus alternatives and the semantics of questions (e.g. Beck Reference Beck2006), no such direct interaction may be necessary or warranted. In the case of questions, one reason for not conflating focus alternatives with question meanings is that, given the close relation between focus alternatives and QUDs, this would amount to conflating question meanings and QUDs. In Section 12.4 I will discuss in more detail what QUDs are, elaborating on the idea that, even though both QUDs and (the meanings of) interrogatives can be characterized in terms of alternatives, they represent very different notions, and we must be cautious when considering their possible interactions.

12.3 Alternatives Introduced by Disjunction

It is often assumed that disjunction can introduce its disjuncts as alternatives into the semantics/pragmatics (e.g. ‘alternative semantics’ for disjunction in Alonso-Ovalle Reference Alonso-Ovalle2006; ‘inquisitive semantics’ more recently, Ciardelli et al. Reference Ciardelli, Groenendijk and Roelofsen2013). But what are these alternatives? And why would a disjunction introduce its disjuncts as alternatives, but not, e.g., a conjunction its conjuncts? (Why, that is, besides the various empirical facts that seem to require this.) I will consider two perspectives on this issue, one based on the notion of attention and another based on more formal, algebraic considerations. I argue that the former is ultimately more explanatory.

One perspective on introduced alternatives is the idea that (parts of) utterances can draw attention to the meanings of their constituents. For instance, in Aloni et al. Reference Aloni2003; Schulz and Van Rooij Reference Schulz and van Rooij2006, disjunction is assumed to introduce its disjuncts as discourse referents (Karttunen Reference Karttunen and McCawley1976), a notion closely related to attention. The notion of discourse referent stems from the literature on coreference, where it is assumed that noun phrases make the entities to which they refer attentionally salient in the discourse, thereby making them available as referents for subsequent anaphoric pronouns such as “he”:

Proposals that a disjunction would introduce its disjuncts as discourse referents, as in Aloni et al. Reference Aloni2003; Schulz and Van Rooij Reference Schulz and van Rooij2006, can therefore be understood in attentional terms: a disjunction makes its disjuncts attentionally salient. This attentional perspective on the alternatives introduced by disjunction is made more explicit by Ciardelli et al. (Reference Ciardelli, Groenendijk, Roelofsen, Ito and Cormany2009), who propose an “attentional semantics” (equivalent in the relevant respects to ‘alternative semantics’ for disjunction in Alonso-Ovalle Reference Alonso-Ovalle2006). While intuitive, this attentional perspective on the alternatives introduced by disjunction fails to explain why disjunction but not conjunction would draw attention to its two coordinates. After all, surely a conjunction, too, draws attention to its conjuncts? I will offer an answer to this question further below, that allows us to maintain the attentional perspective on this notion of alternative. Before giving that answer, let me summarize an alternative perspective altogether, namely the algebraic motivation of ‘inquisitive semantics’ (Roelofsen Reference Roelofsen2013a).

An Algebraic Perspective

In a classical, information-only semantics, where meanings are propositions, i.e. sets of worlds, conjunction expresses the intersection operation on sets of worlds, and disjunction the union operation. If we enrich our notion of meaning to include alternatives, such that the meaning of an expression is now a set of propositions, and if we assume that each disjunct puts forward only a single proposition, i.e. denotes a singleton set, then taking the union of these singleton sets automatically yields a set containing both propositions, one for each disjunct:

1. (9)

   John was at the protest, or Mary.
   $\text{information}:\left\{w,,|,,\mathit{Pj}\text{is true in}w\right\}\cup \left\{w,,|,,\mathit{Pm}\text{is true in}w\right\}=$
   	$\left\{w,,|,,\mathit{Pj}\text{is true in}w\text{or}\mathit{Pm}\text{is true in}w\right\}$
   $\text{alternatives}:\left\{\left\{w,,|,,\mathit{Pj}\text{is true in}w\right\}\right\}\cup \left\{\left\{w,,|,,\mathit{Pm}\text{is true in}w\right\}\right\}=$
   	$\left\{\left\{w,,|,,\mathit{Pj}\text{is true in}w\right\},\left\{w,,|,,\mathit{Pm}\text{is true in}w\right\}\right\}$

Thus, generalizing the treatment of disjunction as union to sets of alternatives immediately explains why disjunction ends up introducing multiple alternatives, typically one for each disjunct.

But this perspective is not completely satisfactory. For one, it is not obvious that the assumption should be granted that the informational and alternative-introducing contributions of parts of an utterance ought to compose according to the same operation. Although it may seem minimal and elegant, this subjective assessment may well point to wishful thinking rather than truth. But more severely, although the treatment of disjunction as union works well, the analogous treatment of conjunction as intersection requires a constraint on alternative sets, namely that they be downward-closed (Roelofsen Reference Roelofsen2013a): if the set contains a proposition, it should also contain all propositions that are logically stronger (i.e. all the propositions that entail it). The reason is that, although treating disjunction as union works well if each disjunct is associated with a singleton set, it will not work for conjunction, as the intersection of two distinct singleton sets is the empty set:

1. (10)

   John was at the protest, and Mary (too).

   $\text{alternatives}:\left\{\left\{w,,|,,\mathit{Pj}\text{is true in}w\right\}\right\}\cap \left\{\left\{w,,|,,\mathit{Pm}\text{is true in}w\right\}\right\}=\varnothing$

Downward closure avoids this empty set: by adding all stronger propositions to the set on each side, and in particular the proposition that both John and Mary were at the protest, their intersection will contain at least this proposition (along with all stronger propositions). Downward closure has its own downside, however. If any stronger propositions are automatically among the alternatives, then the same set of alternatives is assigned to both of the following variants:

1. (11)

   a.	John was there, or Mary.
   b.	John was there, or Mary, or both.

It is, I take it, highly counterintuitive that these two disjunctions would introduce the same alternatives; intuitively (11) has one more, namely the conjunction (and not just intuitively; see Westera Reference Westera2017a for empirical consequences of this difference). I conclude that the algebraic perspective is not entirely satisfactory as an explanation for why disjunction but not conjunction can introduce alternatives. Instead, let us return to the attentional perspective with which this section began.

The Attentional Perspective

The challenge faced by the attentional approach was that, intuitively, conjunction draws attention to its conjuncts as much as a disjunction to its disjuncts, so why would only disjunction serve to introduce alternatives? I propose a pragmatic answer to this puzzle in Westera Reference Westera2017b, by adopting the view in Ciardelli et al. Reference Ciardelli, Groenendijk, Roelofsen, Ito and Cormany2009 that drawing attention to introduce alternatives is not merely something that happens, but that happens intentionally, i.e. as a communicative intention, governed by pragmatic rules, or maxims. Crucially, one need not intend the side effects of one’s intention (Bratman Reference Bratman1987). Hence, just as an utterance normally provides more information than what the speaker intended to convey, an utterance normally draws attention to many more things than just the alternatives which the speaker intended to introduce. Accordingly, although both disjunction and conjunction introduce alternatives semantically, in the sense of drawing attention to their disjuncts/conjuncts, perhaps we can explain why, in the pragmatics, only those introduced by means of a disjunction have any role to play.

To explain the latter, we need to make some pragmatic assumptions about what a reasonable speaker can cooperatively intend to draw attention to, i.e. a set of ‘attentional’ conversational maxims, alongside the usual Gricean ones. I develop such a theory, Attentional Pragmatics, in Westera Reference Westera2017b, but the various principles on which it builds have been considered in the literature before:

• Maxims: A rational, cooperative speaker, addressing a certain QUD, should:

  • – assert all and only propositions in the QUD which they consider true (roughly Grice Reference Grice, Cole and Morgan1975);

  • – intend to draw attention to all and only propositions in the QUD which they consider possible.

The intuitive motivation for the second, attentional addition to Grice’s original maxims should be clear: the propositions in the QUD being relevant, i.e. worth making common ground, it is generally rational to try to keep track of those propositions in the QUD which are possible, i.e. those immediate discourse goals which might be achievable. Moreover, similar constraints have been proposed in the literature. For instance, that propositions to which one draws attention should be considered possible corresponds in essence to “attentive sincerity” in Roelofsen Reference Roelofsen, Aloni, Franke and Roelofsen2013b (building on Ciardelli et al. Reference Ciardelli, Groenendijk, Roelofsen, Ito and Cormany2009), “Genuineness” in Zimmermann Reference Zimmermann2000 (p. 270); and “Viability” in Biezma and Rawlins Reference Biezma and Rawlins2012 (p. 46). Biezma and Rawlins moreover assume that the alternatives one introduces (albeit with an interrogative) ought to be relevant to the QUD, Simons (Reference Simons2001) assumes a comparable “relatedness condition” on disjunctions, and in fact the same idea is found already in Grice Reference Grice1989: that disjunction serves to specify possibilities “that relate in the same way to a given topic.” For a more precise definition of the attentional maxims, more detailed motivation and a number of applications I refer to Westera Reference Westera2017b.

What matters for present purposes is that the pragmatic requirements on attention, along with some other assumptions (e.g. that the QUD is closed under intersection), entail that the asserted proposition must always be equivalent to the union of the set of propositions to which the speaker intended to draw attention. This is because, in a nutshell, if something weaker was asserted, they should have drawn attention to more or weaker things, and if something stronger was asserted, they should have drawn attention to fewer or more specific things. In any case, it follows from this fact that a disjunction can be used to draw attention to the disjuncts (because the disjuncts both lie within the information conveyed by the disjunction as a whole), but a conjunction cannot be used to draw attention to the conjuncts (which fall outside of the information conveyed by the conjunction as a whole). What this means is that, if attention-drawing is indeed a type of communicative intention constrained by the pragmatic considerations given above, then even if both disjunction and conjunction intuitively draw attention to their disjuncts/conjuncts, this can only be intentional in the case of disjunctions; in the case of conjunctions, the attention drawn to the conjuncts must be considered a mere side effect. Pragmatics thus provides a possible explanation for why a disjunction but not conjunction has been perceived in the literature as introducing its coordinates as alternatives.Footnote ¹ I will end this section on the nature of the alternatives introduced by disjunction by highlighting an interesting consequence of attentional, pragmatics-mediated conception of introduced alternatives outlined above: it immediately predicts that the ability of disjunction to introduce alternatives depends on focus intonation. That is, when each disjunct bears focus (now indicated by square brackets) these disjuncts are introduced as alternatives, otherwise only the disjunction as a whole is introduced (e.g. Roelofsen & Van Gool Reference Roelofsen, van Gool, Aloni, Bastiaanse, de Jager and Schulz2010; Pruitt & Roelofsen Reference Pruitt and Roelofsen2011; Biezma & Rawlins Reference Biezma and Rawlins2012):

1. (12)

   a.	[ALPH]F or [BETH]F attended the conference.
   b.	[Alph or BETH]F attended the conference.

This theoretically postulated difference in introduced alternatives is thought to correlate for instance with the robustness of a “not both” inference (in (12a) but not (12b)) and with the naturalness of certain responses. Drawing inspiration from Beaver and Clark 2009, who explain the apparent focus-sensitivity of “only” as a side effect of its more direct sensitivity to the Question Under Discussion (QUD), a partially isomorphic explanation can be found for the apparent focus-sensitivity of the alternative-introducing behavior of disjunction. The standard view on focus (Roberts Reference Roberts, Yoon and Kathol1996; Beaver & Clark Reference Beaver and Clark2009, building on Rooth Reference Rooth1992 and before) is compatible with two kinds of QUDs for the example in (12a): a single-wh QUD to which each disjunct provides a possible answer (“Who attended the conference?”), or a disjunctive multi-wh QUD (“Who attended the conference or who attended the conference?”). Although the latter can occur in the right sort of context (e.g. with different implicit domain restrictions on the two wh-words), it is very odd out of the blue, so I will be assuming the former QUD for (12a), (i.e. “Who attended the conference?”). For (12b) we can assume that the QUD contains the disjunction as a whole but not the individual disjuncts, given the lack of a contrastive accent on “Alph.” Given this, from the different QUDs it follows directly that (12a) can and should be used to draw attention to each disjunct, while (12b) can be used to draw attention to the disjunction as a whole but not to the individual disjuncts (which are irrelevant).

Summary

Summing up, I discussed two conceptions of the alternatives introduced by disjunction. The first, the algebraic perspective, puts this behavior centrally into the semantics, but the explanatory value of the algebraic perspective itself is not entirely clear, and it comes with the downside of imposing downward closure on alternative sets, rendering disjuncts such as “or both” semantically vacuous. The second perspective is based on the more minimal (uninformed) assumption that sentences can drawn attention to basically any of their constituents, while relying on pragmatics to explain why disjunction but not conjunction can be used to intentionally introduce alternatives. The choice between the two perspectives concerns the nature of a particular notion of alternative (one of many), namely the alternatives introduced by disjunction, and has implications for the way in which this notion can be assumed to interact (or be conflated) with others. For instance, the attentional-pragmatic perspective is less conducive to treating the alternatives introduced by disjunction as directly available to the compositional semantics.

12.4 QUDs as Ways of Organizing Discourse Goals

A fruitful and influential perspective on discourse and pragmatics has been to conceive of discourse as being organized around the raising and resolution of Questions Under Discussion (QUD; e.g. Carlson Reference Carlson1983; Van Kuppevelt Reference Van Kuppevelt1995; Ginzburg Reference Ginzburg, Seligman and Westerståhl1996; Roberts Reference Roberts, Yoon and Kathol1996), where QUDs are commonly represented as sets of alternatives: sets of relevant propositions. As we saw before, accounts of focus rely on a notion of QUD, as did the attentional perspective on the alternatives introduced by disjunction outlined in the previous section. It is, therefore, important to be clear about what QUDs are. As in the previous section, I summarize an existing perspective (the predominant one), and a more novel perspective, and present some arguments in favor of the second.

The Predominant Perspective: Linguistic Questions as Discourse Goals

QUDs are often talked about as if they are questions in a linguistic sense, i.e. interrogative sentences (Carlson Reference Carlson1983; Büring Reference Büring2003) or the kinds of speech acts or semantic objects typically expressed by means of such sentences (Van Kuppevelt Reference Van Kuppevelt1995; Roberts Reference Roberts, Yoon and Kathol1996). This tendency is apparent, for instance, in the way in which QUD annotation typically mixes explicit linguistic questions and supposed implicit QUDs in a single representation. Consider the following constructed example (modified from (1) in Riester Reference Riester, Zimmermann, von Heusinger and Gaspar2019), with a possible QUD analysis shown as a discourse tree (Büring Reference Büring2003) in Figure 12.1.Footnote ²

1. (13)

   A: Max had a lovely evening.

   B: What did he do?

   A: He had a great meal. He ate salmon. He devoured cheese. He won a dancing competition.

Figure 12.1 A possible QUD structure for (13)

(slightly modified from Figure 3 in Riester Reference Riester, Zimmermann, von Heusinger and Gaspar2019)

In the figure, following Riester Reference Riester, Zimmermann, von Heusinger and Gaspar2019, questions in curly braces are implicit entities whereas the unbraced question (Q_0.1) was explicit in the original discourse – thus, explicit and implicit questions are assumed to occupy the same kinds of nodes in a discourse tree.

This kind of terminological and perhaps conceptual conflation of discourse goals and linguistic questions is risky, as it may cause us to overlook the fact that discourse goals and the speech acts directed at them are, in principle, very different kinds of things. For instance, in Section 12.2 I argued, illustrated by (7), that the meaning of an interrogative should not be assumed to be equivalent to its QUD: just as declaratives can provide only a partial answer to their QUD, so too can interrogatives highlight only part of their QUD, as indicated for instance by final rising intonation as a marker of nonexhaustivity. Although linguistic questions are a prime instrument for setting discourse goals, we should not conflate the instrument with the goal.

Another characteristic of the predominant perspective on QUDs, besides the aforementioned linguistic stance on QUDs, is that it tends to regard the QUDs themselves, not the propositions they contain, as the ultimate discourse goals. That is, the goal of a given stretch of discourse is identified with the resolution of a particular question, not the making common ground of certain pieces of information. This view on QUDs is in principle independent from the tendency to regard them as linguistic questions, but they fit together nicely: linguistic questions are a prime instrument for setting new discourse goals, so a close relation between linguistic questions and discourse goals seems desirable. Nevertheless, I think that regarding QUDs as discourse goals, rather than the propositions they contain, is conducive to a view on QUDs that does insufficient justice to their dynamicity, i.e. to the ability of speakers to shift from one QUD to another, as I will explain after outlining an alternative perspective.

QUDs as Ways of Organizing Discourse Goals

I propose to conceive of the making common ground of any individual piece of information as a goal in itself, that is, if n pieces of information are worth sharing, let that count as there being n distinguishable conversational goals. QUDs then enter the picture by assuming that a given utterance can potentially serve a number of these goals simultaneously, by providing or requesting several pieces of information at once. Of course, not just any arbitary set of goals is a suitable combination of goals for a single utterance to serve. The subset of goals that a single utterance can be reasonably aimed at must be chosen on the basis of, among other things, subject matter (goals for a single utterance must be topically related), general importance (important goals first), and orderly discourse (e.g. sets of goals shouldn’t be too big or too mixed, and resolving one should naturally lead to the next). We can think of QUDs as sets of goals in this sense, that are grouped together in accordance with certain organizational principles.

Regarding QUDs as ways of organizing goals, instead of regarding the resolution of questions itself as a goal, has a number of advantages. First, it is conducive to a more dynamic view of QUDs, where changing the QUD does not entail changing the discourse goals: the same discourse goals can be organized and reorganized in various ways throughout a conversation. I return to this in the next section.

Second, the proposed perspective makes certain limitations of the QUD-based approach easier to recognize and formulate. One such limitation is that a set of propositions – the typical representation of a QUD – cannot model dependencies between the goals these propositions represent, i.e. the goals of making them common ground. I think so-called mention-some contexts are an example where this matters:

1. (14)

   A: Where can I buy an Italian newspaper?

   B: In the kiosk around the corner.

If I am looking for a place to buy a newspaper, I may want to know if I can buy one in the kiosk around the corner, and also if I can buy one in the equally nearby bookstore, but I don’t need to know both – after achieving one of these goals I will no longer pursue the other. We cannot easily represent such dependencies between the individual pieces of information in the QUD if we only regard the resolution of the entire QUD as the discourse goal, represented as a set of propositions. Accordingly, a QUD approach is prone to conflate this kind of mention-some context with a mention-all context, e.g. where one is compiling an exhaustive list of nearby places that sell newspapers. If, instead, we conceive of QUDs as mere ways of organizing the more elementary goals, i.e. the individual propositions, we are less prone to overlook that these elementary goals can have a life of their own, with interdependencies that cannot be represented at the QUD level.

Third, regarding QUDs as ways of organizing discourse goals, as opposed to treating QUDs themselves as discourse goals, can help decouple the notion of QUD from linguistic notions of question, i.e. one of the characteristics of the predominant approach mentioned above. This is because there is nothing essentially linguistic about organizing our goals in sensible ways: we would organize our goals also when, say, fixing a bike, based in part on something like subject matter; we would perhaps first pursue all goals related to the chain and gears, then everything related to the position of the cyclist (saddle, handlebars), and so on. Indeed, our assumptions about the organization of discourse goals into QUDs should be, as much as possible, grounded in extralinguistic cognition/behavior, as opposed to, say, a semantics of interrogative sentences.

Summary

Whereas the predominant view of QUDs treats them as linguistic questions and regards them as discourse goals in their own right, I have proposed a view of QUDs as mere ways of organizing the more elementary goals, i.e. single propositions that ought to be made common ground. This helps decouple the notion of QUD from the linguistic notion of question, lets us acknowledge that the more elementary discourse goals can have a life of their own (e.g. dependencies between goals), and invites a more dynamic view of QUDs. I return to the latter in the next section.

12.5 Alternative QUDs

The view on QUDs described above favors a view of QUDs as being more fluid and dynamic. It is the underlying discourse goals, i.e. the pieces of information worth making common ground, that are relatively stable from one discourse move to the next, while their organization into QUDs can more easily change. Although it is generally acknowledged that QUDs can be strategically decomposed into sub-QUDs in a systematic way (Roberts Reference Roberts2012), I think that this is only one of many permissible QUD-maneuvers, and that the amount of freedom speakers have in changing the QUD tends to be underestimated. I will give three examples of this tendency. Altogether, this section will emphasize that, when theorizing about a given discourse move, we should consider not just the alternative things a speaker might have said given a certain QUD, but also the alternative QUDs the speaker might have chosen to address.

Summary

This section illustrated the importance of reasoning about alternative QUDs, i.e. of the freedom speakers have in choosing their QUDs. Conceiving of QUDs as more dynamic and fluid than the underlying discourse goals prevents applying perceived constraints on relevance (such as symmetry) directly to QUDs, lets one maintain a strict maxim of Relation (e.g. in the face of indirect answers), and enables a singleton treatment of yes/no questions.

12.6 Conclusion

I started by distinguishing two perspectives on focus alternatives, criticizing the conflation of the set of focus alternatives with the meaning of an interrogative. I also discussed two conceptions of the alternatives introduced by disjunction, favoring an explanation in terms of intentional attention-drawing, which predicts that disjunction can (depending on focus) but conjunction cannot serve to introduce alternatives. All of this relied crucially on the notion of QUD, which are predominantly regarded as, essentially, linguistic questions that represent discourse goals. Departing slightly from this predominant perspective, I proposed to regard QUDs as ways of organizing more primitive discourse goals, namely, single propositions, arguing that this perspective has several advantages: it helps decouple the notion of QUD from the linguistic notion of question, lets us acknowledge that the more elementary discourse goals can have a life of their own (e.g. dependencies between goals), and invites a more dynamic view of QUDs. This more dynamic view requires that we reason not just about alternative utterances aimed at a given QUD, but also about alternative QUDs. I illustrated this with the symmetry problem, indirect answers and yes/no questions.

Altogether, I hope that this chapter encourages us to reflect more deeply on what various notions of alternatives really signify and how they can be assumed to interact, and proceed cautiously when making assumptions about the specific set of alternatives for a given example – what notion of alternatives is being used, and, given how that notion is grounded, are these assumptions really justified?