The Neglect of the Triggering Question

Accounts of generalized quantifiers predict an occurrence of a sentence such as ‘Every bottle is empty’ to be true if and only if the set of bottles in the domain of discourse is a subset of the set of empty things in the domain. However, it is widely acknowledged that there are situations wheredomain restriction occurs: a sentence is understood in such a way that the first argument of the standard extension of a determiner within that sentence is taken to be a proper subset of the extension of the restrictor. For instance, Stanley and Szab ´o (2000) observe that assessors frequently take occurrences of ‘Every bottle is empty’ to be true when the relevant relation holds with respect to some subset of the set of all bottles that exist at that context, such as all of the bottles that Yan bought that day. To refer to the propositions assessors naturally consider in such situations, along with the process of their considering these propositions, I shall use the neutral terminology ‘restricted (unrestricted)

understanding’. The matter ofwhenrestricted understandings arise will be the topic of this chapter, a question I shall refer to as the ‘the Triggering Question’.

The literature on domain restriction includes extensive discussion of the mechanisms that should be invoked to formally analyse domain restriction (e.g. Westerst˚ahl (1985), Partee (1989), von Fintel (1994), Roberts (1995), Eckardt (1999), Geurts and van der Sandt (1999), Bach (2000), Herburger (2000), Stanley and Szab ´o (2000), Stanley (2002), Breheny (2003), Mart´ı (2003), Kratzer (2004), Bach (2005) and Rast (2013)). However, while much has been written abouthowdomain restriction occurs when it does occur, less has been written aboutwhenit occurs. I will begin by giving an overview of the literature on the mechanism underlying domain restriction, before arguing that the Triggering Question is sufficiently important to deserve attention.

It is standard to distinguish accounts of domain restriction according to whether they invoke syntactic, semantic or pragmatic mechanisms.1 Imagine a contextc0where an occur- rence of a sentence S (e.g. ‘Every bottle is empty’) receives a restricted understanding that is naturally paraphrased by an occurrence of a distinct sentence S0 (e.g. ‘Every bottle Yan bought todayis empty’). According to asyntacticapproach to domain restriction, S contains silent morphemes that render it lexically equivalent to S0. Asemanticapproach holds that S and S0 are lexically distinct sentences, but semantic mechanisms mean that the occurrence of S expresses the same proposition as an occurrence of S0 relative toc0. Finally, apragmatic

approach claims that the occurrence of S expresses a proposition corresponding to the un- restricted understanding, but pragmatic mechanisms have allowed the use of S to convey the proposition expressed by an occurrence of S0relative toc0. I shall set aside the syntactic approach, since it has been widely criticised in the literature (e.g. Bach (1994), Stanley and Szab ´o (2000)) and therefore lacks any contemporary advocates. Two accounts paradigmatic of the semantic and pragmatic approaches will now be briefly discussed.

Von Fintel (1994) proposes a semantic account of domain restriction, postulating a re- source domain variable, which is an index attached to certain quantifier expressions. The

context assigns to the resource domain variable a value of the type corresponding to the quantifier’s first argument. He then gives a semantics where a quantifier’s first argument is the extension of the appropriate lexical material intersected with the value of the resource domain variable. For example, whereiis the covert variable andgis a variable assignment, a simplified version of von Fintel’s semantics state that an occurrence of ‘EveryiNβ’ is true

when tokened and assessed relative tocif and only ifJEveryKc(JNKc∩g(i))(JβKc)holds at c.2 All cases of domain restricted understandings of sentences are then attributed to the mechanism of the resource domain variable’s value’s constraining a quantifier’s first argu- ment. For example, the resource domain variable in an occurrence of the sentence ‘Everyi

bottle is empty’ may receive as its value the set of things Yan bought on that day, causing the proposition expressed to be the same as the one that would be expressed by an occurrence of ‘Every bottle Yan bought today is empty’ relative to the same context.

In contrast, Bach proposes a pragmatic account of domain restriction. Bach’s (2000) (p.262) view is that ‘[w]e generally speak loosely, omitting words that could have made what we meant more explicit and letting our audience fill in the gaps’. Domain restriction, he claims, is just a variety of this tendency to omit constituents in cases where we expect in- terlocutors to grasp the proposition we mean to communicate. Bach (2000) (p.268) suggests that it is the ‘lack of relevant specificity’ of the proposition literally expressed that causes the hearer to perceive an instance of loose talk and seek an alternative understanding. For exam- ple, he holds that an occurrence of ‘Every bottle is empty’ always expresses the proposition that every bottle in the domain of discourse is empty; however, it may be used to convey the proposition expressed by an occurrence of ‘Every bottle Yan bought today is empty’, provided the hearer perceives a lack of relevant specificity and succeeds in reconstructing the missing material.

Neither of these accounts of the mechanism of domain restriction provide clear predic- tions about which occurrences of sentences are likely to receive restricted understandings.3

Indeed, a discussion of the Triggering Question is largely absent from the literature. One reason that the Triggering Question has been neglected is that it is often taken for granted that some degree of contextual domain restrictionalwaysoccurs. If this were so, then there could be no interesting, non-trivial answer to the Triggering Question. However, examples such as the following demonstrate that it is not the case that every actual occurrence of a sentence receives a restricted understanding:

1. (a) Everything is part of the natural world.

(b) Every prime number is divisible by itself and one. (c) Every bottle Yan bought today is empty.

(d) It is not the case that every actual occurrence of a sentence receives a restricted understanding.

Firstly, there are rare examples like (1a), where the restrictor ‘thing’ seemingly denotes the entire domain of discourse (that is, including everyday objects, particles, numbers, etc.).

2_{Note that von Fintel defines resource variables as functor variables that apply to contextually-determined}

arguments, in order to handle ‘bound’ readings of quantifier expressions where the resource domain appears to vary for each item in some set denoted by another expression. This complication may be overlooked for current purposes.

Williamson (2003) (p.416) observes that we should understand an ontological naturalist who issues (1a) as generalizing without any restriction whatsoever, as we would otherwise be ‘failing to appreciate the radical extent of their claim’. In seeking examples of sentences that have an unrestricted understanding, people tend to have these rare sentences in mind, with their rarity perhaps contributing to the sense that unrestricted understandings are marked. However, (1b) – (1d) are examples of sentences that have an unrestricted understanding provided the quantifier’s first argument ends up as the standard extension of the restrictor at the context. For instance, an unrestricted understanding will arise with respect to an occurrence of (1b) or (1c) if the quantifier’s first argument ends up as, respectively, the set of all primes (rather than, say, the set of primes that the speaker has ever reached by counting), or the set of all bottles that Yan bought on the relevant day (rather than, say, the set of beer bottles Yan bought that day).

Of course, the possibility of such understandings does not establish that interlocutors would ever actually use or understand sentences such as (1b) and (1c) in an unrestricted manner. However, I am fairly sure that my own use of (1d) in the previous paragraph is naturally understood as a claim about the set ofabsolutely allactual occurrences of a sentence. While some occurrences of (1a) – (1d) may indeed be understood in a restricted way, this only serves to emphasise the importance of addressing the Triggering Question.

A complete answer to the Triggering Question would involve specifying every factor that triggers and blocks domain restricted understandings. However, the complexity and breadth of the pragmatic factors that influence communication raise doubts about the pos- sibility of describing a complete answer. Fortunately, partial answers may be illuminating, where a proper subset of the set of factors that trigger and block restricted understandings is identified. In this chapter, I will propose that observations pertaining to information struc- ture allow the provision of a partial answer. For example, the position to be developed predicts that, relative to a context where all of the bottles Yan bought that day are empty but some of the bottles Yasma bought are full, and relative to the indicated QUD and pitch accents, (1e) will naturally be judged as false and (1f) as true:

1. (e) (I’m looking for empty containers to store stuff in. What’s empty?) Every BOTtle is empty.

(f) (What happened to the bottles Yan bought today?) Every bottle is EMPty.

Having considered extant accounts of domain restriction and the Triggering Question, it has become clear that the question of which mechanisms should be used to model re- stricted understandings is separable from the question of which factors trigger and block the initiating of these mechanisms. While the literature has focused on the former question, I have argued that addressing the latter question is crucial, on the grounds that occurrences of sentences demonstrably vary with respect to whether or not a restricted understanding is natural.