1.2 Overview of the Chapters
1.2.4 Chapter 6: Under and over generation in scalar reasoning
In the standard Gricean approach, scalar implicatures arise from the hearer reasoning about rele- vant stronger alternatives that the speaker could have uttered (Grice 1975; see also Gamut 1991). Recently, however, various cases have been pointed out in the literature, for which reasoning only over stronger alternatives fails to predict inferences that are intuitively attested and that could be derived if we were to add also logically independent alternatives in scalar reasoning (see Spector 2007a and Chierchia et al. (To appear) among others). In this chapter, I first sum- marize the existing arguments for logically independent alternatives and present some novel ones coming from sentences with existential modals and from the phenomenon of so-called “free choice permission” (Fox 2007). I then show that while allowing logically independent alternatives makes the right predictions in such cases, it also causes both an under-generation and an over-generation problem (see also Fox 2007:fn. 35 and Magri 2010a). I propose a so- lution to the over-generation problem based on a novel recursive algorithm for checking which alternatives are to be considered in the computation of scalar implicatures. The gist of the idea is that alternatives are not considered altogether at the same time, but rather through a recursive algorithm that proceeds in steps and decide at each step which alternatives is to be included in the computation of scalar implicatures. I also argue for a solution to the under-generation
problem based on the role of focus in the computation of scalar implicatures (Rooth 1992, Fox and Katzir 2011). Finally, I discuss and compare the proposal of this chapter with the ones of Fox (2007) and Chemla (in preparation).
A scalar implicature-based approach
to neg-raising inferences
It is an old observation in the literature that certain sentence embedding predicates such as thinkand want interact with negation in a surprising way: when negated, these predicates are generally interpreted as if the negation was taking scope in the embedded clause. In brief, sentences like (1a) and (2a) are generally interpreted as (1b) and (2b), respectively.
(1) a. John doesn’t think Bill left.
b. John thinks Bill didn’t leave.
(2) a. John doesn’t want Bill to leave.
b. John wants Bill not to leave.
The traditional name for this phenomenon is “neg-raising”, and predicates like think and want are called “neg-raising predicates”.1 The fact that the sentence with wide scope negation ap-
pears to imply the one with narrow scope is not predicted by the standard semantics of such
1Beyond think and want, there are many other neg-raising predicates, the following in (3) is a list from Horn
predicates.2 Furthermore, other sentence-embedding predicates do not exhibit this property; compare (1a) and (2a) above with a sentence with a non-neg-raising predicate like be certain in (6a): the latter does not imply at all the corresponding sentence with internal negation in (6b).
(6) a. John isn’t certain that Bill left. b. John is certain that Bill didn’t leave.
There are three main approaches to neg-raising in the literature: a syntactic, an implicature- based, and a presuppositional approach. The syntactic approach, which also gave the name to the phenomenon, postulates that in a sentence like (1a) above negation is actually generated in the embedded clause and interpreted there, but it then raises above the predicate and appears linearly before it (Fillmore 1963 among others). I do not discuss the syntactic approach here, for compelling arguments against it see Horn 1978, Gajewski 2005, 2007, and Homer 2012a. An alternative approach is a pragmatic analysis in terms of a type of implicature (Horn 1978). Horn (1989) calls such implicatures “short-circuited implicatures”, implicatures that would be in principle calculable but in fact are conventional properties of some constructions. The main problem of this account is that there does not appear to be any independent motivation for this
(3) a. believe, suppose, imagine, expect, reckon, feel b. seem, appear, look like, sound like, feel like c. be probable, be likely, figure to
d. intend, choose, plan
e. be supposed to, ought, should, be desirable, advise, suggest
See Horn 1978 for a general introduction to neg-raising and Homer 2012a for an extensive discussion of neg-raising modals.
2The standard way to analyze such predicates, originally proposed by Hintikka (1969), is as universal quantifiers
over possible worlds, restricted to some modal base. So for instance the semantics of believe is in (4), where M is a function from worlds and individuals to sets of worlds, in this case the set of worlds compatible with the beliefs of a in w.
(4) [[believe]](p)(a)(w) = ∀w0∈ M(w, a)[p(w)]
It is clear that negating (4) as in (5a) is not equivalent to (5b), where negation takes narrow scope. (5) a. ¬[∀w0∈ M(w, a)[p(w)]]
type of calculable but conventional implicatures (for extensive discussion of the implicature- based account see Gajewski 2005). The presupposition-based approach is defended in Bartsch 1973 and Gajewski 2005, 2007 and, as I discuss below in detail, is successful in accounting for a variety of data relating to neg-raising. However, it also faces the problem of explaining why the presupposition that it postulates does not behave like other presuppositions in embeddings other than negation. Gajewski (2007) tries to overcome this problem by connecting neg-raising predicates to “soft” presuppositional triggers, in the sense of Abusch (2002, 2010), a class of triggers whose presupposition is particularly weak and context-dependent, which I discuss ex- tensively inCHAPTERS3 and 4. I argue that, nonetheless, the behavior of neg-raising predicates is different from that of this class of presuppositional triggers. Furthermore, as I discuss below, by adopting Abusch’s (2010) account of soft triggers, Gajewski (2007) inherits some empirical issues and extra non-standard assumptions about the semantics-pragmatic interface associated with that view.
In this chapter, following ideas in Chemla 2009a and Abusch (2002, 2010), I propose a scalar implicature-based account of the inferences associated with neg-raising predicates (“neg- raising inferences”, henceforth). I discuss two main arguments which favor this approach over the presuppositional one: first, it can straightforwardly account for the differences between between neg-raising predicates and presuppositional triggers. Second, it is based on an inde- pendently justified theory of scalar implicatures and it does not need to adopt the system in Abusch 2010, which, as I discuss below, has conceptual and empirical problems. Finally, I show that it can also account for those aspects of the behavior of neg-raising inferences that do appear presuppositional. While being based on implicatures, the account that I propose is different from Horn’s (1978) in that it only uses regular and independently motivated scalar implicatures.
This chapter is organized as follows: in section 2.2, I summarize the version of the presup- positional approach by Gajewski (2005, 2007) and the account of soft triggers by Abusch (2010) that he adopts. In section 2.3, I discuss the aspects of the behavior of neg-raising predicates that the presuppositional approach gets right and those that it gets wrong. The latter constitute the
motivations for the scalar implicature-based analysis of neg-raising that I outline in section 2.4. In section 2.5, I discuss its predictions and in particular how the proposal accounts for the dif- ferences between neg-raising inferences and presuppositions. In section 2.6, I show how it can also account for what the presuppositional account can explain with respect to the suspension of neg-raising inferences, the interaction with polarity, the neg-raising inferences from the scope of negative quantifiers and negated universals, and the behavior of stacked neg-raising predi- cates. I conclude the chapter in section 2.7. Finally, in appendix A, I explore the interaction between neg-raising inferences and conditional perfection, in section B, I discuss an open is- sue connected to the treatment of stacked neg-raising predicates that I propose in this chapter, and in Appendix C, I summarize the recent approach to the licensing of the so-called “strong” negative polarity items (Gajewski 2011, Chierchia to appear) and I show that neg-raising desire predicates constitute a challenge for this approach. Finally, I propose a tentative solution to it.