Taking Scope: The Natural Semantics of Quantifiers

Chapter 8 Inverse Scope

Chapter 8 Inverse Scope A complete history of every start is available. —The Linguist’s Search Engine We will assume that the universal quantifier determiners every and each and their relatives are syntactically and semantically polarity-preserving, despite being in addition downward-monotone-entailing on the restrictor property. 8.1 How True Universal Quantifiers Invert Scope Because certain universals, by contrast with the plural existentials, are genuine quantifiers, they and they alone can truly invert scope in both right- and leftbranching derivations. For example, every can invert as follows (once again the left-branching inverting reading and the noninverting readings for both derivations are suggested as an exercise): (1) Some farmer owns every donkey S/(S\NP3SG) (S\NP3SG)/NP (S\NP)\((S\NP)/NP) : λp.p(skolem′farmer′) : λxλy.own′xy : λqλy.∀x[donkey′x → qxy] S : ∀x[donkey′x → own′x(skolem′farmer′)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S : ∀x[donkey′x → own′x sk (x) farmer′ ] Such inversion cannot engender violations of the “strong-crossover” condition on binding like the following, because such examples violate binding conditions B and C on the binding of pronouns at the level of logical form (see SS&I, 52–53): (2) *Hei admires every mani However, the theory allows violations of “weak crossover,” as in the derivation in figure 8.1, for much the same reason that the reconstruction example in figure 7.2 is allowed. 128 Chapter 8 ?Hisi mother loves every boyi S/(S\NP3SG) (S\NP3SG)/NP (S\NP)\((S\NP)/NP) : λp.p(skolem′λy.mother′y∧of′(pronoun′him′)y) : λxλy.loves′xy : λqλy.∀x[boy′x → qxy] S : ∀x[boy′x → loves′x(skolem′λy.mother′y∧of′(pronoun′him′)y)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S : ∀x[boy′x → loves′x sk (x) λy.mother′y∧of′xy] Figure 8.1: “Weak Crossover” Inverse Scope 129 Weak crossover is, as its name suggests, a much less compelling effect than strong crossover, and the constraint can be overridden by context or intonation . It seems reasonable to assume that its source is not grammatical, as Shan and Barker (2006) do under their related account of scope inversion, unlike Jacobson (1999). Similar derivations correctly allow the universals every and each to invert over most nonuniversals, such as the counting quantifiers(at least/exactly/at most) two and proportional quantifiers several, many, most. The exceptions to this pattern include few and no, which seem not to permit inversion: (3) a. Few farmers feed every donkey. (few∀/?∀few) b. No farmer owns every donkey. (no∀/?∀no) c. Some critic didn’t like every play. (some not∀/?∀some not) However, this seems symptomatic of a more general reluctance of universals to take scope over negation, including few and no (Jesperson 1917, 87, and 1940, 462; Horn 2001, 226–231): (4) a. Every farmer owns few donkeys. (few∀/#∀few) b. Every farmer owns no donkey. (no∀/#∀no) c. Every farmer doesn’t own a donkey. (not∀/#∀not) Ladd (1980, 145–162) points out that readings where the universal takes wide scope can be obtained in contexts where questions like Does any farmer own few donkeys? are in play, when they attract a distinctive intonation contour, with a “fall” accent on Every and low pitch on everything that follows. We return to these cases in chapter 11. 8.2 “Inverse Linking” Examples like the following (from May 1985; cf. Heim and Kratzer 1998) seem to allow a universal to invert scope over a matrix indefinite from inside that indefinite’s noun modifier: (5) a. Some apple in every barrel was rotten. b. Some representative of every company saw some sample. Such sentences (which are widespread in corpora and on the web, as exempli fied by the epigraph to this chapter) are at first glance puzzling, since relativization out of NPs, and in particular out of subjects, is usually regarded as unacceptable, although opinions differ as to what degree: 130 Chapter 8 (6) a. #(This is) the barrel that some apple in was rotten. b. #Which barrel was some apple in rotten? c. #Every barrel, some apple in was rotten! d. #Some apple in, and the bottom of, every barrel was rotten. May points out that any movement analysis that allows every barrel to directly adjoin to S in the usual quantifier position requires that we provide some other explanation for the anomalies in (6). May’s solution (1985, 69...