QR Obeys Superiority: Frozen Scope and ACD

Abstract

The phenomenon of "frozen scope" in double object and spray-load constructions is shown to hold robustly across contexts, constructions, and quantifier types. Nevertheless, frozen scope is not absolute, holding only between two objects but not between an object and a subject or an object and some other operator. The rigidity of two object quantifiers follows the pattern of multiple instances of movement crosslinguistically (multiple wh-movement, multiple A-scrambling, multiple object shift): movement paths cross, recreating the hierarchical order of the moving elements (Richards 1997). Hypothesizing that quantifier scope is derived by quantifier-specific syntactic movement, movement that is constrained in the same way as other types of movement, permits these phenomena to be unified under accounts of Relativized Minimality effects generally.

1 Introduction: Scope in English

The facts of quantifier scope interaction in English have motivated claims that the covert raising of quantifiers (QR; May 1977, 1985, and much subsequent work) can change the hierarchical order of quantifiers. Thus, for example, following May (1977), one might generate different readings for the sentence in (1a) by applying QR first to the direct object, as in (1b), or to the object of the preposition, as in (1c). Since adjunction might be thought to create successively higher positions, the quantifier that moves last will take widest scope. In this way (1c) has the surface scope reading, where a different boy is interpreted contextually (i.e., different with respect to some contextually salient boy or set of boys), while (1b) has the inverse scope reading, where boys vary with houses.

(1)

1. a. Jill saw a different boy in each house.

2. b. [IP each house₂ [_IP a different boy₁ [_IP Jill saw t₁ in t₂]]]                each < a

3. c. [_IP a different boy₂ [_IP each house1 [_IP Jill saw t₂ in t₁]]]                a > each

This view of QR is motivated by the fact that scope is generally ambiguous in English, at least in simple cases. Permitting quantifiers to adjoin in any order captures this ambiguity.¹

Theories of QR have attempted to constrain its application. Fox (1995b), for example, suggests limiting the application of QR to those instances where raising a quantifier would have some semantic effect. If QR changes scope relations, it is allowed; if it does not, it is not permitted. As Fox shows, this hypothesis correctly accounts for the lack of certain readings in ellipsis constructions (see also Fox 2000). Even with this restriction, however, QR is still expected to reorder quantifiers by moving and adjoining them in any order. In fact, it is expected that the order of quantifiers should be able to change, as this is exactly what would derive a different interpretation—a necessary condition for QR according to Fox's Scope Economy principle. Thus, without additional restrictions we would expect that any quantifier should be able to take scope over any other quantifier in the same clause.²

Double object constructions are then mysterious in not permitting the second object to take scope over the first. For instance, each doll in (2a) is unable to take scope over a child. Children cannot vary with dolls in this sentence; there must be a single child receiving all of the dolls. In contrast, scope relations in the dative counterpart of (2a) are entirely free (2b).

(2)

1. a. I gave a child each doll.                                        a > each, *each > a

2. b. I gave a doll to each child.                                      a > each, each > a

The phenomenon illustrated in (2a), dubbed "scope freezing," is problematic for every version of QR. Scope freezing holds not only of the double object construction, but of several related constructions as well—for instance, the spray-load alternation (see Larson 1990, where this observation is credited to David Lebeaux). The facts are laid out in section 2, where scope freezing is shown to hold robustly in these constructions.

Most accounts of scope freezing attribute it to an inability of the second object to move in double object constructions (e.g., Larson 1988, 1990, Aoun and Li 1989, 1993, Marantz 1993...