Restriction and saturation (review)

The main thesis of this book is that natural language possesses a previously undiscovered mode of semantic composition, Restrict. The primary empirical corollary of the proposal is that languages can overtly signal which mode of composition is to be used—Restrict, or more standard modes involving functional application. The core proposal is simple, yet has far-reaching and intriguing consequences. The presentation is very clear and the empirical predictions are thoroughly tested on the basis of an extensive review of published sources as well as primary fieldwork. This is an important piece of work whose crosslinguistic predictions deserve further investigation.

Restrict is illustrated in 1. A transitive verb (of type <e,<e,t>>) composes directly with an indefinite NP (of type <e,t>), without type-shiftingof either element being necessary. The operation does not decrease semantic valency; a function is returned that still has two unsaturated argument places.

(1) Restrict (λyλx [feed’(y)(x)], dog’)

 = λyλx [feed’(y)(x) ⋀ dog’(y)]     (p. 5)

These unsaturated argument positions are available for saturation later on, either by Functional Application (FA), or by Existential Closure (EC). In 2, for example, the predicate’s internal argument is existentially closed, and the external argument denotes an individual and composes via FA.

(2) FA (EC (Restrict (λyλx [feed’(y)(x)], dog’)), j)

 = ∃y [feed’(y)(j) ⋀ dog’(y)]     (p. 5)

Restrict contrasts with Specify, a more standard (compound) composition mode whereby an indefinite (of type <e,t>) is shifted to type e by a choice function, and then saturates the relevant argument position via FA. C&L adopt a Tanya Reinhart/Yoad Winter version of choice functions, in which the choice function variable is bound by EC at any level.

The truth conditions resulting from the application of Restrict are equivalent to those of a subset of cases where Specify applies. Ex. 2, for instance, is equivalent to 3, which employs Specify with EC over the choice function variable.

(3) FA (FA (λyλx [feed’(y)(x)], CF (dog’)), j)

 = ∃f [feed’(f(dog’))(j)]     (p. 5)

But the two composition modes differ with respect to scope possibilities. C&L introduce a principle requiring that all arguments are semantically saturated by the level at which the event argument is closed off (11). Argument positions that are initially targeted by Restrict must therefore be saturated by the event level, and obligatorily take narrow scope with respect to anything higher than this level. In contrast, elements composed via Specify are immediately converted to type e and result in saturation in situ. They automatically satisfy the principle enforcing saturation, and are therefore free to take wide scope, by the usual method of existentially closing the choice function from a sufficiently high position.

Ch. 2 applies the analysis to the determiner system of Maori. C&L propose that the Maori determiner he signals composition via Restrict. The requirement that all arguments be saturated by the event level forces he-DPs to take narrow scope with respect to negation.

(4)

The determiner tētahi, in contrast, signals composition via Specify. This means that tētahi-DPs can take either wide or narrow scope.

(5)

Since Restrict does not saturate an argument slot, it is predicted that an argument targeted by Restrict could be later saturated by an overt DP. C&L argue in Ch. 3 that this occurs in Chamorro noun incorporation. Chamorro possesses two predicates that productively allow incorporation: gäi- ‘to have’ and täi- ‘to not have’. Crucially, the incorporated object can be doubled.¹

(6)

C&L show that the incorporated object denotes a property and is syntactically an NP, while the extra object is of argumental semantic type and syntactically a DP. They further argue that the extra object is syntactically an adjunct rather than a direct object,² but that it nevertheless saturates the internal argument of the verb. Evidence for the last claim comes from semantic restrictions on the extra object which...