Comparatives, Indices, Scope
Our knowledge of the natural world leads us to judge a sentence like (1) to be a contradiction.
(1) Smith's yacht is larger than it is.
As noted by Bertrand Russell (1905), however, when a sentence like (1) is embedded under an intensional predicate, the resulting sentence is ambiguous.
(2) Jones thinks Smith's yacht is larger than it is.
Russell observed that (2) can either be interpreted as a claim that Jones has a mistaken belief about the size of Smith's yacht, or as a claim that Jones believes a contradiction. Russell derived the ambiguity from the principles of his theory of definite descriptions: comparatives are a type of description (of degrees), descriptions may take scope over intensional predicates, therefore (2) is ambiguous.
The majority of subsequent work on the syntax and semantics of comparative constructions retains the core of Russell's explanation. In these accounts, the ambiguity of (2) and related sentences follows from the assumption that some component of the comparative construction may have wide or narrow scope with respect to an intensional predicate or operator, where scope is determined by the structural relationship which holds between these expressions in a logical form.
This paper develops an indexical account of Russell's ambiguity, in which the scope of a comparative is a function of its indexical value, where its index identifies the world with respect to which its denotation is determined. Following Heim 1985, comparatives are analyzed as degree descriptions--restrictions on the possible values of the degree argument of a gradable predicate. Building on Farkas' (1993, 1994, 1995) indexical account of the scope of indefinite NPs, the scope of comparatives--like the scope of indefinites--is shown to be determined by indexical dependencies rather than configurational relations at LF.