ZASPiL 44 = Proceedings of the Sinn und Bedeutung 10
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This paper looks at sentences with "quantificational indefinites," discussed by Diesing (1992) and others. I propose that these sentences generate sets of alternatives of the form {p, not p and it's possible that p}, which restrict the quantification by an extension of familiar focus principles. For example, in the sentence "I usually read a book about slugs" (on the relevant reading), "usually" quantifies over pairs <x,t> such that x is a book about slugs, t is a time interval, and one alternative is true from the set {I read x at t, I can but do not read x at t}. In addition to accounting for a well-known contrast between creation and non-creation verbs, this also explains a second contrast that Diesing’s analysis cannot account for.
The expressions few and a few are typically considered to be separate quantifiers. I challenge this assumption, showing that with the appropriate definition of few, a few can be derived compositionally as a + few. The core of the analysis is a proposal that few has a denotation as a one-place predicate which incorporates a negation operator. From this, argument interpretations can be derived for expressions such as few students and a few students, differing only in the scope of negation. I show that this approach adequately captures the interpretive differences between few and a few. I further show that other such pairs are blocked by a constraint against the vacuous application of a.
Modifiability by almost has been used as a test for the quantificational force of a DP without stating the meaning of almost explicitly. The aim of this paper is to give a semantics for almost applying across categories and to evaluate the validity of the almost test as a diagnosis for universal quantifiers. It is argued that almost is similar to other cross-categorial modifiers such as at least or exactly in referring to alternatives ordered on a scale. I propose that almost evaluates alternatives in which the modified expression is replaced by a value close by on the corresponding Horn scale. It is shown that a semantics for almost that refers to scalar alternatives derives the correct truth conditions for almost and explains selectional restrictions. At the same time, taking the semantics of almost seriously invalidates the almost test as a simple diagnosis for the nature of quantifiers.