Indefinite t ime phrases, in situ scope, and dual-perspective intensionality

This paper is concerned with expressions like three times in Dafna jumped three times. These expressions look like bare noun phrases in adverbial position, and one could, at first sight, think of them as PPs with an empty preposition. Such an analysis, however, would leave two major properties of these expressions unexplained: 1. They show definiteness effects in interpretation. 2. They don't show wide-scope, or very-wide scope interpretations. I will argue that the crux to explaining these facts lies in Doetjes 1997's assumption that the expression time(s) does not pattern with nouns, but with classifiers/measures. Using a semantic interpretation inspired by Categorial Grammar, and the Adjectival Theory of indefinites from Landman 2004, I argue that indefinite time phrases, and only indefinite time phrases, have an interpretation directly as modifiers; and this will, in essence, account for the definiteness effects. I then argue that this analysis treats indefinite time phrases on a par with intensional adverbial modifiers. At first sight, this seems problematic, because these time phrases don't show the intensionality of, say, modal adverbials. But I argue that the intensionality of modals and of the indefinite time phrases are instances of a deeper form of intensionality, dualperspective intensionality. I then argue that the intensionality involved in indefinite time phrases is what we can call gridding. Indefinite time phrases count pluralities in a set of pluralities of events. Following the theory of plurality of Landman 1989a,b, pluralities cannot be counted directly, only atoms can be counted. The interpretation of the indefinite time phrase as an intensional modifier induces the operation of gridding: gridding shifts a set of pluralities, which cannot be counted, to a set of corresponding singularities, group atoms, which can be counted. I show that gridding has precisely the effects on scope that we observe for indefinite time phrases: gridding creates scope, but not wide scope and 'very wide scope' interpretations.