Directionality in numeral quantifiers: the case of up to

As far as I know, the semantics of such modified numerals has so far only been discussed in Corver and Zwarts (2006), who focus on the close relation between the locative spatial semantics of prepositions like under and their use in numeral quantifiers. In this paper, I will turn to directional prepositions and investigate the role of directionality in numeral modification. I will zoom in on the case of up to, as exemplified in (1-d), show that this modifier has a rather quirky distribution and claim that this can be explained by assuming that the use of a spatial preposition in the numeral domain is governed by the same constraints as is its use in the spatial or temporal domain. The article is structured as follows. First, in Section 2, I will motivate why looking at individual numeral modifiers is an interesting enterprise. Then, I will give some background on prepositional numerals (Section 3), before turning to the crucial data in Section 4. In Section 5, I will propose an analysis in terms of a semantics for up to which expresses a homogeneity requirement. Section 6 concludes.