Counting individuals and their halves. - Bale, Alan; Nicolas, David (Linguistics & Philosophy, 2024)
Expressions like two novels are traditionally taken to convey information about cardinality and are analyzed using a cardinality function. Salmon (Philosop Perspect 11:1–15, 1997), Liebesman (Australasian J Philos 93:21–42, 2015; Philos' Impr 16:1–25, 2016; In D. W. Zimmerman (ed.), Oxford studies in metaphysics, Oxford University Press, Oxford, forthcoming), and Haida and Trinh (in: Dočekal, Wagiel (eds) Formal approaches to number in Slavic and beyond, Language Science Press, Berlin, 2001) argue against this traditional account, claiming that it can't explain our use of expressions like two and a half novels. According to them, the proper analysis of such expressions requires a partiality measure, which maps entities to rational numbers such as 2.5. In this paper, we set out to defend the traditional account. To do so, we demonstrate that an analysis based on a partiality measure is inconsistent with the truth conditions of plural comparatives and equatives. We also show that such an account doesn't provide an adequate analysis for expressions like two novels and a half, nor for their French counterparts (e.g., deux romans et demi). Critically, such expressions contain no constituent that could refer to the number 2.5. We provide an alternative analysis for all these expressions, based on cardinality and an operation of non-overlapping summation.