How to Count 2 1/2 Oranges

Abstract: We address a puzzle about the meanings of fraction words due to Nathan Salmon. Counting 2 1/2 oranges seemingly requires enumerating a collection of objects with a non-whole cardinal number, which is incoherent by the lights of traditional analyses of cardinality expressions. Thus, some argue that counting 2 1/2 oranges really amounts to measuring quantities of orange-stuff . However, we claim that `2 1/2 oranges' is ambiguous between counting and measuring interpretations, and recognizing this affords a novel solution to Salmon's puzzle which is consistent with traditional analyses.

Click here for an official copy of the paper.

Click here for an unofficial copy of the paper