On the semantics of unit fractions

We present two novel observations concerning the linguistic behavior of unit fractions, e.g., ‘half‘, ‘third‘ etc., which challenge their analysis as proportional quantifiers/modifiers, arguing instead that in certain environments fractions presuppose ‘contextually salient‘ partitions over individuals. We distinguish environments that require a salient partition from those that do not, and propose a syntax and semantics for fractions that derives the distinction.