Portion readings are count readings, not measure readings

We assume, following Rothstein 2010, 2011, 2016 and Landman 2011, 2013, 2015, a semantic theory of the mass-count distinction which defines the notion of count in terms of disjointness, non-overlap, and in which the mass-count distinction applies to noun phrases of any complexity (i.e. not just lexical nouns). We derive, following Rothstein 2011, two interpretations for pseudo-partitives like three glasses of wine, a container classifier interpretation which we show to be count and a measure interpretation which we argue to be mass. We then address portion readings. Partee and Borschev 2012 discussed portion readings as a subcase of measure readings. We argue, against this, that portion readings do not pattern with measure readings, because portion readings are count. We discuss three ways of deriving portion readings. This adds, for three glasses of wine, two new portion interpretations: a contents-classifier interpretation and a free portion interpretation. We show that, in the semantic framework given, all portion interpretations come out as count, setting them apart from measure interpretations. We show that the distinctions between measure interpretations and portion interpretations derived here hold cross-linguistically in a number of typologically distinct languages.