Proportional readings of many and few: the case for an underspecified measure function

Abstract

In the so-called reverse proportional reading (Herburger in Nat Lang Semant 5(1):53, 1997), the truth conditions of statements of the form many/few $$\phi $$ $$\psi $$ appear to make reference to the ratio of the individuals that are in the extensions of both $$\phi $$ and $$\psi $$ to the individuals that are in the extension of $$\psi $$ . The analysis of such readings is controversial. One prominent approach assumes they are a symptom of many and few making reference to a context dependent standard of comparison. We observe that this initially attractive approach systematically undergenerates, failing to capture pervasive reverse proportionality in environments that remove context dependency of the standard. Instead, we propose that reverse proportionality in such cases can arise from the underspecification of the measure function underlying the meanings of many and few.