The many readings of many: POS in the reverse proportional reading

Abstract

Besides their ordinary cardinal and proportional meanings, many and few have been argued to allow for a ‘reverse proportional’ reading (Westerstahl in Linguist and Philos 8:387–413, 1985). This reading has later been characterised in two opposite directions: Cohen’s (Nat Lang Semant 69:41–67, 2001) reading where the proportion $$|P\cap Q|:|P|$$ matters and Herburger’s (Nat Lang Semant 5:53–78, 1997) where it does not. We develop a compositional analysis that derives the correct truth conditions for both characterisations of Westerstahl-style sentences while (i) maintaining conservativity, (ii) assuming a standard syntax/semantics mapping and (iii) reducing their context-dependence to mechanisms independently needed for degree constructions in general. In a nutshell, mirroring the decomposition of other degree expressions like tall, many is decomposed into the parametrized determiner many and the operator POS, where POS combines with a contextually salient comparison class C matching the alternatives triggered by some element X $$_{\text {ALT}}$$ in the sentence. Non-reverse readings obtain when X $$_{\text {ALT}}$$ is external to the original host NP and reverse readings when X $$_{\text {ALT}}$$ is internal to the host NP. Cohen’s (2001) (amended) truth conditions for Westerstahl-style sentences are derived as a (true) reverse proportional reading and Herburger’s (1997) interpretation as a sub-case of the non-reverse cardinal reading.