Besides their ordinary cardinal and proportional meanings, many and few have been argued to allow for a ‘reverse proportional’ reading. This reading has later been characterised in two opposite directions: Cohen’s reading where the proportion \ matters and Herburger’s where it does not. We develop a compositional analysis that derives the correct truth conditions for both characterisations of Westerståhl-style sentences while maintaining conservativity, assuming a standard syntax/semantics mapping and 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\ in the sentence. Non-reverse readings obtain when X\ is external to the original host NP and reverse readings when X\ is internal to the host NP. Cohen’s truth conditions for Westerståhl-style sentences are derived as a reverse proportional reading and Herburger’s interpretation as a sub-case of the non-reverse cardinal reading. (shrink)