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

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Besides their ordinary cardinal and proportional meanings, many and few have been argued to allow for a ‘reverse proportional’ reading (Westerståhl 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 Westerståhl-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 Westerståhl-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.

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Correspondence to Maribel Romero.

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I would like to thank Lucas Champollion, Irene Heim, Sven Lauer, Sophia Malamud, Doris Penka, Robert van Rooij, Bernhard Schwarz, Yasutada Sudo and the audiences of the Amsterdam Colloquium 20, NELS 46 and SALT 27 for their valuable input. Special thanks to three reviewers, from whose comments this paper has benefited significantly. Remaining errors are mine.

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Romero, M. The many readings of many: POS in the reverse proportional reading. Linguist and Philos (2020) doi:10.1007/s10988-019-09288-1

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