Cross-linguistic representations of numerals and number marking

Alan Bale, Michaël Gagnon, Hrayr Khanjian

Inspired by Partee (2010), this paper defends a broad thesis that all modifiers, including numeral modifiers, are restrictive in the sense that they can only restrict the denotation of the NP or VP they modify. However, the paper concentrates more narrowly on numeral modification, demonstrating that the evidence that motivated Ionin & Matushansky (2006) to assign non-restrictive, privative interpretations to numerals – assigning them functions that map singular sets to sets containing groups – is in fact consistent with restrictive modification. Ionin & Matushansky (2006)’s argument for this type of interpretation is partly based on the distribution of Turkish numerals which exclusively combine with singular bare nouns. Section 2 demonstrates that Turkish singular bare nouns are not semantically singular, but rather are unspecified for number. Western Armenian has similar characteristics. Building on some of the observations in section 2, section 3 demonstrates that restrictive modification can account for three different types of languages with respect to the distribution of numerals and plural nouns: (i) languages where numerals exclusively combine with plural nouns (e.g., English), (ii) languages where they exclusively combine with singular bare nouns (e.g., Turkish), (iii) languages where they optionally combine with either type of noun (e.g., Western Armenian). Accounting for these differences crucially involves making a distinction between two kinds of restrictive modification among the numerals: subsective vs. intersective modification. Section 3 also discusses why privative interpretations of numerals have trouble accounting for these different language types.