The counting principle makes number words unique

Following Ariel (2021. Why it's hard to construct ad hoc number concepts. In Caterina Mauri, Ilaria Fiorentini, & Eugenio Goria (eds.), Building categories in interaction: Linguistic resources at work, 439-462. Amsterdam: John Benjamins), we argue that number words manifest distinct distributional patterns from open-class lexical items. When modified, open-class words typically take selectors (as in kinda table), which select a subset of their potential denotations (e.g., "nonprototypical table"). They are typically not modified by loosening operators (e.g., approximately), since even if bare, typical lexemes can broaden their interpretation (e.g., table referring to a rock used as a table). Number words, on the other hand, have a single, precise meaning and denotation and cannot take a selector, which would need to select a subset of their (single) denotation (??kinda seven). However, they are often overtly broadened (approximately seven), creating a range of values around N. First, we extend Ariel's empirical examination to the larger COCA and to Hebrew (HeTenTen). Second, we propose that open-class and number words belong to sparse versus dense lexical domains, respectively, because the former exhibit prototypicality effects, but the latter do not. Third, we further support the contrast between sparse and dense domains by reference to: synchronic word2vec models of sparse and dense lexemes, which testify to their differential distributions, numeral use in noncounting communities, and different renewal rates for the two lexical types.