Core concepts and indirect alternatives: on the anti-duality of quantifiers

Abstract This paper proposes an analysis for the long-standing puzzle observed by Chemla (2007) regarding the anti-duality of the French universal quantifier tous, which arises even though French has no word for ‘both’ to feed a Maximize Presupposition competition. This phenomenon has been cited as an example in language where a dual ‘conceptual alternative’ is at play (Buccola et al. , 2018), but no formal account of it has been put forth. Furthermore, a naive implementation of the idea overgenerates anti-duality inferences in other expressions, such as each, which, and one in English and French, which might be expected to be observed due to anti-dual counterparts in some languages like Icelandic and Japanese. We propose an account where French tous has an unpronounceable dual universal alternative built from a dual core concept, competition with which is licensed by the existence of a pronounceable expression equivalent in meaning, which we call an ‘Indirect Alternative’. This proposal accounts for tous’s anti-duality and lack of anti-n-ality for n2, as well as the lack of anti-duality in other quantifiers.