Does language make use of unpronounced, ‘conceptual’ alternatives? Buccola et al. 2018 argue that it does. One of the cases they cite to make this point is the observation by Chemla [2007] that the French universal quantifier tous is anti-dual (i.e. odd when its domain consists of two individuals), even though French has no word for ‘both’ to feed a Maximize Presupposition competition. This suggests that a dual conceptual alternative is at play. However, 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 analysis 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 ‘Indirect Alternative’. This proposal accounts for tous’s anti-duality and lack of anti-n-ality for n > 2, as well as the lack of anti-duality in other quantifiers.