Why 'not numeral NP' requires 'but' but not 'not many NP'

Abstract

This paper observes that negated numerals require but (e.g. Not three *(but four) students arrived), whereas not many doesn’t (e.g. Not many students arrived). Drawing on the additional observation that negated non-quantifier DPs require but (e.g. Max eats not spinach *(but chard)), I propose that constituent negation presupposes that the utterance containing the negation must entail a true alternative utterance, if there exists such a true alternative. This is generally satisfied by an overt but-phrase, except with the not-many-sentence because it entails an alternative sentence on its own–Some students arrived. I also take the contrast between not many and negated numerals as evidence that they have different types of assertion, in support of Kennedy (2013, 2015): many asserts at least n, while numerals assert at least n and at most n at the same time. Therefore, in contrast to not many, which entails some, not three does not entail not one or not two, and thus requires the but-phrase to introduce the true alternative.