Ever since Horn 1972, it has been a received view that the lexical meaning of scalar quantifiers specifies only a lower bound. Most, it is assumed, codes 'more than half', also covering 'all'. To account for most's common interpretation, 'more than half but less than all', linguists have assumed a 'not all' implicature. I argue that the implicature analysis cannot account for most of the discourse data, and that the upper bound on most is independent of a 'not all' implicature. Furthermore, based on questionnaire results, I propose a different semantics-pragmatics division of labor. Most denotes 'a proper subset which is the largest subset given any partitioning of the complement subsets'. Thus, most's lexical meaning does provide an upper bound, but pragmatic inferences may nonetheless sometimes render its use compatible with states of affairs in which 'all' is true.