The traditional analysis of the quantifiers some and some ... not is customarily given via the concepts of scalar implicature, Horn's scales and the logical relations implied by the logical square. In this contribution, I challenge this view by arguing that the pragmatic relation between these particulars is not an implicature, but rather an explicature, that is, a pragmatic development of an utterance's propositional form. To this end, I provide a Boolean semantics and pragmatics for the particulars at hand, and discuss the consequences of my account for pragmatic analysis, especially in relation to the properties of calculability and cancellability that implicatures are associated with. In closing, I propose a possible answer to Horn's conjecture about the well-known issue of the non-lexicalisation of negative particulars (the O vertex in the logical square).