 It would be unconventional (unusual, idiosyncratic, even unprecedented) for people who say “Some athletes smoke” to conversationally implicate that some physically fit people will develop bladder cancer, but conventional (customary, normal, standard practice) for them to implicate that not all athletes smoke. The customary implicature is not conventional in Grice’s sense, though. For “Not all athletes smoke” is not determined by the meaning of “Some athletes smoke”. Speakers can and often do use  (5a)  while implicating something other than  [5b],  as  (6)  will illustrate. The practice of using sentences of the form “Some NP VP” to mean “Not all NP VP” is not a semantic or syntactic convention. It is a pragmatic convention. To avoid confusion, I will describe implicatures that are conventional in Grice’s sense as semantic. When not modified by “in Grice’s sense”, “conventional” will have the broader sense of customary.