In this paper, I distinguish between linguistic and non-linguistic presuppositions. I also propose that we should be interested in conversational presuppositions, which could also be called speaker-meant presuppositions or speaker's presuppositions. I also distinguish between potential and actual presuppositions. I propose that, in some cases, presuppositions can be conversationally implicated and cancellation is possible. I specify what the hard cases are and I try to explain them through ontological considerations. I try to reduce the hard cases through (a) the notion that all actual presuppositions are speaker-meant; (b) the distinction between ontological and linguistic presuppositions; and (c) the uncontroversial notion that even ontol...