First, K. and P. give an overview of different phenomena (preconditions on the smooth functioning of communicative acts) which have generally been regarded as presuppositions. Then they briefly discuss semantic and pragmatic presupposition, i.e. two proposals about what it is for a proposition to be presupposed by a sentence. They come to the conclusion that all the different cases of presupposition they mentioned do not constitute one single phenomenon: some should be treated as particularized conversational implicatures, others as generalized conversational implicatures, others as conventional implicatures and still others as preparatory conditions on illocutionary acts. They abandon the notion 'presupposition'.