B. and L. argue (i) that the thesis that there are semantic presuppositions is false, i.e. the thesis that certain sorts of sentences carry certain quasi-logical implications distinct from and yet closely related to ordinary entailments; (ii) that themethodological corollary of this thesis, i.e. the fact that grammars operating with a 'natural logic' must complicate their semantic theories by adding formal apparatus to account for semantic oddities arising when presuppositions fail, is without support; (iii) that the cases of semantic presupposition do not form a natural kind. The standpoint from which the criticism is brought forward is congenial to generative semantics and the performative analysis.