 Presupposition has been treated as a semantic phenomenon and as a pragmatic phenomenon. Arguably, each of (1)-(5) and its corresponding negation would have the same presupposition. This has led to the semantic conception of presupposition as a non-trivial entailment that is shared by a statement and its negation. Semantical approaches to presupposition encounter some tricky problems, the most important of which is “the projection problem.” If presupposition is semantic, then it seems the presuppositions of complex sentences should be a function of the presuppositions of the simple sentences that make them up, but it is at least not obvious that this is so. Consider, for example,