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This paper discusses a recent opposition between the influential dynamic semantic account of presupposition projection and a recent Gricean-pragmatic theory. The Gricean-pragmatic theory is partly motivated by an influential ob- jection to dynamic semantics based on the compatibility of dynamic systems with connectives and operators exhibiting deviant projection behaviors. By identifying key features of the role of prediction and explanation in semantics, it is argued that the objection is based on a mistaken conception of the involve- ment of empirical foundations in semantic theories. The paper shows that the dynamic paradigm does not suffer from either predictive or explanatory inad- equacy. The chapter concludes that while it is too early to decide in favor of either approach, the Gricean alternative to dynamic semantics cannot be seen as motivated by a flaw in the latter theories.