Pragmatic effects triggered by embedded structure have caused problems to Grice’s Theory of Conversational Implicature. This long-standing view is challenged by local pragmatics proposed by Mandy Simons. As to the theoretical development, Robyn Carston, Francois Recanati, and Emma Borg respectively raise their comments, while Simons positively responds to these commentaries and further elaborates her stance. In this article, the argumentation among these scholars is presented first, and much attention is paid to the value and influence of the argumentation, which would shed light on the current debate between semantics and pragmatics.