In this article, our goal is twofold. First, we would like to present a model, the Semantic Core Model, that challenges a way of interpreting Grice's proposal that has come to be dominant in the field. According to the dominant view, one first retrieves the semantics of a whole root sentence and then processes the implicatures associated with it (in a strictly modular way). The Semantic Core Model proposes, instead, that semantic and pragmatic processing takes place in tandem. Implicatures are factored in recursively, in parallel with truth conditions. Our second goal is to present experimental evidence from adults and children that is consistent with this new model.