In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing proposals by Hinrichs, Krifka and Jackendoff which takes Jackendoff's cross-cutting sortal distinctions as its point of departure. To show that the account is well-suited for computational purposes, I also sketch an implemented calculus of eventualities which yields many of the desired inferences. Further details on both the model-theoretic semantics and the implementation can be found in (White, 1994).