Drawing on the work of Charles Peirce and Bernard Lonergan, I argue (1) that inferences are essentially related to a process of inquiry, (2) that there is a normative pattern to this process, one in which each of Peirce's three distinct types of inferenceabductive, deductive, and inductive-plays a distinct cognitive role, and (3) that each type of inference answers a distinct type of question and thereby resolves a distinct kind of interrogative intentionality.