This paper analyses conceptual change. A rejection of pure experience has prompted philosophers of science to adopt a certain perspective from which to view changes of belief. Popper, Kuhn, and others have analysed conceptual change in terms of problems or anomalies, that is, in terms of contingent reasoning about issues posed in the context of an inherited web of belief. This paper explores a more general analysis of conceptual change in dialogue with these philosophers of science. Still, because changes of belief are not all changes in scientific belief, we seek to unpack conceptual change in terms of dilemmas, as opposed to anomalies or problems. For a start, the notion of a dilemma differ has to be broader than that of an anomaly since it purports to apply to conceptual change as a whole, not just the transition from one era of normal science to another. In addition, we should detach the notion of a dilemma from the objectivism of Popper’s world-3 problems.