How do we explain what constitutes genuine scientific endeavour, as opposed to non-scientific endeavours? We considered a famous ruling by Judge William Overton, who was trying to decide whether creationism could be taught in publicly funded schools as an alternative to evolutionary theory. The key question at issue was whether creationism is a genuine scientific theory, or merely a pseudo-scientific view. To settle this issue Judge Overton put forward five conditions which genuine science had to satisfy. These were: (1) it is guided by natural law; (2) it has to be explanatory by reference to natural law; (3) it is testable against the empirical world; (4) its conclusions are tentative (i.e. are not necessarily the final word); and (5) it is falsifiable. We examine the case for all five conditions. A radically different way of thinking about scientific thinking proposes that the kind of scientific change that takes place when scientific revolutions occur is not to be thought of as an incremental, rational process from an old scientific theory to a new one. Instead, the revolutionary scientific theory is held to be incommensurable with the old theory, in the sense that there is no significant commonality between the two. This means that the two theories will not only disagree about what the scientific evidence demonstrates, but will also disagree about what counts as scientific evidence in the first place. This conception of scientific change challenges a traditional way of thinking about scientific knowledge as the accumulation of knowledge, and it is also potentially incompatible with some of Judge Overton’s conditions for genuine science.