Until recently, the dominant philosophy of science was that due to Karl Popper, with its doctrine that the proper task of science was the formulation of hypotheses followed by attempts at refuting them. In spite of the close analogy with significance testing, these ideas do not fit well with the practice of medical statistics. The same can be said of the later philosophy of Thomas Kuhn, who maintains that science proceeds by way of revolutionary upheavals separated by periods of relatively pedestrian research which are governed by what Kuhn refers to as paradigms. Through there have been paradigm shifts in the history of statistics, a degree of continuity can also be discerned. A current paradigm shift is embodied in the spread of Bayesian ideas. It may be that a future paradigm will emphasise the pragmatic approach to statistics that is associated with the name of Daniel Schwartz.