Abstract
Imre Lakatos and Paul Feyerabend initially both accepted Popper's philosophy of science, but then reacted against it, and developed it in different directions. Lakatos sought to reconcile Kuhn and Popper by characterizing science as a process of competing research programmes, competing fragments of Kuhn's normal science. Feyerabend emphasized the need to develop rival theories to facilitate severe empirical testing of accepted theories, but then, as a result of a disastrous mistake, came to hold that theories that are incompatible with one another cannot be compared empirically. He ended up rejecting method in science. All four philosophers, Popper, Kuhn, Lakatos and Feyerabend missed the decisive defect in Popper's philosophy of science: persistent acceptance of unified theories only when endlessly many empirically more successful disunified rivals are available means that physics makes a big, highly problematic metaphysical assumption about the nature of the universe: it is such that some kind of underlying unity exists in nature. We need to adopt a new conception of science. In order to subject this implicit metaphysical conjecture to sustained critical assessment in an attempt to improve it, we need to see science as making a hierarchy of metaphysical assumptions about the knowability and comprehensibility of the universe, these assumptions becoming less substantial and more likely to be true as we ascend the hierarchy. Elements of Popper, Kuhn and Lakatos are to be found in this picture, but it also differs radically from all three. It more closely resembles Einstein's mature views about the nature of science.