 In his landmark 1962 “Explanation, Reduction and Empiricism”, Paul Feyerabend initially introduced the term ‘incommensurable’ as part of a criticism of the conceptual conservativism that he found in Nagel’s theory of reduction and the Hempel-Oppenheim theory of explanation. He argued that formal accounts of reduction and explanation are impossible for general theories because they cannot accommodate the development of incommensurable concepts in the course of scientific advance. Feyerabend used the notion of incommensurability to characterize the relation between two successive fundamental, universal scientific theories interpreted realistically; i.e. as purported descriptions of reality. By limiting incommensurability to universal theories, Feyerabend meant only those that apply to all objects in the universe. By limiting incommensurability to fundamental theories, Feyerabend meant those that have ontological implications; i.e., those that have implications about the very nature of reality. Universal, fundamental scientific theories can be incommensurable only if they are interpreted realistically, according to Feyerabend, because otherwise they cannot compete as the one true theory, and are thus not mutually exclusive. By calling two such theories incommensurable, Feyerabend meant that they were conceptually incompatible: The main concepts of one could neither be defined on the basis of the primitive descriptive terms of the other, nor related to them via a correct empirical statement (1962, 74, 90). As a consequence, it is impossible to reduce incommensurable theories formally.