This chapter explores relevant aspects of Mary Hesse’s epistemology, with special attention to her attempt to outline a post-empiricist account of scientific knowledge based on criticisms of the received positivist view that were discussed at the time. Key features of Hesse’s view of language and meaning will be considered, and it will be shown that there is a certain consistency between her conception of the growth of scientific knowledge and Thomas Kuhn’s mature philosophy. An account of Hesse’s and Kuhn’s attempts to stress that interpretive activity occurs at various levels of scientific inquiry will allow us to delve into their shared idea that the hermeneutic approach that has traditionally been considered the most appropriate to the human sciences may be appropriate to the natural sciences as well.