Peirce and Dewey were generally more concerned with the process of scientific activity than purely mathematical work. However, their accounts of knowledge production afford some insights into the epistemology of mathematical postulates, especially definition and axioms. Their rejection of rationalist metaphysics and their emphasis on continuity in inquiry provides the pretext for the pragmatic a priori – hypothetical and operational assumptions whose justification relies on their fruitfulness in the long run. This paper focuses on the application of this idea to the epistemology of definitions and an account of progress in mathematics, although it has broader implications for the study of conceptual change and the function and basis of presuppositions in the sciences
