In an Isis 2008 review of research in History and Philosophy of Science (HPS), Galison opened discussion on ten on-going HPS problems. It is however unclear to what extent these problems, and constraints on their solutions, are of HPS’s own making. Recent research provides a basic resolution of these issues. In a recent paper Hooker (Perspect Sci 26(2): 266–291, 2018b) proposed that the discipline(s) of HPS should themselves also be understood to employ paradigms in HPS to understand science, analogously to (...) those employed in science to understand scientific domains. The paper argued for recognising at least two paradigms, one based on logic, and analytic forms more generally, the other based on deliberative judgement making. The present paper aims to use paradigmatic responses to Galison’s problems to explore the differing natures, merits and limitations of these two paradigms. This exploration also reveals the basic inadequacy of the analytic paradigm to illuminate the conduct of science, thereby permitting many of his problems to be dissolved rather than solved. (shrink)