DIAPHORA was a joint European research and training platform for collaborative research on the nature of philosophical problems, their resilience, the sources of persistent divergence of expert opinion about their resolution, and the similarities and dissimilarities they bear to certain hard problems in the practical sphere that would likewise seem to give rise to persistent disagreement among the well-informed. DIAPHORA’s research programme was driven by three overarching objectives: to diagnose what makes philosophical problems so resilient and to clarify to what extent the sustained lack of convergence in philosophy can successfully be explained by the hardness of its problems; to explain why the tendency has not been towards a general agnosticism about candidate solutions, but rather towards divergence, and to identify features of philosophical method that allow for such persistent peer disagreement; and to explore whether the dynamics of philosophical debate bears important and instructive resemblances to the dynamics of debates about more practical matters. The network resolved to approach these issues, from the bottom up, by studying particularly hard philosophical problems arising in the philosophies of logic and language, metaphysics and epistemology, by clarifying the structure and preconditions of reasoned debate itself, and by interacting with non-academic players in the practical sphere. It offered different diagnoses for different areas of philosophical thought. In many such areas, much of the work of philosophers consists in the rational reconstruction of extant theories, and the discernment of viable, perhaps hitherto unexplored alternatives. Progress does not here consist in convergence on a single theory, but recognition of the range of epistemically possible alternatives. In other areas of philosophy, theories are often laced with normative and axiological considerations whose relevance in each case is a matter of negotiation whose outcome helps to shape the subject matter. In yet other areas, a high degree of specialisation, the need for idealisation in the construction of models, and the precisification of research questions often conceal that progress is being made, but in the end are the symptoms of a mature and healthy science.