To mark the publication of a new translation of Jean Cavaillès’s On Logic and the Theory of Science, Robin Mackay is joined by Knox Peden and Matt Hare to provide an introduction to Cavaillès's philosophical project for the uninitiated, and to examine what is at stake in On Logic’s confrontation with Kantianism, logicism, and Husserlian phenomenology. Among the many subjects covered in this wide-ranging conversation: optimism, extreme protestantism, and Spinozism; Heidegger and Cassirer’s Davos debate; mathematics as a necessary dynamism; the virtues and vices of phenomenology; philosophical style and the ethics of concision; foucault, archaeology, and the historical a priori; life and rational activity; abnegation in life and in thought; Cavaillès’s philosophical legacy and how reading his work ‘fundamentally changes our understanding of 20th-Century French philosophy’. Music: ‘23’ from Newtables by SND (SNDSE2)