This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists.
Comment (from this Blueprint): This book by Dutilh Novaes recently won the coveted Lakatos Award. In it, she develops a dialogical account of deduction, where she argues that deduction is implicitly dialogical. Proofs represent dialogues between Prover, who is aiming to establish the theorem, and Skeptic, who is trying to block the theorem. However, the dialogue is both partially adversarial (the two characters have opposite goals) and partially cooperative: the Skeptic’s objections make sure that the Prover must make their proof clear, convincing, and correct. In this chapter, Dutilh Novaes applies her model to mathematical practice, and looks at the way social features of maths embody the Prover-Skeptic dialogical model.