Poincaré and the Philosophy of Mathematics (Studies in Contemporary Philosophy)

This book is a sympathetic reconstruction of Henri Poincar's anti-realist philosophy of mathematics. Although Poincar is recognized as the greatest mathematician of the late 19th century, his contribution to the philosophy of mathematics is not highly regarded. Many regard his remarks as idiosyncratic, and based upon a misunderstanding of logic and logicism. This book argues that Poincar's critiques are not based on misunderstanding; rather, they are grounded in a coherent and attractive foundation of neo-Kantian constructivism. Front Matter....Pages i-xvii Kant and Mathematics, an Outline....Pages 1-29 Introduction to Poincaré’s Theory of the Synthetic A Priori....Pages 30-40 Defending Mathematical Apriorism....Pages 41-70 Logic and Intuition....Pages 71-92 The Attack on Logicism....Pages 93-111 Set Theory and the Continuum....Pages 112-144 Poincaré’s Theory of Predicativity....Pages 145-173 Poincaré’s Theory of Meaning....Pages 174-189 Conclusion....Pages 190-192 Back Matter....Pages 193-202