Naturalizing Logico-Mathematical Knowledge

<p>This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. <i>Naturalizing Logico-Mathematical Knowledge </i>contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.</p> <p>1. Introduction. A Naturalist Landscape <i>Sorin Bangu</i></p><p>2. Psychology and the A Priori Sciences <i>Penelope Maddy</i></p><p>3. Reasoning, Rules, and Representation <i>Paul D. Robinson and Richard Samuels</i></p><p>4. Numerical Cognition and Mathematical Knowledge: The Plural Property View <i>Byeong-uk Yi</i></p><p>5. Intuitions, Naturalism, and Benacerraf’s Problem <i>Mark Fedyk</i></p><p>6. Origins of Numerical Knowledge <i>Karen Wynn</i></p><p>7. What Happens When a Child Learns to Count?: The Development of the Number Concept <i>Kristy vanMarle</i></p><p>8. Seeing Numbers as Affordances <i>Max Jones</i></p><p>9. Testimony and Children’s Acquisition of Number Concepts <i>Helen De Cruz</i></p><p>10. Which Came First, the Number or the Numeral? <i>Jean-Charles Pelland</i></p><p>11. Numbers through Numerals: The Role of External Representations <i>Dirk Schlimm</i></p><p>12. Making Sense of Numbers without a Number Sense <i>Karim Zahidi and Erik Myin</i></p><p>13. Beyond Peano: Looking Into the Unnaturalness of Natural Numbers <i>Josephine Relaford-Doyle and Rafael Núñez</i></p><p>14. Beauty and Truth in Mathematics: Evidence from Cognitive Psychology <i>Rolf Reber</i></p><p>15. Mathematical Knowledge, the Analytic Method, and Naturalism <i>Fabio Sterpetti</i></p>