Platonism, Naturalism, and Mathematical Knowledge
Routledge – 2012 – 182 pages
This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.
Preface 1. Mathematical Explanation 2. What is Naturalism? 3. Perception, Practice, and Ideal Agents: Kitcher’s Naturalism 4. Just Metaphor?: Lakoff’s Language 5. Semi-Naturalists and Reluctant Realists 6. A Life of its Own?: Maddy and Mathematical Autonomy 7. Seeing with the Mind’s Eye: The Platonist Alternative 8. Afterword
James Robert Brown is Professor of Philosophy at the University of Toronto. His interests include foundational issues in mathematics and physics, thought experiments, and the relations of science to society. Recent books include: Who Rules? An Opinionated Guide to the Epistemology and Politics of the Science Wars, Harvard, and new editions of The Laboratory of the Mind: Thought Experiments in the Natural Sciences, Routledge, and Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures, Routledge.