Platonism, Naturalism, and Mathematical Knowledge by Brown, James Robert;

Short description:

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.

Long description:

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.

"Brown argues that mathematics does not explain physical phenomena in the sense of accounting for them, but that it does explain them in the sense of making them comprehensible...this is a clear and engaging book, mainly for professional philosophers or graduate students in philosophy, that contains many on-target criticisms of naturalism." - A.C. Paseau, Wadham College, University of Oxford, UK in Philosophia Mathematica

"Brown’s book is a useful addition to recent debates in the philosophy of mathematics." - Christopher Pincock, The Ohio State University, US in Mind

Table of Contents:

Preface  1. Mathematical Explanation  2. What is Naturalism?  3. Perception, Practice, and Ideal Agents: Kitcher’s Naturalism  4. Just Metaphor?: Lakoff’s Language  5. Seeing with the Mind’s Eye: The Platonist Alternative  6. Semi-Naturalists and Reluctant Realists  7. A Life of its Own?: Maddy and Mathematical Autonomy  8. Afterword