Kant's Mathematical World: Mathematics, Cognition, and Experience

by Daniel Sutherland

Overview

Kant's Mathematical World aims to transform our understanding of Kant's philosophy of mathematics and his account of the mathematical character of the world. Daniel Sutherland reconstructs Kant's project of explaining both mathematical cognition and our cognition of the world in terms of our most basic cognitive capacities. He situates Kant in a long mathematical tradition with roots in Euclid's Elements, and thereby recovers the very different way of thinking about mathematics which existed prior to its 'arithmetization' in the nineteenth century. He shows that Kant thought of mathematics as a science of magnitudes and their measurement, and all objects of experience as extensive magnitudes whose real properties have intensive magnitudes, thus tying mathematics directly to the world. His book will appeal to anyone interested in Kant's critical philosophy — either his account of the world of experience, or his philosophy of mathematics, or how the two inform each other.

Product Details

ISBN-13:	9781108455107
Publisher:	Cambridge University Press
Publication date:	10/19/2023
Pages:	315
Product dimensions:	6.00(w) x 9.00(h) x 0.66(d)

About the Author

Daniel Sutherland is Associate Professor of Philosophy at the University of Illinois at Chicago. He has published numerous articles on Kant's philosophy of mathematics and science, including their relation to Euclid, Newton, Leibniz, Frege, and others.

Table of Contents

Preface and acknowledgements; 1. Introduction: mathematics and the world of experience; Part I. Mathematics, Magnitudes and the Conditions of Experience: 2. Space, time and mathematics in the Critique of Pure Reason; 3. Magnitudes, mathematics, and experience in the Axioms of Intuition; 4. Extensive and intensive magnitudes and continuity; 5. Conceptual and intuitive representation: singularity, continuity, and concreteness; Interlude: the Greek mathematical tradition as background to Kant: 6. Euclid, the Euclidean mathematical tradition, and the theory of magnitudes; Part II. Kant's Theory of Magnitudes and the Role of Intuition: 7. Kant's reworking of the theory of magnitudes; 8. Kant's reformation of the metaphysics of quantity; 9. From mereology to mathematics; 10. Concluding remarks; Bibliography; Index.

Editorial Reviews

‘Daniel Sutherland's Kant's Mathematical World is a remarkable scholarly achievement. The meticulously detailed analysis of Kant's theory of magnitude opens up into a comprehensive account of the mathematical character of experience, shedding new light on virtually every aspect of the first Critique and engaging with many of the liveliest current debates surrounding it. It is essential reading for scholars of Kant's theoretical philosophy.' Emily Carson, McGill University

‘simply outstanding … Highly recommended.’ D. C. Kolb, Choice Connect

From the Publisher