Kant: Studies on Mathematics in the Critical Philosophy Studies on Mathematics in the Critical Philosophy

There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason, Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason, Kant compares the Formula of Universal Law, central to his theory of moral judgement, to a mathematical postulate; in the Critique of Judgement, where he considers aesthetic judgment, Kant distinguishes the mathematical sublime from the dynamical sublime. This last point rests on the distinction that shapes the Transcendental Analytic of Concepts at the heart of Kant’s Critical philosophy, that between the mathematical and the dynamical categories. These examples make it clear that Kant's transcendental philosophy is strongly influenced by the importance and special status of mathematics. The contributions to this book explore this theme of the centrality of mathematics to Kant’s philosophy as a whole. This book was originally published as a special issue of the Canadian Journal of Philosophy.

Introduction Emily Carson and Lisa Shabel 1. Spatial representation, magnitude and the two stems of cognition Thomas Land 2. Infinity and givenness: Kant on the intuitive origin of spatial representation Daniel Smyth 3. Kant on the Acquisition of Geometrical Concepts John J. Callanan 4. Kant (vs. Leibniz, Wolff and Lambert) on real definitions in geometry Jeremy Heis 5. Definitions of Kant’s categories Tyke Nunez 6. Arbitrary combination and the use of signs in mathematics: Kant’s 1763 Prize Essay and its Wolffian background Katherine Dunlop 7. Kant on the construction and composition of motion in the Phoronomy Daniel Sutherland 8. Kant on conic sections Alison Laywine 9. ‘With a Philosophical Eye’: the role of mathematical beauty in Kant’s intellectual development Courtney David Fugate

Emily Carson is Associate Professor of Philosophy at McGill University, Montreal, Canada. She works in early modern philosophy, with a focus on Kant and the philosophy of mathematics, and is a member of the Editorial Board of the Canadian Journal of Philosophy. Lisa Shabel is Associate Professor in the Department of Philosophy at Ohio State University, Columbus, USA. Her primary interests are in the history and philosophy of mathematics and Kant’s Critical philosophy.