Kant's Philosophy of Mathematics: Volume 1, The Critical Philosophy and its Roots The Critical Philosophy and Its Roots

The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant.

Introduction; Part I. Roots: 1. Kant and Mendelssohn on the use of signs in mathematics Katherine Dunlop; 2. Of griffins and horses: mathematics, metaphysics and Kant's critical turn Carl Posy; 3. Kant on mathematics and the metaphysics of corporeal nature: the role of the infinitesimal Daniel Warren; Part II. Method and Logic: 4. Kant's theory of mathematics: what theory of what mathematics? Jaakko Hintikka; 5. Singular terms and intuitions in Kant: a reappraisal Mirella Capozzi; 6. Kant and the character of mathematical inference Desmond Hogan; Part III. Space and Geometry: 7. Kant on parallel lines: definitions, postulates, and axioms Jeremy Heis; 8. Continuity, constructibility, and intuitivity Gordon Brittan; 9. Space and geometry in the B deduction Michael Friedman; Part IV. Arithmetic and Number: 10. Arithmetic and the conditions of possible experience Emily Carson; 11. Kant's philosophy of arithmetic: an outline of a new approach Daniel Sutherland; 12. The critique of pure reason on arithmetic W. W. Tait.

Carl Posy is Professor Emeritus of Philosophy at the Hebrew University of Jerusalem. He is editor of Kant's Philosophy of Mathematics: Modern Essays (1992) and has written extensively on the philosophy of mathematics as well as on Kant.
Ofra Rechter is a member of the philosophy department at Tel-Aviv University. Her work focuses on Kant within the philosophy of mathematics and its history, and she has published a number of papers on Kant's philosophy of arithmetic.