Kant's Philosophy of Mathematics: The Critical Philosophy and Its Roots

Cambridge University Press, 9/2/2021
EAN 9781108717083, ISBN10: 110871708X

Paperback, 332 pages, 22.9 x 15.2 x 1.9 cm
Language: English
Originally published in English

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.