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. (shrink)

This book provides a reading of Kant's theory of the construction of mathematical concepts through a fully contextualised analysis. In this work the author argues that it is only through an understanding of the relevant eighteenth century mathematics textbooks, and the related mathematical practice, that the material and context necessary for a successful interpretation of Kant's philosophy can be provided.

In the chapter of the Critique of Pure Reason entitled ‘The Discipline of Pure Reason in Dogmatic Use’, Kant contrasts mathematical and philosophical knowledge in order to show that pure reason does not (and, indeed, cannot) pursue philosophical truth according to the same method that it uses to pursue and attain the apodictically certain truths of mathematics. In the process of this comparison, Kant gives the most explicit statement of his critical philosophy of mathematics; accordingly, scholars have typically focused their (...) interpretations and criticisms of Kant’s conception of mathematics on this small section of the Critique. (shrink)

: Kant's 'argument from geometry' is usually interpreted to be a regressive transcendental argument in support of the claim that we have a pure intuition of space. In this paper I defend an alternative interpretation of this argument according to which it is rather a progressive synthetic argument meant to identify and establish the essential role of pure spatial intuition in geometric cognition. In the course of reinterpreting the 'argument from geometry' I reassess the arguments of the Aesthetic and illustrate (...) the origin of Kant's view of the role of pure intuition in geometry. (shrink)

In this paper, I investigate an important aspect of Kant’s theory of pure sensible intuition. I argue that, according to Kant, a pure concept of space warrants and constrains intuitions of finite regions of space. That is, an a priori conceptual representation of space provides a governing principle for all spatial construction, which is necessary for mathematical demonstration as Kant understood it.Author Keywords: Kant; Space; Pure sensible intuition; Philosophy of mathematics.

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. (shrink)

In the 17th and 18th centuries, mathematics was understood to be the science that systematized our knowledge of magnitude, or quantity. But the mathematical notion of magnitude and the methods used to investigate it underwent a period of radical transformation during the modern period, which forced philosophers of mathematics to confront a changing mathematical landscape. In this context, the modern philosopher of mathematics had to provide an account of the apriority and applicability of mathematical reasoning, as such reasoning was then (...) understood. Early modern mathematical reasoning and the accounts of such reasoning offered by Newton, Descartes, Leibniz, and Kant are explained and discussed. (shrink)

In this interesting and engaging book, Shabel offers an interpretation of Kant's philosophy of mathematics as expressed in his critical writings. Shabel's analysis is based on the insight that Kant's philosophical standpoint on mathematics cannot be understood without an investigation into his perception of mathematical practice in the seventeenth and eighteenth centuries. She aims to illuminate Kant's theory of the construction of concepts in pure intuition—the basis for his conclusion that mathematical knowledge is synthetic a priori. She does this through (...) a contextualized interpretation of his notion of mathematical construction, which she argues can be approached by looking at Euclid's Elements and Christian Wolff's mathematical textbooks. The importance of the former for her interpretation is justified by the fact that nearly all of Kant's mathematical examples in the Critique are Euclidean propositions. The importance of the latter is revealed through the fact that Wolff's textbooks were not only widely read and representative of the state of elementary mathematics during Kant's time; Kant was also intimately familiar with them. During the thirty years prior to the publication of the Critique, he used the textbooks in the college-level introductory courses in mathematics and physics that he taught.In the introduction to her book, Shabel helpfully distinguishes her approach to Kant's philosophy of mathematics from that of previous commentators. She points out that most commentators assessed Kant's thoughts on mathematics in terms of the ‘supposedly devastating effects of the discovery of non-Euclidean geometry on his theory of space’.1 Bertrand Russell, for example, criticized Kant for his lack of a proper …. (shrink)