Emily Carson – författare

The mathematical method and the nature of mathematical knowledge were subjects of intense philosophical discussion in the 17th and 18th centuries. In particular, there was a debate over whether metaphysical truths admit of distinct proof as geometrical truths do, and whether they may be known with the same degree of certainty. This comparison between geometry and philosophy required a proper understanding of how Euclidean demonstration secured certainty. This element examines attempts by Descartes, Locke, Leibniz, Wolff, Lambert, Mendelssohn and Kant to address this question. The emphasis is on metaphysical and epistemological questions about geometrical demonstration in the 17th- and 18th-centuries.

The mathematical method and the nature of mathematical knowledge were subjects of intense philosophical discussion in the 17th and 18th centuries. In particular, there was a debate over whether metaphysical truths admit of distinct proof as geometrical truths do, and whether they may be known with the same degree of certainty. This comparison between geometry and philosophy required a proper understanding of how Euclidean demonstration secured certainty. This element examines attempts by Descartes, Locke, Leibniz, Wolff, Lambert, Mendelssohn and Kant to address this question. The emphasis is on metaphysical and epistemological questions about geometrical demonstration in the 17th- and 18th-centuries.

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.

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.

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.