Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter April 5, 2009

Kant on Geometrical Intuition and the Foundations of Mathematics

  • Frode Kjosavik
From the journal Kant-Studien

Abstract

It is argued that geometrical intuition, as conceived in Kant, is still crucial to the epistemological foundations of mathematics. For this purpose, I have chosen to target one of the most sympathetic interpreters of Kant's philosophy of mathematics – Michael Friedman – because he has formulated the possible historical limitations of Kant's views most sharply. I claim that there are important insights in Kant's theory that have survived the developments of modern mathematics, and thus, that they are not so intrinsically bound up with the logic and mathematics of Kant's time as Friedman will have it. These insights include the idea that mathematical knowledge relies on the manipulation of objects given in quasi-perceptual intuition, as Charles Parsons has argued, and that pure intuition is a source of knowledge of space itself that cannot be replaced by mere propositional knowledge. In particular, it is pointed out that it is the isomorphism between Kantian intuition and a spatial manifold that underlies both the epistemic intimacy of the most fundamental type of geometrical intuition as well as that of perceptual acquaintance.

Published Online: 2009-04-05
Published in Print: 2009-March

© Walter de Gruyter 2009

Downloaded on 19.3.2024 from https://www.degruyter.com/document/doi/10.1515/KANT.2009.001/html
Scroll to top button