Philosophische Zeitschrift der Kant-Gesellschaft
Ed. by Baum, Manfred / Dörflinger, Bernd / Klemme, Heiner F.
SCImago Journal Rank (SJR) 2014: 0.161
Source Normalized Impact per Paper (SNIP) 2014: 0.421
Impact per Publication (IPP) 2014: 0.115
Kant on Geometrical Intuition and the Foundations of Mathematics
Citation Information: Kant-Studien. Volume 100, Issue 1, Pages 1–27, ISSN (Online) 1613-1134, ISSN (Print) 0022-8877, DOI: 10.1515/KANT.2009.001, April 2009
- Published Online:
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.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.