Kant-Studien 100 (1):1-27 (2009)
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
Similar books and articles
Completions, Constructions, and Corollaries.Thomas Mormann - 2009 - In H. Pulte, G. Hanna & H.-J. Jahnke (eds.), Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. Springer.
Reflections on Kant's Concept (and Intuition) of Space.Lisa Shabel - 2003 - Studies in History and Philosophy of Science Part A 34 (1):45-57.
Intuition and Immediacy in Kant's Critique of Pure Reason.Andrew Kelley - 1997 - Journal of Philosophical Research 22:289-298.
Coffa's Kant and the Evolution of Accounts of Mathematical Necessity.William Mark Goodwin - 2010 - Synthese 172 (3):361 - 379.
Mathematical Intuition Vs. Mathematical Monsters.Solomon Feferman - 2000 - Synthese 125 (3):317-332.
Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics.Pierre Cassou-Nogués - 2006 - Theoria 21 (1):89-104.
Added to index2009-04-07
Total downloads174 ( #25,679 of 2,158,287 )
Recent downloads (6 months)11 ( #32,227 of 2,158,287 )
How can I increase my downloads?