David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Margit Ruffing (2011). Kant-Bibliographie 2009. Kant-Studien 102 (4):499-540.
Similar books and articles
Alexander George (ed.) (1994). Mathematics and Mind. Oxford University Press.
Thomas Mormann (2009). Completions, Constructions, and Corollaries. In H. Pulte, G. Hanna & H.-J. Jahnke (eds.), Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. Springer
Lisa Shabel (2003). Reflections on Kant's Concept (and Intuition) of Space. Studies in History and Philosophy of Science Part A 34 (1):45-57.
Jaakko Hintikka (1972). III. Kantian Intuitions. Inquiry 15 (1-4):341 – 345.
Andrew Kelley (1997). Intuition and Immediacy in Kant's Critique of Pure Reason. Journal of Philosophical Research 22:289-298.
William Mark Goodwin (2010). Coffa's Kant and the Evolution of Accounts of Mathematical Necessity. Synthese 172 (3):361 - 379.
Solomon Feferman (2000). Mathematical Intuition Vs. Mathematical Monsters. Synthese 125 (3):317-332.
Michael Dummett (1982). Frege and Kant on Geometry. Inquiry 25 (2):233 – 254.
Pierre Cassou-Nogués (2006). Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics. Theoria 21 (1):89-104.
Michael Friedman (2012). Kant on Geometry and Spatial Intuition. Synthese 186 (1):231-255.
Added to index2009-04-07
Total downloads152 ( #11,530 of 1,725,611 )
Recent downloads (6 months)2 ( #268,736 of 1,725,611 )
How can I increase my downloads?