Kant on geometry and spatial intuition Article First Online: 07 March 2012 Received: 14 January 2010 Accepted: 27 July 2010 DOI :
10.1007/s11229-012-0066-2

Cite this article as: Friedman, M. Synthese (2012) 186: 231. doi:10.1007/s11229-012-0066-2
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Abstract I use recent work on Kant and diagrammatic reasoning to develop a reconsideration of central aspects of Kant’s philosophy of geometry and its relation to spatial intuition. In particular, I reconsider in this light the relations between geometrical concepts and their schemata, and the relationship between pure and empirical intuition. I argue that diagrammatic interpretations of Kant’s theory of geometrical intuition can, at best, capture only part of what Kant’s conception involves and that, for example, they cannot explain why Kant takes geometrical constructions in the style of Euclid to provide us with an a priori framework for physical space. I attempt, along the way, to shed new light on the relationship between Kant’s theory of space and the debate between Newton and Leibniz to which he was reacting, and also on the role of geometry and spatial intuition in the transcendental deduction of the categories.

Keywords Geometry Diagrammatic reasoning Space Intuition Schematism Transcendental deduction An earlier version of this paper was presented at the second meeting of the Stanford-Paris workshop on diagrams in mathematics in the Fall of 2008 from which the present special issue is drawn, and it was originally inspired by a paper presented by Marco Panza on diagrammatic reasoning in Euclid at the first meeting of the Stanford-Paris workshop in the Fall of 2007. Panza’s paper in the present issue is based, in turn, on his earlier presentation. Since Panza’s paper, as it now appears, has since been substantially revised, I have taken the opportunity substantially to revise my paper as well, and, in particular, I have chosen to take as my main target work of the Kant scholar Lisa Shabel that is very much in the spirit of Kenneth Manders’s original discussion of the Euclidean diagram (note 1 below). I am also indebted, in this connection, to comments on the earlier version of my paper from Jeremy Avigad. For helpful comments on the penultimate version of this paper I am further indebted to Daniel Sutherland and to an anonymous referee for Synthese .

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Authors and Affiliations 1. Department of Philosophy Stanford University Stanford USA