Kant on geometry and spatial intuition

Synthese 186 (1):231-255 (2012)
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
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DOI 10.1007/s11229-012-0066-2
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References found in this work BETA
Kant's Transcendental Idealism.Henry E. Allison - 2004 - Yale University Press.
Kant and the Exact Sciences.Michael Friedman - 1992 - Harvard University Press.
Kant on Arithmetic, Algebra, and the Theory of Proportions.Daniel Sutherland - 2006 - Journal of the History of Philosophy 44 (4):533-558.
Kant on the `Symbolic Construction' of Mathematical Concepts.Lisa Shabel - 1998 - Studies in History and Philosophy of Science Part A 29 (4):589-621.

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Citations of this work BETA
The Kantian (Non)‐Conceptualism Debate.Colin McLear - 2014 - Philosophy Compass 9 (11):769-790.
Self-Affection and Pure Intuition in Kant.Jonas Jervell Indregard - 2017 - Australasian Journal of Philosophy:1-17.
Spatial Representation, Magnitude and the Two Stems of Cognition.Thomas Land - 2014 - Canadian Journal of Philosophy 44 (5-6):524-550.

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