Kant's theory of arithmetic: A constructive approach? [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245 - 271 (2008)
Kant’s theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant’s theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant’s theory of arithmetic can be picked up, improved by reconstruction and defended under a contemporary perspective: the theory of numbers as products of rule following construction presupposing successive synthesis in time and the theory of arithmetic equations, sentences or “formulas”—as Kant says—as synthetic a priori. In order to do so, two calculi in terms of modern mathematics are introduced which formalise Kant’s theory of addition as a form of synthetic operation.
|Keywords||Kant Arithmetic Construction Numbers Time|
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References found in this work BETA
W. V. Quine (1960). Word and Object. The MIT Press.
Henry E. Allison (2004). Kant's Transcendental Idealism. Yale University Press.
Immanuel Kant (1998). Critique of Pure Reason (Translated and Edited by Paul Guyer & Allen W. Wood). Cambridge.
Béatrice Longuenesse (1998). Kant and the Capacity to Judge: Sensibility and Discursivity in the Transcendental Analytic of the "Critique of Pure Reason". Princeton University Press.
John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.
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