Kant’s Theory of Arithmetic: A Constructive Approach?

Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245-271 (2008)
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Abstract

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.

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Kristina Engelhard
Universität Trier

Citations of this work

Two Models of Kantian Construction.Aljoša Kravanja - 2023 - Journal of Transcendental Philosophy 4 (2):137-155.
Maimon's Post-Kantian Skepticism.Emily Fitton - 2017 - Dissertation, University of Essex

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References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Cambridge, MA, USA: MIT Press.
Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press. Edited by J. M. D. Meiklejohn. Translated by Paul Guyer & Allen W. Wood.
Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Kant's Transcendental Idealism.Henry E. Allison - 1988 - Yale University Press.

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