Journal for General Philosophy of Science

, Volume 39, Issue 2, pp 245–271

Kant’s Theory of Arithmetic: A Constructive Approach?


DOI: 10.1007/s10838-008-9072-y

Cite this article as:
Engelhard, K. & Mittelstaedt, P. J Gen Philos Sci (2008) 39: 245. doi:10.1007/s10838-008-9072-y


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.


Kant Arithmetic Construction Numbers Time 

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Philosophisches Seminar der Universität zu KölnKölnGermany
  2. 2.Institut für Theoretische Physik der Universität zu KölnKölnGermany

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