Apriority and Application: Philosophy of Mathematics in the Modern Period

In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press. pp. 29--50 (2005)
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Abstract

In the 17th and 18th centuries, mathematics was understood to be the science that systematized our knowledge of magnitude, or quantity. But the mathematical notion of magnitude and the methods used to investigate it underwent a period of radical transformation during the modern period, which forced philosophers of mathematics to confront a changing mathematical landscape. In this context, the modern philosopher of mathematics had to provide an account of the apriority and applicability of mathematical reasoning, as such reasoning was then understood. Early modern mathematical reasoning and the accounts of such reasoning offered by Newton, Descartes, Leibniz, and Kant are explained and discussed.

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10.1093/0195148770.003.0002

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Lisa Shabel
Ohio State University

Citations of this work

Spatial representation, magnitude and the two stems of cognition.Thomas Land - 2014 - Canadian Journal of Philosophy 44 (5-6):524-550.
Kant and Newton on the a priori necessity of geometry.Mary Domski - 2013 - Studies in History and Philosophy of Science Part A 44 (3):438-447.
Kant Versus Frege on Arithmetic.Nora Grigore - 2022 - Axiomathes 32 (2):263-281.

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The Senses and the Fleshless Eye: The Meditations as Cognitive Exercises.Gary Hatfield - 1986 - In Amélie Rorty (ed.), Rorty. Univ of California Press. pp. 45–76.

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