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.