Three Infinities in Early Modern Philosophy

Abstract

Abstract Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three central figures in the period: Locke (for quantitative infinity), Descartes (ontic infinity), and Leibniz (iterative infinity).