Newton’s Mathematics and Empiricism

Abstract

Abstract This article examines Newton’s approach to applying mathematics to natural evidence by attending to the proposals concerning space and mathematical knowledge that are presented in the unpublished pre-1687 manuscript De Gravitatione. In this work, Newton identifies the form of space studied in geometry with the empirically real form of space in which natural bodies are situated, and thereby collapses the classic Platonic divide between the certainty of mathematical knowledge and the uncertainty of empirical knowledge. As a result, the question of whether it is possible to apply mathematics to the empirical realm is not, for Newton, to be answered independently of mathematics. As shown in De Gravitatione, this application is part and parcel of the mathematical enterprise. To highlight the novelty of Newton’s blending of mathematics and empiricism, his views are contrasted with those put forward in Descartes’s Meditations on First Philosophy (1641) and Locke’s An Essay Concerning Human Understanding (1690).