This book presents a historical and critical study of a controversy that raged among all the leading figures of early modern natural philosophy. The issue at stake is the constitution and internal architecture of matter. On the one hand, an array of a priori arguments seems to show that matter must be infinitely divisible: it must be fundamentally continuous and altogether without simple first parts. On the other hand, an opposing battery of a priori arguments seems to show that matter cannot be divisible ad infinitum: it must be fundamentally discrete in its fine structure, resolving to a finite base of logically unsplittable first elements.
The conflict between these rival sets of arguments greatly discomfited philosophers of the seventeenth and eighteenth centuries. Since arguments on both sides of the question seemed compelling, the clash between them appeared to expose a paradox or antinomy in the new world-view pioneered by Galileo, Descartes, and Newton. The new science's account of a fundamentally geometrical Creation, mathematicizable and intelligible to the human inquirer, seemed to be under threat. This was of course a great scandal, and the philosophers of the period accordingly made various attempts to disarm the conflict and resolve the paradox. All the great figures address the issue: most famously Leibniz ('the labyrinth of the continuum') and Kant (the 'Second Antinomy'), but also Galileo, Descartes, Newton, and Hume, in addition to a crowd of lesser figures. This book ties together all of these discussions and offers an overarching interpretation of the controversy.
A pivotal interpretative thesis of this study is that the historical debate turns crucially on certain metaphysical doctrines concerning the status of material parts. The problems of infinite divisibility in fact brought out an underlying tension at the heart of early modern natural philosophy, between the geometrization of Nature on the one hand, and the dominant metaphysical account of material parts on the other. This interpretation can be contrasted with a rival view of the early modern controversy over