INTRODUCTION

In 1686, in a short article published in the Acta Eruditorum and titled “A Brief Demonstration of Memorable Errors of Descartes and Others Concerning a Natural Law,” Leibniz claimed to demonstrate that one of Descartes's fundamental laws of motion was false. Specifically, Descartes held that, due to God's immutability, the ‘quantity of motion’ in the world must be conserved, where the quantity of motion was to be represented as the product of the size and the speed of matter in motion. Translated into contemporary terms and modified somewhat, this quantity is called ‘momentum’ and is represented by mv. Moreover, Descartes's law of the conservation of the quantity of motion formed an integral part of his broader philosophical position, not only because it followed immediately, on his view, from the necessity of God's immutable nature, but also because it had to be consistent with Descartes's distinctive and rather restrictive account of the nature of matter, namely as consisting solely in extension, including its modes, such as size, shape, place, and changes therein such as motion. For whatever quantity God conserves in the world must be a quantity that matter actually has, and since size and velocity are modes of extension, Descartes's account of matter goes hand in hand with his conservation law. As a consequence, however, if Leibniz's objection to Descartes's conservation law is correct, then it does not concern an inessential detail of Descartes's position, but rather goes to the heart of his natural philosophy and entails that significant features of that account must be rejected.