Descartes and His Critics on Conserved Rectilinear Motion

David Marshall Miller

Iowa State University

The modern principle of rectilinear inertia—uniform rectilinear motion is conserved—is often attributed to Descartes. But where in Descartes’s work is the modern principle found? I argue that the commonly accepted locus of attribution is misplaced. The origin of rectilinear inertia is not to be found in the mature metaphysics of the Principles of Philosophy, but rather in Descartes’s physical work, specifically in his Optics. From early in his career, Descartes held that a motion is conserved. The question at issue here is how Descartes coordinated that explanatory tenet with phenomena. That is, what did Descartes count as ‘a motion’? The modern theory of inertia includes two fundamental suppositions. First, ‘motion’ is a directed quantity, such that changing the direction changes the motion. Second, parallel directions are identified, such that two bodies moving parallel to one another are said to move in the same direction. A conserved motion is therefore a uniform rectilinear translation—a constant displacement directed along a path that is always parallel to itself. But did Descartes accept these components of the modern theory? If so, where do they appear in his works? Many authors (e.g., Garber, Schmaltz, Gaukroger, Machamer and McGuire) locate the inertial principle in Descartes’s mature metaphysics of body and motion. They point to the Principles of Philosophy’s first two Laws of Nature, derived from divine immutability and the nature of body, as a statement of the inertial principle. However, the first two Laws separate ‘motion’ from ‘direction’ or (in Descartes’s idiom) ‘determination’: the first Law says that motion alone is conserved; the second Law says that bodies tend to move rectilinearly. Hence, the Laws do not require that motion is directed and that unidirectional motion is rectilinear. Indeed, Descartes admits cases, such as vortices, that satisfy the Laws but violate the modern principle. Descartes’s Laws of Nature are not equivalent to rectilinear inertia, and cannot be its origin. However, in the earlier Optics, Descartes had presumed both that motion is a directed quantity and that the directions of parallel displacements are to be identified. The Optics therefore contains an implicit version of the modern principle. (Explicitly, Descartes distinguishes motion from its direction—the distinction that persists in his later work.) The necessity of rectilinear inertia for the validity of the proofs was recognized by Descartes’s contemporary critics. Remarking on Descartes’s discussion, Pierre de Fermat brought the implicit assumption into the open. The conservation of rectilinear motion was then formalized as a fundamental physical principle by Gilles Personne de Roberval. Thus, Descartes is indeed the source of the modern principle of rectilinear inertia, but it emerged from his physical science, in opposition to his systematic metaphysics. Rectilinear inertia became the foundation of modern physics both because of Descartes and in spite of him.