Kurt Smith. “Was Descartes's Physics Mathematical?” History of Philosophy Quarterly, 20 (3): 245–256. 2003.

Extract:

One aim of a mathematical physics is to produce equations. Descartes’s physics does not, and some will even argue can not, produce mathematical equations?at least, there is no systematic procedure for doing so. Any equations that he does produce seem at best to be produced ad hoc. Explanations are rooted entirely in his metaphysics and are not mathematical in form. To be sure, Descartes’s Optics meets the standard of a mathematical project, but the mathematization in his treatment of light is limited to this particular subject and does not extend itself to his physics as a whole. And so, although Descartes’s Optics was mathematical, his physics was not. This conclusion is intended by many commentators to be a criticism. For, given Descartes’s insight into the possibility of a mathematical physics, this conclusion is supposed to point out his failure to bring this insight to fruition. The first section of this paper discusses what it is for a physics to be mathematical. It is argued that a quantitative physics is a mathematical one. Working from the position that Descartes’s physics meets the necessary criteria for being a quantitative physics, the second section discusses how a quantitative physics and the possibility of constructing equations are connected. It is argued that the connection is rooted in a specific sort of conceptual scheme that Descartes calls an “enumeration.” A sketch of how Descartes’s physics can, and in fact does, produce and support mathematical equations is offered. Lastly, the paper takes a brief but critical look at how Leibniz reacted

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