Mixed mathematics and metaphysical physics: Descartes and the mechanics of the flow of water

Descartes' systematic physics had little to do with his quantitative accounts of natural phenomena. The former was metaphysical and was concerned with uncovering the causes operating in nature, while the latter dealt with establishing mathematical relations between various natural quantities. I reconstruct a dominant interpretation in recent literature which argues that the two practices are autonomous, and that quantitative problem-solving is normatively subordinated to metaphysical physics. However, a substantial episode of Descartes' practice resists these claims in an interesting way. Descartes' 1643 explanation of the flow of water should be, on the above reading, autonomous from metaphysically grounded physics or matter theory. Yet the explanation had unifying intentions: It is explicitly based on Descartes' laws of motion and considers the material properties of water. Additionally, because quantitative problem-solving should be subordinated to systematic physics, we would expect that Descartes' explanation is coherent with his physics of liquids. However, if we search for such a coherence, the autonomy between the two practices resurfaces as a problem. Even on a charitable reading, the physical features assumed and modelled in the 1643 explanation cannot be accounted for by Descartes' systematic physics. They are simply underdetermined in his natural philosophy. The outcome is that Descartes' quantitative solution navigated its way around the physical constraints in a creative and opportunistic fashion.