Rene Descartes (1596 – 1650) is considered the founder of modern philosophy. Profoundly influenced by the new physics and astronomy of Kepler and Galileo, Descartes was a scientist and mathematician whose most long-lasting contributions in science were the invention of Cartesian coordinates, the application of algebra to geometry, and the discovery of the law of refraction, what we now call Snell’s law.His most important books on philosophy were The discourse on method(1637) and The meditations(1642). Descartes’ writings display an exemplary degree (...) of clarity and an aversion to pedantry. I explore Descartes' break with Aristotle, but also shine a light on the intellectual continuity Descartes had with Aristotle's thought. I also draw attention to some overlooked but interesting possibilities for an experimental test of a dualistic theory of mind. (shrink)

: Although Galileo's struggle to mathematize the study of nature is well known and oft discussed, less discussed is the form this struggle takes in relation to Galileo's first new science, the science of the second day of the Discorsi. This essay argues that Galileo's first science ought to be understood as the science of matter—not, as it is usually understood, the science of the strength of materials. This understanding sheds light on the convoluted structure of the Discorsi's first day. (...) It suggests that the day's meandering discussions of the continuum, infinity, the vacuum, and condensation and rarefaction establish that a formal treatment of the "eternal and necessary" properties of matter is possible; i.e., that matter as such can be considered mathematically. This would have been a necessary, and indeed revolutionary, preliminary to the mathematical science of the second day because matter itself was thought in the Aristotelian tradition to be responsible for the departure of natural bodies from the unchanging and thus mathematizable character of abstract objects. In addition, the first day establishes that when considered physically, these properties account for matter's force of cohesion and resistance to fracture. This essay closes by showing that this dual style of reasoning accords with the conceptual structure of mixed mathematics. (shrink)