Descartes' Mathematical Physics: Between Metaphysical Deduction and Mathematical Experiment

Abstract

This study analyzes the nature of Descartes' mathematical physics by examining the relationship he established between mathematics and physics during the scientific transformations of the 17th century. Descartes considered mathematics a model of certain knowledge and sought to use it in interpreting natural phenomena through deduction and experience within mechanistic and metaphysical frameworks. The research demonstrates that Descartes grounded his physics in first philosophy principles (cogito, causality, clarity of ideas), prioritizing innate ideas over experience—a key distinction from Galileo, who developed a mathematical physics independent of metaphysics. The study also reveals that rational certainty served as the foundation of physical truth for Descartes, resulting in internal coherence at the expense of empirical precision. The research concludes that Descartes was a transitional figure who bridged scholastic philosophy and mathematical modernity, and that his project helped establish mathematical physics as a cornerstone of modern science, despite the challenges it later posed to the development of experimental science.