On Isaac Newton's Concept of Mathematical Force

This dissertation presents a philosophical and developmental account of the mathematical conceptualization of force in Isaac Newton’s writings, starting from the early dynamical writings in the 1660s and ending with the first edition of the Principia of 1687. Broadly speaking, this project is a contribution to the epistemology and metaphysics comprised in (i) the mathematical practices underlying the birth of dynamics and (ii) the philosophical foundations of the transition from natural philosophy to mathematical physics. As a project in the history of ideas, it casts a new light on the foundations of modern science by focusing on the conceptualization of force as a mathematical quantity. As a contribution to the philosophy of science, it introduces a novel understanding of Newton’s philosophy of science centered on the use of what have come to be called models based on mathematical concepts.