Historians of fourteenth-century science have long recognized the extraordinary work at both Oxford and Paris in which natural philosophy was becoming highly mathematical. The movement to subject natural philosophy to a mathematical analysis and to quantify such qualities as heat, color, and of course speed surely stands as one of the most significant aspects of late medieval science. Yet as Edith Sylla has observed, because qualities and quantities pertain to different categories in Aristotelian theory, one might expect Aristotelian theorists to (...) avoid quantifying qualities. Even more serious still, the very task of quantifying physical qualities exposes a tension in the nature of science that was discussed first by Aristotle in his Posterior Analytics. (shrink)

The article investigates the role of symbolic means of knowledge representation in concept development using the historical example of medieval diagrams of change employed in early modern work on the motion of fall. The parallel cases of Galileo Galilei, Thomas Harriot, and René Descartes and Isaac Beeckman are discussed. It is argued that the similarities concerning the achievements as well as the shortcomings of their respective work on the motion of fall can to a large extent be attributed to their (...) shared use of means of knowledge representation handed down from antiquity and the Middle Ages. While the interpretation of medieval diagrams was unproblematic in the scholastic context from which they arose, in the early modern context, which was characterized by the confluence of natural philosophy and practical mathematics, it became ambiguous. It was the early modern mathematicians’ work within this contradictory framework that brought about a new conceptualization of motion which, in particular, eventually led to an infinitesimal concept of velocity. In this process, the diagrams themselves remained largely unchanged and thus functioned as a catalyst for concept development. (shrink)