Between Nature and Analysis: On the History of the Law of Continuity in the XVIIIth Century

The XVIIIth century is called "the age of continuity." The law of continuity is one of its leading ideas. The pursuit of the notion of continuity marked the destiny of the previous century, especially in the case of the "new science" rooted in the Galilean geometrization of motion on the one hand and Cartesian laws of impact on the other. The whole enterprise of the new science thus required invention of a deeper principle that might incorporate both of these roots and account for the notion of force: the law of continuity. The goal of the essay is to follow the development of the law of continuity against the background of the tension between Newtonian physics and Leibnizian metaphysics, mainly based on the example of the two most famous controversies of the century: the vis viva dispute and the vibrating string controversy. We shall distinguish three stages of the history of the law of continuity: the law of continuity as the universal law of nature and geometry; the split between the geometrical and physical branches; and the decline of the law of continuity as it turned into a condition a priori of geometrical science on the one hand and into a law of learned ignorance law within an inaccessible nature on the other.