Continuity and elasticity in Leibniz's dynamics - Philosophy Department Seminar - with Tzu Chien Tho (University of Bristol)
Cotham House G2
Abstract: Leibniz's well-known doctrine of the principle of continuity famously accounts for the structure of the physical world and the aptness of the infinitesimal calculus for its description. However, Leibniz also holds to the imaginary status of continuous extension, stating that only the discrete can be actual. These two theses combine to form the basis of Leibniz's claims about the "actual" infinity of the world. With this Leibniz avoids the classical antinomy concerning the constitution of finite extended bodies from the "very small". That is, he avoids the traditional contradiction implied in the Atomistic division of the continuum into indivisibles. Here insofar as he qualifies the continuous as "imaginary", he affirms the indefinite (interminable) Eleatic division of the continuum as only approximate to the discrete and actual infinite nature of reality. As such the mereological stucture of Leibnizian bodies is indefinite; there is no final division for any Zenonic subdivision just as there is no final indivisible element from which bodies are composed.
The clearest and most obvious way that the continuous and discrete comes together is through the metaphysical model of the monadic universe: simple unextended discrete substances constitute the relations (among them continuity of space) responsible for generating a coherent cosmos of physical phenomena. However, this synthesis of the continuous and discrete equally applies to Leibniz’s dynamics. Here Leibniz requires both the continuity of corporeal motion and the discreteness of metaphysical reality to explain the gap between the dynamics and the kinematics of collision, a solution that appeals to the infra-phenomenal dimension of the "very small" without requiring atoms of indivisibles. I will argue for an interpretation for Leibniz's theory of the infinitesimal in dynamics starting from the centrality of the mathematical synthesis of the continuous and the discrete set forth in the infinitesimal calculus. It will also clarify the fluid-dynamical conception that Leibniz had already begun to develop in order to resolve the problem of elastic collisions in the late 17th century.