tzuchien tho equivocation infinitesimals

This article aims to treat the question of the reality of Leibniz’s infinitesimals from the perspective of their application in his account of corporeal motion. Focusing on three instances of Leibniz’s treatment of contingency in physics, this paper argues that, in order to account for the contingency of physical laws, Leibniz maintained that final causes, in addition to efficient and mechanical ones, must operate in physical processes and operations. Hence the actuality of physical laws results from a causal power that is inherent to substances rather than being the mere consequence of the way God arranged the relations between physical objects. On the contrary, Leibniz understood the status of natural laws as arising from the action internal to physical substances. However, in addition to this, the contingency of natural laws does not consist only in the fact that God has chosen them over other possible ones.

As a consequence, the set of laws that regulate the physical laws could have been created otherwise by God. While geometrical truths, being necessary, do not require the use of the principle of sufficient reason, physical laws are not strictly determined by geometry and therefore are logically distinct from geometrical laws. For Leibniz, the contingency of physical laws entailed the assumption of the existence of an additional form of causality beyond mechanical or efficient ones. The core of Leibniz’s investigation of the modality of natural laws lays in the distinction between necessary, geometrical laws on the one hand, and contingent, physical laws of nature on the other. This paper focuses on Leibniz’s conception of modality and its application to the issue of natural laws. In examining the evolution of the quantity mv2 in the refinement of the force concept from potentia to actio, I argue that Leibniz’s systematic limitations help clarify dynamical causality as neither strictly metaphysical nor mechanical but a distinct level of reality to which Leibniz dedicates the “dynamica” as “nova scientia”. This “error”, resulting from the limits of Leibniz’s methodology, reveals the systematic role of this quantity mv2 in the dynamics. To defend this view, we examine one of the most important theoretical discrepancies of Leibniz’s dynamics with classical mechanics, the measure of vis viva as mv2 rather than ½ mv2. The measure of living force by mv2 must then be understood as an organizational property of motion conceptually distinct from the geometrical or otherwise quantitative magnitudes exchanged in mechanical phenomena. It presents an interpretation of the dynamics that characterizes physical causation as the structural organization of phenomena. This article aims to interpret Leibniz’s dynamics project through a theory of the causation of corporeal motion.

Tzuchien tho equivocation infinitesimals