The Sense of the a Priori Method in Leibniz’s Dynamics

Abstract

In the opuscule De primae philosophiae emendatione notione substantiae (1694), Leibniz mentions that he has devoted a special science, dynamics, to the notion of force, and that this methodological elaboration clarifies the metaphysics of substance.1 To a certain extent this assertion causes problems. The scientific papers published by Leibniz up to that time do not support this claim to have founded a science of dynamics. Certainly, since the Brevis demonstratio erroris memorabibis cartesii (1686), Leibniz had been working to invalidate demonstratively the Cartesian principle of the conservation of quantity of motion. He proposes as an alternative a new measure of the motive force which would be conserved in mechanical exchanges, a measure based on the estimate of absolute force (potentia absoluta) or living force (vis viva), expressed by the product mv 2. Since then, a stormy quarrel with the Cartesians concerning the possibility of deducing the new principle as foundation of the system of the laws of nature had broken out2. But on what basis was Leibniz able to claim that he had founded a science of dynamics? One factor in the answer to this question emerges from a more careful examination of the appeals to the a priori method of demonstration which appear progressively in his unpublished work and in certain exchanges of letters, in particular with De Volder, Johann Bernouilli, and Christian Wolff. Our ambition here will be limited to presenting some reasons which militate in favor of such a re-examination, then to initiate the process of analysis through a study of the first part of the Dynamica de potentia (1689-90) where recourse to the a priori method is first sketched.