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  • Leibniz’s Theoretical Shift in the Phoranomus and Dynamica de Potentia
  • François Duchesneau (bio)

This paper is concerned with the final stage in the invention of the dynamics or theory of force, which forms the core of Leibniz’s contribution to physics. It tries to determine the reasons why this final stage took place and to unravel the arguments Leibniz developed to establish the mature version of his theory. In his article De primæ philosophiæ emendatione et notione substantiæ, published in 1694 in the Acta Eruditorum, Leibniz mentions for the first time in print that he has set the ground for a new science called dynamica and centered on the notion of force (GP IV, pp. 468–70). He adds that he expects the notion of force will bring much light to our understanding of the notion of substance (GP IV, p. 469). 1 Indeed, his use of the term “dynamics” (dynamica, dynamice) can be traced back in various correspondences to an apparently initial occurrence in the exchange of letters, begun in 1689, with Rudolf Christian von Bodenhausen. It is also quite evident that the principles of the new science form the subject matter of the Dynamica de potentia et legibus naturæ corporeæ, a major scientific work Leibniz started working on in late summer 1689. Just previous to setting on that ambitious project, Leibniz, in July 1689, had undertaken to write the Phoranomus, a dialogue which was left incomplete, but wherein he sketched some of the arguments that, appropriately modified, found their way into the Dynamica. My larger project is to understand the genesis, finality, and argumentative structure of the theoretical constructs which form the dynamics. But this paper will focus more specifically on describing the methodological shift in the analysis of force that took place in the Phoranomus. The shortcomings of this initial attempt seem to have occasioned [End Page 77] the arguments Leibniz recast and developed in the Dynamica. 2 The Phoranomus may thus serve as a key opening to one of Leibniz’s major and less known intellectual achievements in the area of physical science.

First, I shall briefly recall the initial steps, beginning in 1676, that led to the 1689 project, and present the circumstances, structure and objectives of the Phoranomus. Second, I intend to show that the main theoretical challenge Leibniz was faced with at the time he wrote the Phoranomus was that of counteracting the Cartesians’ objections against his demonstration of the principle of conservation of vis viva. Third, I shall try to characterize the new way of proof Leibniz puts in place which abstracts from our particular system of things in an effort to determine a priori how the moving force is expressed in uniform unconstrained motion. Certain methodological principles guide this attempt, especially the principle of the equality between full cause and entire effect. Fourth, I shall investigate the concepts and models framing the mathesis mechanica which is supposed to uncover the “formal effect” of moving force as it expresses the form of the subjacent, self-restoring agent. The main problem in this case is to find means of equating mathematical expressions and metaphysical reasons and to provide models more general than those pertaining to the experience of falling bodies and gravitational effects. The strategy to cope with this problem consists in forming a system of abstract definitions according to which models can be constructed, so to speak, a priori. Finally, it seems appropriate to turn to the Dynamica de potentia to discover how the same methodological pattern overcomes the shortcomings of the Phoranomus. The central ingredient of the new theory is a concept of “formal action” which grounds the various models of the dynamics defined as the science of “power and action.” This concept is a truly Leibnizian invention which determines the structure and significance of the mature dynamics.

1. Leibniz’s Reformed Mechanics and the Project of the Phoranomus

A complete genealogy of Leibniz’s views on mechanics should take into account the initial physics which he formulated in the Theoria motus abstracti and Hypothesis physica nova (1671). But those views were to be drastically revised at a later time. The real story begins when Leibniz, upon his return...

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