Leibniz’s mature physics is most noted for the centrality of the notion of force and the development of the dynamics, the science of force. This chapter examines the development and challenges of this “dynamics project,” active from 1676–c. 1700, from its initial motivations and methodological maturation to its important convergence with the systematic metaphysics of his later writings. The chapter begins with Leibniz’s early approach to physical questions and his development in Paris (1672–76), then turns to the emerging theory of power or force from the late 1670s to the late 1680s. In 1689, Leibniz coined the term “dynamica” and composed the two most significant texts of the project. Finally, during the period after 1690, Leibniz not only developed the internal structure of the dynamics but also employed its results toward a convergence between his scientific work and his systematic metaphysics of substantial forms.
This paper argues that Cantorian transfinite cardinality is not a necessary assumption for the ontological claims in Badiou’s L’Être et l’Événement (Vol. 1). The necessary structure for Badiou’s mathematical ontology in this work was only the ordinality of sets. The method for reckoning the sizes of sets was only assumed to follow the standard Cantorian measure. In the face of different and compelling forms of measuring non-finite sets (following Benci and Di Nasso, and Mancosu), it is argued that Badiou’s project can indeed accommodate this pluralism of measurement. In turn, this plurality of measurement implies that Badiou’s insistence on the “subtraction of the one”, the move to affirm the unconditioned being of the “inconsistent multiple”, results in the virtuality of the one, a pluralism of counting that further complicates the relationship between the one and the multiple in the post-Cantorian era.
General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/userguides/explore-bristol-research/ebr-terms/ AGPh 2018; 100(4): Tzuchien Tho* Potentia, actio, vis: the Quantity mv 2 and its Causal RoleAbstract: This article aims to interpret Leibniz's dynamics project (circa 1678-1700) through a theory of the causation of corporeal motion. It presents an interpretation of the dynamics that characterizes physical causation as the structural organization of phenomena. The measure of living force (vis viva) by mv 2 must then be understood as an organizational property of motion conceptually distinct from the geometrical or otherwise quantitative magnitudes exchanged in mechanical phenomena. 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 mv 2 rather than ½ mv 2 . This "error", resulting from the limits of Leibniz's methodology, reveals the systematic role of this quantity mv 2 in the dynamics. In examining the evolution of the quantity mv 2 in the refinement of the force concept (vis) 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".
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