Primitive and Derivative Forces in Leibnizian Bodies

In H. Poser (ed.), Nihil Sine Ratione: Mensch, Natur und Technik im Wirken von G. W. Leibniz. pp. 720-727 (2001)
It is well known that Leibniz believes that the motion of bodies is caused by an internal force.1 Moreover, he distinguishes between two kinds of force that are associated with bodies, which he calls primitive and derivative forces respectively. My aim is to explain Leibniz’s account of the relation between these two kinds of force, and to address a puzzle that arises in connection with this relation. In fact Leibniz speaks of two different kinds of derivative force. The first, and most fundamental, kind of derivative force is the momentary tendency to move from one perception to another within a simple substance, or monad. Sometimes these are called “appetitions”.2 The second kind are the forces of bodies that are found in the mechanical explanations of Leibnizian Dynamics.3 We shall be concerned primarily with the latter in what follows. However, the derivative forces of monads will also play an important role in the discussion. As one might expect, Leibniz holds that derivative forces are derived from the primitive ones. This idea is more usually expressed in terms of the notion of modification. Thus, derivative forces are said to be “nothing but the modifications and results of primitive forces”4 and to “arise as shapes arise from modification of extension”.5 Here it is natural to assume that Leibniz understands the relation between primitive and derivative force in something like the way in which Descartes understood the relation between modes of extended and thinking substances and the substances themselves, namely as particular ways of being an extended or thinking thing that inhere in their subjects.6 Although this account of derivative forces as modifications of primitive forces may seem plausible at first, difficulties arise when we try to understand how it could apply to the derivative forces in Leibnizian bodies. For it seems to be in conflict with two further aspects of Leibniz’s philosophy. Both can be found in the following passage from a letter to De Volder of 1705..
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