On Leibniz: Expanded Edition

12. The Contributions of the Paris Period (1672–1676) to Leibniz’s Metaphysics

205 1. Overview of Cardinal Theses of Leibniz’s Metaphysics This essay seeks to elucidate the biographical background of the preceding discussion of Leibniz’s recourse to the idea of perfection maximization through infinitistic comparisons. In pursuing this goal, it will assess the extent to which the philosophical and mathematical work of Leibniz’s Parisian period contributed to the formation of his entire metaphysical system.1 To determine the extent to which a part contributes to a whole we must begin by setting before our minds just what this whole actually is. In the present case, this is by no means all that simple. For there can be considerable dispute as to just what the central, salient features of Leibniz’s metaphysics in fact are. Yet in the confines of a rather brief discussion one cannot but be somewhat dogmatic about this.2 As I see it, the really major building blocks of Leibniz’s monadological system are as follows: I. Substantival Atomism Thesis: The natural universe is composed of punctiform (“simple,” in Leibniz’s sense of this term—i.e., partless) substances differentiated by “points of view”: the so-called “metaphysical points,” which are indestructible and exist throughout time. Chronology: This idea figures prominently in Leibniz’s early philosophizing and was clearly developed already during the Mainz period. It is one of the fundamental ideas of his early physical tract Theoria motus abstracti of  12 The Contributions of the Paris Period (1672–1676) to Leibniz’s Metaphysics 206 the contributions of the paris period 1671.3 And it is a central feature of the “geometry of indivisibles” of which Leibniz speaks in his early letter to Arnauld, and regarding which he says: From these propositions I have reaped a great harvest, not merely in proving the laws of motion, but also in the doctrine of mind. For I demonstrated that the true locus of our mind is in a certain point or center, and from this I deduced some remarkable conclusions about the imperishability of that mind, the impossibility of ceasing from thinking, the impossibility of forgetting, and the true internal difference between motion and thought.4 II. The Idea of a Complete Individual Concept A. Concept Comprehensiveness Thesis: Each substance has its own characteristic nature, its proper haecceity , its own definitive individual concept. This encompasses its entire “fate” throughout the whole history of its existence—the totality of everything that happens to it—in line with the decrees of God. Chronology: These Leibnizian doctrines are also early. His ideas on individuation go back to his youthful essay De Principio individui. From his earliest days as a philosopher Leibniz held that substances exist in—and throughout—time, and that their individual notion is omnitemporal in coverage and includes everything that happens to the substance. The corresponding conceptions about the necessity of a substance’s descriptive makeup —that with respect to substances “whatever has happened, is happening, or will happen is best, and also necessary” is also early; for example, it is explicitly present in the letter to Magnus Wedderkopf of May 1671 (Loemker, pp. 146–47). B. Historical Dynamism Thesis: The individual notion of a substance must be conceived in dynamic terms. Not only does a substance have a developmental conatus that sweeps it along over the course of time, but its sequential unfolding is always prefigured in its earlier states. Its history is akin to the inherent dynamism of a mathematical formula with the increase of a temporal parameter, like a curve in Cartesian analytic geometry. Its temporal development accords with a characteristic relationship that embodies an infinitely varying detail of historical changes within a single all-comprising relationship.5 Encapsulated the contributions of the paris period 207 within the individual notion of each monad is a characteristic “program” (in modern cybernetic terminology), a plan that encompasses its whole history in the manner in which differential equation synthesizes a complex course of development. Chronology: This idea of the functional dynamics of substances is a product of the Parisian period, although it did not come to prominence until the important essay Primae veritates of 1680/1684 (Loemker, pp. 267 ff). It is worth noting that this important idea of the characterizing “program” or defining mathematical formula (or function) introduces a clearly mathematical conception into the framework of an otherwise essentially logical framework of a subject/predicate system. III. The Proliferation of...