This essay reviews Robert Merrihew Adams’ approaches to the philosophy of Leibniz, both his general methodological approaches, and some of the main themes of his work. It attempts to assess his contribution both to the study of Leibniz and to the history of philosophy more generally.

This essay considers Spinoza’s responses to two questions: what is responsible for the variety in the physical world and by what mechanism do finite bodies causally interact? I begin by elucidating Spinoza’s solution to the problem of variety by considering his comments on Cartesian physics in an epistolary exchange with Tschirnhaus late in Spinoza’s life. I go on to reconstruct Spinoza’s unique account of causation among finite bodies by considering Leibniz’s attack on the Spinozist explanation of variety. It turns out that Spinoza’s explanations of the variety of bodies, on the one hand, and of causation among finite bodies, on the other, generate a tension in his system that can only be resolved by taking Spinoza to employ two notions of “existence.” I conclude by offering evidence that this is in fact what Spinoza does.

Leibniz’s infinite-analysis theory of contingency says a truth is contingent if and only if it cannot be proved via analysis in finitely many steps. Some have argued that this theory faces the Problem of Lucky Proof—we might, by luck, complete our proof early in the analysis, and thus have a finite proof of a contingent truth—and the related Problem of Guaranteed Proof—even if we do not complete our proof early in the analysis, we are guaranteed to complete it in finitely many steps. I aim to solve both problems. For Leibniz, analysis is constrained by three rules: an analysis begins with the conclusion; subsequent steps replace a term by (part of) its real definition; and the analysis is finished only when an identity is reached. Furthermore, real definitions of complete concepts are infinitely complex, and Leibniz thinks infinities lack parts. From these observations, a solution to our problems follows: an analysis of a truth containing a complete concept cannot be completed in a finite number of steps—indeed, the first step of the analysis cannot be completed. I conclude by defusing some alleged counterexamples to my account.

It is well-known that Leibniz ends and crowns the 1714 “Monadologie” with a version of his notion of jurisprudence universelle or “justice as the charity [love] of the wise:” for sections 83-90 of the Vienna manuscript claim that “the totality of all spirits must compose the City of God . . . this perfect government . . . the most perfect state that is possible . . . this truly universal monarchy [which is] a moral world in the natural world”—a moral world of iustitia in which “no good action would be unrewarded” for those “citizens” who “find pleasure . . . in the contemplation of [God’s] perfections, as is the way of genuine ‘pure love.’” But the opening four-fifths of the work offer Leibniz’ theory of “substance” (or monad) viewed as the necessary pre-condition of justice: for “on the knowledge of substance, and in the consequence of the soul, depends the knowledge of virtue and of justice” (to Pierre Coste, 1712). Thus without a complete and correct notion of substance/monad, no complete and correct notion commune de la justice would be conceivable. Hence the entire “Monadologie” can be understood as a theory of justice underpinned by a Grundlegung of moral “monads” or justice-loving rational “substances.” In this connection it is revelatory that Leibniz cites the relevant sections of the 1710 Théodicée in most of the 90 articles of the “Monadologie” (beginning indeed with article #1): for Théodicée (theos-dike) is (Leibniz says) “the justice of God,” and Leibniz makes that justice “appear” in the opening lines of the “Monadologie” (in effect) by referring the reader immediately to Théodicée #10 (“Preliminary Dissertation”) —which relates “im­mortal spirits” to a just God who is cherished through “genuine pure love.” This means that “the justice of God” as “higher love” colors the “Monadologie” instantly. Thus one need not “wait” for sections 83-90 to arrive in order for the “Monadologie” to be(come) a “theory of justice:” it is such ab initio.

Recent scholarship has established that, until the mid-1670s, Leibniz did not hold the possibilist ontology which, in his mature philosophy, provides the foundation for both his account of human freedom and of eternal truth. Concentrating on the Mainz period (1667-1672), this paper examines the conciliation, in those early writings, of an actualist ontology and a conception of necessary truth as analytical. The first section questions the view that Leibniz was educated in a “Platonist” tradition; the second section presents the actualist metaphysics that he adopted in the wake of his teachers; the third section shows how Leibniz could, contrary to those same teachers, hold an analytical view of eternal truth, even without the support of his later possibilist ontology and doctrine of real definitions.

We argue in this paper that Leibniz’s characterization of a substance as “un être” in his correspondence with Arnauld stresses the per se unity of substance rather than oneness in number. We employ two central lines of reasoning. The first is a response to Mogens Lærke’s claim that one can mark the difference between Spinoza and Leibniz by observing that, while Spinoza’s notion of substance is essentially non-numerical, Leibniz’s view of substance is numerical. We argue that Leibniz, like Spinoza, qualifies the substance as “one” primarily in a non-numerical sense, where non-numerical means per se unity or qualitative uniqueness. The second line of reasoning suggests that the term “one” should be understood as a-unity-presupposed-by-multiplicity in two senses: a) externally, in the sense of being presupposed by higher complex structures, such as aggregates, and, b) internally, in the sense of having itself a complex structure. We develop an analogy along these lines between the role the notion of a fundamental unity plays in Leibniz’s view of numbers and his view of substance. In other words, we suggest that looking at the role units play in Leibniz’s view of mathematics can shed some light on the role they play in his metaphysics.