In this paper, I address a topic that has been mostly neglected in Leibniz scholarship: Leibniz’s conception of number. I argue that Leibniz thinks of numbers as a certain kind of relation, and that as such, numbers have a privileged place in his metaphysical system as entities that express a certain kind of possibility. Establishing the relational view requires reconciling two seemingly inconsistent definitions of number in Leibniz’s corpus; establishing where numbers fit in Leibniz’s ontology requires confronting a challenge from the well-known nominalist reading of Leibniz most forcefully articulated in Mates (1986). While my main focus is limited to the positive integers, I also argue that Leibniz intends to subsume them under a more general conception of number.

The question of Leibniz’s relationship to mysticism has been a topic of some debate since the early part of the 20th Century. An initial wave of scholarship led by Jean Baruzi pre­sented Leibniz as a mystic. However, later in the 20th Century the mood turned against this view and the negative appraisal holds sway today. In this paper I do two things: First I provide a detailed account of the ways in which Leibniz is critical of mysticism; second, I argue that there is, nonetheless, an important sense in which Leibniz should be regarded as an advocate of mysticism. However, the approach that I take does not focus on an effort to overturn the kinds of considerations that led people to reject the views of Baruzi. Instead, I try to reframe the discussion and explore more complex and interesting relationships that exist between mysticism and Leibniz’s philosophical theology than have been articulated previously. Here I draw on some recent discussions of mysticism in the philosophical literature to illuminate Leibniz’s own distinction between “false mysticism” and “true mystical theology” and his assessment of the views of a number of other people who might plausibly be identified as mystics.

The question why Leibniz continues to fascinate and perplex us 300 years after his death is one I approach with both hesitation and enthusiasm. Rather than attempting a survey of currrent controversies in Leibniz scholarship, as useful and interesting as such a survey would be, I take the opportunity to explain the underlying basis of our interest in Leibniz.

My aim in this paper is to elucidate Leibniz’s account of moral normativity and the relation between motivation and obligation. I argue against the recent interpretation of Christopher Johns, according to which Leibniz’s moral theory is actually a deontological theory, having more in common with Kantian moral theory than with any form of consequentialism. I argue that for Leibniz reason is not itself the source of practical normativity and real obligation; the source of that is rather the agent’s desire for his own happiness or perfection. For Leibniz, reason in its practical role functions instrumentally: the desire for one’s own happiness is the source of practical normativity, and reason functions only to transfer that normativity from the end that it does not determine to the means to those ends that it does determine.

In 1996, Manuel Luna Alcoba published a transcription of LH XXXVII, IV, 57 r°-58v°, a manuscript written by Leibniz after 1693 and containing historical and systematic reflections on the problem of the continuum. The present article aims to show that the manuscript, to which Luna Alcoba attributed the title Geschichte des Kontinuumproblems, consists mainly of excerpts from, paraphrases of, and comments on the Labyrinthus sive de compositione continui (1631), a book by the Louvain philosopher and theologian Libert Froidmont to which Leibniz often referred in his writings. By comparing LH XXXVII, IV, 57 r°-58v° with the Labyrinthus, I try to understand which parts of Fromondus’ book attracted Leibniz’ attention and why the latter, as late as 1693, still found it worth brooding over an Aristotelian treatise on the composition of the continuum.

Relying on an analogy Leibniz makes in On The Ultimate Origin of Things between God’s creation of substances and a tiling board game, Jeffrey McDonough argues that the challenge of the problem of incompossibility is finding the optimal balance of net-goodness and plenitude given certain existential constraints that God must respect. For McDonough the ordering that optimizes the greatest number of substances is the best of all possible worlds. In this paper I argue that McDonough’s solution cannot be an admissible interpretation of compossibility as Leibniz perceived it because he misinterprets the aim of the tiling analogy: Leibniz did not intend for the tiling analogy to be applied to the problem of compossibility. In my view Leibniz used the tiling analogy to argue for simplicity as a necessary feature of the nomological makeup of the best set of already-compossible substances.

Following the lead of Hans Reichenbach in the early twentieth century, many authors have attributed a causal theory of time to Leibniz. My exposition of Leibniz’s theory of time in a paper of 1985 has been interpreted as a version of such a causal theory, even though I was critical of the idea that Leibniz would have tried to reduce relations among monadic states to causal relations holding only among phenomena. Since that time previously unpublished texts by Leibniz have become available in which he himself explains temporal precedence in terms of causal precedence, and these texts have been given careful scrutiny by other scholars, such as Jan Cover, Stefano Di Bella and Michael Futch. In this paper I respond to their analyses, and try to make precise the way in which Leibniz’s views on time and on causality fit together in his metaphysics.

I propose a straightforward reconciliation of Leibniz’s conception of bodies as aggregates of simple substances (i.e., monads) with his doctrine that bodies are the phenomena of perceivers, without in the process saddling him with any equivocations. The reconciliation relies on the familiar idea that in Leibniz’s idiolect, an aggregate of Fs is that which immediately presupposes those Fs, or in other words, has those Fs as immediate requisites. But I take this idea in a new direction. I argue that a phenomenon having its being in one perceiving substance (monad) can plausibly be understood to presuppose other perceiving substances (monads) in the requisite sense. Accordingly, a phenomenon in one monad can indeed be an aggregate of other monads, in Leibniz’s technical sense, just as the latter monads can be constituents of the phenomenon. So understood, the two conceptions of body are perfectly compatible, just as Leibniz seems to think.

This paper develops some important observations from a recent article by Maria Rosa Antognazza published in The Leibniz Review 2015 under the title “The Hypercategorematic Infinite”, from which I take up the characterization of God, the most perfect Being, as infinite in a hypercategorematic sense, i.e., as a being beyond any determination. By contrast, creatures are determinate beings, and are thus limited and particular expressions of the divine essence. But since Leibniz takes both God and creatures to be infinite, creatures are simultaneously infinite and limited. This leads to seeing creatures as infinite in kind, in distinction from the absolute and hypercategorematic infinity of God. I present three lines of argument to substantiate this point: (1) seeing creatures as entailing a particular sequence of perfections and imperfections; (2) seeing creatures under the rubric of an intermediate degree of infinity and perfection that Leibniz, in 1676, calls “maximum in kind”; and (3) observing that primitive force, a defining feature of created substance, may be seen as infinite in a metaphysical sense. This leads to viewing Leibniz’s use of infinity within a Neoplatonic framework of descending degrees of Being: from the hypercategorematic infinite, identified with the most perfect Being; to the intermediate degree of maximum in kind, identified with creatures; to the lowest degree of entia rationis (or beings of reason), identified with mathematical and abstract entities.

Marco Messeri (2017) offers a new solution to the problem of lucky proof (an influen­tial objection to Leibniz’s infinite-analysis theory of contingency. Messeri claims that contingent truths like “Peter denies Jesus” cannot be proved by a finite analysis because predicates like “denies Jesus” are infinitely complex. I argue that infinitely complex predicates appear in some necessary truths, and that some contingent truths have finitely complex predicates. Messeri’s official account is disjunctive: a truth is contingent just in case either it contains an infinitely complex predicate or it concerns existence. I argue against Messeri’s official account and suggest that some other disjunctive account might be appropriate.

Several scholars have argued that Leibniz’s infinite analysis theory of contingency faces the Problem of Lucky Proof. This problem will be discussed here and a solution offered, trying to show that Leibniz’s proof-theory does not generate the alleged paradox. It will be stressed that only the opportunity to be proved by God, and not by us, is relevant to the issue of modality. At the heart of our proposal lies the claim that, on the one hand, Leibniz’s individual concepts are saturated conceptual conjunctions, i.e., infinite conjunctions that contain either the concept itself or its privation for every primitive concept; and that, on the other hand, also certain universal concepts of states and acts are infinite conjunctions of primitive concepts and privations, even if insaturated ones. This will suffice to allow that some truths regarding individuals can’t be demonstrated, although they are included in the concept of their subject.

Not unlike many contemporary philosophers, Leibniz admitted the existence of temporary truths, true propositions that have not always been or will not always be true. In contrast with contemporary philosophers, though, Leibniz conceived of truth in terms of analytic containment: on his view, the truth of a predicative sentence consists in the analytic containment of the concept expressed by the predicate in the concept expressed by the subject. Given that analytic relations among concepts are eternal and unchanging, the problem arises of explaining how Leibniz reconciled one commitment with the other: how can truth be temporary, if concept-containment is not? This paper presents a new approach to this problem, based on the idea that a concept can be consistent at one time and inconsistent at another. It is argued that, given a proper understanding of what it is for a concept to be consistent, this idea is not as problematic as it may seem at first, and is in fact implied by Leibniz’s general views about propositions, in conjunction with the thesis that some propositions are only temporarily true.

The young Spinoza and the mature Leibniz both characterize the soul as a self-moving spiritual automaton. Though it is unclear if Leibniz’s use of the term was suggested to him from his reading of Spinoza, Leibniz was aware of its presence in Spinoza’s Treatise on the Emendation of the Intellect. Considering Leibniz’s staunch opposition to Spinozism, the question arises as to why he was willing to adopt this term. I propose an answer to this question by comparing the spiritual automaton in both philosophers. For Spinoza, the soul acts as a spiritual automaton when it overcomes imaginative ideas and produces true ideas. For Leibniz, the soul acts as a spiritual automaton when it spontaneously produces its perceptions according to the universal harmony preestablished by God. Thus, for Leibniz contra Spinoza, the spiritual automaton is a means to render intelligible a providential order in which everything happens for the best.