Adam Harmer

Leibniz famously argues that there must be simple substances, since there are composites, and a composite is nothing but a collection of simples. I reconstruct Leibniz’s argument, showing that it relies on a commitment to mereological nihilism (i.e., the view that composites cannot be true beings). I show further that Leibniz endorses mereological nihilism as early as the 1680s and offers both direct and indirect support for this commitment: indirect support via the notion of unity and direct support via the notion of persistence. I then assess the alignment of Leibniz’s mereological nihilism with his other commitments during the 1680s, including his potential commitment to corporeal substances. I argue that any viable interpretation of Leibniz’s commitment to corporeal substances is compatible with mereological nihilism, which provides a new perspective both on Leibniz’s developing theory of substance and on his mature theory of simple substance.

Leibniz argues against Descartes’s conception of material substance based on considerations of unity. I examine a key premise of Leibniz’s argument, what I call the Plurality Thesis—the claim that matter (i.e. extension alone) is a plurality of parts. More specifically, I engage an objection to the Plurality Thesis stemming from what I call Material Monism—the claim that the physical world is a single material substance. I argue that Leibniz can productively engage this objection based on his view that matter is discrete. The discreteness of matter provides two aspects of support for the Plurality Thesis. First, it indicates that the parts of matter do not share boundaries and are, therefore, independent in an important sense. Second, it indicates that the parts of matter are determinate and are, therefore, ontologically prior to the wholes they compose.

Encountering Leibniz for the first time can be a dizzying experience. Unlike many early modern thinkers, Leibniz did not produce a treatise, which outlines his philosophical system step by step. Rather, each of Leibniz’s texts provides a kaleidoscopic view of the whole, a complex mixture of elements, some in the foreground, some receding into the background, present but not altogether in focus. Furthermore, Leibniz produced philosophical work over 6 decades, and the extent to which his views changed over that time is an ongoing subject of scholarly disagreement. The perpetual challenge for readers and teachers of Leibniz is, then, where to start: which fragment of the whole provides a viable entry point into Leibniz’s philosophy? Leibniz’s Key Philosophical Writings engages this challenge, providing an introduction to Leibniz’s thought, not by focusing on particular themes, doctrines, or threads running through his entire corpus, but by engaging complete texts in all their complexity.

As José Benardete observes, "the concept of the infinite is found to impinge on almost the whole schedule of ontological questions" (Infinity, viii). This is especially true for the early moderns, for whom questions like the following were still very much in play: Does the world have a beginning? Are there bounds to the spatial extent of the world? How does an imperfect creation flow from an infinitely perfect creator? How does the infinite divisibility of the continuum relate to the structure of the material world? How are human actions related to the (possibly) infinite chain of causes or influences that shape our behaviors? Far from being an esoteric topic, which is best relegated to the outskirts of metaphysics or mathematics, infinity has tendrils reaching into nearly every philosophical domain.

I argue that Leibniz’s well-known Argument from Unity is equally an argument from plurality. I detail two main claims about plurality that drive the argument, and I provide evidence that they structure Leibniz’s argument from the late 1670s onwards. First, there is what I call Mereological Nihilism (i.e., the claim that a plurality cannot be made into a true unity by any available means). Second, there is what I call the Plurality Thesis (i.e., the claim that matter is a plurality in need of unity in the first place). I suggest that the Plurality Thesis offers a general analysis of materiality that, in some sense, is the most important aspect of Leibniz’s argument. Finally, I connect these claims about plurality to the common 17th & 18th century commitment known as the actual parts doctrine.

Leibniz argues that Cartesian extension lacks the unity required to be a substance. A key premise of Leibniz’s argument is that matter is a collection or aggregation. I consider an objection to this premise raised by Leibniz’s correspondent Burchard de Volder and consider a variety of ways that Leibniz might be able to respond to De Volder’s objection. I argue that it is not easy for Leibniz to provide a dialectically relevant response and, further, that the difficulty arises from Leibniz’s commitment to part-whole priority in the case of material wholes, a commitment not shared by De Volder. One major implication is that Leibniz relies on a bottom-up conception of material things, which makes his argument vulnerable to objections stemming from certain types of monist positions.

Leibniz argues that God doesn't create everything possible because not all possible things are compossible, that is, compatible with each other. Much recent debate has focused on Leibniz's conception of compossibility. One important aspect of this debate, which has not been examined directly, is the distinction between possible worlds and possible creations: the notion of possible world is more robust than simply whatever God can create. Many commentators have relied on this distinction without a clear formulation of it. I develop the distinction between possible worlds and possible creations by looking at how Leibniz characterizes what God is capable of creating. I argue that possible creations must be both logically consistent and determinate. Possible creations differ from possible worlds insofar as possible creations fail to be either maximal or harmonious. I conclude, therefore, that focusing on the notion of determinateness offers a new approach to answering the question why doesn't God create everything possible?

Leibniz's World-Apart Doctrine states that every created substance is independent of everything except God. Commentators have connected the independence of substance asserted by World-Apart to a variety of important aspects of Leibniz's modal metaphysics, including his theory of compossibility and his notion of a possible world (including what possible worlds there are). But what sort of independence is at stake in World-Apart? I argue that there is not a single sense of "independence" at stake, but at least three: what I call "causal", "phenomenal", and "ontological" independence. Further, I distinguish two versions of each type of independence: what I call "basic" and "strict" versions. I argue that only basic versions can be legitimately attributed to Leibniz. In light of this result, I conclude, pace previous commentators, that World-Apart has little impact on Leibniz's modal metaphysics.

This chapter discusses Gottfried Wilhelm Leibniz’s philosophical reflections on mind and body. It first considers Leibniz’s distinction between substance and aggregate, referring to the former as a being that must have true unity (what he calls unum per se) and to the latter as simply a collection of other beings. It then describes Leibniz’s extension of the term “substance” to monads and other things such as animals and living beings. It also examines Leibniz’s views about the union of mind and body, whether mind and body interact, and how interaction is related to union. More specifically, it asks whether mind and body together constitute an unum per se and analyzes Leibniz’s account of the per se unity of mind-body composites. In addition, the chapter explores the problem of soul-body union as opposed to mind-body union and concludes by discussing Leibniz’s explanation of soul-body interaction using a system of pre-established harmony.

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz’s argument against the world soul relies on his rejection of infinite number, and, as such, Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz’s rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’– collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts.