Ohad Nachtomy

In her stimulating article, Catherine Wilson considers the moment of worlds-making in Leibniz’s philosophy. She raises the following question: “How do possible substances give rise to possible worlds?“ and observes that the moment of world-making is as puzzling as it is interesting. In section 2 of her article, Wilson considers two approaches to the question. According to the first, possible individuals logically precede possible worlds and possible worlds are constituted either by combinations of possible individuals or by mechanically checking the compossibility relations among them. This approach assumes that possible individuals are given and complete and that worlds result from their various conjunctions. On this approach, a world is a set of compossible individuals, i.e., a set of complete individuals whose co-existence is possible.

This paper argues that God's immanent causation and Spinoza's account of activity as adequate causation (of finite modes) do not always go together in Spinoza's thought. We show that there is good reason to doubt that this is the case in Spinoza's early Short Treatise on God, Man and His Well‐being. In the Short Treatise, Spinoza defends an account of God's immanent causation without fully endorsing the account of activity as adequate causation that he will later introduce in the Ethics (E3def2). We turn to an examination of how God's immanent causation relates to the activity of finite things in the Ethics. We consider two ways to think about the link between God, seen as immanent cause, and the activity of finite things: namely, in terms of entailment and in terms of production. We argue that the productive model is most promising for understanding the way in which the activity of finite things and God's immanent causality are connected in Spinoza's (mature) philosophy.

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.

In notes from 1675-76 Leibniz is using the notion of an infinite number as an illustration of an impossible notion. In the same notes, he is also using this notion in contrast to the possibility of the ‘Ens perfectissumum’ (A.6.3 572; Pk 91; A.6.3 325). I suggest that Leibniz’s concern about the possibility of the notion of ‘the greatest or the most perfect being’ is partly motivated by his observation that similar notions, such as ‘the greatest number’, are impossible. This leads to the question how Leibniz convinced himself that the notion of the greatest number is self-contradictory and that of the greatest being is not. I consider two suggestions, one that stress the difference between beings and numbers and one that stress the difference between two notions of infinity, and conclude that neither of them provides a satisfactory solution to this question.

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.

This chapter seeks to highlight some of the main threads that Leibniz used in developing his views on infinity in his early years in Paris. In particular, I will be focusing on Leibniz’s encounters with Descartes, Galileo, and Spinoza. Through these encounters, some of the most significant features of Leibniz’s view of infinity will begin to emerge. Leibniz’s response to Descartes reveals his positive attitude to infinity. He rejects Descartes’s view that, since we are finite, we cannot comprehend the infinite and therefore should refrain from studying it. Likewise, Leibniz rejects Descartes’s view that the term ‘infinite’ should be reserved to God alone, as well as Descartes’s distinction between the infinite and the indefinite. Leibniz’s encounter with Galileo brings out his rejection of infinite number in response to Galileo’s paradox. This, in turn, leads him to face another formidable challenge, viz., to defend the claim that an infinite being is possible, while an infinite number is not. Leibniz’s encounter with Spinoza, I suggest, highlights the way he is approaching this problem by distinguishing between quantitative and non- quantitative senses of infinity. The strategy of employing different senses of infinity in different contexts will remain central in Leibniz’s approach to infinity for the rest of his career.