On Oneness and Substance in Leibniz’s Middle Years 1 Ohad Nachtomy and Tamar Levanon, Bar Ilan University Abstract 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 frst 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, qualifes 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. …as all numbers are derived from one plus one, so must all multiplicity be derived from unity (LBr, 389). And it would be the subject of a fne inquiry to discover whether, out of the entire totality of fnite numbers, one number can be defned which is the most beautiful of all - unless perhaps this is the number one, which represents all power at the same time (A 6.3, 477). 2 1. Infnity and Oneness: One is Said in Many Ways T raditional theology typically captures God as unique and infnite substance. The conjunction of oneness and infnity, however, is intriguing. If both these features are understood at the same time in a numerical, quantitative sense, they are incompatible. 3 More particularly, if the notion of God is considered as both one and infnite, then either oneness or infnity (or both) must be held in a non- The Leibniz Review, Vol. 24, 2014 69