Leibniz Reads Spinoza

Having argued in chapter 2 that Leibniz was preoccupied with the difference between the notion of infinite number and that of the infinite being, in this chapter the author examines Spinoza’s solution to a similar problem. The gist of “Spinoza’s solution” is to distinguish between various kinds of infinity and, in particular, between one that applies to substance and one that applies to numbers, seen as auxiliaries of the imagination. Leibniz, the author argues, accepts this kind of approach and adapts it to his own purposes. Leibniz recasts Spinoza’s distinctions between different types of infinity (A 6.3:282; LLC 114–15) in terms of degrees of infinity. These degrees are (1) Omnia (absolute infinity), which applies to God alone; (2) Omnia sui generis, or maximum in its own kind; and (3) Infinitum tantum, or mere infinity, which applies to numbers and other entia rationis (in a syncategorematic sense).