By developing the use of infinity in mathematics and changing the prevailing negative attitude towards it, Leibniz played a central role in introducing infinity into our depiction of nature. Against the Scholastics and the anxiety evoked by Pascal, Leibniz recommends a rational study of infinity and a celebration of its marvels, since “in nature everything goes to infinity.” This is consistent with the omnipresence of infinity in his metaphysics, where infinitely many possible worlds are conceived in God’s infinite understanding, the actual world consists of infinitely many individual beings (substances or monads), and each of these involves infinity.
One of Leibniz’s prime models for such substances is mathematical laws of series that diverge or converge to infinity. At the same time, he holds that the notion of an infinite number—indeed, any infinite magnitude or a whole—is strictly impossible. Faced with this apparent contradiction, Leibniz develops a subtle approach to infinity using a cluster of fine distinctions. For example, while he holds that true infinite entities (or wholes) have no place in mathematics, he accepts infinity in metaphysics and theology. Leibniz’s nuanced approach to infinity presents a host of intriguing challenges.
My project seeks to address some of these by examining how infinity figures in Leibniz’s definitions of individual substances; the nature of individual substances as manifestations of God’s infinity under the imago dei doctrine; and the relations between time and infinity vis-à-vis the labyrinth of the continuum and new methods for time measurement.