Productive Ambiguity in Leibniz's Representation of Infinitesimals

In this essay, I argue that Leibniz believed that mathematics is best investigated by means of a variety of modes of representation, often stemming from a variety of traditions of research, like our investigations of the natural world and of the moral law. I expound this belief with respect to two of his great metaphysical principles, the Principle of Perfection and the Principle of Continuity, both versions of the Principle of Sufficient Reason; the tension between the latter and the Principle of Contradiction is what keeps Leibniz's metaphysics from triviality. I then illustrate my exposition with two case studies from Leibniz's mathematical research, his development of the infinitesimal calculus, and his investigations of transcendental curves.