Abstract

In this chapter we outline the main issues that have arisen in the interpretation of the status of infinitesimals in Leibniz’s Differential Calculus, and difficulties affecting their resolution. Then we give an overview of our interpretation, based on a thorough consideration of Leibniz’s writings, many of them unknown to previous interpreters. This is based on a firm distinction between the issues of the existence of infinitesimals, their use in mathematics, and the justification of the differential algorithm itself.