The Leibnizian infinitesimal calculus: A synthesis of the perspectives of Brunschvicg and Ishiguro

Abstract

This article studies Leibniz's treatment of infinitesimals: their application to the calculus and his opinion that they did not exist. In partial agreement with Brunschvicg's and Ishiguro's commentaries on the paradoxical status of Leibniz's infinitesimals, this study proposes a synthesis of both interpretations, which is based on the algorithmic nature of infinitesimals and on the assumption of continuity, and which renders possible the application of the Infinitesimal Calculus to physics. Leibnizian Infinitesimal Calculus is one of the best examples of his Universal Characteristic, particularly because of its usefulness in the Art of Invention.