Leibniz's Laws of Continuity and Homogeneity

Abstract

We explore Leibniz's understanding of the differential calculus, and argue that his methods were more coherent than is generally recognized. The foundations of the historical infinitesimal calculus of Newton and Leibniz have been a target of numerous criticisms. Some of the critics believed to have found logical fallacies in its foundations. We present a detailed textual analysis of Leibniz's seminal text Cum Prodiisset, and argue that Leibniz's system for differential calculus was free of contradictions.

19 pages, 1 figure. See http://www.ams.org/notices/201211. arXiv admin note: text overlap with arXiv:1205.0174

References in corpus (3)

• Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
• Ten Misconceptions from the History of Analysis and Their Debunking
• Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics

Cited by in corpus (8)

• Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
• Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics
• A Cauchy-Dirac delta function
• Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks
• Toward a history of mathematics focused on procedures
• Toward a clarity of the extreme value theorem
• Historical infinitesimalists and modern historiography of infinitesimals
• Infinitesimals as an issue in neo-Kantian philosophy of science