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.

arXiv comment19 pages, 1 figure. See http://www.ams.org/notices/201211. arXiv admin note: text overlap with arXiv:1205.0174

References in corpus (8)

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• Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus
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Cited by in corpus (18)

• Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
• Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus
• Approaches to analysis with infinitesimals following Robinson, Nelson, and others
• Almost equal: Method of adequality from Diophantus to Fermat and beyond
• Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics
• A Cauchy-Dirac delta function
• Interpreting the infinitesimal mathematics of Leibniz and Euler
• Procedures of Leibnizian infinitesimal calculus: An account in three modern frameworks
• Toward a history of mathematics focused on procedures
• Leibniz's well-founded fictions and their interpretations
• An integer construction of infinitesimals: Toward a theory of Eudoxus hyperreals
• Euler's lute and Edwards' oud
• Toward a clarity of the extreme value theorem
• Controversies in the foundations of analysis: Comments on Schubring's Conflicts
• Historical infinitesimalists and modern historiography of infinitesimals
• The Mathematical Intelligencer flunks the Olympics
• Is Leibnizian calculus embeddable in first order logic?
• Infinitesimals as an issue in neo-Kantian philosophy of science