Leibnizian and Nonstandard Analysis: Philosophical Problematization of an Alleged Continuity


In the present paper the philosophical and mathematical continuity alleged by A. Robinson in Nonstandard Analysis (1966) between his theory and Leibniz’s calculus is investigated. In Section 1, after a brief overview of the history of analysis, we expose the historical, mathematical and philosophical aspects of Leibniz’s calculus. In Section 2 the main technical aspects of nonstandard analysis are presented, and Robinson’s philosophy is discussed. In Section 2.1 we claim the absence of a complete and direct continuity and the only possibility of a conceptual similarity between Leibniz’s and Robinson’s theories, both at the philosophical and at the mathematical level.

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Ivano Zanzarella
Ruhr-Universität Bochum


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