Infinitesimal Differences: Controversies between Leibniz and his Contemporaries

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Ursula Goldenbaum, Douglas Jesseph
Walter de Gruyter, 3 de nov. 2008 - 633 pàgines

The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes overstatus of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its procedures seemed to lack an adequate metaphysical or methodological justification. The topic is also of philosophical interest, because Leibniz freely employed the language of infinitesimal quantities in the foundations of his dynamics and theory of forces. Thus, philosophical disputes over the Leibnizian science of bodies naturally involve questions about the nature of infinitesimals. The volume also includes newly discovered Leibnizian marginalia in the mathematical writings of Hobbes.

 

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Continguts

Introduction
1
Newton and Leibniz on the Status of Infinitesimals
7
John Wallis and his Critics
31
Indivisibilia Vera How Leibniz Came to Love Mathematics
53
Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz
95
On Leibnizs Fictionalism
107
Infinitesimals Differentials and the Leibnizian Calculus
135
Productive Ambiguity in Leibnizs Representation of Infinitesimals
153
Leibnizs Calculation with Compendia
185
Nieuwentijt Leibniz and Jacob Hermann on Infinitesimals
199
Origins and Consequences of Leibnizs Doctrine of Infinitesimal Magnitudes
215
Rule of Continuity and Infinitesimals in Leibnizs Physics
235
Leibniz on Infinitesimals and the Reality of Force
255
Dead Force Infinitesimals and the Mathematicization of Nature
281
Backmatter
307
Copyright

Generality and Infinitely Small Quantities in Leibnizs Mathematics The Case of his Arithmetical Quadrature of Conic Sections and Related Curves
171

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Sobre l'autor (2008)

Ursula Goldenbaum, Emory University, Atlanta, GA, USA and Institute for Advanced Study at Princeton; Douglas Jesseph, North Carolina State University, Raleigh, USA.

Informació bibliogràfica