Infinitesimal Differences: Controversies between Leibniz and his Contemporaries

Published by De Gruyter 2008

Infinitesimal Differences

Controversies between Leibniz and his Contemporaries

Edited by: Ursula Goldenbaum and Douglas Jesseph

https://doi.org/10.1515/9783110211863

Overview
Contents

About this book

The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes over status 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.

Author / Editor information

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

Reviews

"As a philosopher, Leibniz thought deeply about the nature of the infinite and the infinitesimal. [...] Infinitesimal Differences makes compulsory reading for anyone interested in how Leibniz defined and manipulated infinitesimals as geometrical, algebraic, and physical magnitudes, and how Leibniz’s ideas on infinitesimals were received–and often misunderstood–by his contemporaries, including acolytes of his, such as Johann Bernoulli."
Niccolò Guicciardini in: NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin, Band 18/ 2010

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	I
Table of Contents Requires Authentication Unlicensed Licensed Download PDF	V
Introduction Ursula Goldenbaum and Douglas Jesseph Requires Authentication Unlicensed Licensed Download PDF	1
Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals Richard Arthur Requires Authentication Unlicensed Licensed Download PDF	7
Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics Philip Beeley Requires Authentication Unlicensed Licensed Download PDF	31
Indivisibilia Vera – How Leibniz Came to Love Mathematics Ursula Goldenbaum Requires Authentication Unlicensed Licensed Download PDF	53
Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz Siegmund Probst Requires Authentication Unlicensed Licensed Download PDF	95
Archimedes, Infinitesimals and the Law of Continuity: On Leibniz’s Fictionalism Samuel Levey Requires Authentication Unlicensed Licensed Download PDF	107
An Enticing (Im)Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus O. Bradley Bassler Requires Authentication Unlicensed Licensed Download PDF	135
Productive Ambiguity in Leibniz’s Representation of Infinitesimals Emily Grosholz Requires Authentication Unlicensed Licensed Download PDF	153
Generality and Infinitely Small Quantities in Leibniz’s Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves Eberhard Knobloch Requires Authentication Unlicensed Licensed Download PDF	171
Leibniz’s Calculation with Compendia Herbert Breger Requires Authentication Unlicensed Licensed Download PDF	185
Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals Fritz Nagel Requires Authentication Unlicensed Licensed Download PDF	199
Truth in Fiction: Origins and Consequences of Leibniz’s Doctrine of Infinitesimal Magnitudes Douglas Jesseph Requires Authentication Unlicensed Licensed Download PDF	215
Rule of Continuity and Infinitesimals in Leibniz’s Physics François Duchesneau Requires Authentication Unlicensed Licensed Download PDF	235
Leibniz on Infinitesimals and the Reality of Force Donald Rutherford Requires Authentication Unlicensed Licensed Download PDF	255
Dead Force, Infinitesimals, and the Mathematicization of Nature Daniel Garber Requires Authentication Unlicensed Licensed Download PDF	281
Backmatter Requires Authentication Unlicensed Licensed Download PDF	307

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Academics, Libraries, Institutes
Pages
- Front matter: 6
- Main content: 627
Keywords: Infinitesimals; Leibniz; Controversy on the Calculus; Infinity; Fictionality of Mathematical Concepts

eBook

Published: November 3, 2008
ISBN: 9783110211863

Hardcover

Published: August 19, 2008
ISBN: 9783110202168