Infinitesimal differences : controversies between leibniz and his contemporaries / edited by Ursula Goldenbaum and Douglas Jesseph.

Format:

Book

Contributor:

Goldenbaum, Ursula.

Jesseph, Douglas Michael.

Language:

English

Subjects (All):

Physics--Philosophy--Congresses.

Physics.

Mathematics--Philosophy--Congresses.

Mathematics.

Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716--Criticism and interpretation--Congresses.

Leibniz, Gottfried Wilhelm.

Physical Description:

1 online resource (336 p.)

Place of Publication:

Berlin ; New York : Walter De Gruyter, c2008.

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Table of Contents

Introduction

Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals

Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics

Indivisibilia Vera - How Leibniz Came to Love Mathematics

Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz

Archimedes, Infinitesimals and the Law of Continuity: On Leibniz's Fictionalism

An Enticing (Im)Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus

Productive Ambiguity in Leibniz's Representation of Infinitesimals

Generality and Infinitely Small Quantities in Leibniz's Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves

Leibniz's Calculation with Compendia

Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals

Truth in Fiction: Origins and Consequences of Leibniz's Doctrine of Infinitesimal Magnitudes

Rule of Continuity and Infinitesimals in Leibniz's Physics

Leibniz on Infinitesimals and the Reality of Force

Dead Force, Infinitesimals, and the Mathematicization of Nature

Backmatter

Notes:

"This volume had its beginnings in a conference entitled The Metaphysical and Mathematical Discussion os the Status of Infinitesimals in Leibniz's Time held in April 2006 at Emory University"--Introd.

Includes bibliographical references (p. [309]-323) and index.

ISBN:

9786613398284

9781283398282

1283398281

9783110211863

3110211866

OCLC:

476206249