Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries

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Walter de Gruyter (2008)
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Abstract

"The development of the calculus during the 17th century was successful in mathematical practice, but raised questions about the nature of infinitesimals: were they real or rather fictitious? This collection of essays, by scholars from Canada, the US, Germany, United Kingdom and Switzerland, gives a comprehensive study of the controversies over the nature and status of the infinitesimal. Aside from Leibniz, the scholars considered are Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. The collection also contains newly discovered marginalia of Leibniz to the writings of Hobbes."--BOOK JACKET.

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9783110202168   9783110211863   3110202166

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10.1515/9783110211863
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Chapters

An Enticing Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus.Bradley Bassler
Archimedes, Infinitesimals and the Law of Continuity: On Leibniz’s Fictionalism.Samuel Levey
Dead Force, Infinitesimals, and the Mathematicization of Nature.Daniel Garber
Generality and Infinitely Small Quantities in Leibniz’s Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves.Eberhard Knobloch
Introduction.Douglas Jesseph & Ursula Goldenbaum
Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz.Siegmund Probst
Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics.Philip Beeley
Indivisibilia Vera – How Leibniz Came to Love Mathematics.Douglas Jesseph & Ursula Goldenbaum
Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals.Richard Arthur
Leibniz’s Calculation with Compendia.Herbert Breger
Leibniz on Infinitesimals and the Reality of Force.Donald Rutherford
Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals.Fritz Nagel
Productive Ambiguity in Leibniz’s Representation of Infinitesimals.Emily Grosholz
Rule of Continuity and Infinitesimals in Leibniz’s Physics.François Duchesneau
Truth in Fiction: Origins and Consequences of Leibniz’s Doctrine of Infinitesimal Magnitudes.Douglas Jesseph

Similar books and articles

Truth in Fiction: Origins and Consequences of Leibniz’s Doctrine of Infinitesimal Magnitudes.Douglas Jesseph - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Leibniz’s Calculation with Compendia.Herbert Breger - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Leibniz on Infinitesimals and the Reality of Force.Donald Rutherford - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Rule of Continuity and Infinitesimals in Leibniz’s Physics.François Duchesneau - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Productive Ambiguity in Leibniz’s Representation of Infinitesimals.Emily Grosholz - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Indivisibilia Vera – How Leibniz Came to Love Mathematics.Douglas Jesseph & Ursula Goldenbaum - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals.Fritz Nagel - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Archimedes, Infinitesimals and the Law of Continuity: On Leibniz’s Fictionalism.Samuel Levey - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Introduction.Douglas Jesseph & Ursula Goldenbaum - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals.Richard Arthur - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz.Siegmund Probst - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Dead Force, Infinitesimals, and the Mathematicization of Nature.Daniel Garber - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
An Enticing Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus.Bradley Bassler - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Generality and Infinitely Small Quantities in Leibniz’s Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves.Eberhard Knobloch - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics.Philip Beeley - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.

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Author Profiles

Ursula Goldenbaum
Emory University
Douglas Jesseph
University of South Florida

Citations of this work

Leibniz versus Ishiguro: Closing a Quarter Century of Syncategoremania.Tiziana Bascelli, Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, David M. Schaps & David Sherry - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):117-147.

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