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" Infinitesimal differences : "
edited by Ursula Goldenbaum and Douglas Jesseph.
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BL
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| Record Number
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863278
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| Title & Author
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Infinitesimal differences : : controversies between Leibniz and his contemporaries /\ edited by Ursula Goldenbaum and Douglas Jesseph.
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| Publication Statement
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Berlin ;New York :: Walter De Gruyter,, ©2008.
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| Page. NO
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1 online resource (vi, 327 pages) :: illustrations
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| ISBN
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1283398281
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: 3110211866
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: 6613398284
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: 9781283398282
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: 9783110211863
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: 9786613398284
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3110202166
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9783110202168
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| Notes
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"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"--Introduction.
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| Bibliographies/Indexes
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Includes bibliographical references (pages 309-323) and index.
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| Contents
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Leery bedfellows : Newton and Leibniz on the status of infinitesimals / Richard Arthur -- Infinity, infinitesimals, and the reform of Cavalieri : John Wallis and his critics / Philip Beeley -- Indivisibilia vera : how Leibniz came to love mathematics. Appendix : Leibniz's marginalia in Hobbes' Opera philosophica and De corpore / Ursula Goldenbaum -- Indivisibles and infinitesimals in early mathematical texts of Leibniz / Siegmund Probst -- Archimedes, infinitesimals and the law of continuity : on Leibniz's fictionalism / Samuel Levey -- An enticing (im)possibility : infinitesimals, differentials, and the Leibnizian calculus / O. Bradley Bassler -- Productive ambiguity in Leibniz's representation of infinitesimals / Emily Grosholz -- Generality and infinitely small quantities in Leibniz's mathematics : the case of his arithmetical quadrature of conic sections and related curves / Eberhard Knobloch -- Leibniz's calculation with compendia / Herbert Breger -- Nieuwentijt, Leibniz, and Jacob Hermann on infinitesimals / Fritz Nagel -- Truth in fiction : origins and consequences of Leibniz's doctrine of infinitesimal magnitudes / Douglas Jesseph -- Rule of continuity and infinitesimals in Leibniz's physics / François Duchesneau -- Leibniz on infinitesimals and the reality of force / Donald Rutherford -- Dead force, infinitesimals, and the mathematicization of nature / Daniel Garber.
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| Abstract
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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 pr.
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Leibniz, Gottfried Wilhelm,1646-1716-- Criticism and interpretation
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Leibniz, Gottfried Wilhelm,1646-1716.
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| Subject
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Mathematics-- Philosophy, Congresses.
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Physics-- Philosophy, Congresses.
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Infinitesimalrechnung
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Mathematics-- Philosophy.
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PHILOSOPHY-- History Surveys-- Modern.
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Physics-- Philosophy.
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Filosofische aspecten.
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Infinitesimaalrekening.
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| Dewey Classification
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193
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| LC Classification
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B2598.I54 2008eb
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| NLM classification
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31.02bcl
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| Added Entry
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Goldenbaum, Ursula.
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Jesseph, Douglas Michael.
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