TY  - BOOK
AU  - Goldenbaum,Ursula
AU  - Jesseph,Douglas
TI  - Infinitesimal Differences: Controversies between Leibniz and his Contemporaries 
SN  - 9783110202168
AV  - B2598 .I54 2008eb
U1  - 193 22
PY  - 2008///]
CY  - Berlin, Boston : 
PB  - De Gruyter, 
KW  - Mathematics
KW  - Philosophy
KW  - Congresses
KW  - Physics
KW  - Controversy on the Calculus
KW  - Fictionality of Mathematical Concepts
KW  - Infinitesimalrechnung
KW  - Infinitesimals
KW  - Infinity
KW  - Leibniz, Gottfried Wilhelm
KW  - Leibniz
KW  - Unendlichkeit
KW  - PHILOSOPHY / History & Surveys / Modern
KW  - bisacsh
N1  -  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; restricted access
N2  - 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.
UR  - https://doi.org/10.1515/9783110211863
UR  - https://www.degruyter.com/cover/covers/9783110211863.jpg
ER  -