Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Name: Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
Price: 15.9 USD
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ISBN: 9780195132441

ISBN-10: 0195132440

ISBN-13: 9780195132441

Edition: 1999

Authors: Paolo Mancosu

List price: $98.00

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The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader…

Book details

List price: $98.00
Copyright year: 1999
Publisher: Oxford University Press, Incorporated
Publication date: 7/8/1999
Binding: Paperback
Pages: 288
Size: 6.10" wide x 9.09" long x 0.79" tall
Weight: 0.968
Language: English

Paolo Mancosu is Assistant Professor of Philosophy at the University of California at Berkeley. His main interests are in mathematical logic and philosophy of mathematics. He is the author of Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (OUP, 1996).




Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century



The Quaestio de Certitudine Mathematicarum



The Quaestio in the Seventeenth Century



The Quaestio and Mathematical Practice



Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity



Magnitudes, Ratios, and the Method of Exhaustion



Cavalieri's Two Methods of Indivisibles



Guldin's Objections to Cavalieri's Geometry of Indivisibles



Guldin's Centrobaryca and Cavalieri's Objections



Descartes' Geometrie



Descartes' Geometrie



The Algebraization of Mathematics



The Problem of Continuity



Motion and Genetic Definitions



The "Causal" Theories in Arnauld and Bolzano



Proofs by Contradiction from Kant to the Present



Paradoxes of the Infinite



Indivisibles and Infinitely Small Quantities



The Infinitely Large



Leibniz's Differential Calculus and Its Opponents



Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits



Early Debates with Cluver and Nieuwentijt



The Foundational Debate in the Paris Academy of Sciences



Giuseppe Biancani's De Mathematicarum Natura


Notes


References


Index