Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Paperback | June 15, 1999

byPaolo Mancosu

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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, thearithmetic 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 mathematicsof the period. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, thefoundational relevance of Descartes' Geometrie, the relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies betweentechnical development and philosophical reflection in seventeenth century mathematics.

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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, thearithmetic of infinites, and the calculus had been...

Paolo Mancosu is at University of California at Berkeley.

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Format:PaperbackPublished:June 15, 1999Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195132440

ISBN - 13:9780195132441

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Table of Contents

1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century1.1. The Quaestio de Certitudine Mathematicarum1.2. The Quaestio in the Seventeenth Century1.3. The Quaestio and Mathematical Practice2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity2.1. Magnitudes, Ratios, and the Method of Exhaustion2.2. Cavalieri's Two Methods of Indivisibles2.3. Guldin's Objections to Cavalieri's Geometry of Indivisibles2.4. Guldin's Centrobaryca and Cavalieri's Objections3. Descartes' Geometrie3.1. Descartes' Geometrie3.2. The Algebraization of Mathematics4. The Problem of Continuity4.1. Motion and Genetic Definitions4.2. The "Casual" Theories in Arnauld and Bolzano4.3. Proofs by Contradiction from Kant to the Present5. Paradoxes of the Infinite5.1. Indivisibles and Infinitely Small Quantities5.2. The Infinitely Large6. Leibniz's Differential Calculus and Its Opponents6.1. Leibniz's Nova Methodus and L'Hopital's Alalyse des Infiniment Petits6.2. Early Debates with Cluver and Nieuwentijt6.3. The Foundational Debate in the Paris Academy of SciencesAppendix: Giuseppe Biancani's De Mathematicarum Natura, Translated by Gyula KlimaNotesReferencesIndex

Editorial Reviews

"Mancosu's scholarly book is very carefully researched, but it is also clearly written and fascinating to read. It is not to be missed by anyone with a serious interest in philosophy of mathematics."--Philosophia Mathematica