Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

by Paolo Mancosu

Overview

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 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, the foundational 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 between technical development and philosophical reflection in seventeenth century mathematics.

Product Details

ISBN-13:	9780195132441
Publisher:	Oxford University Press
Publication date:	07/08/1999
Edition description:	New Edition
Pages:	288
Sales rank:	729,412
Product dimensions:	9.10(w) x 6.02(h) x 0.74(d)
Lexile:	1500L (what's this?)

About the Author

University of California at Berkeley

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' Géométrie3.1. Descartes' Géométrie3.2. 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'Hôpital's Alalyse des Infiniment Petits6.2. Early Debates with Clüver and Nieuwentijt6.3. The Foundational Debate in the Paris Academy of SciencesAppendix: Giuseppe Biancani's De Mathematicarum Natura, Translated by Gyula KlimaNotesReferencesIndex

Editorial Reviews

"Students of the history of mathematics and philosophers of mathematics will find this a valuable addition to the literature."—Choice

"Mancosu's book shows philosophical acumen as well as high technical competence—and it makes good reading even as it explores abstruse notions or involved technicalities. For historians of early modern mathematics, it is essential reading."—Isis

"Mancosu tells the story well and is good at bringing out significant points"—International Philosophical Quarterly

"Mancosu's book shows philosophical acumen as well as high technical competence—and it makes good reading even as it explores abstruse notions or involved technicalities. For historians of early modern mathematics, it is essential reading."—Isis

"This is a very carefully researched and documented analysis of the rich relationship between philosophy of mathematics and mathematical practice during the 17th century."—Mathematical Reviews

From the Publisher