Description
Book SynopsisProvides an account of the relationship between mathematical advances of the 17th century and the philosophy of mathematics of the period. Starting with the Renaissance debates on the certainty of mathematics, the book explores the issues raised by the emergence of these mathematical techniques.
Trade ReviewStudents 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 *
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 *
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 *
Table of Contents1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century 1.1: The Quaestio de Certitudine Mathematicarum 1.2: The Quaestio in the Seventeenth Century 1.3: The Quaestio and Mathematical Practice 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity 2.1: Magnitudes, Ratios, and the Method of Exhaustion 2.2: Cavalieri's Two Methods of Indivisibles 2.3: Guldin's Objections to Cavalieri's Geometry of Indivisibles 2.4: Guldin's Centrobaryca and Cavalieri's Objections 3. Descartes' Géométrie 3.1: Descartes' Géométrie 3.2: The Algebraization of Mathematics 4. The Problem of Continuity 4.1: Motion and Genetic Definitions 4.2: The "Casual" Theories in Arnauld and Bolzano 4.3: Proofs by Contradiction from Kant to the Present 5. Paradoxes of the Infinite 5.1: Indivisibles and Infinitely Small Quantities 5.2: The Infinitely Large 6. Leibniz's Differential Calculus and Its Opponents 6.1: Leibniz's Nova Methodus and L'Hôpital's Alalyse des Infiniment Petits 6.2: Early Debates with Clüver and Nieuwentijt 6.3: The Foundational Debate in the Paris Academy of Sciences Appendix: Giuseppe Biancani's De Mathematicarum Natura, Translated by Gyula Klima Notes References Index
