Philosophy of mathematics and mathematical practice in the seventeenth century

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Philosophy of mathematics and mathematical practice in the seventeenth century

Paolo Mancosu

Oxford University Press, 1999, c1996

  • : pbk

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注記

Bibliography: p. 249-265

Includes index

内容説明・目次

内容説明

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting 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 relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.

目次

1. 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' Geometrie 3.1: Descartes' Geometrie 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'Hopital's Alalyse des Infiniment Petits 6.2: Early Debates with Cluver 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

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