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The philosophy of mathematics and mathematical practice in the seventeenth century

Author: Paolo Mancosu
Publisher: New York : Oxford University Press, 1996.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Provides 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  Read more...

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Genre/Form: History
Document Type: Book
All Authors / Contributors: Paolo Mancosu
ISBN: 0195084632 9780195084634 0195132440 9780195132441
OCLC Number: 185508974
Description: 275 s. : illustrations
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
Responsibility: Paolo Mancosu.

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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. Read more...

 
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