Philosophy of mathematics and mathematical practice in the seventeenth century:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York
Oxford University Press
1996
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 249-265) and index Cover -- Contents -- 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' 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 "Causal" 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 Analyse 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 -- Notes -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y. This book provides the first comprehensive account of the relationship between philosophy of mathematics and the mathematical practice of the seventeenth century - the most eventful period of mathematical development in history. Starting with the Renaissance debates on the certainty of mathematics, the author leads the readers through the foundational issues raised by the emergence of new mathematical techniques including the influence of the Aristotelian conception of science in Cavalieri and Guldin. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical developments and philosophical reflection in seventeenth century mathematics |
| Beschreibung: | 1 Online-Ressource (viii, 275 p.) |
| ISBN: | 0195359151 1280443669 9780195359152 9781280443664 |
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Datensatz im Suchindex
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| author | Mancosu, Paolo |
| author_facet | Mancosu, Paolo |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.9/032 |
| dewey-search | 510.9/032 |
| dewey-sort | 3510.9 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | 1600 - 1699 fast Geschichte 1600-1700 Geschichte 1600-1700 gnd |
| era_facet | 1600 - 1699 Geschichte 1600-1700 |
| format | Electronic eBook |
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| spelling | Mancosu, Paolo Verfasser aut Philosophy of mathematics and mathematical practice in the seventeenth century Paolo Mancosu New York Oxford University Press 1996 1 Online-Ressource (viii, 275 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 249-265) and index Cover -- Contents -- 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' 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 "Causal" 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 Analyse 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 -- Notes -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y. This book provides the first comprehensive account of the relationship between philosophy of mathematics and the mathematical practice of the seventeenth century - the most eventful period of mathematical development in history. Starting with the Renaissance debates on the certainty of mathematics, the author leads the readers through the foundational issues raised by the emergence of new mathematical techniques including the influence of the Aristotelian conception of science in Cavalieri and Guldin. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical developments and philosophical reflection in seventeenth century mathematics 1600 - 1699 fast Geschichte 1600-1700 Geschichte 1600-1700 gnd rswk-swf MATHEMATICS / History & Philosophy bisacsh Filosofie gtt Wiskunde gtt Mathematics / Philosophy fast Geschichte Mathematik Philosophie Mathematics Europe Philosophy History 17th century Mathematik (DE-588)4037944-9 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Europa Europa (DE-588)4015701-5 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s Geschichte 1600-1700 z 1\p DE-604 Europa (DE-588)4015701-5 g 2\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=176335 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mancosu, Paolo Philosophy of mathematics and mathematical practice in the seventeenth century MATHEMATICS / History & Philosophy bisacsh Filosofie gtt Wiskunde gtt Mathematics / Philosophy fast Geschichte Mathematik Philosophie Mathematics Europe Philosophy History 17th century Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
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| title | Philosophy of mathematics and mathematical practice in the seventeenth century |
| title_auth | Philosophy of mathematics and mathematical practice in the seventeenth century |
| title_exact_search | Philosophy of mathematics and mathematical practice in the seventeenth century |
| title_full | Philosophy of mathematics and mathematical practice in the seventeenth century Paolo Mancosu |
| title_fullStr | Philosophy of mathematics and mathematical practice in the seventeenth century Paolo Mancosu |
| title_full_unstemmed | Philosophy of mathematics and mathematical practice in the seventeenth century Paolo Mancosu |
| title_short | Philosophy of mathematics and mathematical practice in the seventeenth century |
| title_sort | philosophy of mathematics and mathematical practice in the seventeenth century |
| topic | MATHEMATICS / History & Philosophy bisacsh Filosofie gtt Wiskunde gtt Mathematics / Philosophy fast Geschichte Mathematik Philosophie Mathematics Europe Philosophy History 17th century Mathematik (DE-588)4037944-9 gnd Philosophie (DE-588)4045791-6 gnd |
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