Reasoning with the infinite : from the closed world to the mathematical universe
著者
書誌事項
Reasoning with the infinite : from the closed world to the mathematical universe
University of Chicago Press, 1998
- タイトル別名
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Les raisons de l'infini : du monde clos à l'univers mathématique
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注記
Translation of: Les raisons de l'infini. Paris : Gallimard, 1993
Bibliography: p. [193]-209
Includes index
内容説明・目次
内容説明
The nature and motions of heavenly objects had always been mysterious and unpredicatable. But the "Scientific Revolution" was revolutionary in part because it saw the advent of many mathematical tools - chief among them calculus - that natural philosophers could use to explain and predict cosmic motions. Michel Blay traces the origins of this revolutionary mathematization of the world, and considers the profound philosophical consequences of submitting the infinite to rational analysis. Blay begins by showing how a metaphysical debate over infinity undermined Galileo's claim that Euclidean geometry was the key to universal knowledge: a complete account of an object's motion required that the concept of infinity be addressed, yet the name of the infinite was reserved to God alone. This insoluble quandary spurred the adoption of Leibniz's new differential and integral calculus, which enabled natural philosophers to begin building a coherent mathematical framework through which the phenomena of nature could be understood.
目次
- Translator's Note Introduction 1: Infinity Eliminated
- or, Huygens's Theory of the Motion of Heavy Bodies 1: Establishing the General Fact of Gravity 2: Mathematical Speculations about Curvilinear Falls 3: The Deductive Scheme of the Science of Motion of Heavy Bodies 2: First and Last Ratios in the Newtonian Theory of Central Forces 1: The Construction of Circular Motion 2: Mechanist Interlude: Centrifugal Force and Weight 3: The Deductive Scheme of Newton's Principia 3: The Science of Motion in the Workshops of Infinity 1: Satisfying Reason 2: Ratios of the Beginnings, Ends, and Continuous Evolution of Motions 4: Motion Algorithmized 1: Introduction and Import of the Leibnizian Calculus 2: The New Algorithmic Science of Motion Epilogue: Fontenelle and the Reasons of Infinity 1: The Mathematics of Infinity 2: Mathematical Physics and the Rationalization of Infinites Notes Bibliography Index
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