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In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution.
Jesseph begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a "science of abstractions." Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique treatments of geometry and arithmetic and his famous critique of the calculus in "The Analyst."
By putting Berkeley's mathematical writings in the perspective of his larger philosophical project and examining their impact on eighteenth-century British mathematics, Jesseph makes a major contribution to philosophy and to the history and philosophy of science.
| Preface | |
| Works Frequently | |
| Cited Introduction | |
| Abstraction and the Berkeleyan Philosophy of Mathematics | |
| Aristotelian and Scholastic | |
| Background Seventeenth-Century | |
| Background Berkeley's Case against Abstract Ideas | |
| Sources of Berkeley's Antiabstractionism | |
| Berkeley's New Foundations for Geometry | |
| The Early View | |
| Abstraction and Geometry in thePrinciples | |
| Geometry in theNew Theory of Vision | |
| Geometry and Abstraction in the Later Works | |
| Berkeley's New Foundations for Arithmetic Geometry versus Arithmetic Numbers as Creatures of the Mind | |
| The Nonabstract Nature of Numbers | |
| Berkeley's Arithmetical Formalism | |
| Algebra as an Extension of Arithmetic | |
| The Primacy of Practice over Theory | |
| Berkeley's Formalism Evaluated | |
| Berkeley and the Calculus: The Background Classical Geometry and the Proof by Exhaustion Infinitesimal Mathematics | |
| The Method of Indivisibles Leibniz and the Differential Calculus | |
| The Newtonian Method of Fluxions | |
| Berkeley and the Calculus: Writings before theAnalyst | |
| The Calculus in thePhilosophical Commentaries | |
| The Essay "Of Infinites" | |
| ThePrinciplesand Other Works | |
| Berkeley and the Calculus: TheAnalyst The Object of the Calculus | |
| The Principles and Demonstrations of the Calculus | |
| The Compensation of Errors | |
| Thesis Ghosts of Departed Quantities and Other Vain Abstractions | |
| TheAnalystEvaluated | |
| The Aftermath of theAnalyst Berkeley's Disputes with Jurin and Walton | |
| Other Reponses to Berkeley | |
| The Significance of theAnalyst | |
| Conclusions | |
| Bibliography | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9780226398983
ISBN-10: 0226398986
Series: Science & Its Conceptual Foundations S.
Audience:
Professional
Format:
Paperback
Language:
English
Number Of Pages: 334
Published: 15th September 1993
Publisher: The University of Chicago Press
Country of Publication: US
Dimensions (cm): 22.8 x 15.2
x 1.91
Weight (kg): 0.47
Edition Number: 2
