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Berkeleys Philosophy of Mathematics

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Overview

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.

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Product Details

Meet the Author

Douglas M. Jesseph is assistant professor of philosophy at North Carolina State University.

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Table of Contents

Preface Works Frequently Cited Introduction
1. 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
2. Berkeley's New Foundations for Geometry The Early View Abstraction and Geometry in the Principles
Geometry in the New Theory of Vision
Geometry and Abstraction in the Later Works
3. 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
4. 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
5. Berkeley and the Calculus: Writings before the Analyst
The Calculus in the Philosophical Commentaries
The Essay "Of Infinites"
The Principles and Other Works
6. Berkeley and the Calculus: The Analyst
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 The Analyst Evaluated
7. The Aftermath of the Analyst
Berkeley's Disputes with Jurin and Walton Other Reponses to Berkeley The Significance of the Analyst
Conclusions Bibliography Index

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