Berkeley's Philosophy of Mathematics : Science and Its Conceptual Foundations series - Douglas M. Jesseph

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Berkeley's Philosophy of Mathematics

By: Douglas M. Jesseph

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Paperback | 15 September 1993 | Edition Number 1

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329 Pages

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2.32 x 1.67 x 0.18

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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.

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Non-Fiction Philosophy History of Western Philosophy Mathematics History of Mathematics Philosophy of Mathematics

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.

Berkeley's Philosophy of Mathematics

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