Berkeley's Philosophy of Mathematics

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University of Chicago Press, Sep 15, 1993 - Mathematics - 322 pages
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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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Contents

Abstraction and the Berkeleyan Philosophy of Mathematics
9
SeventeenthCentury Background
13
Berkeleys Case against Abstract Ideas
20
Sources of Berkeleys Antiabstractionism
38
Berkeleys New Foundations for Geometry
44
The Early View
45
Abstraction and Geometry in the Principles
69
Geometry in the New Theory of Vision
78
Leibniz and the Differential Calculus
138
The Newtonian Method of Fluxions
143
Berkeley and the Calculus Writings before the Analyst
152
The Calculus in the Philosophical Commentaries
153
The Essay Of Infinities
162
The Principles and Other Works
173
Berkeley and the Calculus The Analyst
178
The Object of the Calculus
183

Geometry and Abstraction in the Later Works
83
Berkeleys New Foundations for Arithmetic
88
Geometry versus Arithmetic
89
Numbers as Creatures of the Mind
95
The Nonabstract Nature of Numbers
99
Berkeleys Arithmetical Formalism
106
Algebra as an Extension of Arithmetic
114
The Primacy of Practice over Theory
117
Berkeleys Formalism Evaluated
118
Berkeley and the Calculus The Background
123
Classical Geometry and the Proof by Exhaustion
124
Infinitesimal Mathematics
129
The Method of Indivisibles
132
The Principles and Demonstrations of the Calculus
189
The Compensation of Errors Thesis
199
Ghosts of Departed Quantities and Other Vain Abstractions
215
The Analyst Evaluated
226
The Aftermath of the Analyst
231
Berkeleys Disputes with Jurin and Walton
233
Other Responses to Berkeley
259
The Significance of the Analyst
292
Conclusions
297
Bibliography
301
Index
317
Copyright

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About the author (1993)

Elizabeth A. Kaye specializes in communications as part of her coaching and consulting practice. She has edited Requirements for Certification since the 2000-01 edition.


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