Berkeley's Philosophy of MathematicsUniversity of Chicago Press, 15 sept. 1993 - 322 pagini 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. |
Cuprins
Introduction | 1 |
1 Abstraction and the Berkeleyan Philosophy of Mathematics | 9 |
2 Berkeleys New Foundations for Geometry | 44 |
3 Berkeleys New Foundations for Arithmetic | 88 |
The Background | 123 |
Writings before the Analyst | 152 |
The Analyst | 178 |
7 The Aftermath of the Analyst | 231 |
Conclusions | 297 |
301 | |
317 | |
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Termeni și expresii frecvente
abstract general idea abstract ideas Alciphron algebra Analyst argues argument from impossibility arithmetic Arithmetica Barrow Berkeley Berkeley's account Berkeley's claim Berkeley's critique Berkeley's New Foundations Berkeley's philosophy Berkeley's views Berkeleyan calculus circle classical geometry Colin Maclaurin Commentaries conceive conception consider curve declares demonstration difference differential calculus doctrine of abstract epistemology equal equation Euclidean geometry evanescent exist extension figures flowing quantity formalistic idea of number indivisibles infinite divisibility infinite number infinitely small infinitesimal magnitudes Infinities insists Jurin Leibniz Leibnizian limit Maclaurin Malebranche mathe mathematicians Mathesis Universalis matics method of exhaustion Method of Fluxions metic mind minima motion Newton Newton's Method Newtonian Nieuwentijt object of geometry Paman perceived philosophy of mathematics prime and ultimate Principles problems procedure proof proportion Quadrature reason rejection represent rigor Robins signs Sir Isaac subtangent supposed supposition theorem Theory of Vision thesis of infinite things tion Treatise triangle truth ultimate ratios vanish Wallis Walton
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