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The Oxford Handbook of Generality in Mathematics and the Sciences

Online ISBN:
9780191859243
Print ISBN:
9780198777267
Publisher:
Oxford University Press
Book

The Oxford Handbook of Generality in Mathematics and the Sciences

Karine Chemla (ed.),
Karine Chemla
(ed.)
Physics, Université Paris 7
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Laboratoire SPHERE UMR 7219 (ex-REHSEIS), Université Paris 7—CNRS

Renaud Chorlay (ed.),
Renaud Chorlay
(ed.)
Physics, Université Paris 7
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Laboratoire SPHERE UMR 7219 (ex-REHSEIS), Université Paris 7— CNRS

David Rabouin (ed.)
David Rabouin
(ed.)
Physics, Université Paris 7
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Laboratoire SPHERE UMR 7219 (ex-REHSEIS), Université Paris 7—CNRS

Published online:
6 July 2017
Published in print:
14 July 2016
Online ISBN:
9780191859243
Print ISBN:
9780198777267
Publisher:
Oxford University Press

Abstract

This handbook examines how actors have valued generality in mathematics and the sciences and how they worked with specific types of “general” entities, procedures, and arguments. It argues that actors have shaped these various types of generality, mainly by introducing specific terminologies to distinguish between different levels or forms of generality, as well as designing means to work with them, or to work in relation to them. The book is organized into three parts. Part I deals with the meaning and value of generality, and more specifically the value of generality in Michel Chasles’s historiography of geometry and generality in Gottfried Leibniz’s mathematics. Part II focuses on statements and concepts that make up the general, covering topics such as Henri Poincaré’s work on the recurrence theorem and the role of genericity in the history of dynamical systems theory. Part III explores the practices of generality, including the dispute over tangents between René Descartes and Pierre de Fermat, generality in James Clerk Maxwell’s theory of electromagnetism, and practices of generalization in mathematical physics, biology, and evolutionary strategies.

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