The Oxford Handbook of Generality in Mathematics and the Sciences
The Oxford Handbook of Generality in Mathematics and the Sciences
Laboratoire SPHERE UMR 7219 (ex-REHSEIS), Université Paris 7—CNRS
Laboratoire SPHERE UMR 7219 (ex-REHSEIS), Université Paris 7— CNRS
Laboratoire SPHERE UMR 7219 (ex-REHSEIS), Université Paris 7—CNRS
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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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Front Matter
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1
Prologue: generality as a component of an epistemological culture
Karine Chemla and others
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Part I The meaning and value of generality
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Section I.1 Epistemic and epistemological values
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Section I.2 Actors’ reflections on generality in science
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Part II Statements and concepts: the formulation of the general
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Section II.1 Developing a new kind of statement
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Section II.2 A diachronic approach: continuity and reinterpretation
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Section II.3 Circulation between epistemological cultures
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Part III Practices of generality
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Section III.1 Scientists at work
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Section III.2 A diachronic approach: continuity and contrasts
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Section III.3 A synchronic approach: controversies
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15
Universality versus generality: an interpretation of the dispute over tangents between Descartes and Fermat
Evelyne Barbin
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16
Algebraic generality versus arithmetic generality in the 1874 controversy between C. Jordan and L. Kronecker
Frédéric Brechenmacher
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17
Practices of generalization in mathematical physics, in biology, and in evolutionary strategies
Evelyn Fox Keller
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15
Universality versus generality: an interpretation of the dispute over tangents between Descartes and Fermat
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Section III.4 Circulation between epistemological cultures
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End Matter
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