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The Oxford Handbook of Generality in Mathematics and the Sciences

Karine Chemla, Renaud Chorlay, David Rabouin

Contributeurs : Jean-Gaël Barbara, Evelyne Barbin, Jacqueline Boniface, Frédéric Brechenmacher, Yves Cambefort, Karine Chemla, Renaud Chorlay, Olivier Darrigol, Emily Grosholz, Frédéric Jaëck, Evelyn Fox Keller, Eberhard Knobloch, Igor Ly, Anne Robadey, Tatiana Roque, Stéphane Schmitt

Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how collectives have valued generality and how they have worked with specific types of "general" entities, procedures, and arguments.

Range of scientific disciplines and historical periods represented
Clear introduction spelling out the key features and the main connections between the chapters
Many excerpts of significant texts translated into English for the first time
Contributions from an outstanding international team

 :: Oxford University Press
 :: 528 p.
 :: June 2016
 :: 9780198777267


1 : Prologue : Generality as a Component of an Epistemological Culture, Karine Chemla, Renaud Chorlay, David Rabouin
Part I : The Meaning of Value of Generality
2 : The Value of Generality in Michel Chasles’s Historiography of Geometry, Karine Chemla
3 : Generality in Leibniz’s Mathematics, Eberhard Knobloch
4 : The Problem of a "General" Theory in Mathematics : Aristotle and Euclid, David Rabouin
5 : Generality and Generalization in Poincaré’s Philosophy, Igor Ly

Part II : Statements and Concepts : The Formulation of the General
6 : Elaboration of a Statement on the Degree of Generality of a Property : Poincaré’s Work on Recurrence Theorem, Anne Robadey
7 : Structures in Functional Analysis and Generality in Banach’s Ph.D. Dissertation, Frédéric Jaëck
8 : How General are Genera ? The Genus in Systematic Zoology, Yves Cambefort
9 : Homology : An Expression of Generality in the Life Sciences, Stéphane Schmitt
10 : Different Notions of Genericity in the Classification Problem of Dynamical Systems, Tatiana Roque

Part III : Practices of Generality
11 : Leibnizian Analysis, Canonical Objects, and Generlization, Emily Grosholz
12 : Models, Structure and the Generality in Clerk Maxwell’s Theory of Electromagnetism, Olivier Darrigol
13 : Biological Generality : General Anatomy from Xavier Bichat to Louis Ranvier, Jean-Gaël Barbara
14 : Questions of Generality as Probes into Nineteenth Century Analysis, Renaud Chorlay
15 : Universality versus Generality : An Interpretation of the Dispute over Tangents between Descartes and Fermat, Evelyne Barbin
16 : Algebraic Generality versus Arithmetic Generality in the Controversy between C. Jordan and L. Kronecker (1874), Frédéric Brechenmacher
17 : Practices of Generalization in Mathematical Physics, in Biology, and in Evolution, Evelyn Fox Keller
18 : Kummer’s Generalization of Arithmetical Properties as Applied to Certain Complex Numbers, Jacqueline Boniface