The Oxford Handbook of Generality in Mathematics and the Sciences

by Karine Chemla (Editor), Renaud Chorlay (Editor), David Rabouin (Editor)

Overview

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.

The books connects history and philosophy of mathematics and the sciences at the intersection of two of the most fruitful contemporary lines of research: historical epistemology, in which values (e.g. "objectivity", "accuracy") are studied from a historical viewpoint; and the philosophy of scientific practice, in which conceptual developments are seen as embedded in networks of social, instrumental, and textual practices. Each chapter provides a self-contained case-study, with a clear exposition of the scientific content at stake. The collection covers a wide range of scientific domains - with an emphasis on mathematics - and historical periods. It thus allows a comparative perspective which suggests a non-linear pattern for a history of generality. The introductory chapter spells out the key issues and points to the connections between the chapters.

Product Details

ISBN-13:	9780198777267
Publisher:	Oxford University Press
Publication date:	09/15/2016
Series:	Oxford Handbooks
Pages:	528
Product dimensions:	6.90(w) x 9.70(h) x 1.50(d)

About the Author

Karine Chemla is currently Senior Researcher at the French National Center for Scientific Research (CNRS), in the research group SPHERE. Her interest is in the history of mathematics in ancient China within the context of a world history. She also researches modern European mathematics. She focuses, from a historical anthropology viewpoint, on the relationship between mathematics and the various cultures in the context of which it is practiced and cultivated. Chemla published, with Guo Shuchun, Les neuf chapitres (2004). She edited The History of Mathematical Proof in Ancient Traditions (2012), and co-edited with J. Virbel Texts, Textual acts and the History of Science (2015). Since 2011, she works with Agathe Keller and Christine Proust on the ERC project "Mathematical Sciences in the Ancient World" (SAW).

Renaud Chorlay was trained in the social sciences at Sciences-Po Paris, and in mathematics and history of mathematics at Paris Diderot University. He works in the teacher-training department of Paris Sorbonne University. His main research field is the history of mathematics in the modern period, with specific interests in qualitative analysis, topology and differential geometry. He also works on the connections between history of mathematics and teaching of mathematics, either in the classroom, in teacher-training, or in theoretical didactics.

David Rabouin is a Senior Research Fellow (CR1) at the French National Center for Scientific Research (CNRS), in the research group SPHERE. His interest is in the history of philosophy and mathematics in early Modern Times, with special focus on Descartes and Leibniz. He also works in contemporary French Philosophy.

Table of Contents

1. Prologue: Generality as a Component of an Epistemological Culture, Karine Chemla, Renaud Chorlay, David RabouinPart I: The Meaning of Value of Generality2. The Value of Generality in Michel Chasles's Historiography of Geometry, Karine Chemla3. Generality in Leibniz's Mathematics, Eberhard Knobloch4. The Problem of a "General" Theory in Mathematics: Aristotle and Euclid, David Rabouin5. Generality and Generalization in Poincare's Philosophy, Igor LyPart II: Statements and Concepts: The Formulation of the General6. Elaboration of a Statement on the Degree of Generality of a Property: Poincare's Work on Recurrence Theorem, Anne Robadey7. Structures in Functional Analysis and Generality in Banach's Ph.D. Dissertation, Frederic Jaeck8. How General are Genera? The Genus in Systematic Zoology, Yves Cambefort9. Homology: An Expression of Generality in the Life Sciences, Stephane Schmitt10. Different Notions of Genericity in the Classification Problem of Dynamical Systems, Tatiana RoquePart III: Practices of Generality11. Leibnizian Analysis, Canonical Objects, and Generlization, Emily Grosholz12. Models, Structure and the Generality in Clerk Maxwell's Theory of Electromagnetism, Olivier Darrigol13. Biological Generality: General Anatomy from Xavier Bichat to Louis Ranvier, Jean-Gael Barbara14. Questions of Generality as Probes into Nineteenth Century Analysis, Renaud Chorlay15. Universality versus Generality: An Interpretation of the Dispute over Tangents between Descartes and Fermat, Evelyne Barbin16. Algebraic Generality versus Arithmetic Generality in the Controversy between C. Jordan and L. Kronecker (1874), Frederic Brechenmacher17. Practices of Generalization in Mathematical Physics, in Biology, and in Evolution, Evelyn Fox Keller18. Kummer's Generalization of Arithmetical Properties as Applied to Certain Complex Numbers, Jacqueline Boniface

Editorial Reviews

"This book astonishes with its richness, its methodological relevance, and its novelty. We must recommend this book to a readership specializing in the history and philosophy of science because of the variety of approaches grouped together and because of its undeniable programmatic virtue." — The Journal of the International Society for the History of Philosophy of Science

"[T]his book contains many very good things... Several of the contributors to this volume succeed in showing how careful attention to the special meanings attached to "the general" and its cognates can lead to deeper historical insights." — Isis Journal

...this collective book proposes an interesting theoretical framework as well as a collection of studies which are original and important for the history of science, both from a historical and a methodological viewpoint." — Revue d'histoire des sciences (translated from French)

"Early mathematicians and scientists seldom discussed their use of generality; the authors expertly examine their work to determine how this concept evolved...This is an important resource for practitioners in the areas of the history and philosophy of science and mathematics...Recommended."—CHOICE

"The accessibility of the essays is such that not only the specialist, but anyone engaged in the history of science or one of the book's historical key figures will benefit from them. Its ideal audience will be composed of historians of science with epistemological interests, and epistemologists wishing to engage with historical matters." — Vincenzo De Risi, Early Science and Medicine

From the Publisher