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 :

1 – Karine Chemla, Renaud Chorlay and David Rabouin : Prologue: Generality as a Component of an Epistemological Culture

Part I: The Meaning of Value of Generality

Section I.1 Epistemic and epistemological values

2 – Karine Chemla: The Value of Generality in Michel Chasles’s Historiography of Geometry

3 – Eberhard Knobloch: Generality in Leibniz’s Mathematics

Section I.2 Actors’ reflections on generality in science

4 – David Rabouin: The Problem of a « General » Theory in Mathematics: Aristotle and Euclid

5 – Igor Ly: Generality and Generalization in Poincaré’s Philosophy

Part II: Statements and Concepts: The Formulation of the General

Section II.1 Developing a new kind of statement

6 – Anne Robadey: Elaboration of a Statement on the Degree of Generality of a Property: Poincaré’s Work on Recurrence Theorem
7 – Frédéric Jaëck: Structures in Functional Analysis and Generality in Banach’s Ph.D. Dissertation

Section II.2 A diachronic approach: continuity and reinterpretation

8 – Yves Cambefort: How General are Genera? The Genus in Systematic Zoology

9 – Stéphane Schmitt: Homology: An Expression of Generality in the Life Sciences

Section II.3 Circulation between epistemological cultures

10 – Tatiana Roque: The role of genericity in the history of dynamical systems theory

Part III: Practices of Generality

Section III.1 Scientists at work

11 – Emily Grosholz: Leibnizian Analysis, Canonical Objects, and Generlization

12 – Olivier Darrigol: Models, structure, and generality in Clerk Maxwell’s theory of electromagnetism

Section III.2 A diachronic approach: continuity and contrasts

13 – Jean-Gaël Barbara: Biological Generality: General Anatomy from Xavier Bichat to Louis Ranvier

14 – Renaud Chorlay: Questions of Generality as Probes into Nineteenth Century Analysis

15 – Evelyne Barbin: Universality versus Generality: An Interpretation of the Dispute over Tangents between Descartes and Fermat

16 – Frédéric Brechenmacher: Algebraic Generality versus Arithmetic Generality in the Controversy between C. Jordan and L. Kronecker (1874)

17 – Evelyn Fox Keller: Practices of generalization in mathematical physics, in biology, and in evolutionary strategies

Section III.4 Circulation between epistemological cultures

18 – Jacqueline Boniface: A process of generalization: Kummer’s creation of ideal numbers