The Oxford Handbook of Generality in Mathematics and the Sciences

Description

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. Content: Prologue: generality as a component of an epistemological culture / Karine Chemla, Renaud Chorlay, David Rabouin -- The role of genericity in the history of dynamical systems theory / Tatiana Roque -- Leibnizian analysis, canonical objects, and generalization / Emily Grosholz -- Models, structure, and generality in Clerk Maxwell's theory of electromagnetism / Olivier Darrigol -- Biological generality: general anatomy from Xavier Bichat to Louis Ranvier / Jean- Gaël Barbara -- Questions of generality as probes into nineteenth- century mathematical analysis / Renaud Chorlay -- Universality versus generality: an interpretation of the dispute over tangents between Descartes and Fermat / Evelyne Barbin -- Algebraic generality versus arithmetic generality in the 1874 controversy between C. Jordan and L. Kronecker / Frédéric Brechenmacher -- Practices of generalization in mathematical physics, in biology, and in evolutionary strategies / Evelyn Fox Keller -- A process of generalization: Kummer's creation of ideal numbers / Jacqueline Boniface -- The value of generality in Michel Chasles's historiography of geometry / Karine Chemla -- Generality in Leibniz's mathematics / Eberhard Knobloch -- The problem of a zgeneraly theory in mathematics: Aristotle and Euclid / David Rabouin -- Generality, generalization, and induction in Poincaré's philosophy / Igor Ly -- Elaboration of a statement on the degree of generality of a property: Poincaré's work on the recurrence theorem / Anne Robadey -- Generality and structures in functional analysis: the influence of Stefan Banach / Frédéric Jaëck -- How general are genera? The genus in systematic zoology / Yves Cambefort -- Homology: an expression of generality in the life sciences / Stéphane Schmitt.