Description
From pebbles to planets, tigers to tables, pine trees to people; animate and inanimate, natural and artificial; bodies are everywhere. Bodies populate the world, acting and interacting with one another, and they are the subject-matter of Newton's laws of motion. But what is a body? And how can we know how they behave? In Philosophical Mechanics in the Age of Reason, Katherine Brading and Marius Stan examine the struggle for a theory of bodies.At the beginning of the 18th century, physics was the branch of philosophy that studied bodies in general. Its primary task was to provide a qualitative account of the nature of bodies, including their essential properties, causal powers, and generic behaviors. Pursued by a variety of figures both canonical (from Leibniz to Kant) and less familiar (from Du Châtelet and Euler to d'Alembert and Lagrange), this proved a difficult task. At stake were the appropriate epistemologies and methods for theorizing about the natural world. Solutions demanded the combined resources of philosophy, physics, and mechanics: what Brading and Stan call a "philosophical mechanics."Brading and Stan analyze a century of widespread, concerted efforts to solve "the problem of bodies," they examine the consequences of the many failures, both for the problem itself and for philosophy more generally. They reveal relationships among disparate themes of 18th century physics and philosophy, from the nature of matter to the motion of a vibrating string; causation to the principle of least action; and the role of subtle matter in collision theory to analytic mechanics. All of these, Brading and Stan argue, are related to the eventual emergence of physics as an independent discipline, autonomous from philosophy, more than a century after Newton's Principia. This book provides a new framing of natural philosophy and its transformations in the Enlightenment; and it proposes an account of how physics and philosophy evolved into distinct fields of inquiry.
Table of Contents
1. A Golden Age1.1. Introduction1.2. The Problem of Bodies1.3. Philosophical mechanics1.4. Constructive and principle approaches1.5. The Unity of Physical Theory1.6. Collisions and constraints: PCOL and PCON1.7. Methods1.8. Audience1.9. Overview1.10. Conclusions2. Malebranche and French collision theory2.1. Introduction2.2. Correcting Descartes: Malebranche's early theory of collisions2.3. Leibniz's objections to Malebranche's early collision theory2.4. Malebranche's mature theory of collisions2.5. After Malebranche: hard bodies in the competition of 1724 and beyond2.6. After Malebranche: elastic rebound and the prize competition of 17262.7. Open questions, hidden problems2.8. Conclusions3. Beyond Newton and Leibniz: bodies in collision3.1. Introduction3.2. Newtonian collisions3.3. Leibniz on collisions3.4. Leibnizian collisions in Hermann and Wolff3.5. The Problem of Collisions (PCOL)4. The Problem of Bodies4.1. Introduction4.2. The scope and remit of physics4.3. The Problem of Bodies: Nature and Action4.4. The Problem of Bodies: Evidence and Principle4.5. The methods of Newtonian physics4.6. Substance and causation4.7. The goal: a philosophical mechanics5. Body and force in the physics of collisions: Du Châtelet and Euler5.1. Introduction5.2. Nature: extension as a property of bodies5.3. Action5.4. Du Châtelet and Action5.5. Euler and Action5.6. Conclusions6. Searching for a new physics: Kant and Boscovich6.1. Introduction6.2. The physics of bodies in Kant and Boscovich6.3. Kant's philosophical mechanics6.4. Boscovich's philosophical mechanics6.5. Conclusions7. Shifting sands in philosophical mechanics7.1. Introduction7.2. Methodology7.3. Elusive mass7.4. Contact action7.5. A general theory of bodies in motion7.6. Shifting sands7.7. From rational to philosophical mechanics7.8. Rational mechanics ascendant7.9. Conclusions8. Early work in the rational mechanics of constrained motion8.1. Introduction8.2. Personnel and work sites8.3. New territory: oscillating systems8.4. The compound pendulum8.5. From special problems to general principles8.6. Implications for philosophical mechanics8.7. Conclusions9. Constructive and principle approaches in d'Alembert's Treatise9.1. Introduction9.2. Constructive and principle approaches9.3. D'Alembert's Treatise on Dynamics: its structure and contents9.4. The Treatise as rational mechanics9.5. The Treatise as philosophical mechanics: a constructive reading9.6. The Treatise as philosophical mechanics: a principle reading9.7. The unity of philosophical mechanics: ontic and nomic9.8. Nature, Action, Evidence, and Principle9.9. Conclusions10. Building bodies: Euler and impressed force mechanics10.1. Introduction10.2. Solving MCON10.3. Newton's Lex Secunda, Euler's principles, Cauchy's laws of motion10.4. Solving MCON110.5. Assessment10.6. Conclusions11. External obstacles: Lagrange and the mechanics of constraints11.1. Introduction11.2. The Principle of Virtual Velocities and Lagrange's Principle11.3. Constraints: equations of condition11.4. Lagrange's Relaxation Postulate: the kinematics and dynamics of constraints11.5. Philosophical mechanics and Lagrange's Mechanique11.6. Action11.7. Evidence11.8. Assessment11.9. Conclusions12. Philosophical mechanics in the Late Enlightenment12.1. Introduction12.2. Makers and spaces12.3. Lagrangian nomic unification12.4. Molecular ontic unification12.5. The Cauchy package12.6. Disunity12.7. Conclusions: A Golden Age
