Philosophical Mechanics in the Age of Reason

Katherine Brading is Professor of Philosophy at Duke University. She is co-editor of Symmetries in Physics: Philosophical Reflections (with Elena Castellani) and author of Emilie Du Châtelet and the Foundations of Physical Science. Marius Stan is Associate Professor of Philosophy at Boston College. He is author of Kant's Natural Philosophy.

• 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. Conclusions 2. 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. Conclusions 3. 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 mechanics 5. 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. Conclusions 6. 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. Conclusions 7. 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. Conclusions 8. Early work in the rational mechanics of constrained motion 8.1. Introduction 8.2. Personnel and work sites 8.3. New territory: oscillating systems 8.4. The compound pendulum 8.5. From special problems to general principles 8.6. Implications for philosophical mechanics 8.7. Conclusions 9. Constructive and principle approaches in d'Alembert's Treatise 9.1. Introduction 9.2. Constructive and principle approaches 9.3. D'Alembert's Treatise on Dynamics: its structure and contents 9.4. The Treatise as rational mechanics 9.5. The Treatise as philosophical mechanics: a constructive reading 9.6. The Treatise as philosophical mechanics: a principle reading 9.7. The unity of philosophical mechanics: ontic and nomic 9.8. Nature, Action, Evidence, and Principle 9.9. Conclusions 10. Building bodies: Euler and impressed force mechanics 10.1. Introduction 10.2. Solving MCON 10.3. Newton's Lex Secunda, Euler's principles, Cauchy's laws of motion 10.4. Solving MCON1 10.5. Assessment 10.6. Conclusions 11. External obstacles: Lagrange and the mechanics of constraints 11.1. Introduction 11.2. The Principle of Virtual Velocities and Lagrange's Principle 11.3. Constraints: equations of condition 11.4. Lagrange's Relaxation Postulate: the kinematics and dynamics of constraints 11.5. Philosophical mechanics and Lagrange's Mechanique 11.6. Action 11.7. Evidence 11.8. Assessment 11.9. Conclusions 12. Philosophical mechanics in the Late Enlightenment 12.1. Introduction 12.2. Makers and spaces 12.3. Lagrangian nomic unification 12.4. Molecular ontic unification 12.5. The Cauchy package 12.6. Disunity 12.7. Conclusions: A Golden Age

The writing is engaging but technical and aimed at specialists. Brading and Stan characterize the book's intended audience as philosophers of physics, science, and metaphysics and those interested in the history of modern philosophy. A strong, nuanced, technical work with a limited audience.