Philosophical Mechanics in the Age of Reason

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.

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 Age
1.1. Introduction
1.2. The Problem of Bodies
1.3. Philosophical mechanics
1.4. Constructive and principle approaches
1.5. The Unity of Physical Theory
1.6. Collisions and constraints: PCOL and PCON
1.7. Methods
1.8. Audience
1.9. Overview
1.10. Conclusions

2. Malebranche and French collision theory
2.1. Introduction
2.2. Correcting Descartes: Malebranche's early theory of collisions
2.3. Leibniz's objections to Malebranche's early collision theory
2.4. Malebranche's mature theory of collisions
2.5. After Malebranche: hard bodies in the competition of 1724 and beyond
2.6. After Malebranche: elastic rebound and the prize competition of 1726
2.7. Open questions, hidden problems
2.8. Conclusions

3. Beyond Newton and Leibniz: bodies in collision
3.1. Introduction
3.2. Newtonian collisions
3.3. Leibniz on collisions
3.4. Leibnizian collisions in Hermann and Wolff
3.5. The Problem of Collisions (PCOL)

4. The Problem of Bodies
4.1. Introduction
4.2. The scope and remit of physics
4.3. The Problem of Bodies: Nature and Action
4.4. The Problem of Bodies: Evidence and Principle
4.5. The methods of Newtonian physics
4.6. Substance and causation
4.7. The goal: a philosophical mechanics

5. Body and force in the physics of collisions: Du Châtelet and Euler
5.1. Introduction
5.2. Nature: extension as a property of bodies
5.3. Action
5.4. Du Châtelet and Action
5.5. Euler and Action
5.6. Conclusions

6. Searching for a new physics: Kant and Boscovich
6.1. Introduction
6.2. The physics of bodies in Kant and Boscovich
6.3. Kant's philosophical mechanics
6.4. Boscovich's philosophical mechanics
6.5. Conclusions

7. Shifting sands in philosophical mechanics
7.1. Introduction
7.2. Methodology
7.3. Elusive mass
7.4. Contact action
7.5. A general theory of bodies in motion
7.6. Shifting sands
7.7. From rational to philosophical mechanics
7.8. Rational mechanics ascendant
7.9. Conclusions