Philosophy of Physics Seminar (Thursday - Week 8, MT25)

Abstract: Lagrangian mechanics is often interpreted in a way that highlights its role in the evolution of the least action principle (or, more accurately, stationary action) and its use of methods of optimisation. This characterisation is indeed true for the historical developments of analytical mechanics before Lagrange (Maupertuis, Euler, etc.) and after Lagrange (Hamilton, etc.) but not true for the mature Lagrange who formulated his methods against the tendencies toward teleology in this field.

This paper focuses on the method of virtual velocities and the principle of (zero) virtual work which Lagrange used to replace the least action methods of his predecessors and examine the metaphysics that it could imply. In particular, focus is placed on Lagrange's turn away from his mentor Euler and association with D’Alembert. By doing this, we develop a sketch of the metaphysical assumptions of the method and use this to assess the deep differences between Lagrange’s innovations and the standard understanding of the least (stationary) action principle. We finally make a case for a Lagrangian theory of causation that is local but not mechanical in the usual sense, and structural but not teleological as his near predecessors would have it.