Some Aspects of Modality in Analytical Mechanics

I commemorate David Lewis by describing some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to Lewis’ work on modality, especially on counterfactuals. The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. The structure of this set of ensembles remains to be explored by philosophers. The second is the way the Lagrangian and Hamiltonian approaches’ variational principles state the law of motion by mentioning contralegal dynamical evolutions. This threatens to contravene the principle that an actual truth, in particular an actual law, is made true by actual states of affairs. Though this threat can be avoided, at least for simple systems, it repays scrutiny; not least because it leads to some open questions. email: [email protected]; [email protected]