This paper discusses 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 David 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 any actual truth,
in particular an actual law, is made true by actual facts. Though this threat
can be avoided, at least for simple mechanical systems, it repays scrutiny; not
least because it leads to some open questions.Comment: 36 pages, no figures. Delivered at a Philosophy of Science
Association Symposium in memory of the distinguished philosopher David Lewis,
Milwaukee, November 2002. This version includes significant additions to
Section 5.1. This version is forthcoming in `Formal Teleology and Causality',
ed. M. Stoeltzner, P. Weingartner, Paderborn, Germany: Mentis. A precis of
the first half of the paper is forthcoming in the journal Philosophy of
Scienc
