Some Aspects of Modality in Analytical Mechanics

Details Some Aspects of Modality in Analytical Mechanics Some Aspects of Modality in Analytical Mechanics

2002-10-19

arxiv.org/abs/physics/0210081v3

Physics

Classical Physics

36 pages, no figures. Delivered at a Philosophy of Science Association Symposium in memory of the distinguished philosopher Da

Scientific paper

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.

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