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Some Aspects of Modality in Analytical Mechanics

Butterfield, Jeremy (2003) Some Aspects of Modality in Analytical Mechanics. UNSPECIFIED. (In Press)


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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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Item Type: Other
Butterfield, Jeremy
Additional Information: Dedicated to the memory of David Lewis. Forthcoming in Formal Teleology and Causality, ed. M. Stoeltzner, P. Weingartner, Paderborn: Mentis.
Keywords: analytical mechanics, variational principles, Hamilton-Jacobi theory, modality, counterfactuals, truthmakers
Subjects: Specific Sciences > Physics > Classical Physics
Depositing User: Jeremy Butterfield
Date Deposited: 30 May 2003
Last Modified: 07 Oct 2010 15:11
Item ID: 1192
Public Domain: No

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