dorsal/arxiv
View SchemaSome Aspects of Modality in Analytical Mechanics
| Authors | Jeremy Butterfield |
|---|---|
| Categories | |
| ArXiv ID | physics/0210081 |
| URL | https://arxiv.org/abs/physics/0210081 |
Abstract
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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"abstract": "This paper discusses some of the modal involvements of analytical mechanics.\nI first review the elementary aspects of the Lagrangian, Hamiltonian and\nHamilton-Jacobi approaches. I then discuss two modal involvements; both are\nrelated to David Lewis\u0027 work on modality, especially on counterfactuals.\n The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of\npossible initial conditions. The structure of this set of ensembles remains to\nbe explored by philosophers.\n The second is the way the Lagrangian and Hamiltonian approaches\u0027 variational\nprinciples state the law of motion by mentioning contralegal dynamical\nevolutions. This threatens to contravene the principle that any actual truth,\nin particular an actual law, is made true by actual facts. Though this threat\ncan be avoided, at least for simple mechanical systems, it repays scrutiny; not\nleast because it leads to some open questions.",
"arxiv_id": "physics/0210081",
"authors": [
"Jeremy Butterfield"
],
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"title": "Some Aspects of Modality in Analytical Mechanics",
"url": "https://arxiv.org/abs/physics/0210081"
},
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