Indeterminism, asymptotic reasoning, and time irreversibility in classical physics

Philosophy of Science 74 (5):943-956 (2007)
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Abstract

A recent proposal by Norton (2003) to show that a simple Newtonian system can exhibit stochastic acausal behavior by giving rise to spontaneous movements of a mass on the dome of a certain shape is examined. We discuss the physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous nontrivial solutions in this and similar cases. We show that the Lipschitz condition is closely linked with the time reversibility of certain solutions in Newtonian mechanics and the failure to incorporate this condition within Newtonian mechanics may unsurprisingly lead to physically impossible solutions that have no serious metaphysical implications. ‡I thank Steven Savitt of the Philosophy Department at the University of British Columbia for drawing my attention to the Lipschitz condition, and Alexei Cheviakov of the Mathematics Department at the University of British Columbia for useful discussions. †To contact the author, please write to: Department of Philosophy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada; e-mail: [email protected]

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Alexandre Korolev
University of British Columbia

Citations of this work

The Dome: An Unexpectedly Simple Failure of Determinism.John D. Norton - 2008 - Philosophy of Science 75 (5):786-798.
The Norton Dome and the Nineteenth Century Foundations of Determinism.Marij van Strien - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):167-185.
What Counts as a Newtonian System? The View From Norton’s Dome.Samuel Craig Fletcher - 2012 - European Journal for Philosophy of Science 2 (3):275-297.
Scientific Theory Eliminativism.Peter Vickers - 2014 - Erkenntnis 79 (1):111-126.

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References found in this work

Galilean Idealization.Ernan McMullin - 1985 - Studies in History and Philosophy of Science Part A 16 (3):247.
Causation as Folk Science.John Norton - 2003 - Philosophers' Imprint 3:1-22.
Models in Physics.Michael Redhead - 1980 - British Journal for the Philosophy of Science 31 (2):145-163.

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