If the force on a particle fails to satisfy a Lipschitz condition at a point, it relaxes one of the conditions necessary for a locally unique solution to the particle's equation of motion. I examine the most discussed example of this failure of determinism in classical mechanics-that of Norton's dome- and the range of current objections against it. Finding there are many different conceptions of classical mechanics appropriate and useful for different purposes, I argue that no single conception is preferred. Instead of arguing for or against determinism, I stress the wide variety of pragmatic considerations that, in a specific context, may lead one usefully and legitimately to adopt one conception over another in which determinism may or may not hold.
Bibliographical noteFunding Information:
Thanks to Jeff Barrett, David Malament, Peter Vickers, Jim Weatherall, and two anonymous referees for helpful comments, and to the audiences of both the Southern California Philosophy of Physics Group and the Sixth Logic, Mathematics, and Physics Graduate Philosophy Conference at the University of Western Ontario for comments on earlier versions. Thanks also to Jennifer C. Herrera for comments on my translation of Poisson. Part of the present work was written with the support of a National Science Foundation Graduate Research Fellowship.
- Classical mechanics
- Newtonian mechanics