Newton’s equations of motion tell us that a mass at rest at the apex of a dome with the shape specified here can spontaneously move. It has been suggested that this indeterminism should be discounted since it draws on an incomplete rendering of Newtonian physics, or it is “unphysical,” or it employs illicit idealizations. I analyze and reject each of these reasons. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA (...) 15260; e‐mail: [email protected]. (shrink)

Determinism is a perennial topic of philosophical discussion. Very little acquaintance with the philosophical literature is needed to reveal the Tower of ...

This article surveys the difficulties in establishing determinism for classical physics within the context of several distinct foundational approaches to the discipline. It explains that such problems commonly emerge due to a deeper problem of ‘missing physics'. The Problems of Formalism Norton's Example Three Species of Classical Mechanics 3.1 Mass point physics 3.2 The physics of perfect constraints 3.3 Continuum mechanics Conclusion CiteULike Connotea Del.icio.us What's this?

In my contribution to the Symposium ("On the Vagaries of Determinism and Indeterminism"), I will identify several issues that arise in trying to decide whether Newtonian particle mechanics qualifies as a deterministic theory. I'll also give a mini-tutorial on the geometry and dynamical properties of Norton's dome surface. The goal is to better understand how his example works, and better appreciate just how wonderfully strange it is.

I present a simple model of Grünbaum’s staccato run in classical mechanics, the staccato roller coaster. It consists of a bead sliding on a frictionless wire shaped like a roller coaster track with infinitely many hills of diminishing size, each of which is a one-dimensional variant of the so-called Norton dome. The staccato roller coaster proves beyond doubt the dynamical (and hence logical) possibility of supertasks in classical mechanics if the Norton dome is a proper system of classical mechanics with (...) metaphysical import. If not, challenges raised against the metaphysical significance of the Norton dome are shown to be challenges against various arguments for the dynamical possibility of supertasks, and the staccato roller coaster clearly shows the importance of meeting these challenges. And the staccato roller coaster can provide, as well as interesting lessons, illuminating analyses of Burke’s (Mod Schoolman 78:1–8, 2000 ) attempt to refute the dynamical possibility of the staccato run and Pérez Laraudogoitia’s (Synthese 148:433–441, 2006 ) rebuttal of it. (shrink)