The recent discovery of an indeterministic system in classical mechanics, the Norton dome, has shown that answering the question whether classical mechanics is deterministic can be a complicated matter. In this paper I show that indeterministic systems similar to the Norton dome were already known in the nineteenth century: I discuss four nineteenth century authors who wrote about such systems, namely Poisson, Duhamel, Boussinesq and Bertrand. However, I argue that their discussion of such systems was very different from the contemporary (...) discussion about the Norton dome, because physicists in the nineteenth century conceived of determinism in essentially different ways: whereas in the contemporary literature on determinism in classical physics, determinism is usually taken to be a property of the equations of physics, in the nineteenth century determinism was primarily taken to be a presupposition of theories in physics, and as such it was not necessarily affected by the possible existence of systems such as the Norton dome. (shrink)

In 1877 the first issue of the Revue des questions scientifiques, published by the Scientific Society of Brussels, appeared in France and Belgium. The new journal was greeted with disdain and hostility by Emile Littrè and George Wyrouboff, the disciples of Auguste Comte and editors of La philosophie positive. The Scientific Society of Brussels was a Catholic organization, and the positivists' opinion was that ‘If science is spoken of in this assembly, it is in order to organize a veritable crusade (...) against it’. But the highly prejudiced assessment by Littré and Wyrouboff completely misread the goals of the society. At the time, the Catholic Church was en pleine crise both in France and Belgium. Church attendance had declined dramatically in recent years, as had the number of young people entering religious orders. Many Catholic laymen and church officials were becoming convinced that some rapprochment with the modern world and modern science was essential. It was to this difficult task that the Catholics of the Brussels Scientific Society addressed themselves with determination. (shrink)

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)

This article discusses the writings of the devout Christian physicist James Clerk Maxwell (best known for his epochal work in electromagnetism and statistical mechanics) on the concept of conscious free-will. To Maxwell a correct understanding of free will, as personified in the example of the railway pointsman, was essential to clear conceptions of both man as a religious creature and of the limits of science. Understanding human volition, then, was not an end unto itself. It was a foundation on which (...) one could build reliable theories of man and matter. (shrink)

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.