Abstract
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.
Highlights
I connect the contemporary discussion in philosophy of physics about the Norton dome with nineteenth century literature on similar physical systems, and I show that what is currently the standard conception of determinism in classical physics was not generally accepted in nineteenth century France
The kind of indeterminism that is at issue in Norton's dome can be called "Lipschitzindeterminism", and amounts to the fact that the differential equations which are the equations of motion of a certain system may not have a unique solution for given initial conditions
In an article about the Norton dome, Malament discusses another possible Lipschitz-indeterministic system in which a particular force acting on a point particle leaves the motion of the particle undetermined.[2]
Summary
I connect the contemporary discussion in philosophy of physics about the Norton dome with nineteenth century literature on similar physical systems, and I show that what is currently the standard conception of determinism in classical physics was not generally accepted in nineteenth century France. The kind of indeterminism that is at issue in Norton's dome can be called "Lipschitzindeterminism", and amounts to the fact that the differential equations which are the equations of motion of a certain system may not have a unique solution for given initial conditions.
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