I deny that the world is fundamentally causal, deriving the skepticism on non-Humean grounds from our enduring failures to find a contingent, universal principle of causality that holds true of our science. I explain the prevalence and fertility of causal notions in science by arguing that a causal character for many sciences can be recovered, when they are restricted to appropriately hospitable domains. There they conform to loose and varying collections of causal notions that form folk sciences of causation. This (...) recovery of causation exploits the same generative power of reduction relations that allows us to recover gravity as a force from Einstein's general relativity and heat as a conserved fluid, the caloric, from modern thermal physics, when each theory is restricted to appropriate domains. Causes are real in science to the same degree as caloric and gravitational forces. (shrink)

This paper explores the possibility that chaos theory might be helpful in explaining free will. I will argue that chaos has little to offer if we construe its role as to resolve the apparent conflict between determinism and freedom. However, I contend that the fundamental problem of freedom is to find a way to preserve intuitions about rational action in a physical brain. New work on dynamic computation provides a framework for viewing free choice as a process that is sensitive (...) and unpredictable, while at the same time organized and intelligent. I conclude that this vision of a chaotic brain may make a modest contribution to an intuitively acceptable physicalist account of free will. (shrink)

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)

Various fault modes of determinism in classical physics are outlined. It is shown how quantum mechanics can cure some forms of classical indeterminism. †To contact the author, please write to: Department of HPS, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected].

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.

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]. (shrink)

It has notoriously been supposed that the doctrine of determinism conflicts with the belief in human freedom. Yet it is not readily apparent how indeterminism, the denial of determinism, makes human freedom any less problematic. It has sometimes been suggested that the arrival of quantum mechanics should immediately have solved the problem of free will and determinism. It was proposed, perhaps more often by scientists than by philosophers, that the brain would need only to be fitted with a device for (...) amplifying indeterministic quantum phenomena for the bogey of determinism to be defeated. Acts of free will could then be those that were initiated by such indeterministic nudges. Recently there has been some inclination to revive such a story as part of the fallout from the trend for chaos theory. Chaotic systems in the brain, being indefinitely sensitive to the precise details of initial conditions, seem to provide fine candidates for the hypothetical amplifiers of quantum events. (shrink)

In this paper I examine the foundations of Laplace's famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace's statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he (...) could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace's determinism was in fact widespread in enlightenment France, and is ultimately based on a re-interpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace's determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation. (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)

During the period 1860-1880, a number of physicists and mathematicians, including Maxwell, Stewart, Cournot and Boussinesq, used theories formulated in terms of physics to argue that the mind, the soul or a vital principle could have an impact on the body. This paper shows that what was primarily at stake for these authors was a concern about the irreducibility of life and the mind to physics, and that their theories can be regarded primarily as reactions to the law of conservation (...) of energy, which was used among others by Helmholtz and Du Bois-Reymond as an argument against the possibility of vital and mental causes in physiology. In light of this development, Maxwell, Stewart, Cournot and Boussinesq showed that it was still possible to argue for the irreducibility of life and the mind to physics, through an appeal to instability or indeterminism in physics: if the body is an unstable or physically indeterministic system, an immaterial principle can act through triggering or directing motions in the body, without violating the laws of physics. (shrink)

Laplacean determinism remains a popular theory among philosophers and scientists alike, in spite of the fact that the Copenhagen Interpretation of quantum mechanics, with which it is inconsistent, has been around for more than fifty years. There are a number of reasons for its continuing popularity. One, recently articulated by Honderich, is that there are too many possible interpretations of quantum mechanics, and the subject is too controversial even among physicists to be an adequate basis for overturning determinism. Nevertheless, quantum (...) mechanics is an enormously successful theory, considering the quantity and variety of its predictions which have been verified under conditions never dreamt of by its originators; and the Copenhagen Interpretation is the only widely accepted interpretation of it. Although a hidden variable theory consistent with the results of quantum mechanics is not impossible, one of its major advocates admits that it is highly speculative, and far from adequately developed. Yet such a theory would be needed to reconcile Laplacean determinism with quantum mechanics; most of the controversies alluded to by Honderich are irrelevant. (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)