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)

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)

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)

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. (shrink)

What grounds the standard claim that classical mechanics is time-reversal invariant? Hutchison (1993, 1995) challenges the conventional reasoning underlying the belief that classical mechanics is time reversal invariant and argues that it is not in any well-defined sense. I find a defensible criterion that will exclude his cases, thereby rescuing a sense in which we can say that classical mechanics is time reversal invariant.

Emphasizing the debt of science to nonspecialist intellectuals, Theodore Porter describes in detail the nineteenth-century background that produced the burst of modern statistical innovation of the early 1900s. Statistics arose as a study of society--the science of the statist--and the pioneering statistical physicists and biologists, Maxwell, Boltzmann, and Galton, each introduced statistical models by pointing to analogies between his discipline and social science.

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

In his Philosophical Inquiry concerning Human Liberty (1717), the English deist Anthony Collins proposed a complete determinist account of the human mind and action, partly inspired by his mentor Locke, but also by elements from Bayle, Leibniz and other Continental sources. It is a determinism which does not neglect the question of the specific status of the mind but rather seeks to provide a causal account of mental activity and volition in particular; it is a ‘volitional determinism’. Some decades later, (...) Diderot articulates a very similar determinism, which seeks to recognize the existence of “causes proper to man” (as he says in the Réfutation d’Helvétius). The difference with Collins is that now biological factors are being taken into account. Obviously both the ‘volitional’ and the ‘biological’ forms of determinism are noteworthy inasmuch as they change our picture of the nature of determinism itself, but my interest here is to compare these two determinist arguments, both of which are broadly Spinozist in nature – and as such belong to what Jonathan Israel called in his recent book “the radical Enlightenment,” i.e. a kind of underground Enlightenment constituted by Spinozism – and to see how Collins’ specifically psychological vision and Diderot’s specifically biological vision correspond to their two separate national contexts: determinism in France in the mid-1750s was a much more medico-biological affair than English determinism, which appears to be on a ‘path’ leading to Mill and associationist psychology. (shrink)

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)

Norton has recently argued that causation is merely a useful folk concept and that it fails to hold for some simple systems even in the supposed paradigm case of a causal physical theory – namely Newtonian mechanics. The purpose of this article is to argue against this devaluation of causality in physics. My main argument is that Norton’s alleged counterexample to causality within standard Newtonian physics fails to obey what I shall call the causal core of Newtonian mechanics. In particular, (...) I argue, Norton’s example is not in conformity with Newton’s first law. Moreover, Norton’s reformulation of this first law seems insufficient as a replacement for the original version since the notion of inertial frames in the resulting reformulated theory lacks a physical justification, and since an intelligible notion of time in Newtonian mechanics appears to be closely tied to Newton’s first law in its standard form. I will finally suggest how, given a plausible relationist account of time, the causal core of Newtonian mechanics may play a central role also in relativity and quantum theory. (shrink)

The singularity arising from the violation of the Lipschitz condition in the simple Newtonian system proposed recently by Norton (2003) is so fragile as to be completely and irreparably destroyed by slightly relaxing certain (infinite) idealizations pertaining to elastic phenomena in this model. I demonstrate that this is also true for several other Lipschitz-indeterministic systems, which, unlike Norton's example, have no surface curvature singularities. As a result, indeterminism in these systems should rather be viewed as an artefact of certain infinite (...) idealizations essential for these models, depriving them of much of their intended metaphysical import. (shrink)