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.

The beauty of electricity, or of any other force, is not that the power is mysterious and unexpected, touching every sense at unawares in turn, but that it is under law... Michael Faraday, Wheatstone's Electric Telegraph's Relation to Science (being an argument in favour of the full recognition of Science as a branch of Education), 1854.

Suppose all of the particles in the universe should happen to come to rest at the same time, in positions so arranged that all of the forces on every particle balance to zero at that time. What would happen next? Or rather, what does Newtonian mechanics say will happen next? Preface Inertia and Stasis 2.1 Stating the Law of Inertia more precisely 2.2 The stasis scenario Indeterministic Examples 3.1 Abstract example 3.2 Second example Non-Lipschitz Forces and Determinism Beyond the Stasis (...) Scenario CiteULike Connotea Del.icio.us What's this? (shrink)

Mark Wilson presents a highly original and broad-ranging investigation of the way we get to grips with the world conceptually, and the way that philosophical problems commonly arise from this. He combines traditional philosophical concerns about human conceptual thinking with illuminating data derived from a large variety of fields including physics and applied mathematics, cognitive psychology, and linguistics. Wandering Significance offers abundant new insights and perspectives for philosophers of language, mind, and science, and will also reward the interest of psychologists, (...) linguists, and anyone curious about the mysterious ways in which useful language obtains its practical applicability. (shrink)

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?

This paper follows up a debate as to the consistency of Newtonian cosmology. Whereas Malament (1995) has shown that Newtonian cosmology *is* not inconsistent, to date there has been no analysis of Norton’s claim (1995) that Newtonian cosmology *was* inconsistent prior to certain advances in the 1930s, and in particular prior to Seeliger’s seminal paper of 1895. In this paper I agree that there are assumptions, Newtonian and cosmological in character, and relevant to the real history of science, which are (...) inconsistent. But there are some important corrections to make to Norton’s account. Here I display for the first time the inconsistencies—four in total—in all their detail. Although this extra detail shows there to be several different inconsistencies, it also goes some way towards explaining why they went unnoticed for two hundred years. (shrink)

This paper follows up a debate as to the consistency of Newtonian cosmology. Whereas Malament has shown that Newtonian cosmology *is* not inconsistent, to date there has been no analysis of Norton’s claim that Newtonian cosmology *was* inconsistent prior to certain advances in the 1930s, and in particular prior to Seeliger’s seminal paper of 1895. In this paper I agree that there are assumptions, Newtonian and cosmological in character, and relevant to the real history of science, which are inconsistent. But (...) there are some important corrections to make to Norton’s account. Here I display for the first time the inconsistencies—four in total—in all their detail. Although this extra detail shows there to be several different inconsistencies, it also goes some way towards explaining why they went unnoticed for two hundred years. (shrink)

This paper follows up a debate as to whether classical electrodynamics is inconsistent. Mathias Frisch makes the claim in Inconsistency, Asymmetry and Non-Locality ([2005]), but this has been quickly countered by F. A. Muller ([2007]) and Gordon Belot ([2007]). Here I argue that both Muller and Belot fail to connect with the background assumptions that support Frisch's claim. Responding to Belot I explicate Frisch's position in more detail, before providing my own criticisms. Correcting Frisch's position, I find that I can (...) present the theory in a way both authors can agree upon. Differences then manifest themselves purely within the reasoning methods employed. Introduction Features of the Theory Frisch's Inconsistency Claim Defending Frisch 4.1 Muller 4.2 Belot Difficulties for Frisch and a Compromise Conclusion CiteULike Connotea Del.icio.us What's this? (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.

We interpret the concept of determinism for a classical system as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally believed to hold for all autonomous classical systems. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension provides counterexamples of this belief. Given the initial conditions of a particular type, the Cauchy problem may have an infinite set of solutions. Therefore, (...) random behavior of closed classical systems is indeed possible. With this finding, we give a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems. (shrink)

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)

This paper argues against a standard view that all deterministic and conservative classical mechanical systems are time-reversible, by asking how the temporal evolution of a system modulates parametric imprecision (either ontological or epistemic). It notes that well-behaved systems (e.g. inertial motion) can possess a dynamics which is unstable enough to fail at reversing uncertainties—even though exact values are reliably reversed. A limited (but significant) source of irreversibility is thus displayed in classical mechanics, closely analogous the lack of predictability revealed by (...) unstable chaotic systems. (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].

Norton (2003 and 2006) 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 (and determinism) 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 (in an instantaneous form) 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)

Disagreements about the definition, nature, structure, ontology, and content of scientific theories are at least partly responsible for disagreements in other debates in the philosophy of science. I argue that available theories of theories and conceptual analyses of *theory* are ineffectual options for overcoming this difficulty. Directing my attention to debates about the properties of particular, named theories, I introduce ‘theory eliminativism’ as a certain type of debate-reformulation. As a methodological tool it has the potential to be a highly effective (...) way to make real progress in the face of the noted problem. After the recommended reformulation questions of genuine importance to philosophy of science can still be asked and answered, but now without any possibility of disagreements about ‘theories’ compromising the debate. (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)

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 a loose collection of causal notions that form a folk science 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)

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)