Sheldon R. Smith

Violated laws, Ceteris paribus clauses, and capacities

It is often claimed that the bulk of the laws of physics –including such venerable laws as Universal Gravitation– are violated in many (or even all) circumstances because they havecounter-instances that result when a system is not isolated fromother systems. Various accounts of how one should interpretthese (apparently) violated laws have been provided. In thispaper, I examine two accounts of (apparently) violated laws, thatthey are merely ceteris paribus laws and that they aremanifestations of capacities. Through an examination of theprimary example that motivated these views, I show that given aproper understanding of the situation, neither view is optimalbecause the law is not even apparently violated. Along the way, Iam able to diagnose what has led to the mistaken belief: I showthat it originates from an element of the standard empiricistconception of laws. I then evaluate the suggestions of how tointerpret violated laws with respect to other examples and findthem wanting there too.

Are instantaneous velocities real and really instantaneous?: an argument for the affirmative

Abstract Frank Arntzenius has recently suggested that we should reject the standard view that the instantaneous state in classical mechanics consists of both the position and the velocity. In his view, the velocity as ordinarily defined—as the derivative of position with respect to time—cannot be genuinely instantaneous, and, thus, it should be excluded from the instantaneous state. After reviewing Bertrand Russells traditional objections to the notion of an instantaneous velocity and suggesting that Russells concerns can be effectively answered, I argue that Arntzenius’ attempt to show that the standard definition of velocity fails to yield an instantaneous property is not compelling either. Although I review several suggestions that Arntzenius makes against the existence of instantaneous velocity, much of his case rests upon an intuition, which has also appeared in the work of David Albert, about what is required of genuine instantaneous states. I argue in part that there is no reason to accept this intuition, and, thus, no reason to revise standard physical practice when it comes to the classical, instantaneous state.

Continuous Bodies, Impenetrability, and Contact Interactions: The View from the Applied Mathematics of Continuum Mechanics

Many philosophers have claimed that there is a tension between the impenetrability of matter and the possibility of contact between continuous bodies. This tension has led some to claim that impenetrable continuous bodies could not ever be in contact, and it has led others to posit certain structural features to continuous bodies that they believe would resolve the tension. Unfortunately, such philosophical discussions rarely borrow much from the investigation of actual matter. This is probably largely because actual matter is not continuous, and so it might seem as if discussion of the structure of continuous bodies is merely within the realm of philosophical thought experiments rather than actual scientific investigation. However, classical continuum mechanics models actual matter as if it were continuous, and it has implications about the structure of continuous bodies and about what contact and impenetrability are. This paper describes the relevant notions from classical continuum mechanics so as to resolve the alleged tension between contact and impenetrability. 1. The ‘Problem’ of Contact Interaction in a Continuous Medium: the Root Argument2. The ‘Axiom of Impenetrability’ in Continuum Mechanics2.1. The status of Kinematical principles in continuum mechanics2.1.1. Vortex sheets (slip surfaces)2.2. Violations of the axiom of impenetrability on sets of measure zero3. Axioms of Body4. Contact Forces and Equations of Motion5. Contact Action and the Structure of Continuous Bodies6. ‘Real Contact’ and Contact in Continuum Mechanics7. Bodies as Open or Closed Sets8. Contact Action and Fields of Force9. Conclusion The ‘Problem’ of Contact Interaction in a Continuous Medium: the Root Argument The ‘Axiom of Impenetrability’ in Continuum Mechanics The status of Kinematical principles in continuum mechanics Vortex sheets (slip surfaces) Violations of the axiom of impenetrability on sets of measure zero Axioms of Body Contact Forces and Equations of Motion Contact Action and the Structure of Continuous Bodies ‘Real Contact’ and Contact in Continuum Mechanics Bodies as Open or Closed Sets Contact Action and Fields of Force Conclusion

Models and the Unity of Classical Physics: Nancy Cartwright's Dappled World

In this paper, I examine the claim that any physical theory will have an extremely limited domain of application because 1) we have to use distinct theories to model different situations in the world and 2) no theory has enough textbook models to handle anything beyond a highly simplified situation. Against the first claim, I show that many examples used to bolster it are actually instances of application of the very same classical theory rather than disjoint theories. Thus, there is a hidden unity to the world of classical physics that is usually overlooked (by, for example, Nancy Cartwright who argues for the claims above). Against the second claim, I show that the practice of classical physics involves an enormous (infinite) number of models the use of which cannot be written off as merely ad hoc. Thus, although classical physics cannot, of course, model every situation in nature, it has a much larger domain than some would have us believe.

Causation and Its Relation to 'Causal Laws'

Many have found attractive views according to which the veracity of specific causal judgements is underwritten by general causal laws. This paper describes various variants of that view and explores complications that appear when one looks at a certain simple type of example from physics. To capture certain causal dependencies, physics is driven to look at equations which, I argue, are not causal laws. One place where physics is forced to look at such equations (and not the only place) is in its handling of Greens functions which reveal point-wise causal dependencies. Thus, I claim that there is no simple relationship between causal dependence and causal laws of the sort often pictured. Rather, this paper explores the complexity of the relationship in a certain well-understood case. 1. Introduction2. The Causal Covering-Law Thesis3. The Laws of String Motion4. Greens Functions and Causation5. Greens Functions and Boundary Conditions6. The Greens Function as a Violation of the Wave Equation6.1. The Greens Function and other Senses of ‘Causal Law’: Temporal Propagation and Local Propagation7. The Distributional Wave Equation8. Why is not the Greens Function a ‘Causal Law’?9. Conclusion Introduction The Causal Covering-Law Thesis The Laws of String Motion Greens Functions and Causation Greens Functions and Boundary Conditions The Greens Function as a Violation of the Wave Equation6.1. The Greens Function and other Senses of ‘Causal Law’: Temporal Propagation and Local Propagation The Greens Function and other Senses of ‘Causal Law’: Temporal Propagation and Local Propagation The Distributional Wave Equation Why is not the Greens Function a ‘Causal Law’? Conclusion

Elementary classical mechanics and the principle of the Composition of Causes

In this paper, I explore whether elementary classical mechanics adheres to the Principle of Composition of Causes as Mill claimed and as certain contemporary authors still seem to believe. Among other things, I provide a proof that if one reads Mill’s description of the principle literally (as I think many do), it does not hold in any general sense. In addition, I explore a separate notion of Composition of Causes and note that it too does not hold in elementary classical mechanics. Among the major morals is that there is no utility to describing classical mechanics in terms of Composition of Causes. This is both because the stated principles do not hold and because when one describes what actually does hold in classical mechanics in terms of the Composition of Causes, one introduces misleading associations that can generate errors just as claimed by Russell (Mysticism and logic, 1981).