Sheldon Smith

Many have claimed that ceteris paribus (CP) laws are a quite legitimate feature of scientific theories, some even going so far as to claim that laws of all scientific theories currently on offer are merely CP. We argue here that one of the common props of such a thesis, that there are numerous examples of CP laws in physics, is false. Moreover, besides the absence of genuine examples from physics, we suggest that otherwise unproblematic claims are rendered untestable by the mere addition of the CP operator. Thus, “CP all Fs are Gs” when read as a straightforward statement of fact, cannot be the stuff of scientific theory. Rather, we suggest that when ``ceteris paribus'' appears in scientific works it plays a pragmatic role of pointing to more respectable claims.

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

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 Green's 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

Many philosophers have discussed the ability of thinkers to think thoughts that the thinker cannot justify because the thoughts involve concepts that the thinker incompletely understands. A standard example of this phenomenon involves the concept of the derivative in the early days of the calculus: Newton and Leibniz incompletely understood the derivative concept and, hence, as Berkeley noted, they could not justify their thoughts involving it. Later, Weierstrass justified their thoughts by giving a correct explication of the derivative concept. This paper discusses various accounts of how a thinker manages to think with a concept that they incompletely understand and finds them wanting in the case at hand. Part of the overlooked complexity is that there are many derivative concepts, and it is unclear in virtue of what a thinker would be thinking with one of them rather than another. After critical evaluation of standard accounts, this paper suggests a novel account of how one should think about the derivative concepts with which Newton and Leibniz thought and how Weierstrass could have managed to justify their thoughts even if their thoughts did not involve the same derivative concept as Weierstrass’s

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

I discuss the applicability of mathematics via a detailed case study involving a family of mathematical concepts known as ‘fractional derivatives.’ Certain formulations of the mystery of applied mathematics would lead one to believe that there ought to be a mystery about the applicability of fractional derivatives. I argue, however, that there is no clear mystery about their applicability. Thus, via this case study, I think that one can come to see more clearly why certain formulations of the mystery of applied mathematics are not convincing

In "On the Notion of Cause," Bertrand Russell expressed an eliminativist view about causation driven by an examination of the contents of mathematical physics. Russell's primary reason for thinking that the notion of causation is absent in physics was that laws of nature are mere "functional dependencies" and not "causal laws." In this paper, I show that several ordinary notions of causation can be found within the functional dependencies of physics. Not only does this show that Russell's eliminitivism was misguided, but it shows that Russell's opponents, such as Nancy Cartwright, who think that mere functional dependenciescannot capture causal claims, also underestimate the causal content of such equations.

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.

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, 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

Many have thought that symmetries of a Lagrangian explain the standard laws of energy, momentum, and angular momentum conservation in a rather straightforward way. In this paper, I argue that the explanation of conservation laws via symmetries of Lagrangians involves complications that have not been adequately noted in the philosophical literature and some of the physics literature on the subject. In fact, such complications show that the principles that are commonly appealed to to drive explanations of conservation laws are not generally correct without caveats. I hope here to give a clearer picture of the relationship between symmetries and conservation laws in Lagrangian mechanics via an examination of the bearing that results in the inverse problem in the calculus of variations have on this topic.