Philosophy and Phenomenological Research, Volume 103, Issue 2, Page 462-465, September 2021.

Explanations in physics commonly appeal to data drawn from different length or time scales, as when a “top-down” macroscopic constraint such as rigidity is used to evade the complexities one would confront in attempting to model the situation in a purely “bottom-up” fashion. Such techniques commonly embody rather complex shifts in explanatory strategy.

The quality of philosophical diagnosis within the philosophy of science will be greatly improved if the original distinctions of applied mathematics are employed instead of the inadequate substitutes provided by the logical empiricists. The problem of evaluating counterfactual claims is examined from this point of view.

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)

For several decades now philosophers have discussed apparent examples of internally inconsistent scientific theories. However, there is still much controversy over how exactly we should conceive of scientific theories in the first place. Here I argue for a new approach, whereby all of the truly important questions about inconsistency in science can be asked and answered without disagreements about theories and theory-content getting in the way. Three examples commonly described as ‘internally inconsistent theories’ are analysed in the light of this (...) approach. In the process, the question ‘Is the theory inconsistent or not?’ is identified as a bad, or at least unimportant, question. (shrink)

The philosopher of science faces overwhelming disagreement in the literature on the definition, nature, structure, ontology, and content of scientific theories. These disagreements are at least partly responsible for disagreements in many of the debates in the discipline which put weight on the concept scientific theory. I argue that available theories of theories and conceptual analyses of theory are ineffectual options for addressing this difficulty: they do not move debates forward in a significant way. 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 progress in the face of the noted problem: post-reformulation disagreements about theory cannot compromise the debate, and the questions that really matter can still be asked and answered. In addition the reformulation process demands that philosophers engage with science and the history of science in a more serious way than is usual in order to answer important questions about the justification for targeting a particular set of propositions (say) in a given context. All things considered, we should expect the benefits of a theory-eliminating debate-reformulation to heavily outweigh the costs for a highly significant number of debates of the relevant type. (shrink)

The semantic approach to scientific representation is now long established as a favourite amongst philosophers of science. One of the foremost strains of this approach—the model-theoretic approach —is to represent scientific theories as families of models, all of which satisfy or ‘make true’ a given set of constraints. However some authors have criticised the approach on the grounds that certain scientific theories are logically inconsistent, and there can be no models of an inconsistent set of constraints. Thus it would seem (...) that the MTA fails to represent inconsistent scientific theories at all, and this raises concerns about the way it represents in general. In a series of papers and a recent book da Costa and French have developed a variant of the MTA approach which they call ‘partial structures’, and which they claim can accommodate inconsistent theories. I assess this claim, looking to two theories which have been called ‘inconsistent’: Bohr’s theory of the atom and classical electrodynamics. (shrink)

Pluralist and eliminativist positions have proliferated within both science and philosophy of science in recent decades. This paper asks the question why this shift of thinking has occurred, and where it is leading us. We provide an explanation which, if correct, entails that we should expect pluralism and eliminativism to transform other debates currently unaffected, and for good reasons. We then consider the question under what circumstances eliminativism will be appropriate, arguing that it depends not only on the term in (...) question, but also on the context of discussion and details of the debate at hand. The resultant selective eliminativism is an appealing compromise for various ‘pluralists’ and ‘eliminativists’ who are currently locking horns. (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)

This is a critical notice of Mark Wilson's Wandering Significance.

It is argued that explanations of shock waves display explanatory emergence in two different ways. Firstly, the use of discontinuities to model jumps in flow variables is an example of “physics avoidance”. This is where microphysical details can be ignored in an abstract model thus allowing us access to modal information which cannot be attained in principle in any other way. Secondly, Whitham’s interleaving criterion for continuous shock structure is an example of the way different characteristic scales interact in shock (...) dynamics. To fully explain the shock structure one must take account of these different scales, and by doing so explanations of shock structure have irreducible aspects. Lastly, the implications of this explanatory irreducibility are examined in the context of explanatory indispensability arguments used in realism debates elsewhere in the philosophy of science. It is concluded that explanatory emergence on its own only supports an epistemic form of emergence. Yet this epistemic emergence is fully objective. (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)

I present a simple model of Grünbaum’s staccato run in classical mechanics, the staccato roller coaster. It consists of a bead sliding on a frictionless wire shaped like a roller coaster track with infinitely many hills of diminishing size, each of which is a one-dimensional variant of the so-called Norton dome. The staccato roller coaster proves beyond doubt the dynamical (and hence logical) possibility of supertasks in classical mechanics if the Norton dome is a proper system of classical mechanics with (...) metaphysical import. If not, challenges raised against the metaphysical significance of the Norton dome are shown to be challenges against various arguments for the dynamical possibility of supertasks, and the staccato roller coaster clearly shows the importance of meeting these challenges. And the staccato roller coaster can provide, as well as interesting lessons, illuminating analyses of Burke’s (Mod Schoolman 78:1–8, 2000 ) attempt to refute the dynamical possibility of the staccato run and Pérez Laraudogoitia’s (Synthese 148:433–441, 2006 ) rebuttal of it. (shrink)

Norton’s very simple case of indeterminism in classical mechanics has given rise to a literature critical of his result. I am interested here in posing a new objection different from the ones made to date. The first section of the paper expounds the essence of Norton’s model and my criticism of it. I then propose a specific modification in the absence of gravitational interaction. The final section takes into consideration a surprising consequence for classical mechanics from the new model introduced (...) here. (shrink)

We describe a case of indeterminacy in general relativity for homogeneous and isotropic cosmologies for a class of dark energy fluids. The cosmologies are parametrized by an equation of state variable, with one instance giving the same solution as Norton’s mechanical dome. Our example goes beyond previously studied cases in that indeterminacy lies in the evolution of spacetime itself: the onset of the Big Bang is indeterminate. We show further that the indeterminacy is resolved if the dynamics is viewed relationally.

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)

John Norton has proposed a position of “material induction” that denies the existence of a universal inductive inference schema behind scientific reasoning. In this vein, Norton has recently presented a “dome scenario” based on Newtonian physics that, in his understanding, is at variance with Bayesianism. The present note points out that a closer analysis of the dome scenario reveals incompatibilities with material inductivism itself.

The problem of theoretical equivalence is traditionally understood as the problem of specifying when superficially dissimilar accounts of the world are reformulations of a single underlying theory. One important strategy for answering this question has been to appeal to formal relations between theoretical structures. This article presents two reasons to think that such an approach will be unsuccessful and suggests an alternative account of theoretical equivalence, based on the notion of interpretive equivalence, in which the problem is merely an instance (...) of a broader problem in the philosophy of physics. I thus conclude that there is no distinctive problem of theoretical equivalence at all. Two difficulties my approach raises for realist replies to the threat of underdetermination are then discussed, with particular emphasis on a recent reply by Norton. 1 Introduction2 Methodological Confusion3 Asymmetrical Equivalence3.1 Maxwell’s field equations3.2 Classical Lagrangian dynamics4 Formal Approaches: Quine and Glymour5 Theoretical Equivalence as Interpretive Equivalence6 Theoretical Equivalence without Interpretive Judgement?7 Lessons for Underdetermination. (shrink)

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.

This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.

It is commonly thought that before the introduction of quantum mechanics, determinism was a straightforward consequence of the laws of mechanics. However, around the nineteenth century, many physicists, for various reasons, did not regard determinism as a provable feature of physics. This is not to say that physicists in this period were not committed to determinism; there were some physicists who argued for fundamental indeterminism, but most were committed to determinism in some sense. However, for them, determinism was often not (...) a provable feature of physical theory, but rather an a priori principle or a methodological presupposition. Determinism was strongly connected with principles of causality and continuity and the principle of sufficient reason; this thesis examines the relevance of these principles in the history of physics. Moreover, the history of determinism in this period shows that there were essential changes in the relation between mathematics and physics: whereas in the eighteenth century, there were metaphysical arguments which lent support to differential calculus, by the early twentieth century the development of rigorous foundations of differential calculus led to concerns about its applicability in physics. The thesis consists of six papers. In the first paper, "On the origins and foundations of Laplacian determinism", I argue that Laplace, who is usually pointed out as the first major proponent of scientific determinism, did not derive his statement of determinism directly from the laws of mechanics; rather, his determinism has a background in eighteenth century Leibnizian metaphysics, and is ultimately based on the law of continuity and the principle of sufficient reason. These principles also provided a basis for the idea that one can find laws of nature in the form of differential equations which uniquely determine natural processes. In "The Norton dome and the nineteenth century foundations of determinism", I argue that an example of indeterminism in classical physics which has attracted attention in philosophy of physics in recent years, namely the Norton come, was already discussed during the nineteenth century. However, the significance which this type of indeterminism had back then is very different from the significance which the Norton dome currently has in philosophy of physics. This is explained by the fact that determinism was conceived of in an essentially different way: in particular, the nineteenth century authors who wrote about this type of indeterminism regarded determinism as an a priori principle rather than as a property of the equations of physics. In "Vital instability: life and free will in physics and physiology, 1860-1880", I show how Maxwell, Cournot, Stewart and Boussinesq used the possibility of unstable or indeterministic mechanical systems to argue that the will or a vital principle can intervene in organic processes without violating the laws of physics, so that a strictly dualist account of life and the mind is possible. Moreover, I show that their ideas can be understood as a reaction to the law of conservation of energy and to the way it was used in physiology to exclude vital and mental causes. In "The nineteenth century conflict between mechanism and irreversibility", I show that in the late nineteenth century, there was a widespread conflict between the aim of reducing physical processes to mechanics and the recognition that certain processes are irreversible. Whereas the so-called reversibility objection is known as an objection that was made to the kinetic theory of gases, it in fact appeared in a wide range of arguments, and was susceptible to very different interpretations. It was only when the project of reducing all of physics to mechanics lost favor, in the late nineteenth century, that the reversibility objection came to be used as an argument against mechanism and against the kinetic theory of gases. In "Continuity in nature and in mathematics: Boltzmann and Poincaré", I show that the development of rigorous foundations of differential calculus in the nineteenth century led to concerns about its applicability in physics: through this development, differential calculus was made independent of empirical and intuitive notions of continuity and was instead based on mathematical continuity conditions, and for Boltzmann and Poincaré, the applicability of differential calculus in physics depended on whether these continuity conditions could be given a foundation in intuition or experience. In the final paper, "Determinism around 1900", I briefly discuss the implications of the developments described in the previous two papers for the history of determinism in physics, through a discussion of determinism in Mach, Poincaré and Boltzmann. I show that neither of them regards determinism as a property of the laws of mechanics; rather, for them, determinism is a precondition for science, which can be verified to the extent that science is successful. (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)