I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible.

The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single (...) formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. (shrink)

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and “interpretational” equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including (generalized) definitional (...) equivalence and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality. The article is in two parts; this is Part 2, which addresses categorical equivalence, interpretational equivalence, and duality. (shrink)

I argue that a criterion of theoretical equivalence due to Glymour :227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation.

I point out a radical indeterminism in potential-based formulations of Newtonian gravity once we drop the condition that the potential vanishes at infinity. This indeterminism, which is well known in theoretical cosmology but has received little attention in foundational discussions, can be removed only by specifying boundary conditions at all instants of time, which undermines the theory's claim to be fully cosmological, i.e., to apply to the Universe as a whole. A recent alternative formulation of Newtonian gravity due to Saunders (...) pp.22-48) provides a conceptually satisfactory cosmology but fails to reproduce the Newtonian limit of general relativity in homogenous but anisotropic universes. I conclude that Newtonian gravity lacks a fully satisfactory cosmological formulation. (shrink)

Using as a starting point recent and apparently incompatible conclusions by Saunders and Knox, I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two versions of Newtonian physics make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view—espoused by Knox, and also by Brown —that inertial structure is defined (...) by the dynamics governing subsystems of a larger system. This clarifies some interesting features of Newtonian physics, notably the distinction between using the theory to model subsystems of a larger whole and using it to model complete universes, and the scale-relativity of spacetime structure. _1_ Introduction _2_ Newtonian Mechanics and Galilean Spacetime _3_ Vector Relationism and Maxwellian Spacetime _4_ Recovering the Galilei Group: Dynamics of Subsystems _5_ Knox on Inertial Structure _6_ Connections on Maxwellian Spacetime _7_ Knox on Newtonian Gravity _8_ Vector Relationism and Newton–Cartan Theory _9_ Inertial Structure in Newton–Cartan Gravity _10_ Reconciling Knox and Saunders _11_ Conclusions. (shrink)

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)

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this framework, never absolute (...) ones. (shrink)

History and philosophy complement and overlap each other in subject matter, but the two disciplines exhibit conflict over methodology. Since Hempel's challenge to historians that they should adopt the covering law model of explanation, the methodological conflict has revolved around the respective roles of the general and the particular in each discipline. In recent years, the revival of narrativism in history, coupled with the trend in philosophy of science to rely upon case studies, joins the methodological conflict anew. So long (...) as contemporary philosophy of science relies upon history's methodology to construct its case studies, it subjects itself to a paradoxical situation: the better the history, the worse the philosophy. An example of the methodological conflict is presented in the case of Antoine Lavoisier. This example also serves our ultimateconclusion, which is that distinctively philosophical methods of case-study design promise enhanced prescriptive powers for philosophy of science. (shrink)

That past patterns may continue in many different ways has long been identified as a problem for accounts of induction. The novelty of Goodman’s ”new riddle of induction” lies in a meta-argument that purports to show that no account of induction can discriminate between incompatible continuations. That meta-argument depends on the perfect symmetry of the definitions of grue/bleen and green/blue, so that any evidence that favors the ordinary continuation must equally favor the grue-ified continuation. I argue that this very dependence (...) on the perfect symmetry defeats the novelty of the new riddle. The symmetry can be obtained in contrived circumstances, such as when we grue-ify our total science. However, in all such cases, we cannot preclude the possibility that the original and grue-ified descriptions are merely notationally variant descriptions of the same physical facts; or if there are facts that separate them, these facts are ineffable, so that no account of induction should be expected to pick between them. In ordinary circumstances, there are facts that distinguish the regular and grue-ified descriptions. Since accounts of induction can and do call upon these facts, Goodman’s meta-argument cannot provide principled grounds for the failure of all accounts of induction. It assures us only of the failure of accounts of induction, such as unaugmented enumerative induction, that cannot exploit these symmetry breaking facts. (shrink)

I argue that, contrary to thestandard view, the Newtonian universe containsno contingency. I do this by arguing (i) thatno contingency is introduced into the Newtonianuniverse by the initial conditions of physicalsystems in the universe, and (ii) that theclaim that the Newtonian universe as a wholehas contingent properties leads to incoherence.This result suggests that Newtonian physics iseither inconsistent or incomplete, since thelaws of Newtonian physics are too weak todetermine all the properties of the Newtonianuniverse uniquely.

As a discipline of its own, the philosophy of science can be traced back to the founding of its academic journals, some of which go back to the first half of the twentieth century. While the discipline has been the object of many historical studies, notably focusing on specific schools or major figures of the field, little work has focused on the journals themselves. Here, we investigate contemporary philosophy of science by means of computational text-mining approaches: we apply topic-modeling algorithms (...) to eight major philosophy of science journals, from the 1930s up until 2017. Based on the full-text content of some 15,897 articles, we identified 25 research themes and 8 thematic clusters that show how the research agenda of the philosophy of science has changed in its content over the course of the last eight decades, up to the philosophy of science we now know. We also show how each one of the journals contributed in its own way to this thematic evolution. (shrink)

I argue that the best spacetime setting for Newtonian gravitation (NG) is the curved spacetime setting associated with geometrized Newtonian gravitation (GNG). Appreciation of the ‘Newtonian equivalence principle’ leads us to conclude that the gravitational field in NG itself is a gauge quantity, and that the freely falling frames are naturally identified with inertial frames. In this context, the spacetime structure of NG is represented not by the flat neo-Newtonian connection usually made explicit in formulations, but by the sum of (...) the flat connection and the gravitational field. 1 Introduction2 Newtonian Gravity: The Orthodox Approach3 Newtonian Gravity: Additional Symmetries4 Cosmological Considerations5 A Newtonian Equivalence Principle: Inertial Frames in Newtonian Gravitation6 Theory Equivalence?7 Conclusion. (shrink)

The constrained Hamiltonian formalism is recommended as a means for getting a grip on the concepts of gauge and gauge transformation. This formalism makes it clear how the gauge concept is relevant to understanding Newtonian and classical relativistic theories as well as the theories of elementary particle physics; it provides an explication of the vague notions of “local” and “global” gauge transformations; it explains how and why a fibre bundle structure emerges for theories which do not wear their bundle structure (...) on their sleeves; it illuminates the connections of the gauge concept to issues of determinism and what counts as a genuine “observable”; and it calls attention to problems which arise in attempting to quantize gauge theories. Some of the limitations and problematic aspects of the formalism are also discussed. (shrink)

ABSTRACT I explore the viability of a Galilean relational theory of space-time—a theory that includes a three-place collinearity relation among its stock of basic relations. Two formal results are established. First, I prove the existence of a class of dynamically possible models of Newtonian mechanics in which collinearity is uninstantiated. Second, I prove that the dynamical properties of Newtonian systems fail to supervene on their Galilean relations. On the basis of these two results, I argue that Galilean relational space-time is (...) too weak of a structure to support a relational interpretation of classical mechanics. 1.Introduction 2.Completeness 3.Leibnizian Relationalism 4.Galilean Relationalism 5.Inverse-Cube Force Laws 5.1Warm-up 5.2Model 1: Zero angular momentum 5.3Model 2: Non-zero angular momentum 6.Supervenience 7.Incompleteness 8.Conclusion. (shrink)

In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’’ version and a ‘‘strong’’ version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. (...) Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a ‘‘weak’’ version in Maxwellian spacetime, and a ‘‘strong’’ version in Neo-Newtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism. r 2004 Elsevier Ltd. All rights reserved. (shrink)

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and "interpretational" equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including definitional equivalence (...) and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality. (shrink)

This survey article is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the ``geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its ``causal structure".

This volume is the first systematic presentation of the work of Albert Einstein, comprising fourteen essays by leading historians and philosophers of science that introduce readers to his work. Following an introduction that places Einstein's work in the context of his life and times, the book opens with essays on the papers of Einstein's 'miracle year', 1905, covering Brownian motion, light quanta, and special relativity, as well as his contributions to early quantum theory and the opposition to his light quantum (...) hypothesis. Further essays relate Einstein's path to the general theory of relativity (1915) and the beginnings of two fields it spawned, relativistic cosmology and gravitational waves. Essays on Einstein's later years examine his unified field theory program and his critique of quantum mechanics. The closing essays explore the relation between Einstein's work and twentieth-century philosophy, as well as his political writings. (shrink)

This is the chapter on general relativity for the Cambridge Companion to Einstein which I am co-editing with Christoph Lehner.

It is well-known that Newton’s theory of gravity, commonly held to describe a gravitational force, can be recast in a geometrical form: Newton- Cartan theory. It is less well-known that general relativity, an apparently geometrical theory, can be reformulated in such a way that it resembles a force theory; teleparallel gravity does just this. This raises questions. One of these concerns theoretical underdetermination. I argue that these theories do not, in fact, represent cases of worrying underdetermination. On close examination, the (...) alternative formulations are best interpreted as postulating the same spacetime ontology. In accepting this, we see that the ontological commitments of these theories cannot be directly deduced from their mathematical form. The geometrical nature of a gravitational theory is not a straightforward consequence of anything internal to that theory as a theory of gravity. Rather, it essentially relies on the rest of nature (the nongravitational interactions) conspiring to choose the appropriate set of inertial frames. (shrink)