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This paper does two things. First, it reviews the recent debate between Halvorson and Manchak (2022) and Menon and Read (2024), looking for a reading of the former that is sympathetic to the concerns of the latter. Second, it considers whether there is a notion of determinism for spacetime theories that is adequate for the purposes of (Halvorson & Manchak, 2022); it concludes that there is not, but that we learn much of interest by considering the question.

Philosophers of science spend a lot of time “interpreting” scientific theories. In this paper, I try to get a handle on what it is they might be up to. My main contention is that a certain picture of interpretation is widespread (though implicit) in contemporary philosophy of science: a picture according to which interpretation of theories is relevantly analogous to the interpretation of foreign literature. On this picture, which we might call the external account of theory-interpretation, meaning is to be imported into the equations by putting them in correspondence with some discourse whose signs and symbols are already endowed with significance. However, there is an alternative way of thinking about interpretation—what we can call the “internal” account of interpretation—which instead takes interpretation to be a matter of delineating a theory’s internal semantic architecture.

The goal of this paper is to analyse the role of convention in interpreting physical theories - and, in particular, how the distinction between the conventional and the non-conventional interacts with judgments of equivalence. We will begin with a discussion of what, if anything, distinguishes those statements of a theory that might be dubbed “conventions”. This will lead us to consider the conventions that are not themselves part of a theory’s content, but are rather applied to the theory in interpreting it. Finally, we will consider the idea that what conventions to adopt might, itself, be regarded as a matter of convention.

It is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.

Christian List has recently proposed a category-theoretic model of a system of levels, applying it to various pertinent metaphysical questions. We modify and extend this framework to correct some minor defects and better adapt it to application in philosophy of science. This includes a richer use of category theoretic ideas and some illustrations using social choice theory.

This is an essay about general covariance, and what it says (or doesn't say) about spacetime structure. After outlining a version of the dynamical approach to spacetime theories, and how it struggles to deal with generally covariant theories, I argue that we should think about the symmetry structure of spacetime rather differently in generally-covariant theories compared to non-generally-covariant theories: namely, as a form of internal rather than external symmetry structure.

A central issue in the philosophical debates over general relativity concerns the status of the metric field: should it be regarded as part of the background arena in which physical fields evolve, or as a physical field itself? In this paper, we approach this debate through its relationship to the so-called "Problem of Space": the problem of determining which abstract, mathematical geometries are candidate descriptions of physical space. In particular, we explore the way that Hermann Weyl tackled the Problem of Space in the wake of general relativity, and argue that Weyl’s proposed solution reveals a “middle way” between bare-manifold and manifold-plus-metric accounts of spacetime.

This paper considers the following question: what is the relationship between supervenience and reduction? I investigate this formally, first by introducing a recent argument by Christian List to the effect that one can have supervenience without reduction; then by considering how the notion of Nagelian reduction can be related to the formal apparatus of definability and translation theory; then by showing how, in the context of propositional theories, topological constraints on supervenience serve to enforce reducibility; and finally, how constraints derived from the theory of ultraproducts can enforce reducibility in the context of first-order theories.

In a recent paper, Wigglesworth claims that syntactic criteria of theoretical equivalence are not appropriate for settling questions of equivalence between logical theories, since such criteria judge classical and intuitionistic logic to be equivalent; he concludes that logicians should use semantic criteria instead. However, this is an artefact of the particular syntactic criterion chosen, which is an implausible criterion of theoretical equivalence (even in the non-logical case). Correspondingly, there is nothing to suggest that a more plausible syntactic criterion should not be used to settle questions of equivalence between different logical theories; such a criterion (which may already be found in the literature) is exhibited and shown to judge classical and intuitionistic logic to be inequivalent.

This essay is about how the notion of “structure” in ontic structuralism might be made precise. More specifically, my aim is to make precise the idea that the structure of the world is (somehow) given by the relations inhering in the world, in such a way that the relations are ontologically prior to their relata. The central claim is the following: one can do so by giving due attention to the relationships that hold between those relations, by making use of certain notions from algebraic logic.

There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation (i.e., Newton-Cartan theory). We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized (gauge-free) theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation.

Philosophers of science spend a lot of time “interpreting” scientific theories. In this paper, I try to get a handle on what it is they might be up to. My main contention is that a certain picture of interpretation is widespread (though implicit) in contemporary philosophy of science: a picture according to which interpretation of theories is relevantly analogous to the interpretation of foreign literature. On this picture, which we might call the external account of theory-interpretation, meaning is to be imported into the equations by putting them in correspondence with some discourse whose signs and symbols are already endowed with significance. However, there is an alternative way of thinking about interpretation—what we can call the “internal” account of interpretation—which instead takes interpretation to be a matter of delineating a theory’s internal semantic architecture.

In the literature over the Ramsey-sentence approach to structural realism, there is often debate over whether structural realists can legitimately restrict the range of the second-order quantifiers, in order to avoid the Newman problem. In this paper, I argue that even if they are allowed to, it won’t help: even if the Ramsey sentence is interpreted using such restricted quantifiers, it is still an implausible candidate to capture a theory’s structural content. To do so, I use the following observation: if a Ramsey sentence did encode a theory’s structural content, then two theories would be structurally equivalent just in case they have logically equivalent Ramsey sentences. I then argue that this criterion for structural equivalence is implausible, even where frame or Henkin semantics are used.

There has recently been debate in the literature over whether the metaphysical doctrine popularly known as Humean supervenience can be reconciled—in whole or in part—with certain empirical facts about quantum entanglement. In this paper, I undertake a critical analysis of Humean efforts to effect such a reconciliation.

This paper gives an explicit presentation of Newtonian gravitation on the backdrop of Maxwell spacetime, giving a sense in which acceleration is relative in gravitational theory. However, caution is needed: assessing whether this is a robust or interesting sense of the relativity of acceleration depends upon some subtle technical issues, and upon substantive philosophical questions over how to identify the spacetime structure of a theory.

This essay is about how the notion of “structure” in ontic structuralism might be made precise. More specifically, my aim is to make precise the idea that the structure of the world is (somehow) given by the relations inhering in the world, in such a way that the relations are ontologically prior to their relata. The central claim is the following: one can do so by giving due attention to the relationships that hold between those relations, by making use of certain notions from algebraic logic.

In this paper, I critique the claim that a theory’s Ramsey sentence (or something like it) is a good candidate for encoding that theory’s structural content, by showing that such a claim leads to implausible criteria of the- oretical equivalence.

There has recently been debate in the literature over whether the metaphysical doctrine popularly known as Humean supervenience can be reconciled—in whole or in part—with certain empirical facts about quantum entanglement. In this paper, I undertake a critical analysis of Humean efforts to effect such a reconciliation.

Suppose that one thinks that certain symmetries of a theory reveal “surplus structure”. What would a formalism without that surplus structure look like? The conventional answer is that it would be a reduced theory: a theory which traffics only in structures invariant under the relevant symmetry. In this paper, I argue that there is a neglected alternative: one can work with a sophisticated version of the theory, in which the symmetries act as isomorphisms.

This paper gives an explicit presentation of Newtonian gravitation on the backdrop of Maxwell spacetime, giving a sense in which acceleration is relative in gravitational theory. However, caution is needed: assessing whether this is a robust or interesting sense of the relativity of acceleration depends upon subtle questions over how to identify the spacetime structure of a theory.

This paper seeks to give an account of what could be involved in interpreting a theory. The aim is to try and provide a robust conception of theory-interpretation which operates in terms internal to the representational architecture of the theory, rather than importing meaning by stipulative correspondence to external terms.

In this paper, I build upon and extend Weatherall’s answer to the question posed by Saunders: “What is the relation between a theory of gravity (and other forces) formulated in Maxwell space-time and one based on Newton-Cartan space-time?” I do so by showing how one can give an explicit dynamics for Newtonian gravitation, without presupposing any more structure than that found in Maxwell spacetime. Doing so helps to further illuminate the relationship between geometrised and non-geometrised formulations of Newtonian gravitation.

There has recently been debate in the literature over whether the metaphysical doctrine popularly known as Humean supervenience can be reconciled—in whole or in part—with certain empirical facts about quantum entanglement. In this paper, I undertake a critical analysis of Humean efforts to effect such a reconciliation. I begin with a discussion of the relationship between Humeanism and quantum mechanics; I suggest that there are some difficulties even when considering single-particle quantum mechanics, but agree that the real problems come when considering many-particle quantum mechanics. I then review the available strategies for overcoming this problem, and find them wanting.

In this paper, I consider the role of exact symmetries in theories of physics, working throughout with the example of gravitation set in Newtonian spacetime. First, I spend some time setting up a means of thinking about symmetries in this context; second, I consider arguments from the seeming undetectability of absolute velocities to an anti-realism about velocities; and finally, I claim that the structure of the theory licences (and perhaps requires) us to interpret models which differ only with regards to the absolute velocities of objects as depicting the same physical state of affairs. In defending this last claim, I consider how ideas and resources from the philosophy of language may usefully be brought to bear on this topic.

Christian List (Noûs, forthcoming, 2018, [24]) has recently proposed a category-theoretic model of a system of levels, applying it to various pertinent metaphysical questions. We modify and extend this framework to correct some minor defects and better adapt it to application in philosophy of science. This includes a richer use of category theoretic ideas and some illustrations using social choice theory.