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 Element explores what it means for two theories in physics to be equivalent, and what lessons can be drawn about their structure as a result. It does so through a twofold approach. On the one hand, it provides a synoptic overview of the logical tools that have been employed in recent philosophy of physics to explore these topics: definition, translation, Ramsey sentences, and category theory. On the other, it provides a detailed case study of how these ideas may be (...) applied to understand the dynamical and spatiotemporal structure of Newtonian mechanics - in particular, in light of the symmetries of Newtonian theory. In so doing, it brings together a great deal of exciting recent work in the literature, and is sure to be a valuable companion for all those interested in these topics. (shrink)

Data science, and the related field of big data, is an emerging discipline involving the analysis of data to solve problems and develop insights. This rapidly growing domain promises many benefits to both consumers and businesses. However, the use of big data analytics can also introduce many ethical concerns, stemming from, for example, the possible loss of privacy or the harming of a sub-category of the population via a classification algorithm. To help address these potential ethical challenges, this paper maps (...) and describes the main ethical themes that were identified via systematic literature review. It then identifies a possible structure to integrate these themes within a data science project, thus helping to provide some structure in the on-going debate with respect to the possible ethical situations that can arise when using data science analytics. (shrink)

This article gives an explicit presentation of Newtonian gravitation on the backdrop of Maxwell space-time, 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 on some subtle technical issues and on substantive philosophical questions over how to identify the space-time structure of a theory.

There are well-known problems associated with the idea of gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation. 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 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. (shrink)

This paper argues that much of the literature on interpreting scientific theories presupposes a certain picture of what interpretation involves: a picture according to which interpreting a theory is like translating from one language to another. In place of this “external” approach to interpretation, this paper proposes an “internal” approach, according to which interpretation is more concerned with delineating a theory’s internal semantic architecture.

This is an essay about general covariance, and what it says 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.

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 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. (shrink)

This paper critically assesses whether quantum entanglement can be made compatible with Humean supervenience. After reviewing the prima facie tension between entanglement and Humeanism, I outline a recently-proposed Humean response, and argue that it is subject to two problems: one concerning the determinacy of quantities, and one concerning its relationship to scientific practice.

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. 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 is exhibited and shown to judge classical and intuitionistic logic to be inequivalent. (shrink)

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. (shrink)

Philosophy Compass, Volume 17, Issue 4, April 2022.

This paper critically assesses whether quantum entanglement can be made compatible with Humean supervenience. After reviewing the prima facie tension between entanglement and Humeanism, I outline a recently-proposed Humean response, and argue that it is subject to two problems: one concerning the determinacy of quantities, and one concerning its relationship to scientific practice.

How may we characterize the intrinsic structure of physical quantities such as mass, length, or electric charge? This article shows that group-theoretic methods—specifically, the notion of a free and transitive group action—provide an elegant way of characterizing the structure of scalar quantities, and uses this to give an intrinsic treatment of vector quantities. It also gives a general account of how different scalar or vector quantities may be algebraically combined with one another. Finally, it uses this apparatus to give a (...) simple intrinsic treatment of Newtonian gravitation. (shrink)

This article 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, by showing how (...) constraints derived from the theory of ultraproducts can enforce reducibility in the context of first-order theories. (shrink)

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. (shrink)

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.

If categorical equivalence is a good criterion of theoretical equivalence, then it would seem that if some class of mathematical structures is represented as a category, then any other class of structures categorically equivalent to it will have the same representational capacities. Hudetz (2019a) has presented an apparent counterexample to this claim; in this note, I argue that the counterexample fails.

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.

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. (shrink)

Philosophy Compass, Volume 17, Issue 10, October 2022.

Structural realists contend that the properties and relations in the world are more fundamental than the individuals. However, the standard model theory used to analyse the structure of logical theories can make it difficult to see how such an idea could be coherent or workable: for in that theory, properties and relations are constructed as sets of individuals. In this paper, I look at three ways in which structuralists might hope for an alternative: by appealing to predicate-functor logic, Tractarian geometry, (...) or cylindric algebras. I argue that the first two are problematic, but that the third is promising. (shrink)

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 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. (shrink)

Steven French’s new book is a bold and ambitious look at the question of what sorts of things scientific theories are—or rather, what they are not. For the purp.

Tomasz Bigaj’s new book is an authoritative and comprehensive discussion of recent issues concerning the means and metaphysical implications of individuating identical quantum particles. This review briefly summarises the book’s contributions and considers some of its implications for the debate over indiscernibility in quantum mechanics.