Algebraic structuralism

Forthcoming in Philosophical Studies

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.


On gravitational energy in Newtonian theories (with Jim Weatherall)

Forthcoming in Foundations of Physics

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.

Preprint | Published version

On translating between logics

Forthcoming in Analysis

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.

Preprint | Published version

Ramsey equivalence

Forthcoming in Erkenntnis

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.


Maxwell gravitation

Forthcoming in Philosophy of Science

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.


Interpretation and equivalence; or, equivalence and interpretation

Forthcoming in Curiel and Lutz (eds.), The Semantics of Theories

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.


Sophistication about symmetries

Forthcoming in The British Journal for the Philosophy of Science

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.

Preprint | Published version

Symmetries and the philosophy of language

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52, Part B, 317–327. doi: 10.1016/j.shpsb.2015.09.004

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.

Preprint | Published version