My research is in the philosophy of science and early analytic philosophy, with a particular interest in the late nineteenth and early twentieth century—the period that encompassed the transition from classical to modern physics and the emergence of modern logic. A recurring theme in my research is the topic of representation, from the particular question of how mathematical geometry represents physical space, to the broader question of how formal and natural languages represent the world.
- "Models and Multiplicities" — Journal of the History of Philosophy (forthcoming) [preprint]
Although it is well known that Heinrich Hertz was one of Ludwig Wittgenstein’s earliest influences, Wittgenstein’s explicit references to Hertz in the Tractatus have remained almost entirely uninterpreted. My central claim in this paper is that Wittgenstein’s reference to Hertz’s ‘dynamical models’ has important implications for a long-standing debate concerning whether or not the Tractatus explains the sense of colloquial sentences by offering an account of the fundamental structure of reality. I argue that Wittgenstein’s reference to dynamical models provides strong evidence for the view that the Tractatus contains no such ontological theory. I show that, just as Hertz’s dynamical models capture the essential content of a mechanical description (what all descriptions of the same system have in common), so Tractarian analysis captures the essential content of a sentence (what all sentences that express the same sense have in common). I argue that treating Hertzian analysis as a model of Tractarian analysis provides important insights into how such analysis terminates, and that in neither case is there a need to appeal to an underlying ontology.
- "Hertz's Mechanics and a Unitary Notion of Force" — winning entry for the 2020 Du Châtelet Prize in Philosophy of Physics
Heinrich Hertz dedicated the last four years of his life to a systematic reformulation of mechanics. One of the main issues that troubled Hertz in the traditional formulation was a ‘logical obscurity’ in the notion of force. However, it is unclear what this logical obscurity was, hence it is unclear how Hertz took himself to have avoided this obscurity in his own formulation of mechanics. In this paper I first identify an issue concerning the Newtonian conception of force that lay in the background of Hertz’s concerns. I argue that a subtle ambiguity in Newton’s original laws of motion led to the development of two different notions of force: a vectorial notion and a variational notion. I then show how Hertz employed the mathematical apparatus of differential geometry to arrive at a unitary notion of force, thus avoiding the logical obscurity that lurked in the traditional formulation of mechanics.
- "A Raum with a View" — co-authored with Neil Dewar; Einstein Studies, 15(1): 111–132, 2020 [online] [preprint]
In this paper, we argue that Hermann Weyl’s analysis of the conception of physical geometry implicit in Einstein’s theory of general relativity offers a novel insight into how geometry represents the world. Following the rapid proliferation of geometries in the nineteenth century, consensus developed around the idea that only constant curvature geometries were candidate physical geometries. However, this idea was unequivocally undermined by the use of a variable curvature geometry in general relativity. Indeed, in the wake of general relativity there is no generally accepted account of which geometrical objects represent spatio-temporal structure: although some argue that spacetime is best represented by a bare topological manifold, others argue that such a manifold must be equipped with a metric—a means of determining distances and angles—in order to represent spacetime. We argue that Weyl’s work reveals a level of geometrical structure intermediate between the manifold and the metric, and that there are good reasons to regard this intermediate structure as the mathematical representation of spacetime in general relativity.
- "Mechanics without Mechanisms" — Studies in History and Philosophy of Science Part B, 62: 45–55, 2018 [online] [preprint]
Almost all of Hertz's readers have criticised Principles of Mechanics for the lack of any plausible way to construct a mechanism from the “hidden masses” that are particularly characteristic of Hertz's framework. This issue has seemed especially pressing given the widespread expectation that Hertz's work might have led to a model of the underlying workings of the ether. In this paper, I seek an explanation for why Hertz seemed so unperturbed by the difficulties of constructing such a mechanism. I explore how Hertz's image-theory of representation brings with it an austere view of the “essential content” of mechanical descriptions, only requiring a kind of structural isomorphism between symbolic representations and target phenomena. I argue that bringing this into view makes clear why Hertz felt no need to work out the kinds of mechanisms that many of his readers have looked for. Furthermore, I argue that a crucial role of Hertz's hypothesis of hidden masses has been widely overlooked: far from acting as a proposal for the underlying structure of the ether, I show that Hertz's hypothesis ruled out knowledge of such underlying structure.