• I argue that Isaac Newton's De Gravitatione should not be considered an authoritative expression of his thought about the metaphysics of space and its relation to physical inquiry. I establish the following narrative: In De Gravitatione (circa 1668–84), Newton claimed he had direct experimental evidence for the work's central thesis: that space had "its own manner of existing" as an affection or emanative effect. In the 1710s, however, through the prodding of Roger Cotes and G. W. Leibniz, he ca…Read more
  • Cotes’ Queries: Newton’s Empiricism and Conceptions of Matter
    In Eric Schliesser & Andrew Janiak (eds.), Interpreting Newton, Cambridge University Press. pp. 105-137. 2012.
    We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist methodologies…Read more
  • In his Metaphysische Anfangsgründe der Naturwissenschaft, Kant claims that chemistry is a science, but not a proper science (like physics), because it does not adequately allow for the application of mathematics to its objects. This paper argues that the application of mathematics to a proper science is best thought of as depending upon a coordination between mathematically constructible concepts and those of the science. In physics, the proper science that exhausts the a priori knowledge of obj…Read more
  • Kant on the Mathematical Deficiency of Psychology
    Hopos: The Journal of the International Society for the History of Philosophy of Science 12 (2): 485-509. 2022.
    Kant’s denial that psychology is a properly so-called natural science, owing to the lack of application of mathematics to inner sense, has garnered a great deal of attention from scholars. Although the interpretations of this claim are diverse, commentators by and large fail to ground their views on an account of Kant’s conception of applied mathematics. In this article, I develop such an account, according to which the application of mathematics to a natural science requires both a mathematical…Read more
  • What is Chemistry, for Kant?
    Kant Yearbook 9 (1): 85-112. 2017.
    Kant’s preoccupation with architectonics is a characteristic and noteworthy aspect of his thought. Various features of Kant’s argumentation and philosophical system are founded on the precise definitions of the various subdomains of human knowledge and the derivative borders among them. One science conspicuously absent from Kant’s routine discussions of the organization of knowledge is chemistry. Whereas sciences such as physics, psychology, and anthropology are all explicitly located in the arc…Read more
  • Comparing the structures of mathematical objects
    Synthese 199 (3-4): 6357-6369. 2021.
    A popular method for comparing the structures of mathematical objects, which I call the ‘subset approach’, says that X has more structure than Y just in case X’s automorphisms form a proper subset of Y’s automorphisms. This approach is attractive, in part, because it seems to yield the right results in some comparisons of spacetime structure. But as I show, it yields the wrong results in a number of other cases. The problem is that the subset approach compares structure using automorphism sets. …Read more
  • How electrons spin
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 68 40-50. 2019.
  • Quantum Mechanics as Classical Physics
    Philosophy of Science 82 (2): 266-291. 2015.
    Here I explore a novel no-collapse interpretation of quantum mechanics that combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.
  • Mechanics without Mechanisms
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 62 45-55. 2018.
    At the time of Heinrich Hertz's premature death in 1894, he was regarded as one of the leading scientists of his generation. However, the posthumous publication of his treatise in the foundations of physics, "Principles of Mechanics", presents a curious historical situation. Although Hertz's book was widely praised and admired, it was also met with a general sense of dissatisfaction. Almost all of Hertz's contemporaries criticized "Principles" for the lack of any plausible way to construct a mec…Read more
  • In philosophy, much attention has rightly been paid to the need to diversify teaching with regard to who teaches, who is taught, and which authors and questions are the focus of study. Less attention, however, has been paid to inclusive pedagogy—the teaching methods that are used, and how they can make or fail to make classes as accessible as possible to the diverse students who enter them. By drawing on experiences from our own teaching as well as research on student-centered, inclusive best pr…Read more
  • On the Structure of Classical Mechanics
    British Journal for the Philosophy of Science 66 (4): 801-828. 2015.
    The standard view is that the Lagrangian and Hamiltonian formulations of classical mechanics are theoretically equivalent. Jill North, however, argues that they are not. In particular, she argues that the state-space of Hamiltonian mechanics has less structure than the state-space of Lagrangian mechanics. I will isolate two arguments that North puts forward for this conclusion and argue that neither yet succeeds. 1 Introduction2 Hamiltonian State-space Has less Structure than Lagrangian State-sp…Read more
  • Equivalent and Inequivalent Formulations of Classical Mechanics
    British Journal for the Philosophy of Science 70 (4): 1167-1199. 2019.
    In this article, I examine whether or not the Hamiltonian and Lagrangian formulations of classical mechanics are equivalent theories. I do so by applying a standard for equivalence that was recently introduced into philosophy of science by Halvorson and Weatherall. This case study yields three general philosophical payoffs. The first concerns what a theory is, while the second and third concern how we should interpret what our physical theories say about the world. 1Introduction 2When Are Two Th…Read more