•  39
    The purpose of this paper is to examine in detail a particularly interesting pair of first-order theories. In addition to clarifying the overall geography of notions of equivalence between theories, this simple example yields two surprising conclusions about the relationships that theories might bear to one another. In brief, we see that theories lack both the Cantor-Bernstein and co-Cantor-Bernstein properties.
  •  222
    What Do Symmetries Tell Us About Structure?
    Philosophy of Science (4): 617-639. 2017.
    Mathematicians, physicists, and philosophers of physics often look to the symmetries of an object for insight into the structure and constitution of the object. My aim in this paper is to explain why this practice is successful. In order to do so, I present a collection of results that are closely related to (and in a sense, generalizations of) Beth’s and Svenonius’ theorems.
  •  28
    Equivalent and Inequivalent Formulations of Classical Mechanics
    British Journal for the Philosophy of Science. forthcoming.
    In this paper, 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, Halvorson and Weatherall. This case study yields three general philosophical payo offs. 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.
  •  28
    From Geometry to Conceptual Relativity
    Erkenntnis 82 (5): 1043-1063. 2017.
    The purported fact that geometric theories formulated in terms of points and geometric theories formulated in terms of lines are “equally correct” is often invoked in arguments for conceptual relativity, in particular by Putnam and Goodman. We discuss a few notions of equivalence between first-order theories, and we then demonstrate a precise sense in which this purported fact is true. We argue, however, that this fact does not undermine metaphysical realism.
  •  230
    Quine’s conjecture on many-sorted logic
    Synthese 194 (9): 3563-3582. 2017.
    Quine often argued for a simple, untyped system of logic rather than the typed systems that were championed by Russell and Carnap, among others. He claimed that nothing important would be lost by eliminating sorts, and the result would be additional simplicity and elegance. In support of this claim, Quine conjectured that every many-sorted theory is equivalent to a single-sorted theory. We make this conjecture precise, and prove that it is true, at least according to one reasonable notion of the…Read more
  •  106
    Morita Equivalence
    Review of Symbolic Logic 9 (3): 556-582. 2016.
    Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how these two well-known criteria are related to one another, we investigate an intermediate criterion called Morita equivalence.
  •  150
    Glymour and Quine on Theoretical Equivalence
    Journal of Philosophical Logic 45 (5): 467-483. 2016.
    Glymour and Quine propose two different formal criteria for theoretical equivalence. In this paper we examine the relationships between these criteria.
  •  39
    On Einstein Algebras and Relativistic Spacetimes
    with Sarita Rosenstock and James Owen Weatherall
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B): 309-316. 2015.
    In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson and Weatherall, the two are equivalent theories.
  •  41
    Spacetime structure
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 51 37-43. 2015.
    This paper makes an observation about the ``amount of structure'' that different classical and relativistic spacetimes posit. The observation substantiates a suggestion made by Earman and yields a cautionary remark concerning the scope and applicability of structural parsimony principles.
  •  96
    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