Publications
(for abstracts, click here)
Expressivism about Explanatory Relevance, Philosophical Studies, (2022), available open access online!
Hamiltonian Privilege, Erkenntnis (2023), with Gabriele Carcassi and Christine Aidala (open access!)
Epistemic dependence & Understanding: Reformulating through Symmetry, British Journal for Philosophy of Science, 2023, 74 (4)
Interpreting the Wigner-Eckart Theorem, Studies in History and Philosophy of Science, 2021, 87: 28-43
Understanding and Equivalent Reformulations, Philosophy of Science, Proceedings of 2020 Biennial Meeting, December 2021, issue 88 (5)
Indispensability and the Problem of Compatible Explanations, Synthese, 2016, 193 (2): 451-467
Work in Progress
(comments welcome!)
Dissertation
“Symmetry & Reformulation”
My Ph.D. thesis examines the intellectual significance of mathematical reformulations in science. I focus on cases where we do not need to reformulate a theory or problem-solving procedure, with symmetry arguments providing paradigmatic examples. This leads to a general puzzle about compatible formulations: what do we intellectually gain from having multiple ways of solving the same problem? I argue against both conventionalist responses that seek to deflate the puzzle and joint-carving responses that seek to answer it through expansive (meta-)ontological resources. Instead, I defend a positive but empiricist-friendly solution, which I call conceptualism (or conceptual empiricism). According to conceptualism, science aims not only at empirical adequacy but also at clarifying what we need to know (and what suffices to know) to solve problems and answer why-questions. Through a series of case studies, I examine the implications of reformulations for scientific understanding, explanation, variable choices, and the aims of science.
Director's Cut is linked here
(an extended abstract lies at the end of the preface)
Expressivism about Scientific Concepts
I am actively exploring how expressivism (or quasi-realism) pairs well with empiricism, allowing us to avoid substantial metaphysical commitments while making sense of ordinary scientific practice.
I have a paper developing an expressivist account of explanation. Here is a shorter version (~4k words)! In brief, to judge that an argument or answer is explanatory is to endorse a set of norms for being (intellectually) satisfied by that answer. A set of norms on explanation is good insofar as it facilitates the (non-explanatory) aims of science. Here’s a handout for expressivism about explanation.
I am working on a similar project developing an expressivist account of laws of nature, based on expressivism about counterfactual reasoning: here is a draft and a handout! My dissertation also briefly develops expressivist accounts of comparative understanding and fundamentality.
Interpreting Classical Mechanics
With Gabriele Carcassi and Prof. Christine Aidala, we have a paper (forthcoming at Erkenntnis) clarifying the relationship between Lagrangian and Hamiltonian mechanics. This is a part of their broader project on the Foundations of Physics, called Assumptions of Physics.
Quantum Field Theory
There are many formulations of quantum field theory: Lagrangian, algebraic, axiomatic, etc. Of particular interest for the calculation of scattering amplitudes is a recent reformulation known as the on-shell framework. This formalism eschews writing down a specific Lagrangian, constraining amplitudes instead by appealing to a few basic physical and logical principles, including locality, unitarity, Lorentz invariance, and dimensional analysis. I am investigating the interpretive and methodological significance of this formalism. Although it sheds light on some interpretive problems involving virtual particles and gauge symmetries, it also opens new problems of its own.
Draft manuscript or talk slides available upon request.
History of Physics
I have research interests in the history of symmetry arguments in quantum mechanics and spectroscopy, spanning the 1920’s to the 1980’s. Projects include Dirac’s 1926 non-group theoretic derivation of angular momentum selection rules, Lie-algebraic vs. Lie-group-theoretic approaches to atomic spectroscopy, and the history of the Wigner-Eckart theorem in atomic, molecular, and nuclear spectroscopy.
Philosophy of Mathematics
I have published a paper arguing against indispensability arguments for mathematical Platonism. In brief, the existence of alternative foundations for mathematics prevents inference to the best explanation arguments for mathematical ontology.
My other projects relate primarily to mathematical methodology. Mathematicians frequently reprove theorems that are already known to be true, often through stunningly different methods. These different proofs all provide different understandings of the same theorem. I am investigating the particular epistemic achievements that lie behind these different proof methods and styles.