Research

Philosophy of Science

My work so far on scientific (specifically, physical) theories has been connected by the interwoven thematic threads of pluralism, the pragmatics of application, and the importance of context. I am also developing a research program to use ideas and methods from topology to formalize notions of similarity among mathematical models used in science. These can be put to use giving precise answers to a surprising variety of questions, such as the nature of intertheoretic reduction and emergence, theory change, lawhood and counterfactual reasoning in science, and the epistemology of modeling. Here, the selection of the relevant notion of similarity in a given context is crucial.

Classical Mechanics

There is a longstanding debate on the senses in which classical mechanics can be understood as a deterministic theory.  In one paper, I examine a much recently discussed example of the purported failure of determinism in classical mechanics—that of Norton’s Dome—and the range of current objections against it. These objections all assume a fixed conception of classical mechanics, but I argue that there are in fact many different conceptions appropriate and useful for different purposes, none of which is intrinsically preferred in analyzing the Dome. Instead of also arguing for or against determinism, I stress the wide variety of pragmatic considerations that, in a specific context, may lead one to adopt one conception over another.

Spacetime Theory and Gravitation

In the context of general relativity, Stephen Hawking (among others) has proposed that a necessary condition for a property of spacetime to be “physically significant” is that it is stable: all the spacetimes sufficiently similar to the one in question must also have that property.  Thus whether a property is stable depends on the notion of similarity.  In physics, this is done by introducing a topology on the collection of all spacetimes.  Some have thus suggested that one should find a canonical topology, a single “right” topology for every inquiry.  In another paper, I show how the main candidates—and each possible choice, to some extent—faces the horns of a no-go result. I suggest that instead of trying to decide what the “right” topology is for all problems, one should let the details of particular types of problems guide the choice of an appropriate topology.  This work forms one chapter of my dissertation.

In another chapter, I illustrate the importance of choosing a topology with the relationship between general relativity and Newtonian gravitation.  Accounts of the reduction of the former to the latter usually take one of two approaches. One considers the limit as the speed of light c → ∞, while the other focuses on the approximation of formulas for low velocities. Although the first approach treats the reduction of relativistic spacetimes globally, many have argued that ‘c → ∞’ can at best be interpreted counterfactually, which is of limited value in explaining the past empirical success of Newtonian gravitation. The second, on the other hand, while more applicable to explaining this success, only treats a small fragment of general relativity.  Building on work by Jürgen Ehlers, I propose a different account of the reduction relation that offers the global applicability of the c → ∞ limit while maintaining the explanatory utility of the low velocity approximation. In doing so, I highlight the role that a topology on the collection of all spacetimes plays in defining the relation, and how the choice of topology corresponds with broader or narrower classes of observables that one demands be well-approximated in the limit.

Statistics

My work in philosophy of statistics has centered on the nature of evidence.  In a recent paper I consider the likelihood principle,  a constraint on any measure of evidence arising from a statistical experiment, in light of procedures for model verification—statistical tests of modeling assumptions.  I argue that if model verification is to be at all feasible, and insofar as the results of the verification should bear on the evidence produced by the experiment, the likelihood principle cannot be a universal constraint on any measure of evidence.  Nevertheless, I suggest that proponents of the principle may hold out for a restricted version thereof, either as a kind of idealization or as defining one among many different forms of evidence.

I am also developing a formalization of Deborah G. Mayo’s theory of severe testing and other defenses and elaborations of the foundations of classical statistics. When it comes to statistical schools I am a pluralist, but have found that classical statistics has received much less attention than Bayesian statistics in the philosophy of science literature.