Research

Philosophy of Science

I am developing a research program to use ideas and methods from topology to formalize notions of similarity amongst models used in science. This 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 and idealization. Here, the selection of the relevant notion of similarity in a given context is crucial, as is specificity in just what models one is considering.

On modeling and idealization, one of my papers on Norton’s Dome—see below—also introduces the idea of a “Minimal Approximation,” and unholy but useful admixture of the sort of minimality for explanations one finds in minimal models, but applied only to properties of models rather models themselves, per John D. Norton’s distinction. I’ve also co-edited a special issue of Synthese on infinite idealizations in science, the introduction to which you can read here.

Determinism in 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. Besides extending these ideas to inertial motion in general relativity, I’ve also showed how certain approximations Norton used do not affect the indeterminism of the example; in fact, the approximation are “minimal” in the sense that they elide details of the properties of the classical mechanical model that don’t matter to the inference drawn therefrom.

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. I’ve even constructed a new topology that better captures the similarity of global spacetime properties.

I have also illustrated the importance of choosing a topology when considering 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.

I’m also interested in the foundational interpretational principles of general relativity. For instance, I’ve written a paper with some technical results that justify why the clock hypothesis in general relativity makes sense—that is, why it makes sense to represent the time elapsed along a worldline as the length of that worldline as determined by the spacetime metric. More recently I’ve drawn out a tension between the possibility of time travel in the theory and the usual assumption that timelike worldlines represent the possible histories of massive test particles, with implications for the material ontology that general relativity supports. And I’ve added my two cents on how representation works in the theory, with commentary bearing on discussion around the hole argument.

Finally, most authors don’t consider the role of the dimensionality in interpreting a spacetime theory, but in work with J. B. Manchak, Mike D. Schneider, and James Owen Weatherall I show that in two spacetime dimensions, it is far from clear what general relativity is even supposed to be, as the most obvious formulation has qualitatively different properties than in four spacetime dimensions.

Quantum Foundations

I’m especially interested in structural features of quantum theory that make it (dis)similar to other theories, such as contextualityBen Feintzeig and I applied the Kochen-Specker theorem to derive a sort of no-go theorem for a large class of hidden variable theories that seek to avoid the hard choices of Bell’s theorem by generalizing probability theory. In a word, they can only do so on pain of admitting a finite null cover of events: a finite collection of events whose union is the trivial event (anything happens), but each of which is assigned a (generalized) probability of 0—something impossible for classical (Kolmogorovian) probability spaces.

Philosophy of Statistics

My work in philosophy of statistics has centered on the nature of evidence; I’ve co-edited a special issue of Synthese on evidence amalgamation in the sciences, the introduction to which you can read here.

As for my own work, in one 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.

One consequence of the likelihood principle concerns so-called stopping rules, rules that determine when a sequential experiment should stop. Should the stopping rule of an experiment make a difference, evidentially, to an hypothesis it tests? For instance, consider sequential flips of a coin. One stopping rule prescribes ending after a fixed number of flips, another, say, after a fixed number of heads. Is it the case that how such an experiment bears on the bias of the coin depends on which stopping rule was used? Many think not, but I demur, rebutting five different argument for this conclusion.

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.

Philosophy of Computing

I’m interested in account of computational implementation, i.e., of how physical objects act as computers. With Mike Cuffaro, I edited Physical Perspectives on Computation, Computational Perspectives on Physics with Cambridge University Press. In addition to our introduction, there are twelve commissioned chapters evenly divided amongst four thematic parts:

  1. The Computability of Physical Systems and Physical Systems as Computers
  2. The Implementation of Computation in Physical Systems
  3. Physical Perspectives on Computer Science
  4. Computational Perspectives on Physical Theory

Inspired by the chapter in this volume by Dominic Horsman, Viv Kendon, and Susan Stepney, I developed my own version of their account of physical computation, which I intend to develop further.