I work in the areas of epistemology, decision theory, and the philosophy of mathematics. I am currently thinking about analogies between individual and collective decision making, with lessons to be drawn in both directions. My work in epistemology focuses on the mathematical notions of probability theory, and how they can help clarify the pre-theoretic notions of belief, justification, knowledge, and the like. In particular, my research has focused on cases involving probability zero, and what they can show about the notions of conditional and unconditional probability in other cases. More recent work considers a notion of coherence for full beliefs that is derived from considerations of truth, and shows how this notion can clarify our understanding of degree of belief. In the philosophy of mathematics I am particularly interested in set theory and its foundations. In particular, I am interested in the role that the social practices of mathematics play in the development of mathematical knowledge, and the constraints they put on the notions of proof that are acceptable to mathematicians. My work in decision theory primarily deals with alternatives to expected utility that agree with it in finite cases, but allow for more subtle distinctions among infinitary decision problems.


Research articles

Expository work

Book reviews


"The Foundations of Conditional Probability", UC Berkeley, Group in Logic and the Methodology of Science, 2008.

Committee: Branden Fitelson (chair), John MacFarlane, Paolo Mancosu, Sherrilyn Roush, Tom Griffiths (outside member, psychology)

Abstract: I investigate the Bayesian notion of probability as a measure of degree of belief, and argue that the correct mathematical formalism for conditional probability in this setting is neither P(A&B)/P(B), as traditionally assumed, nor a Popperian account that takes conditional probability as more basic than unconditional probability, but rather an account that is more standard in the mathematics of measure theory. On this account the conditional probability for an agent of an event A given an event B depends additionally on what set of alternatives to B is relevant.

Work in progress

An Opinionated Introduction to the Philosophical Foundations of Bayesianism - a book in eight chapters that is intended for use either by graduate students who are interested in getting into philosophical questions about the foundations of Bayesianism, or active professionals who are looking for an opinionated picture of how they fit together, or people from other fields that would like to see a philosophical perspective on these questions.

"Bullshit Activities" - extends Harry Frankfurt's concept of "bullshit" to speech acts other than statements, and acts other than speech acts, and suggests that this is the same concept of "bullshit" as in David Graeber's Bullshit Jobs.

"Generalizations of Risk-Weighted Expected Utility" - shows some formal properties of generalizations of Lara Buchak's "Risk-Weighted Expected Utility". While her R function maps the [0,1] interval to the [0,1] interval, I show that it can formally be any continuous, monotonically increasing function. If the endpoints are infinite rather than finite, then it encodes a certain kind of "minimax" or "maximax" decision theory, but with additional refinement. Argues that the derivative of this function may be easier to work with than the function itself, and that this may shed some light on parallels between risk sensitivity in decision theory and inequality sensitivity in social choice.

(with Ben Levinstein and Ted Shear) "Causal One-Boxing" - describes a variety of specifications of the Newcomb problem in which causal decision theory recommends one-boxing. This has several implications: philosophers should be more careful in specifying their thought experiments; some one-boxing intuitions may not count against causal decision theory; and some conceptions of the role of decision theory might naturally lead to a theory other than evidential or causal decision theory.

(with Henry Towsner) "Realism in Mathematics: The Case of the Hyperreals" - distinguishes two types of realism one might have about the existence of a class of mathematical objects: factualism (the view that there is a fact of the matter about the existence of the entities, and that they exist in whatever sense any mathematical entities do) and applicabilism (the view that the entities can play a role in accurate description of the physical world). Argues that the hyperreals of non-standard analysis (and in general, any entity whose existence proof depends on the Axiom of Choice) have the former but not the latter. Responds to existing arguments that have claimed the hyperreals either have both or lack both.

(with Reuben Stern) "Diachronic and Interpersonal Coherence" - draws analogies between arguments for diachronic coherence of an individual agent and interpersonal coherence for members of a group. Argues for certain conditions under which these sorts of coherence are or are not required. Suggests that this analysis can provide an interesting account of phenomena like supposition.

(with Reuben Stern) "Two Dimensions of Collective Agency" - argues that collective agency can occur either "horizontally" (when multiple individuals share goals and coordinate their behavior to achieve those goals) or "vertically" (when multiple agents have different goals, but each behaves in a way that gets the other to realize their goal). Argues that most collective action involves aspects of both dimensions.

In hiatus

(with Ryan Muldoon) "The Newcomb Trolley Problem" - argues that a regulatory approach to the Trolley problem for self-driving cars will produce a Newcomb problem for manufacturers that want regulators to predict them to behave socially, while riders reap the benefits of them behaving anti-socially.

"Testimony and Autonomy in Mathematics" - considers the knowledge of the mathematical community as an additional epistemic fact beyond the knowledge of individual mathematicians. Argues that the mathematical community has the goal of achieving "autonomous" knowledge that doesn't depend on the testimony of individual mathematicians, even though individual mathematicians always depend on testimony. Argues that this explains community practices of rejecting certain types of argument that seem fit to give knowledge of mathematical results.

"The Tarski-Gödel thesis" - analyzes the arguments of Tarski and Gödel to show that they depend on a thesis akin to the Church-Turing thesis, namely that the mathematical analysis of the notion of a finite sequence is correct. Shows that, regardless of the ontology of mathematics, this thesis entails that the set of correct mathematical claims is not coextensive with the consequences of a particular set of axioms. Argues that rejection of this thesis requires something like "ultrafinitism" - a radical revision of the practice of applying number theory in understanding finite sets of objects.