Kenny Easwaran

Publications

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, and in the role that the social practices of mathematics play in the development of mathematical knowledge — in particular, the constraints those practices 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.

Media and public writing

Book

Research articles

Expository and survey work

Book reviews

Work in progress

(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 (there is a fact of the matter about whether the entities exist, and they exist in whatever sense any mathematical entities do) and applicabilism (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, responding to existing arguments that they either have both or lack both.

(with Reuben Stern) “Two Dimensions of Collective Agency”. Argues that collective agency can occur either “horizontally” (multiple individuals share goals and coordinate their behavior to achieve them) or “vertically” (multiple agents have different goals, but each behaves in a way that gets the other to realize theirs), and 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 produces a Newcomb problem for manufacturers, who want regulators to predict them to behave socially while riders reap the benefits of anti-social behavior.

“Testimony and Autonomy in Mathematics”. Considers the knowledge of the mathematical community as an epistemic fact beyond the knowledge of individual mathematicians. Argues that the 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 — and that this explains community practices of rejecting certain types of argument that otherwise seem fit to give knowledge.

“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: 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 any particular set of axioms, and that rejecting it requires something like ultrafinitism.

Dissertation

“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, and Tom Griffiths (outside member, psychology).

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.