Research

Kenny Easwaran works in the areas of epistemology, decision theory, and the philosophy of mathematics. His 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, his 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 he is particularly interested in set theory and its foundations. In particular, he is 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. His 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.

Published Work

Research Articles
Expository Pieces
Book Reviews
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, 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 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.

(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) "The Many Ways to Achieve Diachronic Unity" - argues that Bratman-style binding intentions aren't needed for an agent to maintain diachronic unity. Considers three types of formal models of an agent as a sequence of time slices, each with their own utility function, and shows conditions under which they will act as though they were unified. Shows that lesser degrees of unity under each of these types can add up to full behavioral unity.

(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.

"Towards a Classification of Newcomb-Style Problems" - classifies Newcomb-style problems in two respects - the payoff table, and the nature of the correlation between act and state. Using causal graphs (following Pearl, or Spirtes, Glymour and Scheines) we find a variety of different causal decision theories that respond differently to these problems based on whether the correlation occurs at the level of character, decision, intention, or action.

"Uncertainty and Aggregating Utility for Infinitely Many Agents" - uses an analogy between acts that certainly affect multiple agents and acts that have multiple uncertain outcomes to bring uncertainty and aggregation together. Applies techniques from "Decision Theory without Representation Theorems" to aggregation problems involving infinitely many agents, to solve some fundamental problems for utilitarianism raised by Bostrom and Arntzenius.

"Primitive Conditional Probabilities" - considers the nature of conditional probability on several interpretations, philosophical arguments for the idea that conditional probability is prior to unconditional probability, and mathematical arguments for the same claim. Gives in-depth introductions to the formal mathematical theories of Kolmogorov, Popper, Rényi, and Dubins/de Finetti and evaluates the prospects for use of each in philosophical contexts.

In hiatus

"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.