# Research

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.

## Media

Interview at

*The Reasoner*, with Bill D'Alessandro (2021)100 Philosophers, 100 Artworks, Die Walküre, at Aesthetics for Birds (2021)

"What is it like to be a philosopher of Asian-American descent?",

*APA Newsletter on Asian and Asian American Philosophers and Philosophy*(2020)Interview at Think About Sport, with Ben Genta (2019)

(with 71 other authors) "Redefining Statistical Significance".

*Nature Human Behavior*, (2017). (journal)"Mutualistic Anteraction", at the Daily Ant blog, hosted by Benjamin Blanchard (October 16, 2017)

appearance on the "Rationally Speaking" podcast, with Julia Galef (August 9, 2015)

appearance on "Philosophy TV", with Jonathan Weisberg (July 16, 2011)

## Research articles

"A New Method of Value Aggregation".

*Proceedings of the Aristotelian Society*, (2021), 299-326. (journal)(with Matthew Sheldon and collaborators) "Markov chains for modeling complex luminescence, absorption, and scattering in nanophotonic systems".

*Optics Express*, (2021), 4249-4269. (journal)"A Classification of Newcomb Problems and Decision Theories".

*Synthese*, (2019). (journal)"The Concept of Rationality for a City".

*Topoi*, (2019). (journal)(with Reuben Stern) “The Many Ways to Achieve Diachronic Unity”. Chapter 11 of

*Self Control, Decision Theory, and Rationality*, ed. José Luis Bermúdez, Cambridge University Press. (2018), 240-263. (publisher)

"The Tripartite Role of Belief: Evidence, Truth, and Action".

*Res Philosophica*,**94**:2, (2017), 189-206. (journal)"Dr. Truthlove or: How I Learned to Stop Worrying and Love Bayesian Probabilities".

*Noûs,***50**:4, (2016), 816-853*.*(journal) (Selected for inclusion in*The Philosopher's Annual*as one of the ten best papers in philosophy in 2015 - note the difference from the eventual paper publication date)(with Luke Fenton-Glynn, Chris Hitchcock, and Joel Velasco) "Updating on the Credences of Others: Disagreement, Agreement, and Synergy".

*Philosophers' Imprint*,**16**:11, (2016), 1-39. (journal)"Rebutting and Undercutting in Mathematics".

*Philosophical Perspectives*,**29**:1, (2015), 146-162. (journal)(with Branden Fitelson) "Accuracy, Coherence, and Evidence".

*Oxford Studies in Epistemology*,**5**, (2015), 61-96. (publisher)(with Ray Briggs, Fabrizio Cariani, Branden Fitelson) "Individual Coherence and Group Coherence".

*Essays in Collective Epistemology*, ed. Jennifer Lackey. Oxford University Press, (2014), 215-239. (publisher)"Why Physics Uses Second Derivatives".

*British Journal for the Philosophy of Science*,**65**:4, (2014), 845-862*.*(journal)"Principal Values and Weak Expectations".

*Mind*,**123**:490, (2014), 517-531. (journal)"Decision Theory without Representation Theorems".

*Philosophers Imprint*,**14**:27, (2014), 1-30. (journal) (Selected for inclusion in*The Philosopher's Annual*as one of the ten best papers in philosophy in 2014)"Regularity and Hyperreal Credences".

*The Philosophical Review*,**123**:1, (2014), 1-41. (journal)"Why Countable Additivity?"

*Thought*,**1**:4, (2013), 53-61. (journal)"Expected Accuracy Supports Conditionalization - and Conglomerability and Reflection".

*Philosophy of Science*,**80**:1, (2013), 119-142. (journal)(with Branden Fitelson) "An 'Evidentialist' Worry About Joyce's Argument for Probabilism".

*Dialectica,***66**, (2012), 425-433. (journal)(with Bradley Monton) "Mixed Strategies, Uncountable Times, and Pascal's Wager".

*Analysis*,**72**:4, (2012), 681-685. (journal)"Varieties of Conditional Probability". Chapter IIB of

*Handbook for Philosophy of Statistics,*eds. Prasanta Bandyopadhyay and Malcolm Forster. Elsevier, (2011) 137-148. (publisher)“Probabilistic Proofs and Transferability”.

*Philosophia Mathematica*,**17**:3, (2009), 341-362. (journal)“Strong and Weak Expectations”.

*Mind*,**117**:467, (2008), 633-641. (journal)(with Mark Colyvan) “Mathematical and Physical Continuity”.

*The Australasian Journal of Logic*,**6**, (2008), 87-93. (journal)“The Role of Axioms in Mathematics”.

*Erkenntnis*,**68**:3, (2008), 381-391. (journal)

## Expository work

(with Alan Hájek, Paolo Mancosu, and Graham Oppy) "Infinity".

*Stanford Encyclopedia of Philosophy*. (2021)"Conditional Probabilities". Chapter 4 of

*Open Handbook of Formal Epistemology*, eds. Richard Pettigrew and Jonathan Weisberg, (2019), 131-198. (publisher)"Conditional Probability". Chapter 9 of

*Oxford Handbook of Probability and Philosophy*, eds. Chris Hitchcock and Alan Hájek, (2016), 167-182. (publisher)"Formal Epistemology".

*Journal of Philosophical Logic*,**44**:6, (2015), 651-662. (journal)"Probability and Logic".

*Philosophy Compass*,**9**:12, (2014), 876-883. (journal)"Bayesianism".

*Oxford Bibliographies*in "Philosophy"*,*ed. Duncan Pritchard (2013)."Dutch Book Arguments". In

*The Encyclopedia of the Mind*, eds. Hal Pashler*et al*. (2013), 264-266."Bayesianism II: Criticisms and Applications".

*Philosophy Compass*,**6**:5, (2011), 321-332. (journal)"Bayesianism I: Introduction and Arguments in Favor".

*Philosophy Compass*,**6**:5, (2011), 312-320. (journal)"Logic and Probability".

*Journal of the Indian Council for Philosophical Research*,**XXVII**:2, (2010), 229-253."A Cheerful Introduction to Forcing and the Continuum Hypothesis". Unpublished, on the arXiv. (2007)

## Book reviews

Review of

*Infinity, Causation, and Paradox*, by Alexander Pruss.*Mind*, (2019). (journal)Review of

*Probabilistic Knowledge*, by Sarah Moss.*Notre Dame Philosophical Reviews*, (2018), https://ndpr.nd.edu/news/probabilistic-knowledge/Review of

*Reasons without Persons*, by Brian Hedden.*The Journal of Philosophy***114**:2, (2017), 105-110. (journal)Review of

*Accuracy and the Laws of Credence*, by Richard Pettigrew.*Notre Dame Philosophical Reviews*, (2016), http://ndpr.nd.edu/news/70705-accuracy-and-the-laws-of-credence/Review of

*Quitting Certainties*, by Michael Titelbaum.*The Philosophical Review*,**125**:1, (2016), 143-148. (journal)Review of

*From Zeno to Arbitrage: Essays on Quantity, Coherence, and Induction*, by Brian Skyrms.*Notre Dame Philosophical Reviews*, (2013), http://ndpr.nd.edu/news/40323-from-zeno-to-arbitrage-essays-on-quantity-coherence-and-induction/Review of

*The Evolution of Logic*, by W.D. Hart.*The Bulletin of Symbolic Logic*,**17**:4, (2011), 533-535.Review of

*By Parallel Reasoning*, by Paul Bartha.*Notre Dame Philosophical Reviews*, (2011), http://ndpr.nd.edu/review.cfm?id=23890

Review of

*Representation, Evidence, and Justification: Themes from Suppes*, Michael Frauchiger and Wilhelm K. Essler, eds.*Notre Dame Philosophical Reviews*, (2009), http://ndpr.nd.edu/review.cfm?id=14965Review of

*Tracking Reason: Proof, Consequence, and Truth*, by Jody Azzouni.*The Philosophical Review*,**117**:2, (2008), 296-299. (journal)Review of

*Ambiguity and Logic*, by Frederic Schick.*Mind*,**116**(2007), 478-482. (journal)

## 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 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.