
548An 'evidentialist' worry about Joyce's argument for ProbabilismDialetica 66 (3): 425433. 2012.To the extent that we have reasons to avoid these “bad B properties”, these arguments provide reasons not to have an incoherent credence function b — and perhaps even reasons to have a coherent one. But, note that these two traditional arguments for probabilism involve what might be called “pragmatic” reasons (not) to be (in)coherent. In the case of the Dutch Book argument, the “bad” property is pragmatically bad (to the extent that one values money). But, it is not clear whether the DBA pinpoi…Read more

476Regularity and Hyperreal CredencesPhilosophical Review 123 (1): 141. 2014.Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperrea…Read more

449Bayesianism I: Introduction and Arguments in FavorPhilosophy Compass 6 (5): 312320. 2011.Bayesianism is a collection of positions in several related fields, centered on the interpretation of probability as something like degree of belief, as contrasted with relative frequency, or objective chance. However, Bayesianism is far from a unified movement. Bayesians are divided about the nature of the probability functions they discuss; about the normative force of this probability function for ordinary and scientific reasoning and decision making; and about what relation (if any) holds be…Read more

443Bayesianism II: Applications and CriticismsPhilosophy Compass 6 (5): 321332. 2011.In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemol ogy, and statistics, and criticisms of these applications.

420Why Countable Additivity?Thought: A Journal of Philosophy 2 (1): 5361. 2013.It is sometimes alleged that arguments that probability functions should be countably additive show too much, and that they motivate uncountable additivity as well. I show this is false by giving two naturally motivated arguments for countable additivity that do not motivate uncountable additivity

361The Role of Axioms in MathematicsErkenntnis 68 (3): 381391. 2008.To answer the question of whether mathematics needs new axioms, it seems necessary to say what role axioms actually play in mathematics. A first guess is that they are inherently obvious statements that are used to guarantee the truth of theorems proved from them. However, this may neither be possible nor necessary, and it doesn’t seem to fit the historical facts. Instead, I argue that the role of axioms is to systematize uncontroversial facts that mathematicians can accept from a wide variety o…Read more

351Probabilistic proofs and transferabilityPhilosophia Mathematica 17 (3): 341362. 2009.In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have…Read more

297Strong and weak expectationsMind 117 (467): 633641. 2008.Fine has shown that assigning any value to the Pasadena game is consistent with a certain standard set of axioms for decision theory. However, I suggest that it might be reasonable to believe that the value of an individual game is constrained by the longrun payout of repeated plays of the game. Although there is no value that repeated plays of the Pasadena game converges to in the standard strong sense, I show that there is a weaker sort of convergence it exhibits, and use this to define a not…Read more

232Logic and ProbabilityJournal of the Indian Council of Philosophical Research 27 (2): 229253. 2010.As is clear from the other articles in this volume, logic has applications in a broad range of areas of philosophy. If logic is taken to include the mathematical disciplines of set theory, model theory, proof theory, and recursion theory (as well as firstorder logic, secondorder logic, and modal logic), then the only other area of mathematics with such wideranging applications in philosophy is probability theory

214Mixed strategies, uncountable times, and Pascal's Wager: a reply to RobertsonAnalysis 72 (4): 681685. 2012.Pascal’s Wager holds that one has pragmatic reason to believe in God, since that course of action has infinite expected utility. The mixed strategy objection holds that one could just as well follow a course of action that has infinite expected utility but is unlikely to end with one believing in God. Monton (2011. Mixed strategies can’t evade Pascal’s Wager. Analysis 71: 642–45.) has argued that mixed strategies can’t evade Pascal’s Wager, while Robertson (2012. Some mixed strategies can evade …Read more

214Dr. Truthlove or: How I Learned to Stop Worrying and Love Bayesian ProbabilitiesNoûs 50 (4): 816853. 2016.Many philosophers have argued that "degree of belief" or "credence" is a more fundamental state grounding belief. Many other philosophers have been skeptical about the notion of "degree of belief", and take belief to be the only meaningful notion in the vicinity. This paper shows that one can take belief to be fundamental, and ground a notion of "degree of belief" in the patterns of belief, assuming that an agent has a collection of beliefs that isn't dominated by some other collection in terms …Read more

213Conditional ProbabilitiesIn Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology, Philpapers Foundation. pp. 131198. 2019.

187Accuracy, Coherence, and EvidenceOxford Studies in Epistemology 5 6196. 2015.Taking Joyce’s (1998; 2009) recent argument(s) for probabilism as our point of departure, we propose a new way of grounding formal, synchronic, epistemic coherence requirements for (opinionated) full belief. Our approach yields principled alternatives to deductive consistency, sheds new light on the preface and lottery paradoxes, and reveals novel conceptual connections between alethic and evidential epistemic norms

178Updating on the Credences of Others: Disagreement, Agreement, and SynergyPhilosophers’ Imprint 16 139. 2016.We introduce a family of rules for adjusting one's credences in response to learning the credences of others. These rules have a number of desirable features. 1. They yield the posterior credences that would result from updating by standard Bayesian conditionalization on one's peers' reported credences if one's likelihood function takes a particular simple form. 2. In the simplest form, they are symmetric among the agents in the group. 3. They map neatly onto the familiar Condorcet voting result…Read more

148Mathematical and Physical ContinuityAustralasian Journal of Logic 6 8793. 2008.There is general agreement in mathematics about what continuity is. In this paper we examine how well the mathematical definition lines up with common sense notions. We use a recent paper by Hud Hudson as a point of departure. Hudson argues that two objects moving continuously can coincide for all but the last moment of their histories and yet be separated in space at the end of this last moment. It turns out that Hudson’s construction does not deliver mathematically continuous motion, but the n…Read more

138Why Physics Uses Second DerivativesBritish Journal for the Philosophy of Science 65 (4): 845862. 2014.I defend a causal reductionist account of the nature of rates of change like velocity and acceleration. This account identifies velocity with the past derivative of position and acceleration with the future derivative of velocity. Unlike most reductionist accounts, it can preserve the role of velocity as a cause of future positions and acceleration as the effect of current forces. I show that this is possible only if all the fundamental laws are expressed by differential equations of the same or…Read more

129Expected Accuracy Supports Conditionalization—and Conglomerability and ReflectionPhilosophy of Science 80 (1): 119142. 2013.Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew, and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has …Read more

102Formal EpistemologyJournal of Philosophical Logic 44 (6): 651662. 2015.Doxastic TheoriesThe application of formal tools to questions related to epistemology is of course not at all new. However, there has been a surge of interest in the field now known as “formal epistemology” over the past decade, with two annual conference series and an annual summer school at Carnegie Mellon University, in addition to many oneoff events devoted to the field. A glance at the programs of these series illustrates the wideranging set of topics that have been grouped under this nam…Read more

72Decision Theory without Representation TheoremsPhilosophers' Imprint 14. 2014.Naive versions of decision theory take probabilities and utilities as primitive and use expected value to give norms on rational decision. However, standard decision theory takes rational preference as primitive and uses it to construct probability and utility. This paper shows how to justify a version of the naive theory, by taking dominance as the most basic normatively required preference relation, and then extending it by various conditions under which agents should be indifferent between ac…Read more

53Reasons without Persons: Rationality, Identity, and Time (review)Journal of Philosophy 114 (2): 105110. 2017.

52Tracking Reason: Proof, Consequence, and Truth (review)Philosophical Review 117 (2): 296299. 2008.

52Probability and LogicPhilosophy Compass 9 (12): 876883. 2014.Probability and logic are two branches of mathematics that have important philosophical applications. This article discusses several areas of intersection between them. Several involve the role for probability in giving semantics for logic or the role of logic in governing assignments of probability. Some involve probability over nonclassical logic or selfreferential sentences

46Infinity, Causation, and Paradox, by Alexander PrussMind. forthcoming._ Infinity, Causation, and Paradox _, by PrussAlexander. Oxford: Oxford University Press, 2018. Pp. xiii + 207.

42A classification of Newcomb problems and decision theoriesSynthese 120. forthcoming.Newcomblike problems are classified by the payoff table of their actstate pairs, and the causal structure that gives rise to the actstate correlation. Decision theories are classified by the one or more points of intervention whose causal role is taken to be relevant to rationality in various problems. Some decision theories suggest an inherent conflict between different notions of rationality that are all relevant. Some issues with causal modeling raise problems for decision theories in the …Read more

34Principal Values and Weak ExpectationsMind 123 (490): 517531. 2014.This paper evaluates a recent method proposed by Jeremy Gwiazda for calculating the value of gambles that fail to have expected values in the standard sense. I show that Gwiazda’s method fails to give answers for many gambles that do have standardly defined expected values. However, a slight modification of his method (based on the mathematical notion of the ‘Cauchy principal value’ of an integral), is in fact a proper extension of both his method and the method of ‘weak expectations’. I show th…Read more

31The Tripartite Role of Belief: Evidence, Truth, and ActionRes Philosophica 94 (2): 189206. 2017.Belief and credence are often characterized in three different ways—they ought to govern our actions, they ought to be governed by our evidence, and they ought to aim at the truth. If one of these roles is to be central, we need to explain why the others should be features of the same mental state rather than separate ones. If multiple roles are equally central, then this may cause problems for some traditional arguments about what belief and credence must be like. I read the history of formal a…Read more

30The Concept of Rationality for a CityTopoi 113. forthcoming.The central aim of this paper is to argue that there is a meaningful sense in which a concept of rationality can apply to a city. The idea will be that a city is rational to the extent that the collective practices of its people enable diverse inhabitants to simultaneously live the kinds of life they are each trying to live. This has significant implications for the varieties of social practices that constitute being more or less rational. Some of these implications may be welcome to a theorist …Read more

25Review of Michael frauchiger, Wilhelm K. Essler (eds.), Representation, Evidence, and Justification: Themes From Suppes (review)Notre Dame Philosophical Reviews 2009 (1). 2009.

22Rebutting and undercutting in mathematicsPhilosophical Perspectives 29 (1): 146162. 2015.In my () I argued that a central component of mathematical practice is that published proofs must be “transferable” — that is, they must be such that the author's reasons for believing the conclusion are shared directly with the reader, rather than requiring the reader to essentially rely on testimony. The goal of this paper is to explain this requirement of transferability in terms of a more general norm on defeat in mathematical reasoning that I will call “convertibility”. I begin by discussin…Read more
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