•  7
    The evolution of logic
    Bulletin of Symbolic Logic 17 (4): 533-535. 2011.
  •  46
    _ Infinity, Causation, and Paradox _, by PrussAlexander. Oxford: Oxford University Press, 2018. Pp. xiii + 207.
  •  213
    Conditional Probabilities
    In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology, Philpapers Foundation. pp. 131-198. 2019.
  •  42
    Newcomb-like problems are classified by the payoff table of their act-state pairs, and the causal structure that gives rise to the act-state 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
  •  30
    The Concept of Rationality for a City
    Topoi 1-13. 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
  •  148
    Mathematical and Physical Continuity
    with Mark Colyvan
    Australasian Journal of Logic 6 87-93. 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
  •  548
    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
  •  214
    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
  •  187
    Accuracy, Coherence, and Evidence
    Oxford Studies in Epistemology 5 61-96. 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
  •  178
    Updating on the Credences of Others: Disagreement, Agreement, and Synergy
    with Luke Fenton-Glynn, Christopher Hitchcock, and Joel D. Velasco
    Philosophers’ Imprint 16 1--39. 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
  •  53
    Reasons without Persons: Rationality, Identity, and Time (review)
    Journal of Philosophy 114 (2): 105-110. 2017.
  •  31
    The Tripartite Role of Belief: Evidence, Truth, and Action
    Res Philosophica 94 (2): 189-206. 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
  •  129
    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
  •  361
    The Role of Axioms in Mathematics
    Erkenntnis 68 (3): 381-391. 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
  •  351
    Probabilistic proofs and transferability
    Philosophia Mathematica 17 (3): 341-362. 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
  •  449
    Bayesianism I: Introduction and Arguments in Favor
    Philosophy Compass 6 (5): 312-320. 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
  •  22
    Rebutting and undercutting in mathematics
    Philosophical Perspectives 29 (1): 146-162. 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
  •  102
    Formal Epistemology
    Journal of Philosophical Logic 44 (6): 651-662. 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 one-off events devoted to the field. A glance at the programs of these series illustrates the wide-ranging set of topics that have been grouped under this nam…Read more
  •  297
    Strong and weak expectations
    Mind 117 (467): 633-641. 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 long-run 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
  •  420
    Why Countable Additivity?
    Thought: A Journal of Philosophy 2 (1): 53-61. 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
  •  34
    Principal Values and Weak Expectations
    Mind 123 (490): 517-531. 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
  •  214
    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
  •  1
    REVIEWS-WD Hart, The evolution of logic (review)
    Bulletin of Symbolic Logic 17 (4): 533. 2011.
  •  232
    Logic and Probability
    Journal of the Indian Council of Philosophical Research 27 (2): 229-253. 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 first-order logic, second-order logic, and modal logic), then the only other area of mathematics with such wide-ranging applications in philosophy is probability theory
  •  3
    Varieties of Conditional Probability
    In Prasanta Bandyopadhyay & Malcolm Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics, North Holland. 2011.
    I consider the notions of logical probability, degree of belief, and objective chance, and argue that a different formalism for conditional probability is appropriate for each.
  •  138
    Why Physics Uses Second Derivatives
    British Journal for the Philosophy of Science 65 (4): 845-862. 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
  •  15
    Review: Ambiguity and Logic (review)
    Mind 116 (462): 478-482. 2007.