•  3344
    A Tale of Two Epistemologies?
    with Hanti Lin
    Res Philosophica 94 (2): 207-232. 2017.
    So-called “traditional epistemology” and “Bayesian epistemology” share a word, but it may often seem that the enterprises hardly share a subject matter. They differ in their central concepts. They differ in their main concerns. They differ in their main theoretical moves. And they often differ in their methodology. However, in the last decade or so, there have been a number of attempts to build bridges between the two epistemologies. Indeed, many would say that there is just one branch of philos…Read more
  •  874
    Uncertainty governs our lives. From the unknowns of living with the risks of terrorism to developing policies on genetically modified foods, or disaster planning for catastrophic climate change, how we conceptualize, evaluate and cope with uncertainty drives our actions and deployment of resources, decisions and priorities.
  •  658
    What are degrees of belief
    Studia Logica 86 (2): 185-215. 2007.
    Probabilism is committed to two theses: 1) Opinion comes in degrees—call them degrees of belief, or credences. 2) The degrees of belief of a rational agent obey the probability calculus. Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are, and then ii) to show that those things should be probabilities, on pain of irrationality. Most of the action in the literature concerns stage ii). Assuming that stage i) has been adequately discharged…Read more
  •  643
    Bayesian Epistemology
    In DancyJ (ed.), A Companion to Epistemology, Blackwell. 2010.
    Bayesianism is our leading theory of uncertainty. Epistemology is defined as the theory of knowledge. So “Bayesian Epistemology” may sound like an oxymoron. Bayesianism, after all, studies the properties and dynamics of degrees of belief, understood to be probabilities. Traditional epistemology, on the other hand, places the singularly non-probabilistic notion of knowledge at centre stage, and to the extent that it traffics in belief, that notion does not come in degrees. So how can there be a B…Read more
  •  561
    The reference class problem is your problem too
    Synthese 156 (3): 563--585. 2007.
    The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the r…Read more
  •  500
    What conditional probability could not be
    Synthese 137 (3): 273--323. 2003.
    Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.
  •  479
    David Hume, David Lewis, and decision theory
    with Alex Byrne
    Mind 106 (423): 411-728. 1997.
    David Lewis claims that a simple sort of anti-Humeanism-that the rational agent desires something to the extent he believes it to be good-can be given a decision-theoretic formulation, which Lewis calls 'Desire as Belief' (DAB). Given the (widely held) assumption that Jeffrey conditionalising is a rationally permissible way to change one's mind in the face of new evidence, Lewis proves that DAB leads to absurdity. Thus, according to Lewis, the simple form of anti-Humeanism stands refuted. In thi…Read more
  •  430
    Fifteen Arguments Against Hypothetical Frequentism
    Erkenntnis 70 (2): 211-235. 2009.
    This is the sequel to my “Fifteen Arguments Against Finite Frequentism” ( Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A ’s among the B ’s would be p if there were an infinite sequence of B ’s. I offer fifteen arguments against this analysis. I consider various frequentist responses, which…Read more
  •  377
    Desire Beyond Belief
    Australasian Journal of Philosophy 82 (1): 77-92. 2004.
    David Lewis [1988; 1996] canvases an anti-Humean thesis about mental states: that the rational agent desires something to the extent that he or she believes it to be good. Lewis offers and refutes a decision-theoretic formulation of it, the 'Desire-as-Belief Thesis'. Other authors have since added further negative results in the spirit of Lewis's. We explore ways of being anti-Humean that evade all these negative results. We begin by providing background on evidential decision theory and on Lewi…Read more
  •  340
    The Cable Guy paradox
    Analysis 65 (2): 112-119. 2005.
    The Cable Guy is coming. You have to be home in order for him to install your new cable service, but to your chagrin he cannot tell you exactly when he will come. He will definitely come between 8.a.m. and 4 p.m. tomorrow, but you have no more information than that. I offer to keep you company while you wait. To make things more interesting, we decide now to bet on the Cable Guy’s arrival time. We subdivide the relevant part of the day into two 4-hour long intervals, ‘morning’: (8, 12], and ‘aft…Read more
  •  319
    Rationality and indeterminate probabilities
    Synthese 187 (1): 33-48. 2012.
    We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our…Read more
  •  313
    Ramsey + Moore = God
    Analysis 67 (2): 170-172. 2007.
    Frank Ramsey (1931) wrote: If two people are arguing 'if p will q?' and both are in doubt as to p, they are adding p hypothetically to their stock of knowledge and arguing on that basis about q. We can say that they are fixing their degrees of belief in q given p. Let us take the first sentence the way it is often taken, as proposing the following test for the acceptability of an indicative conditional: ‘If p then q’ is acceptable to a subject S iff, were S to accept p and consider q, S would ac…Read more
  •  284
    Declarations of independence
    Synthese 194 (10): 3979-3995. 2017.
    According to orthodox (Kolmogorovian) probability theory, conditional probabilities are by definition certain ratios of unconditional probabilities. As a result, orthodox conditional probabilities are undefined whenever their antecedents have zero unconditional probability. This has important ramifications for the notion of probabilistic independence. Traditionally, independence is defined in terms of unconditional probabilities (the factorization of the relevant joint unconditional probabilitie…Read more
  •  277
    Probability
    In Jessica Pfeifer & Sahotra Sarkar (eds.), The Philosophy of Science: An Encyclopedia, Routledge. 2006.
    There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewh…Read more
  •  267
    – We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot re…Read more
  •  262
    Vexing expectations
    with Harris Nover
    Mind 113 (450): 237-249. 2004.
    We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we want, s…Read more
  •  260
    Pascal's Wager
    Stanford Encyclopedia of Philosophy. 2008.
    “Pascal's Wager” is the name given to an argument due to Blaise Pascal for believing, or for at least taking steps to believe, in God. The name is somewhat misleading, for in a single paragraph of his Pensées, Pascal apparently presents at least three such arguments, each of which might be called a ‘wager’ — it is only the final of these that is traditionally referred to as “Pascal's Wager”. We find in it the extraordinary confluence of several important strands of thought: the justification of …Read more
  •  250
    Crimmins, Gonzales and Moore
    with Daniel Stoljar
    Analysis 61 (3): 208-213. 2001.
    Gonzales tells Mark Crimmins (1992) that Crimmins knows him under two guises, and that under his other guise Crimmins thinks him an idiot. Knowing his cleverness, but not knowing which guise he has in mind, Crimmins trusts Gonzales but does not know which of his beliefs to revise. He therefore asserts to Gonzales. (FBI) I falsely believe that you are an idiot.
  •  248
    Arguments for–or against–Probabilism?
    British Journal for the Philosophy of Science 59 (4): 793-819. 2008.
    Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned.Each argument concludes that rationality requires your credences to be probabilities.I contend that each argument …Read more
  •  215
    Chance
    In Donald Borchert (ed.), Macmillan's Encyclopedia of Philosophy, Macmillan. 2006.
    Much is asked of the concept of chance. It has been thought to play various roles, some in tension with or even incompatible with others. Chance has been characterized negatively, as the absence of causation; yet also positively—the ancient Greek τυχη´ reifies it—as a cause of events that are not governed by laws of nature, or as a feature of the laws themselves. Chance events have been understood epistemically as those whose causes are unknown; yet also objectively as a distinct ontological kin…Read more
  •  213
    Are Miracles Chimerical?
    Oxford Studies in Philosophy of Religion 1 82-104. 2008.
    I analyze David Hume’s "Of Miracles". I vindicate Hume’s argument against two charges: that it (1) defines miracles out of existence; (2) appeals to a suspect principle of balancing probabilities. He argues that miracles are, in a certain sense, maximally improbable. To understand this sense, we must turn to his notion of probability as ’strength of analogy’: miracles are incredible, according to him, because they bear no analogy to anything in our past experience. This reveals as anachronistic …Read more
  •  212
    Scotching Dutch Books?
    Philosophical Perspectives 19 (1): 139-151. 2005.
    The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consist…Read more
  •  210
    Induction and Probability
    with Ned Hall
    In Peter Machamer & Michael Silberstein (eds.), The Blackwell Guide to the Philosophy of Science, Blackwell. pp. 149-172. 2002.
    Arguably, Hume's greatest single contribution to contemporary philosophy of science has been the problem of induction (1739). Before attempting its statement, we need to spend a few words identifying the subject matter of this corner of epistemology. At a first pass, induction concerns ampliative inferences drawn on the basis of evidence (presumably, evidence acquired more or less directly from experience)—that is, inferences whose conclusions are not (validly) entailed by the premises. Philosop…Read more
  •  199
    Subjective Probability and its Dynamics
    In Markus Knauff & Wolfgang Spohn (eds.), MIT Handbook of Rationality, Mit Press. forthcoming.
    This chapter is a philosophical survey of some leading approaches in formal epistemology in the so-called ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and c…Read more
  •  194
    According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.
  •  191
    Conditional Probability Is the Very Guide of Life
    In Kyburg Jr, E. Henry & Mariam Thalos (eds.), Probability is the Very Guide of Life: The Philosophical Uses of Chance, Open Court. pp. 183--203. 2003.
    in Probability is the Very Guide of Life: The Philosophical Uses of Chance, eds. Henry Kyburg, Jr. and Mariam Thalos, Open Court. Abridged version in Proceedings of the International Society for Bayesian Analysis 2002.
  •  182
    Complex Expectations
    with Harris Nover
    Mind 117 (467). 2008.
    In our 2004, we introduced two games in the spirit of the St Petersburg game, the Pasadena and Altadena games. As these latter games lack an expectation, we argued that they pose a paradox for decision theory. Terrence Fine has shown that any finite valuations for the Pasadena, Altadena, and St Petersburg games are consistent with the standard decision-theoretic axioms. In particular, one can value the Pasadena game above the other two, a result that conflicts with both our intuitions and domina…Read more