•  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
  •  5
    On the Plurality of Lewis's Triviality Results
    In Barry Loewer & Jonathan Schaffer (eds.), A Companion to David Lewis, Wiley. 2015.
    David Lewis introduced a new kind of reductio ad absurdum style of argument: while the claims, suitably formalized, do not lead to outright contradiction, he showed they are tenable only in trivial ways. Lewis proved what are known as triviality results against the claims. The claims are "Probabilities of conditionals are conditional probabilities." "Desires are beliefs about what is good." The author argues that the tenuous connections between the claims go considerably further still: the claim…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
  •  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
  •  130
    We examine a distinctive kind of problem for decision theory, involving what we call discontinuity at infinity. Roughly, it arises when an infinite sequence of choices, each apparently sanctioned by plausible principles, converges to a ‘limit choice’ whose utility is much lower than the limit approached by the utilities of the choices in the sequence. We give examples of this phenomenon, focusing on Arntzenius et al.’s Satan’s apple, and give a general characterization of it. In these examples, …Read more
  •  50
    Two objects of valuation are said to be incommensurable if neither is better than the other, nor are they equally good. This negative, coarse-grained characterization fails to capture the nuanced structure of incommensurability. We argue that our evaluative resources are far richer than orthodoxy recognizes. We model value comparisons with the corresponding class of permissible preference orderings. Then, making use of our model, we introduce a potentially infinite set of degrees of approximatio…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
  •  106
    Risky business
    Philosophical Perspectives 35 (1): 189-205. 2021.
    Philosophical Perspectives, Volume 35, Issue 1, Page 189-205, December 2021.
  •  91
    As van Fraassen pointed out in his opening remarks, Henry Kyburg's lottery paradox has long been known to raise difficulties in attempts to represent full belief as a probability greater than or equal to p, where p is some number less than 1. Recently, Patrick Maher has pointed out that to identify full belief with probability equal to 1 presents similar difficulties. In his paper, van Fraassen investigates ways of representing full belief by personal probability which avoid the difficulties rai…Read more
  •  130
    The Oxford Handbook of Probability and Philosophy (edited book)
    Oxford University Press. 2016.
    Probability theory is a key tool of the physical, mathematical, and social sciences. It has also been playing an increasingly significant role in philosophy: in epistemology, philosophy of science, ethics, social philosophy, philosophy of religion, and elsewhere. This Handbook encapsulates and furthers the influence of philosophy on probability, and of probability on philosophy. Nearly forty articles summarise the state of play and present new insights in various areas of research at the interse…Read more
  •  44
    Orthodox Bayesianism tells a story about the epistemic trajectory of an ideally rational agent. The agent begins with a ‘prior’ probability function; thereafter, it conditionalizes on its evidence as it comes in. Consider, then, such an agent at the very beginning of its trajectory. It is ideally rational, but completely ignorant of which world is actual. Call this agent ‘Superbaby’.1 Superbaby personifies the Bayesian story. We argue that it must believe ‘Moorish’ propositions of the form.
  •  25
    Bayesianism tells a story about the epistemic trajectory of an ideally rational agent. The agent begins with a ‘prior’ probability function; thereafter, it conditionalizes on its evidence as it comes in. Consider, then, such an agent at the very beginning of its trajectory. It is ideally rational, but completely ignorant of which world is actual. Let us call this agent ‘superbaby’. We show that superbaby is committed to sincerely asserting propositions of the form [p and I am not justified in be…Read more
  •  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
  •  178
    Counterfactual scepticism and antecedent-contextualism
    Synthese 199 (1-2): 637-659. 2020.
    I have argued for a kind of ‘counterfactual scepticism’: most counterfactuals ever uttered or thought in human history are false. I briefly rehearse my main arguments. Yet common sense recoils. Ordinary speakers judge most counterfactuals that they utter and think to be true. A common defence of such judgments regards counterfactuals as context-dependent: the proposition expressed by a given counterfactual can vary according to the context in which it is uttered. In normal contexts, the counterf…Read more
  •  86
    Two Interpretations of Two Stoic Conditionals
    History of Philosophy & Logical Analysis 12 (1): 206-221. 2009.
    Controversy has surrounded the interpretation of the so-called 'Diodorean' and 'Chrysippean' conditionals of the Stoics. I critically evaluate and reject two interpretations of each of them: as expressing natural laws, and as strict conditionals. In doing so I engage with the work of authors such as Frede, Gould, Hurst, the Kneales, Mates, and Prior. I conclude by offering my own proposal for where these Stoic conditionals should be located on a 'ladder' of logical strength.
  •  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
  •  134
    Contra counterfactism
    Synthese 199 (1-2): 181-210. 2020.
    ‘If I were to toss a coin 1000 times, then it would land heads exactly n times’. Is there a specific value of n that renders this counterfactual true? According to an increasingly influential view, there is. A precursor of the view goes back to the Molinists; more recently it has been inspired by Stalnaker, and versions of it have been advocated by Hawthorne, Bradley, Moss, Schulz, and Stefánsson. More generally, I attribute to these authors what I call Counterfactual Plenitude:For any anteceden…Read more
  •  27
    Bayes or Bust?: A Critical Examination of Bayesian Confirmation Theory (review)
    Philosophical and Phenomenological Research 60 (3): 707-711. 2000.
  •  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
  •  22
    Zakład Pascala
    Roczniki Filozoficzne 67 (1): 199-229. 2019.
    Autor analizuje klasyczne rozumowanie, zwane „zakładem Pascala”, w kontekście teorii decyzji, wyróżniając w nim trzy argumenty: argument z silnej dominacji, argument z wartości oczekiwanej oraz argument z uogólnionej wartości oczekiwanej; dyskutuje zarzuty względem poprawności materialnej i formalnej rozumowania Pascala w jego trzeciej wersji, rozważa kontrowersje natury moralnej względem argumentu, a także docieka znaczenia jego konkluzji.
  •  11
    Probability and Statistics: 5 Questions (edited book)
    Automatic Press. 2009.
    Probability and Statistics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in probability and statistics. We hear their views on the fields, aims, scopes, the future direction of research and how their work fits in these respects. Interviews with Nick Bingham, Luc Bovens, Terrence L. Fine, Haim Gaifman, Donald Gillies, James Hawthorne, Carl Hoefer, James M. Joyce, Joseph B. Kadane Isaac Levi, D.H. Mellor, Patr…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
  •  10
    Saturday Round Table Panel
    with Allan Gibbard, Jim Joyce, and Brian Skyrms
  •  92
    Deliberation welcomes prediction
    Episteme 13 (4): 507-528. 2016.
    According to the so-called ‘deliberation crowds out prediction’ thesis, while deliberating about what you’ll do, you cannot rationally have credences for what you’ll do – you cannot rationally have option-credences. Versions of the thesis have been defended by authors such as Spohn, Levi, Gilboa, Price, Louise, and others. After registering a number of concerns about the thesis, I rehearse and rebut many of the main arguments for it, grouped according to their main themes: agency, vacuity, betti…Read more
  •  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
  •  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.
  •  1
    The Conditional Construal of Conditional Probability
    Dissertation, Princeton University. 1993.
    Very roughly, the conditional construal of conditional probability is the hypothesis that the conditional probability P equals the probability of the conditional 'if A, then B'. My main purposes are to hone this rough statement down to various precise versions of the Hypothesis, as I call it, and to argue that virtually none of them is tenable. ;In S 1, I distinguish four versions of the Hypothesis. The subsequent four sections are largely an opinionated historical survey, tracing the motivation…Read more
  •  148
    This paper is partly a tribute to Richard Jeffrey, partly a reflection on some of his writings, The Logic of Decision in particular. I begin with a brief biography and some fond reminiscences of Dick. I turn to some of the key tenets of his version of Bayesianism. All of these tenets are deployed in my discussion of his response to the St. Petersburg paradox, a notorious problem for decision theory that involves a game of infinite expectation. Prompted by that paradox, I conclude with some sugge…Read more