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Profile: Alan Hajek (Australian National University)
  1. Alan Hájek, Arguments for - or Against? - Probabilism – or Non-Probabilism?
    forthcoming in Degrees of Belief, eds. Franz Huber and Christoph Schmidt-Petri, Oxford University Press, 2006.
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  2. Alan Hájek, A Philosopher’s Guide to Probability.
    in Uncertainty: Multi-disciplinary Perspectives on Risk, Earthscan (the Goolabri symposium organized by Gabriele Bammer and Michael Smithson), 2007.
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  3. Alan Hájek, Interview: “Masses of Formal Philosophy”.
    I came to philosophy as a refugee from mathematics and statistics. I was impressed by their power at codifying and precisifying antecedently understood but rather nebulous concepts, and at clarifying and exploring their interrelations. I enjoyed learning many of the great theorems of probability theory—equations rich in ‘P’s of this and of that. But I wondered what is this ‘P’? What do statements of probability mean? When I asked one of my professors, he looked at me like I needed medication. (...)
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  4. Alan Hájek, Counterfactual Reasoning (Philosophical Aspects)—Quantitative.
    Counterfactuals are a species of conditionals. They are propositions or sentences, expressed by or equivalent to subjunctive conditionals of the form 'if it were the case that A, then it would be the case that B', or 'if it had been the case that A, then it would have been the case that B'; A is called the antecedent, and B the consequent. Counterfactual reasoning typically involves the entertaining of hypothetical states of affairs: the antecedent is believed or presumed to (...)
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  5. Ned Hall & Alan Hájek, Induction and Probability.
    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. Philosophers have historically drawn further distinctions, often appropriating the term (...)
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  6. Branden Fitelson & Alan Hájek, Declarations of Independence.
    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 probabilities). Various “equivalent” formulations of independence can be given using conditional probabilities. But these “equivalences” break down if conditional probabilities are permitted to have (...)
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  7. Alan Hajek, Chance.
    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 (...)
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  8. Alan Hajek, Induction and Probability.
    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. Philosophers have historically drawn further distinctions, often appropriating the term (...)
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  9. Alan Hájek, Australasian Philosophy of Probability, and Probability in Australasian Philosophy.
    The philosophy of probability has been alive and well for several decades in Australia and New Zealand. Some distinctive lines of thought have emerged, resonating with broader themes that have come to be associated with Australasian philosophers: realist/objectivist accounts of various theoretical entities; an ongoing concern with logic, including the development of non­classical logics; and enthusiasm for conceptual analysis, rooted in commonsense but informed by science. In this article I concentrate on work by philosophers on the interpretation of probability, its (...)
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  10. Alan Hájek, Two Interpretations of Two Stoic Conditionals.
    Four different conditionals were known to the Stoics. The so-called ‘first’ (Philonian) conditional has been interpreted fairly uncontroversially as an ancient counterpart to the material conditional of modern logic; the ‘fourth’ conditional is obscure, and seemingly of little historical interest, as it was probably not held widely by any group in antiquity. The ‘second’ (Diodorean) and ‘third’ (Chrysippean) conditionals, on the other hand, pose challenging interpretive questions, raising in the process issues in philosophical logic that are as relevant today as (...)
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  11. Alan Hájek & James M. Joyce, Confirmation.
    I.1. Introduction Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “counter­support” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H.
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  12. Christopher Hitchcock & Alan Hajek (eds.) (forthcoming). Oxford Handbook of Probability and Philosophy. Oxford University Press.
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  13. Paul Bartha, John Barker & Alan Hájek (2014). Satan, Saint Peter and Saint Petersburg. Synthese 191 (4):629-660.
    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, repeated dominance reasoning (...)
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  14. Alan Hájek (2012). Is Strict Coherence Coherent? Dialectica 66 (3):411-424.
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  15. Alan Hájek (2012). The Fall of “Adams' Thesis”? Journal of Logic, Language and Information 21 (2):145-161.
    The so-called ‘Adams’ Thesis’ is often understood as the claim that the assertibility of an indicative conditional equals the corresponding conditional probability—schematically: $${({\rm AT})}\qquad\qquad\quad As(A\rightarrow B)=P({B|A}),{\rm provided}\quad P(A)\neq 0.$$ The Thesis is taken by many to be a touchstone of any theorizing about indicative conditionals. Yet it is unclear exactly what the Thesis is . I suggest some precise statements of it. I then rebut a number of arguments that have been given in its favor. Finally, I offer a new (...)
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  16. Alan Hájek & Michael Smithson (2012). Rationality and Indeterminate Probabilities. Synthese 187 (1):33-48.
    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 second argument begins with our (...)
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  17. Alan Hájek (2011). Triviality Pursuit. Topoi 30 (1):3-15.
    The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I will (...)
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  18. Alan Hájek (2010). David Lewis. In The New Dictionary of Scientific Biography. Scribners.
    David Lewis was one of the most important philosophers of the 20th century working in the Anglo-American analytic tradition. His corpus is extraordinary for its breadth of subject matter and for its systematicity. For both these reasons, it is difficult to do justice to his work in a short space—there are rich interconnections among his myriad writings, and numerous possible entry points. This article approaches Lewis and his work in three passes: first, a biographical tracing of his intellectual influences; second, (...)
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  19. Alan Hájek (2010). The New Dictionary of Scientific Biography. Scribners.
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  20. Alan Hájek & Stephan Hartmann (2010). Bayesian Epistemology. In J. Dancy et al (ed.), A Companion to Epistemology. Blackwell.
    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 Bayesian epistemology?
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  21. Alan Hájek (2009). Arguments For—Or Against—Probabilism?. In. In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer. 229--251.
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  22. Alan Hájek (2009). Fifteen Arguments Against Hypothetical Frequentism. Erkenntnis 70 (2):211 - 235.
    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 (...)
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  23. Alan Hájek (2008). Arguments for–or Against–Probabilism? British Journal for the Philosophy of Science 59 (4):793 - 819.
    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 is invalid as formulated. In each case there is a mirror-image theorem and (...)
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  24. Alan Hajek (2008). Dutch Book Arguments. In Paul Anand, Prasanta Pattanaik & Clemens Puppe (eds.), The Oxford Handbook of Rational and Social Choice. Oxford University Press.
    in The Oxford Handbook of Corporate Social Responsibility, ed. Paul Anand, Prasanta Pattanaik, and Clemens Puppe, forthcoming 2007.
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  25. Alan Hajek (2008). Probability—A Phifosophical Overview. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. 323.
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  26. Alan Hájek (2008). Are Miracles Chimerical? In , Oxford Studies in Philosophy of Religion, Volume 1. Oxford Univ Pr. 82-104.
    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 various recent Bayesian (...)
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  27. Alan Hájek, Interpretations of Probability. Stanford Encyclopedia of Philosophy.
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  28. Alan Hájek (ed.) (2008). Oxford Studies in Philosophy of Religion, Volume 1. Oxford Univ Pr.
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  29. Alan Hájek, Pascal's Wager. Stanford Encyclopedia of Philosophy.
    “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 (...)
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  30. Alan Hájek & Harris Nover (2008). Complex Expectations. Mind 117 (467):643 - 664.
    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 (...)
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  31. Harris Nover & Alan Hájek (2008). Complex Expectations. Mind 117 (467):643 - 664.
    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 (...)
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  32. David J. Chalmers & Alan Hájek (2007). Ramsey + Moore = God. Analysis 67 (294):170–172.
    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’ (...)
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  33. Lina Eriksson & Alan Hájek (2007). What Are Degrees of Belief? Studia Logica 86 (2):185-215.
    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 (...)
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  34. Alan Hájek (2007). Most Counterfactuals Are False. Unpublished Article.
  35. Alan Hájek (2007). My Philosophical Position Says

    and I Don't Believe

    . In Mitchell S. Green & John N. Williams (eds.), Moore's Paradox: New Essays on Belief, Rationality, and the First Person. Oxford University Press.

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  36. Alan Hájek (2007). The Reference Class Problem is Your Problem Too. Synthese 156 (3):563--585.
    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 reference (...)
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  37. Branden Fitelson, Alan Hajek & Ned Hall (2006). Probability. In Jessica Pfeifer & Sahotra Sarkar (eds.), The Philosophy of Science: An Encyclopedia. Routledge.
    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 elsewhere. To see why, observe (...)
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  38. Alan Hájek (2006). Some Reminiscences on Richard Jeffrey, and Some Reflections on The Logic of Decision. In Borchert (ed.), Philosophy of Science. Macmillan. 73--947.
     
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  39. Alan Hájek & Harris Nover (2006). Perplexing Expectations. Mind 115 (459):703 - 720.
    This paper revisits the Pasadena game (Nover and Háyek 2004), a St Petersburg-like game whose expectation is undefined. We discuss serveral respects in which the Pasadena game is even more troublesome for decision theory than the St Petersburg game. Colyvan (2006) argues that the decision problem of whether or not to play the Pasadena game is ‘ill-posed’. He goes on to advocate a ‘pluralism’ regarding decision rules, which embraces dominance reasoning as well as maximizing expected utility. We rebut Colyvan’s argument, (...)
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  40. John Williams & Alan Hajek, 'P, and I Have Absolutely No Justification for Believing That P': The Necessary Falsehood of Orthodox Bayesianism.
    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.
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  41. Alan Hajek (2005). Scotching Dutch Books? Philosophical Perspectives 19 (1):139-151.
  42. Alan Hajek (2005). The Cable Guy Paradox. Analysis 65 (286):112-119.
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  43. Alan Hájek (2005). Scotching Dutch Books? Philosophical Perspectives 19 (1):139–151.
    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 consistency of credences amounts to. The Dutch Book (...)
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  44. Alan Hájek (2005). The Cable Guy Paradox. Analysis 65 (286):112–119.
    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 (...)
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  45. John Williams & Alan Hajek, 'P, And I Have Absolutely No Justification for Believing That P': The Incoherence of Bayesianism.
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  46. Alan Hajek (2004). Vexing Expectations. Mind 113 (450):237 - 249.
    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 (...)
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  47. Frank Jackson, Graham Priest, Alan Hájek & Philip Pettit (2004). Desire Beyond Belief. Australasian Journal of Philosophy 82 (1):77 – 92.
    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 Lewis's negative results. We (...)
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  48. Harris Nover & Alan Hájek (2004). Vexing Expectations. Mind 113 (450):237-249.
    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, simply by reordering (...)
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  49. Alan Hájek (2003). 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. 183--203.
    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.
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  50. Alan Hájek (2003). What Conditional Probability Could Not Be. Synthese 137 (3):273--323.
    Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.
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