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191Conditional Probability Is the Very Guide of LifeIn 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.
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190Counterfactual scepticism and antecedent-contextualismSynthese 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
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188Complex ExpectationsMind 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
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173Dutch Book ArgumentsIn Paul Anand, Prasanta Pattanaik & Clemens Puppe (eds.), The Oxford Handbook of Rational and Social Choice, Oxford University Press. 2008.in The Oxford Handbook of Corporate Social Responsibility, ed. Paul Anand, Prasanta Pattanaik, and Clemens Puppe, forthcoming 2007.
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159In Memory of Richard Jeffrey: Some Reminiscences and Some Reflections on The Logic of DecisionPhilosophy of Science 73 (5): 947-958. 2006.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
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157Triviality PursuitTopoi 30 (1): 3-15. 2011.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…Read more
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155The 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
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154Perplexing expectationsMind 115 (459). 2006.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 r…Read more
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153Minkish dispositionsSynthese 197 (11): 4795-4811. 2020.Start with an ordinary disposition ascription, like ‘the wire is live’ or ‘the glass is fragile’. Lewis gives a canonical template for what he regards as the analysandum of such an ascription:“Something x is disposed at time t to give response r to stimulus s”.For example, the wire is disposed at noon to conduct electrical current when touched by a conductor.What Lewis calls “the simple conditional analysis” gives putatively necessary and sufficient conditions for the analysandum in terms of a c…Read more
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149Contra counterfactismSynthese 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
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144Satan, Saint Peter and Saint Petersburg: Decision theory and discontinuity at infinitySynthese 191 (4): 629-660. 2014.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
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141Arguments For—Or Against—Probabilism?In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief, Springer. pp. 229--251. 2009.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 argumen…Read more
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141Unexpected ExpectationsMind 123 (490): 533-567. 2014.A decade ago, Harris Nover and I introduced the Pasadena game, which we argued gives rise to a new paradox in decision theory even more troubling than the St Petersburg paradox. Gwiazda's and Smith's articles in this volume both offer revisionist solutions. I critically engage with both articles. They invite reflections on a number of deep issues in the foundations of decision theory, which I hope to bring out. These issues include: some ways in which orthodox decision theory might be supplement…Read more
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137The hypothesis of the conditional construal of conditional probabilityIn Ellery Eells, Brian Skyrms & Ernest W. Adams (eds.), Probability and Conditionals: Belief Revision and Rational Decision, Cambridge University Press. pp. 75. 1994.
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128Counterfactual reasoning (philosophical aspects)—quantitativeIn N. J. Smelser & P. B. Baltes (eds.), International Encyclopedia of the Social and Behavioral Sciences, Elsevier. pp. 2872-2874. 2002.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 be false, or contrar…Read more
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121Risky businessPhilosophical Perspectives 35 (1): 189-205. 2021.Philosophical Perspectives, Volume 35, Issue 1, Page 189-205, December 2021.
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116Deliberation welcomes predictionEpisteme 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
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110EprFoundations of Physics 22 (3): 313-332. 1992.We present an exegesis of the Einstein-Podolsky-Rosen argument for the incompleteness of quantum mechanics, and defend it against the critique in Fine. (1) We contend,contra Fine, that it compares favorably with an argument reconstructed by him from a letter by Einstein to Schrödinger; and also with one given by Einstein in a letter to Popper. All three arguments turn on a dubious assumption of “separability,” which accords separate elements of reality to space-like separated systems. We discuss…Read more
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109ConfirmationIn S. Psillos & M. Curd (eds.), The Routledge Companion to the Philosophy of Science, Routledge. 2008.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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98In Defense of Hume’s Balancing of Probabilities in the Miracles ArgumentSouthwest Philosophy Review 11 (1): 111-118. 1995.I vindicate Hume’s argument against belief in miracle reports against a prevalent objection. Hume has us balance the probability of a miracle’s occurrence against the probability of its being falsely attested to, and argues that the latter must inevitably be the greater; thus, reason requires us to reject any miracle report. The "flaw" in this reasoning, according to Butler and many others, is that it proves too much--it counsels us to never believe historians, newspaper reports of lottery resul…Read more
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96Two Interpretations of Two Stoic ConditionalsHistory 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.
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94Full Belief and Probability: Comments on Van FraassenDialogue 36 (1). 1997.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
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88Probabilities of counterfactuals and counterfactual probabilitiesJournal of Applied Logic 12 (3): 235-251. 2014.Probabilities figure centrally in much of the literature on the semantics of conditionals. I find this surprising: it accords a special status to conditionals that other parts of language apparently do not share. I critically discuss two notable ‘probabilities first’ accounts of counterfactuals, due to Edgington and Leitgeb. According to Edgington, counterfactuals lack truth values but have probabilities. I argue that this combination gives rise to a number of problems. According to Leitgeb, cou…Read more
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88Interview: “Masses of formal philosophy”In Vincent F. Hendricks & John Symons (eds.), Masses of Formal Philosophy, Automatic Press/vip. 2006.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. Th…Read more
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75Making Ado Without ExpectationsMind 125 (499): 829-857. 2016.This paper is a response to Paul Bartha’s ‘Making Do Without Expectations’. We provide an assessment of the strengths and limitations of two notable extensions of standard decision theory: relative expectation theory and Paul Bartha’s relative utility theory. These extensions are designed to provide intuitive answers to some well-known problems in decision theory involving gaps in expectations. We argue that both RET and RUT go some way towards providing solutions to the problems in question but…Read more
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73My philosophical position says p and I don't believe pIn Mitchell S. Green & John N. Williams (eds.), Moore's Paradox: New Essays on Belief, Rationality, and the First Person, Oxford University Press. 2007.
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68Is Strict Coherence Coherent?Dialectica 66 (3): 411-424. 2012.Bayesians have a seemingly attractive account of rational credal states in terms of coherence. An agent's set of credences are synchronically coherent just in case they conform to the probability calculus. Some Bayesians impose a further putative coherence constraint called regularity: roughly, if X is possible, then it is assigned positive probability. I look at two versions of regularity – logical and metaphysical – and I canvass various defences of it as a rationality norm. Combining regulari…Read more
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62Degrees of commensurability and the repugnant conclusionNoûs 56 (4): 897-919. 2021.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
Acton, Australian Capital Territory, Australia
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Probability |