¹ Lewis, David, ‘Humean Supervenience Debugged’, Mind, NS, 103 (1994)Google Scholar, Symposium: Chance and Credence, 475 and 483. The various interpretations, as we will see, tone down Lewis's exuberance and then frame the PP in their own terms.

² Four decades ago Kyburg, Henry, in his seminal Logical Foundations of Statistical Inference (Dordrecht: Holland, D. Reidel Publishing Company, 1974)Google Scholar stressed that ‘probability can be attributed only to kinds of events or sets and not (usefully) to individual events or to members of the sets that belong to S ... We cannot talk about the probability that John Smith, a 40-year old coal miner will survive for a year. This fact has been emphasized by Neyman, by Reichenbach, by Salmon, by von Mises, by Cramer – by nearly every serious writer who has adopted an empirical interpretation of probability: probability is applicable only to sets of events or kinds of events’ (8).

³ Lewis himself – in his ‘A Subjectivist's Guide to Objective Chance’, in Studies in Inductive Logic and Probability, Vol. 2, ed., Jeffrey, R.C., (Berkeley: University of California Press, 1980)Google Scholar – grants that chance is ‘at bottom ... really just a “folk” concept', but one that carries with it an objective truth (269). We shall see this idea – that chance, as objective single-case probability, is basic in human belief – variously affirmed throughout the essay.

⁴ Op.cit. note 1, 477, 485.

⁵ Ibid. 481–482.

⁶ Throughout this essay I will slide by two difficult problems – the reference class problem: how, if at all, to determine just what probabilistic distribution a single case best fits into; and the (dis)confirmation problem: how to (dis)confirm idealized ratios – e.g., to determine how long a sequence must be before it can (dis)confirm some probabilistic projection. Whatever answers are given to these questions will not negate or weaken what I say about the inapplicability of probability to the single case. For any view on applied probability faces these two problems; and what I say throughout this essay about single-case probability is independent of one's solutions to either of these problems.

⁷ As Ismael, Jenann puts it – in her ‘A Modest Proposal about Chance’, The Journal of Philosophy, CVII (2011)Google Scholar – while ‘general probabilities apply to classes and do not generally have a time index’, ‘[s]ingle case probabilities ... are unconditional, time-dependent, and pertain to particular occurrences’ – e.g., ‘that this particular roll of these particular dice … on this day comes up double sixes’ (421 and 418). (Ismael's emphases)

⁸ Ibid. 420.

⁹ Ibid. 442 and 441. Ismael later further frames her pragmatic orientation in terms of a block or timeless universe, thereby taking any dynamic chanciness out of probability. But none of this directly bears on her reply to the CA and can be bypassed.

¹⁰ Ibid. 431 and 425. As Ismael writes: ‘The only specific information a situated human agent has about the world is information about past events’ (439). Later, she sharpens this definition to make it more in line with relativistic theories by speaking of the light cones of a point, p, rather than the history of e at t (436) and by placing law and chance within a relativistic timeless or block universe.

¹¹ Op. cit., note 7, 430.

¹² Perhaps Ismael's most impressive advance on Lewis is found in her essay, ‘ Raid! Dissolving the Big, Bad Bug’, Nous 42 (2008), 292–307 CrossRefGoogle Scholar – in which she dissolves Lewis's worry that a probability law, P*, would admit as probable a competing law, P₁, that would in turn contradict the probabilities of P*. To sidestep Lewis's dodgy appeal to ‘inadmissible evidence’, evidence that allows him to rule out competing laws, Ismael distinguished between ‘reasoning within the scope of a theory’ and ‘reasoning about theories’ (296), where reasoning within the scope of the theory does not allow for competing probabilistic laws and so does not generate competing probability claims.

¹³ Ibid. 421.

¹⁴ Ibid. 422.

¹⁵ Ibid. Ismael initially defines probability in terms of quantum mechanics (419) but throughout the essay uses instances from ordinary life, on behalf of ‘creatures like us’ (442).

¹⁶ Glymour, Clark, ‘Instrumental Probability’, Monist 84 (2001), 285 CrossRefGoogle Scholar.

¹⁷ Howson, Colin and Urbach, Peter, Scientific Reasoning: The Bayesian Approach, Third Edition (Chicago: Open Court, 2006), 237Google Scholar. They add here that Bayesians start with a prior probability distribution, which ‘reflects a person's belief before the experimental results are known’ – ‘subjective, ... illusive, idiosyncratic ... likely to vary from person to person’ (237). But that said, they then stress that the formula, ideally, and in fact generally, is sensitive to the accumulation of evidence – the observed frequencies or other evidence – and yields an idealized frequency.

¹⁸ Ibid. 265.

¹⁹ Ibid. 76. And later, given P*(a) = r, ‘then, in the absence of any other relevant information, the appropriate subjective degree of belief that the event will occur is also r’ (174). Whether the ‘data source possesses a definite tendency to produce outcomes as measured by P*’ will be considered in the discussion on propensity theories.

²⁰ Ibid. 77.

²¹ Ibid. 78 (their emphasis).

²² Ibid. 77. They add that this capacity of the sample data to provide such objective information at first glance ‘seems frankly almost beyond belief’.

²³ Ibid. (my emphasis)

²⁴ Mises, Richard von Probability, Statistics, and Truth, second revised English edition prepared by Geiringer, Hilda (London: George Allen and Unwin, Ltd., 1957), 116 Google Scholar and 125

²⁵ As Miller, David W. – in his Critical Rationalism: A Restatement and Defence (Peru, IL: Open Court, 1994)Google Scholar – writes: ‘Propensities depend on the situation today ... Only in this way do we attain the specificity to resolve the problem of the single case’ (186). However, not all propensity theorists hold that propensity is of the single case, whether understood as an object (Peirce), the experimental set up (Popper) or the light cone of one's place in the universe (Miller). For instance, Gillies, Donald – in his ‘Varieties of Propensity’, British Journal of Philosophy of Science 51 (December, 2000), 807–835 CrossRefGoogle Scholar – argues that propensity does not lie in the single case but in the sequence as a whole. He nonetheless believes that probability applies to the single case by in effect accepting a version of the appeal to appropriateness as proposed by Howson and Urbach in their 1993 second edition of Scientific Reasoning, where they argue that ‘single case probabilities ... are not themselves objective’ but ‘subjective probabilities, which considerations of consistency nonetheless dictate must be set equal to the objective probabilities just when all you know about the single case is that it is an instance of the relevant collective’ (813). Again: an inference from the property of the collective to that of an item in the collective.

²⁶ Op.cit., note 16, 284.

²⁷ Suárez, Mauricio, ‘Propensities and Pragmatism’, The Journal of Philosophy CX (2013), 68 Google Scholar. Suárez grounds his view on five Peircean-inspired pragmatic maxims, in brief: (1) Understand concepts in terms of their effects, but also (2) avoid the positivistic simplicities that identify hypothetical entities with their empirical manifestations; (3) see ‘philosophy as continuous with science … bringing its own specific techniques to bear on scientific problems’; (4) ‘avoid reducing causal efficacy and causation to anything empirically accessible, such as frequency or correlation’; and (5) ‘be open to those scientific theories that postulate hypothetical or fictional entities’ via ‘[a]bduction or ... “inference to the best explanation”’ (69–72). Suárez also focuses on ‘Humphrey's Paradox’, where he rejects what he calls the ‘identity thesis’ that equates probability and propensity – holding instead that ‘propensities … are distinct from their probabilistic manifestations’ (89, his note 47) and thus need not, like probability, go ‘both ways’.

²⁸ Ibid. 73. Or: They are ‘theoretical properties ascribed to objects by scientists in an attempt to explain phenomena involving those objects as dispositional properties with probabilistic displays or manifestations’ (87).

²⁹ Ibid. 87 (Suárez's emphasis). While Suárez initially presents propensities as powers or causes, even mentioning ‘Aristotle's efficient causation’ (68), he later, on pragmatist grounds, further refines this and asserts that the relation need not be causal. ‘It is an empirical matter to determine, for any particular property whether it is causally related to its manifestations’ (88). How a manifestation relates to a propensity that does not cause it he does not say, perhaps relying on it being a sui generis relation.

³⁰ Ibid. 76.

³¹ Ibid.

³² Ibid.

³³ Hájek, Alan, “Fifteen Arguments Against Hypothetical Frequentism”, Erkenntnis 70 (2009), 225 CrossRefGoogle Scholar. Hájek makes the same point in his predecessor essay – “‘Mises Redux' – Redux: Fifteen Arguments Against Finite Frequentism’, Erkenntnis 45 (1996), 209–227 Google Scholar: ‘I think the frequentist has things backwards. Surely it is the coin's probability of landing heads that gives rise to its statistics, rather than the other way around’ (216). ‘Gives rise to’ – as if probability is some underlying cause?

³⁴ Aristotle, Physics, trans., Hardie, R.P. and Gaye, R.K., in The Complete Works of Aristotle: The Revised Oxford Translation, ed., Barnes, Jonathan, Volume One, (Princeton, New Jersey: Princeton University Press, 1984), 196:12–13 Google Scholar. Aristotle was not thinking of probability, of which he had not a glimmer, when he spoke of what comes to pass for the most part, but of contingency – as in a boulder not falling because it was lodged on the edge of a cliff.

³⁵ Ibid. 198a 2–3

³⁶ Whether it is possible to put the happenings of irregular irregularities into an idealized sequence I will leave to those who have the courage to define ‘this or that or whatnots’ – or even ‘market surprises’.

³⁷ This is not to deny that probabilistic laws provide a scientific ‘explanation’, just that propensities as underlying causes of such laws provide such an explanation. Just how probabilistic laws explain, of course, is another issue. But even if, as Salmon, Wesley C. argues – in his ‘Explaining Things Probabilistically’, The Monist 84 (2001), 208–217 CrossRefGoogle Scholar – probabilistic laws explain the single case, they are not effective in the single case. As Salmon notes, ‘statistical explanations – in many cases, at least – are not arguments’ (210). For explanation goes one way, from the single case to the law; it is after the fact. In contrast, a guide, like a prediction or argument, goes the other way, from the law to the single case; it is before the fact – a measure we do not have.

³⁸ Hume, David, Treatise on Human Nature, ed., Selby-Bigge, L.A. (Oxford: Clarendon Press, 1967), 125 Google Scholar.

³⁹ This understanding of propensity as involving multiple and varying causes, admittedly, will not address quantum mechanics. Kyburg, Henry E. – in his ‘Propensities and Probabilities’, The British Journal of the Philosophy of Science 25 (1974)Google Scholar – notes the striking difference between radioactive decay and, say, dying. ‘If we could identify people chemically and physically so as to put them in a small number of classes, and that is all we could do, then we would be home free’ in taking radioactive decay and dying as similar. ‘But precisely in distinction to the decay of radioactive elements, we can often identify the cause of a person's demise’ (366). The point is, if we could identify the cause of the half-life, as in discovering the underlying properties of a ‘propensity’, we would have left the swerve of quantum mechanics for some underlying Einsteinean cause. And, whatever, probability would not be of the single case except elliptically.

⁴⁰ Alan Hájek, op. cit, note 33, 218. Similarly, Hitchcock, Christopher – in ‘Causal Generalizations and Good Advice,’ The Monist 84 (2001), 218–241 CrossRefGoogle Scholar – starts with the PP as a ‘useful framework for thinking about the relationship between subjective probabilities and beliefs about objective probabilities’ (235) but adds that the PP needs a supplement, an answer to the reference class problem, by insisting that the probabilistic law is framed as directly as possible to the specific case so that there is less of a gap between them. But a gap in this instance is a chasm – not to be bridged by a magical jump from the real probability of the aggregate to the imaginary probability of the single case.

⁴¹ Op. cit., note 16, 299.

⁴² Van Fraasen, Bas C., ‘Calibration: A Frequency Justification for Personal Probability’, in Physics, Philosophy and Psychoanalysis: Essays in Honor of Adolf Grünbaum, eds, Cohen, R.S. and Lauden, L. (Boston: D. Reidel Publishing Company, 1983)Google Scholar Boston Studies in the Philosophy of Science, vol. 76, 300.

⁴³ Orange County, KO, ‘Mastering Your Reaction to Losses’, Blackjack Forum XXIII (Spring, 2003)Google Scholar. While this is expressed in terms of a frequentist understanding of probability, it could equally well be expressed in Bayesian or propensity terms.

⁴⁴ As interviewed by Justin Rohrlich, in ‘Hunches Mean Squat: How a Professional Gambler Invests in Sports’, Minyanville (July 10, 2012).

⁴⁵ As reported in Boston Globe (2/2/14, A17), the risk of death for donors of part of their liver is one to five for every 1,000 transplants. Dr. Giuliano Testa, Baylor University's Dallas Medical Center's surgical director, is cited as worrying that too much focus on rare donor deaths will decrease the number of donors and so cost lives. In a classic instance of the surgeon's point of view, he observed, ‘Bad things happen all the time. They should not take center stage with the discussions we have with the donors’. No matter how careful you are with regulations and donors, ‘you still cannot totally control unforeseen circumstances’. Clearly, this is the read of the one who is in it for the long run, who knows that most of his bets of this type by far will come out right. (Does it also provide a backdrop for why surgeons are notoriously unsympathetic? – that, like Jimmy, they know it's gambling, after all?) The patients, in sharp contrast, are well advised to know that the long odds of the surgeon are not for them. This is not to say that one should not donate, but let's not downplay what the bet is on, a bundled frequency, and the profound altruism in such donations. (My thanks to Charlene Entwistle for this reference.)

⁴⁶ Kyburg, Henry, ‘Don't Take Unnecessary Chances!’ Synthese 132 (2002), 11 CrossRefGoogle Scholar. This also provides the basis of a reply to speaking of the probability of the universe coming to be – by not seeing it as unique but as a type. While Kyburg speaks here in frequentist terms, I could just as well have spoken in Bayesian or propensity terminology.

⁴⁷ If they had been offered the choice of picking two doors or one, they would have picked two; and the odds would not have changed on those two doors winning two thirds of the time even after one of them had been opened. See Baumann, Peter, ‘Three Doors, Two Players, and Single-Case Probabilities’, The American Philosophical Quarterly 42 (2005), 71–79 Google Scholar. Bauman sees no way out here, arguing that ‘one ought to give up probabilistic arguments for or against switching or sticking in isolated individual cases. They only make sense in the long run’ (76) – which I disagree with because of the practice of bundling. For a delightful discussion of the authoritative vitriol directed against the advice to switch as offered by Marilyn vos Savant of Ask Marilyn fame, see Mlodinow, Leonard, The Drunkard's Walk: How Randomness Rules Our Lives (New York: Pantheon Books, 2008), 42–45 Google Scholar.

⁴⁸ Peirce, Charles Sanders, Philosophical Writings of Peirce, ed., Buchler, Justus (New York: Dover Publications, Inc., 1955, 169 Google Scholar. In his words, a gambler – which here includes everyone – ‘cannot be absolutely certain that the mean result will accord with the probabilities at all. Taking all his risks collectively, then, it cannot be certain that they will not fail,’ for that is what random means (ibid).

⁴⁹ Ibid. 162. It is to the greatness of Peirce that he sees the falsehood of the long-run winner's fallacy and offers a solution – that of epistemic community. ‘I can see but one solution ... that logicality inexorably requires that our interests shall not be limited. They must not stop at our own fate, but must embrace the whole community. … To be logical men should not be “selfish”’ (162). This begins to open up the issue of the morality embedded in reasoning probabilistically and, more generally still, the morality embedded in epistemic vulnerability – of which this piece is a part.

⁵⁰ My thanks to my philosophy department, at Bridgewater State University, where I read a much earlier version of this at a Philosophy Colloquium, and was helped, as always, a great deal. Thanks especially to Professors Matthew Dasti, William Devlin, Robert Fitzgibbons, Gull Kober, Laura McAlinden, James Pearson, Aeon Skoble, Catherine Womack – and, as always, especially, to Professors David Cheney and Steven Sanders. The errors, of course, are mine.