Hume, Probability, Lotteries and Miracles

Hume, Probability, Lotteries and Miracles Bruce Langtry Dorothy P. Coleman has recently offered an interpretation and defence of a central strand of Hume's critique of belief in miracles. Coleman is responding to a line ofargument against Hume which can be identified as early as Butler's Analogy ofReligion, and which has lately reappeared in the work of Robert Hambourger and others. In this paper I assess Coleman's contribution. Hambourger ascribes to Hume the following Principle ofRelative Likelihood (PRL): Suppose that someone, or, perhaps, a group of people testify to the truth of a proposition P that, considered by itself, is improbable. Then to evaluate the testimony, one must weight the probability that P is true against the probability that the informants are lying or mistaken. Ifit is more likely that P is true than that the informants are lying or mistaken, then, on balance, the testimony renders P more likely than not, and it may be reasonable for one to believe that P. However, if it is as likely, or even more likely, that the informants are lying or mistaken than it is that P is true, then, on balance, the testimony does not render P more likely true than false, and it would not be reasonable for one to believe that P. Hambourger argues that PRL is false. He offers as a counter-example reasonable belief, on the basis of a newspaper report, that such-and-such a person has won a particular lottery. Coleman argues that Hume held PRL, given a certain interpretation of"probability." Hambourger's lottery example does not refute PRL rightly understood. When PRL is applied to the evaluation of reports of miracles, it emerges that it would not be reasonable to believe that a miracle has occurred. Coleman begins her defence of Hume as follows: Butler's argument and its reincarnation in Hambourger overlook two senses of probability: probability pertaining to events qua unique occurrences and probability pertaining to events qua instances or tokens ofevent types. This distinction Volume XVI Number 1 67 BRUCE LANGTRY approximates that made by Hume in the Treatise between "probability of chances" and "probability of causes" (Bk. I, Pt. Ill, Sect. XII and XIII). Hume's argument against the believability ofmiracles invokes the second sense, whereas the Butler/Hambourger argument invokes the first. Following the first sense of probability, the likelihood of an event is measured by its degree of predictability as a unique occurrence; following the second sense, it is measured by its degree of conformity to causal laws applicable to events ofits type. An event having low predictability may be credible provided it conforms to relevant causal laws ... Granting that Hume's argument invokes the second sense ofprobability, i.e., probabilities regarding event-types, we can now see why Hambourger's lottery example does not prove to be the counterexample to Hume's principle of relative likelihood he believed it to be. The principle is to be invoked only when evaluating reports of events that do not conform to general rules or laws pertaining to events of its type. But Smith's winning the lottery is not an exception to rules governing lotteries. Here a distinction between two senses of probability is drawn in three ways: (1) Probability pertaining to events qua unique occurrences, contrasted with probability pertaining to events qua instances or tokens of event-types; (2) Probability of chances, contrasted with probability ofcauses; (3) Probability measured by the event's degree ofpredictability as a unique occurrence, contrasted with probabilitymeasuredby the event's degree ofconformity to causal laws applicable to events ofits type. These three characterisations of the distinction are far from equivalent. The probability that a six is thrown with a normal die concerns event-types rather than any particular occurrence, but surely falls under the heading "probability of chances"; so (1) diverges from (2). The measure of this probability is 1/6, but we cannot reasonably take 1/6 to measure the degree of conformity to causal laws of throws of six with a normal die; so (1) diverges from (3). The probability of a woman who has contracted breast cancer dying within five years of onset is a case of probability...