Baconian Probability and Hume's Theory of Testimony

Hume Studies Volume 27, Number 2, November 2001, pp. 195-226 Baconian Probability and Hume's Theory of Testimony DOROTHY COLEMAN Bacon, like Moses, led us forth at last, The barren Wilderness he past, Did on the very Border stand Of the bestpromis'd Land, And from the Mountain Top of his Exalted Wit, Saw it himself, and shewed us it. — Abraham Cowley (1667) I Hume notoriously argued that no testimony is sufficient to justify belief in the occurrence of a miracle, defined as a violation of a law of nature, "unless the testimony be of such a kind, that its falsehood would be more miraculous , than the fact, which it endeavors to establish" (EHU 116). His argument for this thesis relies on the premise that in determining the credibility of testimony to any extraordinary event—whether miraculous or merely anomalous —"the evidence, resulting from testimony, admits of a diminution, greater or less, in proportion as the fact is more or less unusual" (EHU 113). Ironically, both advocates and critics of Hume's "diminution principle"1 have invoked a Bayesian model of conditional probabilities in evaluating his theory of testimony. While this fashionable approach is consistent with Hume's focus on epistemic probability, or probability relative to evidence, I Dorothy Coleman is Adjunct Associate Professor of Philosophy, Northern Illinois University, DeKaIb, IL 60115, USA. e-mail: dcoleman@niu. edu 196 Dorothy Coleman prefer to sidestep this debate because both sides of it assume without argument that all epistemic gradations of probability should be evaluated using a Pascalian model of probability, that is, probability based on the mathematical calculus of chance, of which Bayesianism is one form. I will defend Hume on his own terms by showing that criticisms based on the calculus of chances are irrelevant for assessing his account of testimony because the model of probability on which he bases it is Baconian rather than Pascalian. The foremost advocate of Baconian probability, L. J. Cohen, has credited Hume for being the first to recognize explicitly "that there is an important kind of probability which does not fit into the framework afforded by the calculus of chance," a recognition he finds evident in Hume's distinction between "probabilities arising from analogy and probabilities arising from chance or cause."2 The purpose of this paper is to interpret Hume's account of testimony in light of this insight and to discuss its implications for assessing his argument against the believability of miracles. Critics of Hume's diminution principle, from his contemporaries, George Campbell and Richard Price, to the present,3 argue that even moderately reliable testimony to events having extremely low prior probability is nevertheless credible. Suppose, drawing from one of Price's counterexamples, that a blindfolded individual selects a ball from a container holding 99 white balls and one black ball, that a witness, W, reports that the ball selected was black, and that W's statements about this sort of thing are correct 9 out of 10 times. In this example, the probability that the selected ball is black is 99 to 1, whereas the probability that W's report is true is 9 to 1. Since the former probability is lower than the latter, Hume's diminution principle appears to require that the testimony is not credible, but this is absurd. So Hume's principle, following this reasoning, must be false. Price's criticisms of Hume drew upon the work of Thomas Bayes.4 As a Bayesian, he believed that all degrees of belief or probability are quantifiable and that all rational degrees of belief conform to the Pascalian model of the calculus of chances. Price's criticism evidently made an impression on Hume, who wrote to Price saying that "the light, in which you have put this controversy , is new and plausible and ingenious, and perhaps solid. But I must have some more time to weight it, before I can pronounce this judgment with satisfaction to myself."5 Hume's subsequent revisions to his essay, however, show no departure from his commitment to the principle of diminution or the conclusions he drew from it. This suggests either that he later satisfied himself that Price's criticisms were...

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