This paper defends David Hume's "Of Miracles" from John Earman's (2000) Bayesian attack by showing that Earman misrepresents Hume's argument against believing in miracles and misunderstands Hume's epistemology of probable belief. It argues, moreover, that Hume's account of evidence is fundamentally non-mathematical and thus cannot be properly represented in a Bayesian framework. Hume's account of probability is show to be consistent with a long and laudable tradition of evidential reasoning going back to ancient Roman law.

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume 28, Number 1, April 2002, pp. 113-130 Bayesianism, Analogy, and Hume's Dialogues concerning Natural Religion SALLY FERGUSON Introduction Analyses of the argument from design in Hume's Dialogues concerning Natural Religion have generally treated that argument as an example of reasoning by analogy.1 In this paper I examine whether it is in accord with Hume's thinking about the argument to subsume the version of it given in (...) the Dialogues under the model of probabilistic reasoning offered by Bayes's theorem. Wesley Salmon attempted this project in 1978.2 In related projects, David Owen3 as well as Philip Dawid and Donald Gillies4 have more recently attempted to construct Bayesian analyses of Hume's argument concerning testimony in "Of Miracles." I want to be careful at this stage to note exactly what I will claim. It is not that Bayesian reasoning sheds no light on the argument from design, or on arguments concerning testimony. All of the analyses mentioned above are beneficial in that they have been able to expose subtleties in these arguments that had previously gone unnoticed. Salmon's paper, in particular, contributes nicely to an understanding of just how the design argument may function in relation to contemporary scientific reasoning. In this paper I argue that, nonetheless, the attempt to apply Bayesian reasoning to the argument as presented in the Dialogues is not well supported as a reconstruction of Hume's own approach to the argument from design. Sally Ferguson is Assistant Professor of Philosophy, University of West Florida, UOOO University Parkway, Pensacola, FL 32514, USA. e-mail: [email protected] 114 Sally Ferguson There are two stages to my treatment of the issue. I begin by considering how much Hume knew of Bayes's theorem, and what consequence that knowledge might have had on his treatment of the argument in the Dialogues. This discussion includes a consideration of exactly what has been claimed by other authors on this subject, including what some have argued concerning Hume's reasonings in "Of Miracles," section 10 of An Enquiry concerning Human Understanding. I conclude that, based on the historical data, there is little reason to think of Hume's approach to the argument from design as anything more than proto-Bayesian at best. I then argue further, through a close textual analysis of the Dialogues, that there are good reasons for not treating Hume's reasoning there as even proto-Bayesian. In the end, the benefits that have been claimed for that approach, in terms of exposing both the subtleties of the argument and of Hume's reasoning about it, can equally well be derived from a careful analysis of the argument under a model of analogical reasoning, without need of Bayes's theorem. Section One Perhaps one might think that there is not much use for a consideration of the question whether Hume himself conceived of any of his arguments along specifically Bayesian lines. As Gower argues,5 Hume's knowledge of mathematics in general was fairly limited, and Bayes's theorem was not well known even up until Hume's death. It is important, therefore, for me to establish that there have not only been those who thought that Bayesian reasoning illuminates the arguments Hume gave, but also his own thinking about those arguments. It is also important for me to establish that it is not obvious that knowledge of Bayes's theorem did not affect Hume's reasonings. Each of these points will be addressed in the following. As to the first point, the claims of some authors on the subject are ambiguous. Dawid and Gillie, for example, make no statement to the effect that the probabilities involved in Bayes's theorem were in fact examined in "Of Miracles," nor do they attempt to produce any passages from Hume in support of that view. Thus it would be assumed that they see their attempt not as an attempt to provide an analysis that represents Hume's own approach to the argument, but rather simply as one that provides an illuminating method of analysis and support for an argument that Hume happened to give. Indeed, their conclusion, to the effect that a... (shrink)

This paper presents a new account of Hume’s “probability of causes”. There are two main results attained in this investigation. The first, and perhaps the most significant, is that Hume developed – albeit informally – an essentially sound system of probabilistic inductive logic that turns out to be a powerful forerunner of Carnap’s systems. The Humean set of principles include, along with rules that turn out to be new for us, well known Carnapian principles, such as the axioms of semiregularity, (...) symmetry with respect to individuals (exchangeability), predictive irrelevance and positive instantial relevance. The second result is that Hume developed an original conception of probability, which is subjective in character, although it differs from contemporary personalistic views because it includes constraints that are additional to simple consistency and do not vary between different persons. The final section is a response to Gower’s thesis, by which Hume’s probability of causes is essentially non-Bayesian in character. It is argued that, on closer examination, Gower’s reading of the relevant passages is untenable and that, on the contrary, they are in accordance with the Bayesian reconstruction presented in this paper. (shrink)

The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-nineteenth century physics, neglecting both locality and Noether’s theorem and its converse. The relevance of General Relativity has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, so there (...) is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether’s first theorem, an infinity of conserved energies-momenta. Second, Sean Carroll has asked how one should modify the Dirac–Maxwell–Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR. Such realism also might help to answer an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR. (shrink)

At the beginning of his section “Of Miracles,” Hume mentions an argument of Dr. Tillotson. The doctrine of “the real presence” seems contradicted by our senses. We see a piece of bread, but are asked to believe it consists in the substance of the body of Christ.