A BAYESIAN ARTICULATION OF HUME’S VIEWS IS OFFERED BASED ON A FORM OF THE BAYES-LAPLACE THEOREM THAT IS SUPERFICIALLY LIKE A FORMULA OF CONDORCET’S. INFINITESIMAL PROBABILITIES ARE EMPLOYED FOR MIRACLES AGAINST WHICH THERE ARE ’PROOFS’ THAT ARE NOT OPPOSED BY ’PROOFS’. OBJECTIONS MADE BY RICHARD PRICE ARE DEALT WITH, AND RECENT EXPERIMENTS CONDUCTED BY AMOS TVERSKY AND DANIEL KAHNEMAN ARE CONSIDERED IN WHICH PERSONS TEND TO DISCOUNT PRIOR IMPROBABILITIES WHEN ASSESSING REPORTS OF WITNESSES.

"It is a general maxim...’ That no testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous, than the fact which it endeavors to establish; and even in that case there is a mutual destruction of arguments, and the superior only gives us an assurance suitable to that degree of force, which remains, after deducting the inferior.’" A Bayesian interpretation of the first half is proved as a theorem. (...) A stronger conditional principle, and a biconditional theorem based on it, are substantiated. And a truth that the second part can express is explained. (shrink)

It has often been suggested (1) that according to Hume it is impossible in principle for testimony to prove a miracle, and (2) that an indispensable element in Hume's argument is the claim that a miracle is by definition a violation of the laws of nature. I argue that both (1) and (2) are mistaken, and that, once Hume's 'Of Miracles' is viewed in a proper historical context, it emerges that Hume's argument against miracles is considerably different from what is (...) usually supposed. (shrink)

Hume’s celebrated argument concerning miracles, and an 18th century criticism of it put forward by Richard Price, is here interpreted in terms of the modern controversy over the base-rate fallacy. When considering to what degree we should trust a witness, should we or should we not take into account the prior probability of the event reported? The reliability of the witness (’Pr’(says e/e)) is distinguished from the credibility of the testimony (’Pr’(e/says e)), and it is argued that Hume, as a (...) good proto-Bayesian, argued that the credibility of the testimony should be calculated in terms of both the reliability of the witness and the prior probability of the event reported. (shrink)

George Schlesinger has recently presented a reply to Hume’s argument concerning miracles. Schlesinger argues that probability theory and some simple assumptions about miracles show that testimony for a miracle increases the probability of God existing; furthermore this testimony can raise the probability of God existing enough that it is rational to believe that God exists. I argue that one of the assumptions that Schlesinger makes is false, and that the justification Schlesinger gives for it does not succeed. Thus I claim (...) Schlesinger’s reply to Hume fails. (shrink)

The late John L. Mackie, formerly of University College, Oxford.

Recent attempts to cast Hume’s argument against miracles in a Bayesian form are examined. It is shown how the Bayesian apparatus does serve to clarify the structure and substance of Hume’s argument. But the apparatus does not underwrite Hume’s various claims, such as that no testimony serves to establish the credibility of a miracle; indeed, the Bayesian analysis reveals various conditions under which it would be reasonable to reject the more interesting of Hume’s claims.

1. Causal knowledge is an indispensable element in science. Causal assertions are embedded in both the results and the procedures of scientific investigation. 2. It is therefore worthwhile to investigate the meaning of causal statements and the ways in which we can arrive at causal knowledge.

The best defence against the suggestion that Hume’s use of the laws of nature is question-begging is the both-sides-need-the-laws’ response in its variations. Efforts along these lines by Antony Flew, J L Mackie, and more recently J C Thornton are shown to fail. Hume intends to rule out miracles by ruling out, e.g., resurrections, not just rule out calling resurrections miracles’. The both-sides-need-the-laws’ objection can target only the latter and it fails to do even this.