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Twenty-three years ago Robert Ayers noticed several brief and intriguing comments on miracles in the Collected Papers of Charles Sanders Peirce (CP). Working with just those scraps of information from the CP, he stitched together a rough but helpful starting point for understanding this aspect of Peirce's religious and scientific thought. In the last few years several more articles on this subject have been written, each filling in a gap left by the others: Ayers' is a theological view, based solely on the CP; later articles fill out Peirce's mathematics and his logic. This paper attempts to fill in a genealogical gap by showing how his thought on miracles is directly related to his dialogues with Plato, Hume, and Lutoslawski. My resources are largely unpublished manuscripts, many of which are fragmentary. I show the relationship between these manuscripts and two key published essays, "Philosophy and the Conduct of Life" (1898), and "On the Logic of Drawing History from Ancient Documents, Especially from Testimonies" (1901), and then show how Peirce, in dialogue with Plato, exposes and overcomes the nominalistic and anti-miracle prejudices of historiography in his day. The resulting view of history is fallibilistic, realistic and evolutionary, in which miracles are not violations of laws of nature but are to be expected as evolutionary variations that form part of the ongoing self-revelation of the cosmos. Miracles, like all events in history, must not be viewed prejudicially by adherents or detractors, but must be taken into careful account in the grand induction of history and science.

Hume's argument concerning miracles is interpreted by making approximations to terms in Bayes's theorem. This formulation is then used to analyse the impact of multiple testimony. Individual testimonies which are ‘non-miraculous’ in Hume's sense can in principle be accumulated to yield a high probability both for the occurrence of a single miracle and for the occurrence of at least one of a set of miracles. Conditions are given under which testimony for miracles may provide support for the existence of God.

A recent discussion of Hume’s argument concerning the rationality of accepting a belief that a miracle has occurred is given by J. L. Mackie in The Miracle of Theism. Mackie believes that Hume’s argument is essentially correct, although he attempts to clarify and strengthen it. Any version of Hume’s argument depends upon one’s conception of miracles and laws of nature; I will argue that Mackie commits a simple logical error and that given his conception of laws of nature and miracles there is no reason to reject rational belief in miracles.

Bayesian analyses are prominent among recent and allegedly novel interpretations of Hume’s argument against the justified belief in miracles. However, since there is no consensus on just what Hume’s argument is any Bayesian analysis will beg crucial issues of interpretation. Apart from independent philosophical arguments—arguments that would undermine the relevance of a Bayesian analysis to the question of the credibility of reports of the miraculous—no such analysis can, in principle, prove that no testimony can (or cannot) establish the credibility of a miracle. Bayesian analyses of Hume’s argument are not analyses of Hume’s argument at all—but superfluous representations of it.

An examination of the principles advanced by David Hume, Esq., in An Essay on Miracles; with a correspondence on the subject by Mr Hume, Dr. Campbell, and Dr. Blair. To which are added sermons and tracts. In 1763 Campbell published A Dissertation on Miracles which was intended as a demolition of Hume’s essay On miracles.

With A Defense of Hume on Miracles Robert Fogelin enters the recent discussion on Hume’s treatment of miracles. In this short book Fogelin begins by presenting his interpretation of Hume’s argument concerning miracles. The second chapter is a lengthy treatment of recent work by David Johnson and John Earman, and the third short chapter is a discussion of the relation of Hume’s view on miracles to his broader philosophy. There are also two appendices and the text of “Of Miracles.”.

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.

This vital study offers a new interpretation of Hume's famous "Of Miracles," which notoriously argues against the possibility of miracles. By situating Hume's popular argument in the context of the 18th century debate on miracles, Earman shows Hume's argument to be largely unoriginal and chiefly without merit where it is original. Yet Earman constructively conceives how progress can be made on the issues that Hume's essay so provocatively posed about the ability of eyewitness testimony to establish the credibility of marvelous and miraculous events.