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

In this book, Graham Oppy examines arguments for and against the existence of God. He shows that none of these arguments is powerful enough to change the minds of reasonable participants in debates on the question of the existence of God. His conclusion is supported by detailed analyses of the arguments as well as by the development of a theory about the purpose of arguments and the criteria that should be used in judging whether or not arguments are successful. Oppy (...) discusses the work of a wide array of philosophers, including Anselm, Aquinas, Descartes, Locke, Leibniz, Kant, Hume and, more recently, Plantinga, Dembski, White, Dawkins, Bergman, Gale and Pruss. (shrink)

This is a wide-ranging 2004 book about arguments for and against beliefs in God. The arguments for the belief are analysed in the first six chapters and include ontological arguments from Anselm to Gödel, the cosmological arguments of Aquinas and Leibniz, and arguments from evidence for design and miracles. The next two chapters consider arguments against belief. The last chapter examines Pascalian arguments for and against belief in God. There are discussions of Cantorian problems for omniscience, of challenges to divine (...) omnipotence, and of the compatibility of everlasting complete knowledge of the world with free-will. There are appendices that present formal proofs in a system for quantified modal logic, a theory of possible worlds, notes on Cantorian set theory, and remarks concerning non-standard hyperreal numbers. This book will be a valuable resource for philosophers of religion and theologians and will interest logicians and mathematicians as well. (shrink)

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. (shrink)

Reasons for believing that Jesus rose from the dead.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The first is that a miracle, understood as an event produced by a transcendent agent overriding the usual course of nature, involves a violation of the laws of nature. Larmer argues that events are explained by reference to both relevant laws and units of mass/energy in the sequences to be explained. He contends that a miracle need not be conceived as involving a violation of natural law, but rather as the creation or annihilation of mass/energy by a transcendent agent. In (...) reply to the objection that this account would violate the first law of thermo-dynamics, he distinguishes two forms of the principle -- one metaphysical, one scientific -- and aruges that a miracle would not violate the principle considered as a scientific law. The second assumption is that miracle testimony cannot serve as evidence for theism. Larmer demonstrates that the logical ties connecting the concept of miracle to theism need not imply that one must be a theist to evaluate miracle testimony properly. All that is required is that one is prepared to entertain theism as a hypothesis. Attacking these assumptions allows Larmer to show that Humean balance-of-probabilities arguments, based on a presumed conflict between evidence which establishes belief in the laws of nature and evidence in favour of miracles, miss the point if miracles need not be defined as violations of the laws of nature. He argues that, in the absence of a general argument demonstrating that the testimonial evidence in favour of miracles conflicts with the evidence for the laws of nature, it is up to the atheist to demonstrate, on a case-by-case basis, why the testimonial evidence is to be rejected. His conclusion is that, contrary to what is usually thought, the burden of proof lies not upon the shoulders of the theist, but upon the shoulders of the atheist. (shrink)

In this timely study, Dawes defends the methodological naturalism of the sciences. Though religions offer what appear to be explanations of various facts about the world, the scientist, as scientist, will not take such proposed explanations seriously. Even if no natural explanation were available, she will assume that one exists. Is this merely a sign of atheistic prejudice, as some critics suggest? Or are there good reasons to exclude from science explanations that invoke a supernatural agent? On the one hand, (...) Dawes concedes the bare possibility that talk of divine action could constitute a potential explanation of some state of affairs, while noting that the conditions under which this would be true are unlikely ever to be fulfilled. On the other hand, he argues that a proposed explanation of this kind would rate poorly, when measured against our usual standards of explanatory virtue. (shrink)

A longstanding question at the intersection of science, philosophy, and theology is how God might act, or not, when governing the universe. Many believe that determinism would prevent God from acting at all, since to do so would require violating the laws of nature. However, when a robust view of these laws is coupled with the kind of determinism now used in dynamics, a new model of divine action emerges. This book presents a new approach to divine action beyond the (...) current focus on quantum mechanics and esoteric gaps in the causal order. It bases this approach on two general points. First, that there are laws of nature is not merely a metaphor. Second, laws and physical determinism are now understood in mathematically precise ways that have important implications for metaphysics. The explication of these two claims shows not only that nonviolationist divine action is possible, but there is considerably more freedom available for God to act than current models allow. By bringing a philosophical perspective to an issue often dominated by theologians and scientists, this text redresses an imbalance in the discussion around divine action. It will, therefore, be of keen interest to scholars of Philosophy and Religion, the Philosophy of Science, and Theology. (shrink)

This chapter contains sections titled: Introduction Goal and Scope of the Argument The Concept of a Miracle Textual Assumptions Background Facts: Death and Burial The Salient Facts: W, D, and P Probabilistic Cumulative Case Arguments: Nature and Structure The Testimony of the Women: Bayes Factor Analysis The Testimony of the Disciples: Bayes Factor Analysis The Conversion of Paul: Bayes Factor Analysis The Collective Force of the Salient Facts Independence Hume's Maxim and Worldview Worries Plantinga's Principle of Dwindling Probabilities Knavery, Folly, (...) and the Love of Wonder Conclusion References. (shrink)

AN ASSUMPTION IN DEBATES ABOUT THE PHILOSOPHICAL SIGNIFICANCE OF MIRACLES IS THAT IF A MIRACLE (A VIOLATION OF NATURAL LAW OR A PERMANENTLY INEXPLICABLE EVENT) WERE TO OCCUR, IT WOULD BE EVIDENCE FOR THE EXISTENCE OF THE CHRISTIAN GOD. THE PAPER EXPLORES RESERVATIONS BY SEVERAL PHILOSOPHERS ABOUT THIS CONNECTION BETWEEN GOD AND MIRACLES, AND PRESENTS ARGUMENTS TO SHOW THAT IF A MIRACLE WERE TO OCCUR THERE WOULD BE GOOD REASON TO DENY THAT GOD EXISTS.

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)

This contains an extended and wide ranging bibliography, beginning with the seventeenth century, of works relevant to the problem of miracles and Hume’s essay. It is especially useful for the problem in its historical setting.

The Humean argument concerning miracles says that one should always think it more likely that anyone who testifies to a miracle is lying or deluded than that the alleged miracle actually occurred, and so should always reject any single report of it. A longstanding and widely accepted objection is that even if this is right, the concurring and non-collusive testimony of many witnesses should make it rational to believe in whatever miracle they all report. I argue that on the contrary, (...) even multiple reports from non-collusive witnesses lack the sort of independence that could make trouble for Hume. (shrink)

The Legitimacy of Miracle defends the view that miracles, in the strong sense of being events produced by a supernatural agent overriding the usual course of nature, can take place without violating any laws of nature. This means that the evidence for miracles cannot be judged to be in conflict with the evidence for the laws of nature; the result being that Humean objections to the rationality of belief in miracles fail.

Alexander George’s lucid interpretation of Hume’s “Of Miracles” provides fresh insights into this provocative text, explaining the concepts and claims involved. He also shows why Hume’s argument fails to engage with committed religious thought and why philosophical argumentation so often proves ineffective in shaking people’s deeply held beliefs.

"This book is about miracles -- what they are, what would count as evidence that they have occurred. It is not primarily concerned with historical evidence about whether certain particular miracles (such as Christ rising from the dead or walking on water) have occurred, but it is primarily concerned with whether historical evidence could show anything about such things and whether it matters if it can. It is concerned with the framework within which a historical debate must be conducted. It (...) contains a selection of writings written from different viewpoints by philosophers, classical and modern. The reader is left to form his or her own view on who wins the argument." [Introduction]. (shrink)

ALTHOUGH THE IDEA OF A VIOLATION OF NATURAL LAW IS NOT NECESSARILY INVOLVED IN THE IDEA OF THE MIRACULOUS, THERE IS "ONE KIND" OF MIRACLE WHICH SEEMS TO INVOLVE IT. HUME’S DISCUSSION OF THE EVIDENCE FOR MIRACLES RELATES TO THIS KIND AND IS INTERPRETABLE AS AN ARGUMENT AGAINST ITS POSSIBILITY. ALSO THERE IS AN ARGUMENT THAT THE EXPRESSION "VIOLATION OF NATURAL LAW" SIGNIFIES A CONFUSION IN WHICH THE IDEAS OF NATURAL LAW AND LEGAL LAW COLLAPSE INTO EACH OTHER. NEITHER OF (...) THESE ARGUMENTS IS EFFICACIOUS. FURTHERMORE, THE CONTENTION THAT THERE CAN BE NO SUCH THING AS ESTABLISHING THE "ABSENCE" OF A NATURAL CAUSE IS OPEN TO OBJECTION. HOWEVER, TO BE CONCEIVED AS A VIOLATION OF NATURAL LAW, A MIRACLE MUST BE THOUGHT OF AS AN OCCURRENCE WHICH IS BOTH EMPIRICALLY CERTAIN AND CONCEPTUALLY IMPOSSIBLE--WHICH OUGHT TO MAKE THE NOTION RIDICULOUS. AND YET IT NEED NOT. (shrink)

Newton, along with a number of other seventeenth-century scientists, is frequently charged with having held an inconsistent view of nature and its operations, believing on the one hand in immutable laws of nature, and on the other in divine interventions into the natural order. In this paper I argue that Newton, William Whiston, and Samuel Clarke, came to understand miracles, not as violations of laws of nature, but rather as beneficent coincidences which were remarkable either because they were unusual, or (...) were beyond current understandings of nature. In this manner the Newtonians managed to reconcile their scientific pursuits with their religious convictions. (shrink)

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.

This book is a critical overview of the manner in which the concept of miracle is understood and discussed in contemporary analytic philosophy of religion. In its most basic sense, a miracle is an unusual, unexpected, observable event brought about by direct divine intervention. The focus of this study is on the key conceptual, epistemological, and theological issues that this definition of the miraculous continues to raise. As this topic is of existential as well as theoretical interest to many, there (...) is no reason to believe the concept of miracle won't continue to be of ongoing interest to philosophers. (shrink)

In this paper I outline and discuss the central claims and arguments of J. L. Mackie’s The Miracle of Theism. Mackie argues, in essence, that none of the traditional theistic arguments is successful taken either one at a time or in tandem, that the theist does nothave a satisfactory response to the problem of evil, and that on balance the theistic hypothesis is much less probable than is its denial. He then concludes that theism is unsatisfactory and rationally unacceptable. I (...) argue that he is mistaken in nearly all of his major contentions. (shrink)

RésuméJ'ai soutenu dans un article de 1985 que s'il y avait des miracles, cela parlerait contre l'existence du Dieu judéo-chrétien. Dans son livre de 1988 sur le concept de miracle, Robert Larmer propose une critique de mes arguments. J'évalue ici la force de cette critique. Je montre que la redéfinition de «miracle» que propose Larmer est circulaire; que sa distinction est spécieuse entre violer une hi naturelle et la surmonter grâce à la création ou la destruction d'énergie par Dieu; et (...) que sa tentative de montrer que les miracles sont le produit d'un être rationnel, bienfaisant et tout-puissant est inadéquate. (shrink)

I analyze David Hume’s "Of Miracles". I vindicate Hume’s argument against two charges: that it (1) defines miracles out of existence; (2) appeals to a suspect principle of balancing probabilities. He argues that miracles are, in a certain sense, maximally improbable. To understand this sense, we must turn to his notion of probability as ’strength of analogy’: miracles are incredible, according to him, because they bear no analogy to anything in our past experience. This reveals as anachronistic various recent Bayesian (...) reconstructions of his argument. But it exposes him to other charges, with which I conclude. (shrink)

As this article is published, Robert Larmer and I have been engaged in a debate that is now eighteen years long, often with gaps of many years between ripostes, about the nature and significance of miracles. The Larmer/overall oeuvre now includes six works, including the two published here. I am grateful to the editors of Dialogue for giving me the opportunity to respond to Larmer’s most recent entry in the debate.

This book provides students with a scholarly introduction to miracles, which also covers philosophical, medical and historical issues.

IN "MIRACLES AND CRITERIA" I ARGUE THAT, CONTRARY TO VIEWS OF PHILOSOPHERS SUCH AS GUY ROBINSON, THERE EXIST CRITERIA BY WHICH TO DIFFERENTIATE EVENTS LEGITIMATELY TERMED MIRACLES AND EVENTS BEST INTERPRETED AS MERE INDICES OF AN INADEQUATE UNDERSTANDING OF NATURAL PROCESSES. WHETHER ONE VIEWS AN EXTRAORDINARY EVENT AS A MIRACLE OR AS THE RESULT OF SOME UNKNOWN OR POORLY UNDERSTOOD NATURAL PROCESSES IS NOT, THEREFORE, A MATTER OF WHIM.

Hume says we never have grounds to believe in miracles. He’s right, but many commentators misunderstand his theory of probability and therefore his argument. This book shows that Humean probability descends from Roman law, and once properly contextualized historically and philosophically, Hume’s argument survives the criticisms leveled against it.

In lieu of an abstract, here is a brief excerpt of the content:328 HUME, MIRACLES AND LOTTERIES This paper addresses recent criticisms of Hume's skepticism with regard to miracles, by 1 2 Sorensen and Hambourger who argue that there are counterexamples, illustrated by lotteries, to Hume's account of how the truth of reports of improbable events (either first or second hand) must be evaluated. They believe these counterexamples are sufficient to prove that Hume's argument against the believability of miracles, defined (...) as violations of laws of nature caused by God, is unsound. Their arguments merit consideration not only in their own right but also on the basis of historical precedent, since they have in common an assumption that is found in Butler's criticism of Hume's predecessors in this debate. The bulk of my paper deals with Hambourger, who presents the most detailed version of the 'Butler' criticism. Sorensen's version can be answered in light of the evaluation of Hambourger 's argument. Hume's Argument Hume's argument is not against the possibility of miracles but against the possibility that it could ever be reasonable to believe a miracle 4 had occurred. His argument can be summed up as follows: in judging the credibility of a report of an improbable event, the probability of the event must be weighed against the probability that the report could be mistaken. The probability of an event is determined by the degree to which it conforms to known laws of nature. Laws of nature are formulated on the basis of uniform experience. Assuming that a miracle is a violation of laws of nature, any judgment that an event is miraculous presupposes a 329 judgment that there exists a uniform pattern of causation to which it is opposed, which pattern would constitute empirical proof against the miracle's occurrence. Testimony, on the other hand, is shown by experience not to be uniformly reliable. Consequently, no report of a miracle will have credibility since there will always be a uniform experience that is full proof against it, which therefore outweighs whatever merits testimony may have. In Hume's words, [N]o 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.... When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened.... If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till- then, can he pretend to command my belief or opinion (E 115-116). Hambourger 's Criticism Hambourger maintains that Hume's argument depends on a principle which he calls the "principle of relative likelihood." He restates this principle as follows: 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 (sic) the probability that P is true against the probability that the informants are lying or mistaken. If it is more likely that P is true than that the informants are lying or mistaken, then, on balance, the 330 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. As a counterexample to this principle, Hambourger asks us to suppose that a lottery is held in which there are one million entrants, each of whom has a one in a million chance of winning, and that a reliable newspaper, the New York Times, reports that the winner of the lottery is Smith. He further asks us to suppose that the Times errs only once out of every 10,000 times. Thus, the probability that the Times ' report is wrong is... (shrink)

Christian Overall and I have been debating whether the occurrence of events traditionally viewed as miracles would constitute evidence for theism. In this article, I make some concluding comments regarding our exchanges. My goal in making these comments is twofold. First, I wish to sketch why I think miracles can function as evidence for God. Second, in the course of our discussion, Overall has ascribed to me claims that I do not make and criticized me on the basis of my (...) holding these views. I feel it is important to set the record straight on several issues. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:What Hume Actually Said About Miracles Robert J. Fogelin Two things are commonly said about Hume's treatment ofmiracles in the first part of Section X of the Enquiry Concerning Human Understanding: I.Hume did not put forward an a priori argument intended to show that miracles are not possible. II.Hume did put forward an a priori argument intended to show that testimony, however strong, could never make it reasonable to (...) believe that a miracle had occurred. In a recent article in this journal, Dorothy Coleman calls this the "traditional interpretation," and, since this characterization strikes me as correct, I shall call it that too. Antony Flew stands virtually alone in challenging the traditional interpretation, arguing, in particular, that Hume did not even attempt to provide an a priori argument showing that testimony can never establish the existence of a miracle. On FIeW1S reading, Hume's argument was intended to do no more than place a "check" on arguments put forward to establish the existence of miracles on the basis oftestimony. Along with others, however, Flew accepts the first partofthe traditional interpretation, namely, that whatever Hume was up to, he was certainly not trying to produce a proof showing that miracles cannot exist. He endorses the first part of the traditional interpretation in these words: What [Hume] is trying to demonstrate a priori in Part I is: not that, as amatter offact, miracles do nothappen; but that, from the very nature of the concept — 'from the very nature of the fact' — there must be a conflict of evidence required to show that they do. In opposition to these united voices, I will argue that this consensus on the first part of the traditional interpretation is unfounded, for there are clear texts — at the very heart ofHume's discussion — that go dead against it. Volume XVI Number 1 81 ROBERT J. FOGELIN Two passages, which occur in the same paragraph, are particularly relevant to this discussion: Passage I. A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proofagainst a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined. (E 114, emphasis added) Passage II. There must...bea uniform experience against every miraculous event, otherwise the event would not merit that appellation. And as a uniform experience amounts to a proof, there is here a direct andfullproof, from the nature ofthe fact, against the existence ofany miracle; nor can such aproofbe destroyed, or the miracle rendered credible, but by an opposite proof, which is superior. (E 115, emphasis added in final clause) The clause nor such a proof be destroyed, or miracle rendered credible in Passage II is crucial for our purposes, for it simultaneously expresses two claims which, for clarity's sake, I will state separately. First, when Hume speaks??such a proof, he is referring to the direct and full proof, from the nature ofthe fact, against the existence ofany miracle mentioned in the first part of the same sentence. Thus, one thing that Hume is saying is this: Ci: Nor can such a proof(against the existence ofany miracle) be destroyed, but by an opposite proof which is superior. He is also making the following claim: C2: Nor can such a miracle be rendered credible, but by an opposite proof which is superior. Having sorted things out, it is now possible — using only direct quotations from the immediate text — to show that, contrary to the traditional interpretation, Hume does present an a priori argument against the existence ofmiracles. Argument One 1. there is here a direct and full proof, from the nature ofthe fact, against the existence ofany miracle; nor can such a proof be destroyed... but by an opposite proof, which is superior. (E 115, from Passage II) 82Hume Studies WHAT HUME ACTUALLY SAID ABOUT MIRACLES 2.the proofagainst a miracle, from the very nature ofthe fact, is as entire as any argument from experience can possibly be imagined. (E 114, emphasis added, from Passage I) Therefore: 3.there is... a direct andfullproof, from the nature ofthe fact, against the existence ofany miracle... (shrink)

HUME’S ARGUMENT AGAINST JUSTIFIED BELIEF IN MIRACLES CANNOT BE PROPERLY UNDERSTOOD APART FROM HIS ANALYSIS OF CAUSATION. IT IS ARGUED THAT HUME’S POSITION HAS NEVER BEEN CORRECTLY INTERPRETED BECAUSE ITS CONNECTION WITH HIS MORE GENERAL METAPHYSICS HAS NEVER BEEN ADEQUATELY EXAMINED. TO UNDERSTAND HUME’S VIEW ON MIRACLES THE FOLLOWING QUESTION MUST BE ANSWERED: WHY DID HUME THINK THAT ONE COULD JUSTIFIABLY BELIEVE THAT AN "EXTRAORDINARY" EVENT HAD OCCURRED, BUT THAT ONE COULD "NEVER" JUSTIFIABLY BELIEVE A "MIRACLE" HAD OCCURRED? THIS BOOK (...) OFFERS A SUSTAINED TREATMENT OF THAT QUESTION. IT IS ALSO ARGUED THAT IT MAKES NO SIGNIFICANT DIFFERENCE WHETHER HUME’S CENTRAL ARGUMENT IS INTERPRETED AS AN "A PRIORI" OR AN "A POSTERIORI" ARGUMENT; AND THAT HIS ARGUMENT IS APPLICABLE BOTH TO BELIEF BASED ON TESTIMONY AND DIRECT EXPERIENCE OF A MIRACLE. IN PART II THE CENTRAL QUESTION ADDRESSED IS WHETHER OR NOT ANYONE CAN JUSTIFIABLY BELIEVE A MIRACLE TO HAVE OCCURRED GIVEN A CONTEMPORARY EPISTEMOL. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:David Hume and the Probability of Miracles Barry Gower 1. Introduction Oflate there have been published several discussions ofDavid Hume's famous essay "Of Miracles" which attempt to make precise the reasoning it contains. This, it turns out, requires the use of certain mathematical rules and theorems of the probability calculus which were unknown to Hume or, indeed, to anyone else when the essay was first published. It is suggested, (...) in particular, that the claims he made can best be understood in the light of a theorem of the probability calculus which we now name after a celebrated eighteenth century probabilist, Thomas Bayes. However, the so-called "Bayesian" interpretation of the argument against miracles misrepresents Hume's reasoning in that the manner in which he expressed his thinking does not fit such an interpretation. Moreover, this error needs to be rectified, not just because it involves a mistaken view about the past but, more importantly, because it obscures the legacy of a different mode of thinking evident in Hume's writing about probabilistic inference which deserves to be recovered. Our thinkingisimpoverishedifcertain presumptions aboutprobability become so entrenched that we have great difficulty in seeing them as anything other than obvious. By imputing them to Hume we overlook their contestability and so lose an opportunity to recapture an alternative way of understanding probabilistic reasoning. As is well known, the argument against miracles, though not published until 1748, had been worked out some twelve or thirteen years earlier during Hume's stay at the Jesuit college of La Fleche, where he wrote most of A Treatise of Human Nature. A chapter entitled "Reasonings concerning Miracles" had been written but, at the last moment, it was suppressed for fear that such an explicit attack on religion would give offence and thus deflect attention from the book's main philosophical aim which was to put an end to controversy. On the other hand, Thomas Bayes's famous memoir on probability was not published until 1764, andit is unlikely that Hume knew ofits existence until Richard Price mentionedit, though without identifyingits author, in an elaborate mathematical footnote to a dissertation containing remarks on the probability of miracles, published in 1767. Had Hume taken the trouble to follow up this reference, he would almost certainly Volume XVI Number 1 17 BARRY GOWER have been either baffled by its mathematics or discouraged by its lack of practical advice. That, at least, seems to have been the reaction of Hume's contemporaries, for apart from Price none of them seems to have paid any attention to the memoir. Even today, when anyone with the slightest acquaintance with probability can recite a version of Bayes's theorem, it is hard to follow the reasoning of the memoir and to appreciate the significance of the ideas it contains. As an historian of statistics has recently said, "Bayes's contemporaries were stymied by the work, and modern readers unwilling to devote many hours to it are likely to gain only a superficial understanding ofit." One paradoxical feature of attributing Bayesianism to Hume concerns the role of Richard Price. His dissertation, which had, it seems, been written some years before it was published — perhaps in the early 1750's — is sharply critical of Hume's argument against miracles. Yet it was Price himself who was responsible for the posthumous publication of Bayes's memoir, and his introduction and commentary clearly express approval of its methods and conclusions. We are, then, faced with the suggestion that Hume, not having heard of Bayes, was applying Bayesian ideas about "inverse" inference to miraculous events, whereas Price, who was not only familiar with but also endorsed Bayes's ideas, preferred a quite different approach to reasoning about miracles and about the credibility of testimony generally. Can Hume really be described as a "better intuitive Bayesian" than Price? Before embracing such aparadoxical conclusion we should consider whether it is really justified by what Hume said about the probability ofmiracles. First, though, some attention needs to be paid to a way ofthinking about probable arguments which does not conform to convention, and which implies a non-Bayesian interpretation of the question about miracles. 2. Jakob Bernoulli and the Combination... (shrink)