Hume's Argument Against Miracles: A Failure?, Lecture notes of Religion

Download Hume's Argument Against Miracles: A Failure? and more Lecture notes Religion in PDF only on Docsity! “Se — a Hume's Abject Failure,The Argument Against Miracles John Earman, Professor of the History and Philosophy of Science, University of Pittsburgh Abstract: Hume's famous essay on miracles is set in the context of the larger debate that was taking place in the eighteenth century about the nature of miracles and the ability of eyewitness testimony to establish the credibility of such events. The author contents that Hume's argument against miracles is largely unoriginal and chiefly without merit where it is original. To advance the issues so provocatively posed by Hume's essay requires the tools of the probability calculus being developed by Hume's contemporaries but largely ignored by Hume. Content Part I Hume on Miracles 1. Abstract 1 2 Hume's Religious Orientation 4 3 The Origins of Hume's Essay 6 4 The Puzzles of Hume's Definitions of “Miracles” 8 5 Conceptions of Miracles 9 6 What a Miracle Is for Hume 12 7 The Eighteenth-Century Debate on Miracles 14 8 The Structure of Hume's Essay 20 9 Hume's Straight Rule of Induction and His “Proof” Against Miracles 22 10 Hume, Bayes, and Price 24 11 Bayes and Bayesianism 26 12 The Bayes-Price Rejection of Hume's Straight Rule 29 13 Hume's Stultification of Scientific Inquiry 31 14 The Indian Prince 33 15 Hume's Maxim 38 16 What Is Hume's Thesis? 43 17 Hume's Diminution Principle 49 18 Multiple Witnessing 53 19 More Multiple Witnessing 56 20 What Is Right About Hume's Position 59 21 Fall Back Positions for Hume 61 22 Probabilifying Religious Doctrines 65 23 Hume's Contrary Miracles Argument 67 24 Conclusion 70 Appendix on Probability 75 Works Cited 87 Part I Hume on Miracles John Earman Abstract: Part I contains the author's reconstruction and critical evaluation of Hume's argument against miracles. Especially emphasized is the utility of the probabilistic epistemology that emerges from the work of Hume's contemporaries, Thomas Bayes and Richard Price, for evaluating the evidential value of the testimony of fallible witnesses. Keywords: Bayes, Bayesianism, eyewitness testimony, Hume, miracles, Richard Price, probabilistic epistemology, probability Section X (“Of Miracles”) of Hume's Enquiry Concerning Human Understanding 1 is a failure. In philosophy, where almost all ambitious projects are failures, this may seem a mild criticism. So to be blunt. I contend that “Of Miracles” is an abject failure. It is not simply that Hume's essay does not achieve its goals, but that his goals are ambiguous and confused. Most of Hume's considerations are unoriginal, warmed over versions of arguments that are found in the writings of predecessors and contemporaries. And the parts of “Of Miracles” that set Hume apart do not stand up to scrutiny. Worse still, the essay reveals the weakness and the poverty of Hume's own account of induction and probabilistic reasoning. And to cap it all off, the essay represents the kind of overraching that gives philosophy a bad name. These charges will be detailed and supported below, but at the outset I want to elaborate on the last one. An apt analogy for Hume's project is the search for a “demarcation criterion.” As originally conceived by the logical positivists, such a criterion would separate genuine assertions having cognitive significance from meaningless gibberish. More recently, there has been a quest for a criterion to cleave genuine science from pseudo-science. The history of these twin quests has been a history of failure.2 One of the morals to be drawn from a failure to find a litmus test of the pseudo-scientific is relevant here: namely, it does not much matter what label one sticks on a particular assertion or an enterprise;3 the interesting questions are whether the assertion merits belief and whether the enterprise is conducive to producing well-founded belief.4 The answers cannot be supplied by a simple litmus test, but can only be reached by detailed, case-by-case investigations. Admittedly, however, such investigations are often unrewarding and can be, downright tedious. Charles Berlitz's The Bermuda Triangle (1974) sold several million copies. Larry Kusche's The Mystery of the Bermuda Triangle—Solved (1986) was never a bestseller. It is a careful, if plodding, examination of the claims made about the mysterious disappearance of ships and airplanes in the region known as the Bermuda Triangle. In case after case, Kusche shows that there is no mystery at all (e.g., the Raifuku Maru was seen by another ship to sink in a raging storm) or else that the only mystery is over which of several commonsense explanations is correct. It is not very exciting reading, and after a few chapters the reader hankers after a silver bullet that will spare us further details by putting a merciful end to all the nonsense. And so it is with alleged miracles. Joe Nickell's Looking for a Miracle (1993) casts a skeptical eye on the Shroud of Turin, weeping icons, bleeding effigies. etc. A few chapters are enough to make the reader yearn for a quick knock out blow to spare us further tedium. Hume himself, at the beginning of his miracles essay, confesses the desire to deliver such a blow. Dr. Tillotson, he informs us, supplied a “decisive argument” against the doctrine of transubstantiation that served to “silence the most arrogant bigotry and superstition” (E 110: 141). “I flatter myself.” Hume wrote, “that I have discovered an argument of a like nature which, if just, will, with the wise and learned, be an everlasting check to all kinds of superstitious delusion, and consequently, will be useful as long as the world endures” (E 110: 141).5 The temptation to fashion such an argument is understandable. But it should be resisted. Any epistemology that does not allow for the possibility that evidence, whether from eyewitness testimony or from some other source, can establish the credibility of a UFO landing, a walking on water, or a resurrection is inadequate. At the same time, of course, an adequate epistemology should deliver the conclusion that in most (all?) actual cases, when all the evidence is weighed up, little credibility should be given to such events. Hume's account of inductive reasoning is incapable of satisfying these dual demands. The tools needed for a better account were being fashioned at the very time that Hume wrote his Enquiry, and in succeeding years, they were honed on Hume's skeptical attack on the problem of induction and on his treatment of the problematics of eyewitness testimony. The aim of the current essay is not simply to bash Hume—a comparatively easy exercise—but also to indicate how, given the proper tools, some advance can be made on these problems. The contribution to philosophy of religion is incidental but, I hope, non- negligible. 2 Hume's Religious Orientation John Earman Hume's views on religion have been extensively documented, and there is no need to rehearse the discussion here.6 But a few remarks relevant to the motivation behind “Of Miracles” are in order. There is some evidence that the youthful Hume struggled against religious feeling.7 If there was such a struggle, there is not much doubt about how the mature Hume resolved it. If we take Philo's pronouncements in Dialogues Concerning Natural Religion (1776) as a guide, the mature Hume was a theist, albeit of a vague and weak-kneed sort. He seems to have been convinced by the argument from design of the proposition “That the cause or causes of order in the universe probably bear some remote analogy to human intelligence” (227). But he was also convinced that the argument does not permit this undefined intelligence to be given further shape or specificity, and certainly not the specificity that would be needed to support any inference “that affects human life, or can be the source of any action or forbearance.”8 Hume's inconsequential theism was combined with an abhorrence of organized religion, which Hume saw as composed of superstitions that have had almost uniformly baneful effects for mankind. When Cleanthes averred that “Religion, however corrupted, is still better than no religion at all.” Philo responded as follows: How happens it then, if vulgar superstition be so salutory to society, that all history abounds so much with accounts of its pernicious consequences on public affairs? Factions, civil wars, persecutions, subversions of government, oppression, slavery: these are the dismal consequences which always attend its prevalency over the minds of men. (220) Given such an animus toward organized religion, it is easy to understand why Hume would want to attack religious miracles, for the argument from design and the cosmological argument were supposed to establish the existence of God while miracles were supposed to serve as indicators of what kind of God exists.9 But how to attack? Only the most benighted theists failed to recognize the pitfalls of eyewitness testimony to miracles. Thus, in chapter 37 (“Of Miracles, and Their Uses”) of the Leviathan (1668). Hobbes cautioned that For such is the ignorance and aptitude to error generally of all men, but especially of them that have no much knowledge of naturall causes, and the nature and interests of men: as by innumerable and easie tricks to be abused. (203) Nor was there any need to point to improbabilities in the cases of the miracles of Jesus— as we will see below, that ground was well trodden by Hume's contemporaries. What was left was to launch an in-principle attack on the possibility of establishing the credibility of religious miracles. The strong desire to strike a toppling blow against one of the main pillars of what Hume saw as baneful superstition led him to claim more than he could deliver, and it blinded him to the fact that in stating his arguments against miracles he was exposing the weaknesses in his own account of inductive reasoning. 3 The Origins of Hume's Essay John Earman Hume's Treatise of Human Nature (1739–1740) was written during a three-year stay (1735–1737) in France, first at Reims and then at La Flèche. It was at the latter that Hume received the inspiration for his essay on miracles, as he confessed to George Campbell, the author of A Dissertation on Miracles (1762), one of the better contemporary responses to Hume's essay: It may perhaps amuse you to learn the first hint, which suggested to me that argument which you have so strenuously attacked. I was walking in the cloisters of the Jesuits' College of La Flèche, a town in which I passed two years of my youth, and engaged in a conservation with a Jesuit of some parts and learning, who was relating to me, and urging some nonsensical miracle performed in their convent, when I was tempted to dispute against him; as my head was full of the topics of my Treatise of Human Nature, which I was at that time composing, this argument immediately occurred to me, and I thought that is to take the position that the issue of whether or not a miracle has occurred is a matter that does not turn on the opinions of particular witnesses. There is an even more obvious and troubling puzzle about Hume's first definition: if a miracle is a violation of a law of nature, then whether or not the violation is due to the intervention of the Deity, a miracle is logically impossible since, whatever else a law of nature is, it is an exceptionless regularity. Where then is the need for a complicated essay on the credibility of miracle stories? I will return to these puzzles below. But first I need to explore more of the context in which Hume was operating. end p.8 5 Conceptions of Miracles John Earman The idea behind Hume's first definition of ‘miracle’ as a violation of a law of nature goes back at least as far as St. Thomas Aquinas, who took a miracle to be an occurrence that “lies outside the order of nature” (Summa Theologica, Q. 110, Art 4; Pegis 1944, 1022). In his Theologico-Political Treatise, Spinoza follows this tradition in defining a miracle as “contrary to the order of nature.” But he concluded that a belief in miracles was always due to ignorance: and worse, such a belief was a tacit confession of unsound conceptions of nature and of God and ultimately serves atheism rather than theism. [A]s nothing is necessarily true save only by Divine decree, it is plain that the universal laws of nature are decrees of God following from the necessity and perfection of Divine nature. Hence, any event happening in nature which contravened nature's universal laws, would necessarily also contravene the divine decree, nature, and understanding; or if anyone asserted that God acts in contravention to the laws of nature, he, ipso facto, would be compelled to assert that God acted against his own nature—an evident absurdity.14 (TPT 83; 108) The conclusion is evident: “[I]t most clearly follows that miracles are only intelligible as in relation to human opinions, and merely mean events of which the natural cause cannot be explained by a reference to any ordinary occurrence, either by us, or at any rate, by the writer or narrator of the miracle” (TPT 84; 109). And further: “[W]e cannot gain knowledge of the existence and providence of God by means of miracles, but . . . we can far better infer them from the fixed and immutable order of nature” (TPT 86; 111). For our purposes, there is a crucial implication of Spinoza's view of laws that can be stated in purely secular terms: “nothing happens in nature which does not follow from her laws” (TPT 84; 109). Spinoza held to a strong form of determinism that allowed for no contingency in nature. This is contrary to the modern conception of determinism according to which laws allow for contingency in “initial conditions” and necessitate only conditionals of the form “If the initial conditions are such-and-such, then the state at a later time will be so-and-so.” But this difference makes no difference for present concerns. If laws of nature are conceived as universal truths, applying without exception to all space and all time, then a miracle as a violation of a law of nature is a contradiction in terms. As Spinoza himself put it. “[W]hatsoever is contrary to nature is also contrary to reason, and whatsoever is contrary to reason is absurd end p.9 and, ipso facto, to be rejected” (TPT 92; 114). Since the point is statable in secular terms and does not require Spinoza's notion that laws are decrees of God. it was available to Hume as well. Before turning to the puzzle of why Hume did not avail himself of it, and thus reduce his miracles essay to a single paragraph, some other matters need to be addressed.15 When Spinoza wrote that the term ‘miracle’ “is only intelligible as in relation to human opinions,” he meant to dismiss the subject. Locke begins his “Discourse of Miracles” (1706) with an almost identical definition: “A miracle then I take to be a sensible operation which, being above the comprehension of the spectator, and in his opinion contrary to the established course of nature, is taken by him to be divine” (DM 256; 114). But Locke's intent was quite the opposite of Spinoza's since for Locke miracles are the “foundation on which believers of any divine revelation must ultimately bottom their faith” (DM 264; 119). To the objection that what will be a miracle for one spectator will not be a miracle for another, Locke says: [T]his objection is of no force, but in the mouth of one who can produce a definition of miracle not liable to the same exception, which I think is not so easy to do: for it being agreed that a miracle must be that which surpasses the force of nature in the established, steady laws of causes and effects, nothing can be taken to be a miracle but what is judged to exceed those laws. Now everyone being able to judge of those laws by his own acquaintance with nature, and notions of its force (which are different in different men), it is unavoidable that that should be a miracle for one, which is not so to another. (DM 256– 57; 114) Some members of the Royal Society, such as Robert Boyle (1686) and John Wilkins (1699), continued to hew to the definition of ‘miracle’ as a violation of the laws of nature. They held the charming but muddled idea that miracles are a meeting place for science and religion since natural philosophers, as arbiters of what counts as a law of nature, are best placed to judge what counts as a violation of a law. By contrast. Newton's disciples Samuel Clarke (1705) and William Whiston (1696), and arguably Newton himself, maintained a view closer to Locke's on which ‘miracle’ marks an epistemic rather than an ontic category.16 Such a view seems to undercut the use of miracles as direct demonstrations of the active presence of God in human affairs. But to be puzzled, as some commentators are (see, for example, McKinnon 1967), as to how miracles, non- onticly conceived, can have religious force is to fail to appreciate the strategy adopted by the liberal Anglicans in the late seventeenth and the eighteenth centuries. Their concern was less with providing proofs and demonstrations and more with providing grounds for reasonable belief (see section 22). Miracles, non-onticly conceived, could further this goal by serving as evidence for the existence of God and for his designs and purposes. For Locke and the Newtonians, these miracies gained their religious force from their combination with prophecy, from their timing and coincidence, and from contextual factors.17 But the general evidentiary function of such miracles is independent of the details of Christian apologetics. Suppose, for the sake of illustration, that there is a well developed theology based on the existence of a god called Emuh. who promises an afterlife in return for certain religious observances in this life. Suppose that this theology predicts that on such-and-such a day Emuh will send a sign in the sky. And suppose that on the appointed day, the clouds over America clearly spell out in English the words “Believe in Emuh and you will have everlasting life,” while the same message is spelled out in French over France, in Deutsch over Germany, etc.18 Then even though these cloud formations may not contravene any of the general principles taken at the time in question to be laws of nature and, indeed, may be explicable in terms of those principles, it would not be untoward to take these extraordinary occurrences to be support for Emuh theology. Those who have read Hume may be tempted to dismiss such examples as lying outside of the ambit of Hume's argument against miracles since the phenomena at issue would be counted by Hume as marvels rather than miracles. But as we will see shortly, Hume has a hard time maintaining a principled marvel vs. miracle distinction. And in any case what matters is not how Hume classified examples but how the major participants in the eighteenth-century miracles debate classified them. Unless Hume's argument applies to examples generally taken at the time to be miracles and unless it shows that the occurrence of such events lack credibility and/or that these events, even if their occurrences are rendered credible, cannot serve as the basis for a reasonable belief in religious tenets, his essay must be judged a failure in context.19 Hume's essay shows no sensitivity to the nuances of the changing roles of miracles in Christian apologetics. No such sensitivity was required, Hume thought, because if religious miracles can never be rendered credible (as he proposed to show), then none of the contentious theological issues about miracles is ever reached. Hume's first definition of ‘miracle’ as a violation of a law of nature seems intended in part as a rejection of Locke's epistemic conception in favor of an ontic conception. If correct, this would have left him free to follow the secularized version of Spinoza's line and dismiss miracles as contradictions in terms. That he does not do this should be a signal that the first reading of Hume can be misleading. Hume unquestionably rejects Locke's subjectivism. Whether or not a miracle occurs is for Hume an issue that does not turn on the event being discoverable by us, much less on our opinions of it: “A miracle may either be discoverable by men or not. This alters not its nature and essence . . . The raising of a feather, when the wind wants ever so little of a force requisite for that purpose, is as real a miracle [as the raising of a house or ship], though not so sensible with regards to us” (E fn 115: 154). But first appearances to the contrary. ‘miracle’ for Hume marks an epistemic category in the sense that it is relative to evidence, although for Hume it is not relative to the evidence that any particular person possesses. end p.11 6 What a Miracle Is for Hume John Earman Hume commentators have tied themselves in knots trying to explain Hume's first definition of ‘miracle’ in a way that makes sense of his essay. We can cut part way “Of Miracles”; if it had been, the essay would have had to have been considerably different. My reading of Hume allows an escape between the horns of Curd's dilemma. A Hume miracle, such as a resurrection, is certainly not a contradiction in terms, and one can justifiably believe in the occurrence of such an event without already being committed to theism. Further, once it is rendered credible, such a miracle can serve as inductive evidence for theism, or so I will argue in section 22. But this is getting ahead of the story. The important thing about Hume's concept of miracles is how it functions in his arguments against them. Before I examine the details of the arguments I need to set them in the context of the eighteenth century debate. 7 The Eighteenth-Century Debate on Miracles John Earman “Of Miracles” is often treated as if it were a genuinely original piece of philosophy. But although it does contain some original insights and is cast in Hume's characteristically forceful prose, it is in fact a largely derivative work. Apart from questions of priority, a fair evaluation of Hume's treatment of the issues must start from the way in which they were conceptualized by his predecessors and contemporaries.25 There are many echoes of Locke in Hume's essay. To name two, Locke's definition of miracles is surely one reference point of Hume's own definition, and Locke's king of Siam is transmuted into Hume's Indian prince end p.14 (see section 14). But more fundamentally. Hume owes to Locke the formulation of the general problem of which miracles is a special and especially thorny instance. There are, according to Locke's Essay Concerning Human Understanding (1690), two sources of credibility: ‘common observation in like cases, and particular testimonies in that particular instance” (ECHU 377; 103). But what if these sources pull in opposite directions? Locke was well aware of the difficulty created when such a conflict arises: “The difficulty is, when testimonies contradict common experience, and the reports of history and witnesses clash with the ordinary course of nature, or with one another: there it is, where diligence, attention, and exactness are required, to form a right judgment, and to proportion assent to the different evidence and probability of the thing” (ECHU 377; 103). Having stated the problem. Locke has little to offer beyond the pious admonition to diligence, attention, and exactitude. The evidences are liable to so great variety of contrary observations, circumstances, reports, different qualifications, tempers, designs, oversights, &c., of the reporters, that it is impossible to reduce to precise rules the various degrees wherein men give their assent. This only may be said in general. That as the argument and proofs pro and con, upon due examination, nicely weighing every particular circumstance, shall to anyone appear, upon the whole matter, in a greater or lesser degree to preponderate on either side; so they are fitted to produce in the mind such different entertainments, as we call belief, conjecture, guess, doubt, wavering, distrust, disbelief, &c. (ECHU 377; 103) Locke's waffling was unavoidable, for without the help of the probability calculus, which was being developed when Locke wrote his Essay but of which he was largely innocent, it is impossible to state any precise rules for “nicely weighing” the evidence. Unfortunately, Locke abandons his caution and modesty precisely where it was needed most. He writes: Though the common experience and the ordinary course of things have justly a mighty influence on the minds of men, to make them give or refuse credit to anything proposed to their belief; yet there is one case, wherein the strangeness of the fact lessens not the assent to a fair testimony given to it. . . . This is the proper case of miracles, which, well attested, do not only find credit themselves, but give it also to other truths, which need such confirmation. (ECHU 382; 106) While it is impossible to say whether or not Hume was biting on this bait, it is indisputable that Hume had read Locke's Essay and had advertised his own Treatise as an improvement on Locke's account of probabilistic reasoning (see section 10).26 The bait was offered afresh in a dispute that erupted in the years 1727–1729 with the publication of Thomas Woolston's Six Discourses on the Miracles of Our Savior.27 Woolston used the device of having his friend the “Jewish Rabbi” set out the reasons for thinking that the story of the resurrection of Jesus is undermined by “absurdities, improbabilities, and incredibilities.” The rhetoric is inflamatory: “Was, or can there be, any imposture more against sense and reason palm'd upon the understanding of mankind?” (12); “[S]uch a manifest and indisputable Mark and Indication of Fraud, as not to be equall'd in all or any of the impostures that ever were attempted to be put upon the World” (15). Leslie Stephen may have been a bit severe in characterizing Woolston's performance as that of a “mere buffoon jingling his cap and bells in a sacred shrine” (1962, Vol. 1. 195),28 but Woolston was certainly foolish to turn his undisguised sarcasm on church authorities. Here is a sample: Bishop Gibson is for the Messiahship of Jesus, who cast the Devils out of the Madmen, permitted them to enter into the Herd of Swine, that ran violently down a Precipice, and were choak'd in the Sea: How great a Miracle it was thus to cure the Madmen, the Bishop may know best, being perhaps better acquainted with the Devil than I am; but was it not for the Pity to the Swineherds, for their Losses, I could even now laugh at the Thoughts of the Hoggs running and tumbling down-hill, as if the Devil drove them: But leaving the Bishop calmly, decently, and seriously to admire the Wisdom and Justice of his Jesus in that Act, I am for the spiritual Jesus, who, according to the typical Form of that Story, exorcis'd the furious and diabolical Tempers out of the Jews and gentiles of old, whom no Chains of Reason could hold from doing violence to Christians till they were converted; and tho’ He permitted the like persecuting and diabolical Spirits to enter into Ecclestiastical Swine; yet will they be precipitated into the Sea of the Knowledge of God, wherein they will be absorpt with divine Visions and Contemplations. (56–57) Woolston was convicted of criminal blasphemy. He died in 1733 in prison, unable to pay his fine of £ 100. Gasking (1978) has suggested, not implausibly, that Hume had Woolston's fate in mind when he wrote to his cousin Henry Home in 1737 that he had forborne from including an essay on miracles in his Treatise (recall section 3).29 While there is little of any theoretical interest in the Six Discourses, there is much that is of decisive interest to Hume scholars to be found in one of the many attempted rebuttals of Woolston. Thomas Sherlock's Tryal of the Witnesses of the Resurrection of Jesus was first published in 1728 and subsequently went through fourteen editions. Sherlock's well chosen conceit was a trial in which the Apostles, alleged witness to the resurrection, stand accused of giving false evidence. Mr. A. councel for Woolston, puts the case against them, while Mr. B serves as their defense attorney. A jury hears the evidence and renders a verdict. The “not guilty” verdict is no surprise. But what is remarkable about Sherlock's pamphlet is that it succeeded in framing the objections to the resurrection miracle, and to miracles in general, in a form that was at once more forceful and much more philosophically interesting than anything Woolston had managed. The prosecutor, Mr. A, puts a rhetorical question: “[W]hen the Thing end p.16 testify'd is contrary to the Order of Nature, and, at first sight at least, impossible, what Evidence can be sufficient to overturn the constant Evidence of Nature, which she gives us in the constant and regular Method of her Operation?” (TW 58: 127). There is a distinct echo here of Locke: “Though to a man whose experience has always been quite contrary, and who has never heard anything like it, the most untainted credit of a witness will scarce be able to find belief” (ECHU 367; 99). The illustration Locke gives in his Essay Concerning Human Understanding is a possibly apocryphal tale: As it happened to a Dutch ambassador, who entertaining the king of Siam with the peculiarities of Holland . . . amongst other things told him that the water in his country would sometimes, in cold weather, be so hard, that men walked upon it, and that it would bear an elephant, if he were there. To which the king relied, Hitherto I have believed the strange things you have told me, because I look upon you as a sober fair man, but now I am sure you lie. (ECHU 367; 99) The defense attorney, Mr. B. answers the prosecutor's charge that testimony ought not to be admitted in cases where it is contrary to the order of nature by claiming that this principle leads to absurd results in cases like the one described by Locke. For instance: a Man who lives in a warm Climate, and never saw Ice, ought upon no Evidence to believe that Rivers freeze and grow hard in cold Countries; for it is improbable, contrary to the usual Course of Nature, and impossible according to the Notion of Things: and yet we all know that this is a plain, manifest Case, discernible by the Senses of Men, of which therefore they are qualify'd to be good Witnesses. . . . And what has the Gentleman [Mr. A] said upon this Occasion against the Resurrection, more than any man who never saw Ice might say against an hundred honest Witnesses, who assert that Water turns to Ice in cold Climates? (TW 60; 128) Mr. B then draws a general moral from the example: “It is very true that Men do not so easily believe, upon testimony of others, things which to them seem improbable or impossible, but the reason is not because the thing itself admits of no Evidence, but because the Hearer's pre-conceiv'd Opinion outweighs the Credit of the Reporter, and makes his Veracity to be call'd into question” (TW 60–61; 128). Sherlock illustrates his moral with an example: [F]or instance, it is natural for a Stone to roll down-hill; but a Stone moving up-hill is as much an Object of Sense as a Stone moving down-hill; and all Men in their Senses are as capable of seeing, and judging, and reporting the Fact in one Case as in the other. Should a Man then tell you that he saw a Stone go up-hill of its own accord, you might question Annet seems to be saying that either naive induction by enumeration works, or nothing does. Hume's view, as we will see below, is not much more sophisticated. 8 The Structure of Hume's Essay John Earman I defy the reader to give a short, simple, and accurate summary of the argumentation in “Of Miracles.” What on first reading appears to be a seamless argument is actually a collection of considerations that sometimes mesh and sometimes don't. It will take much work to tease out the components of Hume's argument and to evaluate the soundness of individual components and the effectiveness of the entire package. But it would be useful to have at the outset a rough and ready sketch of the structure of Hume's case against miracles. Unfortunately, commentators cannot even agree on this much, and we will soon see why. Hume opens Part 1 of his essay by representing Tillotson's argument against transubstantiation as a contest: scripture and tradition (which inform us that the bread has turned to flesh and the wine has become blood) vs. the evidence of our senses (which inform us that the bread is just bread and the wine is just wine). But the former “carry not such evidence with them as sense: when they are considered merely as external evidences, and are not brought home to everyone's breast, by the immediate operation of the Holy Spirit” (E 109; 140). Thus, the contest is really no contest at all since “[A] weaker evidence can never destroy a stronger; and therefore, were the doctrine of the real presence ever so clearly revealed in scripture, it were directly contrary to the rules of just reasoning to give our assent to it” (E 109; 140).33 Hume also represents his argument against miracles as a contest: here it is a “contest of two opposite experiences; of which the one destroys the other, as far as its force goes, and the superior can only operate on the mind by the force, which remains” (E 113; 143). On one side, there is uniform experience against the occurrence of the miraculous. On the other, there is testimony, which itself derives its force from experience: It will be sufficient to observe that our assurance in any argument of this kind [i.e., one based on testimony] is derived from no other principle than our observation of the veracity of human testimony, and of the usual conformity of the facts to the reports of witnesses. (E 111: 142) The reason, why we place any credit in witnesses and historians, is not derived from any connexion, which we perceive a priori, between testimony and reality, but because we are accustomed to find a conformity between them. (E 113: 142–43) To many commentators it is clear what Hume took to be the upshot of this contest. Here, for example, is C. D. Broad's summary: So Hume's argument comes to this. Against belief in any alleged miracle we have, by definition of the word miracle, an absolute uniform experience. For believing in the miracle we have only our experience as to the trustworthiness of testimony. And this is not an absolutely uniform experience, however trustworthy we suppose the witness to be. Therefore we have never the right to believe in any alleged miracle however strong the testimony for it may be. (1916–17. 80) Broad's reading is not a twentieth-century invention: it was in fact put forward by contemporaries of Hume such as Richard Price (1767), who took Hume to be saying that to believe in a miracle on the authority of human testimony is to “prefer a weaker proof to a stronger” (FD 385; 158). Price may have had an ulterior motive for this attribution since he thought it led to a a quick refutation of Hume. The regard we give to testimony is not, Price contended, based solely or even largely on data about the frequency with which it delivers the truth. “One action, or one conversation with a man, may convince us of his integrity and induce us to believe his testimony, though we had never, in a single instance, experienced his veracity. His manner of telling the story, its being corroborated by other testimony, and various particulars on the nature and circumstances of it, may satisfy us that it must be true” (FD 399; 161). There certainly are passages, if taken in isolation, that suggest the Price-Broad reading. In the case where the event related is marvelous rather than miraculous, Hume says that the contest of opposing experiences results in a “counterpoise, and mutual destruction of belief and authority” (E 113; 143). But by “counterpoize” and “destruction.” Hume cannot mean that stories of marvelous events are never to be credited since he allows that, under appropriate conditions, historians can be correct in accepting such stories. When the event related is not just marvelous but really miraculous. Hume invites us to suppose that “the testimony considered apart and in itself, amounts to an entire proof.” In that case, he says, “there is proof against proof, of which the strongest must prevail, but with a diminution of its force, in proportion to that of its antagonist” (E 114; 143). But Hume does not say explicitly that what is left after the clash of proofs is never sufficient to ground the credibility of a miracle, and, indeed, he nowhere explicitly states the argument attributed to him by Price and Broad.34 Nor is it plausible that the Price-Broad reading is what Hume thought, even if it is not what he explicitly end p.21 says. For one thing, this reading would make it hard to understand the function of the famous Maxim which Hume enunciates at the close of Part 1 (see section 15). That Maxim sets the conditions under which testimony is sufficient to establish the credibility of a miracle; but if Price and Broad are right, Hume is saying that there are no such conditions and, hence, no role for the Maxim. For another thing, Part 2 would be puzzling since there Hume allows that especially good testimony can establish the credibility of some secular miracles. Thus, I will assume, contra Price and Broad, that in Part 1 Hume did not mean to foreclose the issue of whether testimony could establish the credibility of a miracle, although I acknowledge that the text is ambiguous enough to allow the Price- Broad reading.35 In Part 2 Hume takes back his overgenerous assumption that the falsehood of the testimony to a miracle “would be a real prodigy” (E 116; 144). He enumerates various factors which contribute to the unreliability of eyewitness testimony and gives a cursory review of various Catholic and profane miracle stories. Then he suddenly announces—in the first edition of the Enquiry—that no testimony “for any kind of miracle can ever possibly amount to a Probability much less to a Proof.” From 1768 onward the “can ever” is softened to a “has ever.” And even this latter claim is further qualified to apply only to religious miracles, although initially this qualification was put in a footnote and only after 1768 was it moved into the main text. There is a disturbing slipperiness to Hume's aims and conclusions, which I will address in section 16. But the first order of business is to take up Hume's argument that experience provides a “proof” against miracles. 9 Hume's Straight Rule of Induction and His “Proof” Against Miracles John Earman In Part 1 of “Of Miracles” Hume writes that “A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined” (E 114; 143). If the argument Hume gives for this assertion is correct, then it is irrelevant that the alleged miracle has a divine or supernatural origin. To understand the structure of Hume's argument, it is helpful to try to specify the form that Hume thinks inductive reasoning follows. As a starting point, recall Reichenbach's straight rule of induction: If n As have been examined and m have been found to be Bs, then the probability that the next A examined will be a B is m/n.36 Corollary: If m = n, then end p.22 the probability that the next A will be a B is 1. Hume also thought that induction proceeds by a straight rule which is not easy to formulate in general37 but which takes on a simple form in the case of uniform experience. As a first cut, we can try to state the corollary as: If n As have been examined, all of which were found to be Bs, then if n is sufficiently large, the probability that all As are Bs is 1. How large “sufficiently large” needs to be is presumably a matter to be settled by psychological investigations. The evidence for attributing this straight rule to Hume comes from passages such as: (1) “All probability, then, supposes an opposition of experiments and observations, where the one side is found to overbalance the other, and to produce a degree of evidence, proportioned to the superiority” (E 111; 141). (2) The evidence of testimony is “regarded either as a proof or a probability, according as the conjunction between any particular kind of report and any kind of object has been found to be constant or variable” (E 112; 142). (3) “Why is it more than probable, that all men must die; that lead cannot, of itself, remain suspended in the air; that fire consumes wood, and is extinguished by water; unless it be, that these events are found agreeable to the laws of nature?” (E 114–115; 143). (4) “There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appellation. And as uniform experience amounts to a proof, there is here a direct and full proof, from the very nature of the fact, against the existence of any miracle” (E 115; 143–44). Additional evidence comes from Hume's letter of 1761 to Hugh Blair: “The proof against a miracle, as it is founded on invariable experience, is of that species or kind of proof which is full and certain when taken alone, because it implies no doubt, as is the case with all probabilities” (L. Vol. 1, 350). agreed that the probabilistic form of analysis is wholly appropriate when discussing the credibility of testimony.45 Naysayers will have a hard time explaining away the above quoted letter from Hume to Price, where Hume is implicitly accepting the probabilistic form into which Price cast Hume's argument. In a brilliant analysis of the sources of Hume's essay, Wootton (1990) has identified two preconditions for the emergence of unbelief, or at least of skepticism with respect to religious doctrines. The first is the conviction that unbelievers and skeptics can be of good moral character (see Wootton 1983). The second precondition lay in the new concepts of evidence and probability . . . which made possible a new approach to problems of historical testimony, including those presented in the Gospel story. The “emergence of probability” made it possible to ask, in place of “Can the truth of Christianity be demonstrated?”, or “Is it supported by authority?”, questions such as “Is it likely that the Gospel narrative is accurate?” and “How good is the evidence for God's existence?” Modern irreligion may be said to be born with these new questions. (1990, 193) I agree that the seventeenth and eighteenth centuries saw a decisive turn from the first to the second set of questions. But I also see a double irony in the facts that the most subtle and interesting arguments offered by theists of this era relied on the emergence of probability and that the irreligion promoted by Hume's attempts to answer the second set of questions is, in a word, sophomoric when examined under the lens of Bayesianism. 11 Bayes and Bayesianism John Earman There are many forms of Bayesianism, perhaps more forms than there are practicing Bayesians. But all of the adherents of this persuasion share two central tenets, and many subscribe to a third. First, epistemology is most fruitfully discussed not in terms of all-or- nothing belief but in terms of degrees of belief. Second, rational degrees of belief should be regimented according to the probability calculus.46 Bayes' (1763) essay contains a nascent form of what has come to be known as the Dutch book argument for this tenet, the idea being that if an agent's degrees of belief violate an axiom of probability, then she can be bilked in the sense that she can be presented with a finite set of bets, each of which she judges as fair, but with the net effect that she is guaranteed to lose money come what may.47 Third, when an agent has a learning experience and the content of the experience is fully captured by a proposition E, then the agent's degree of belief function Pr new after the learning experience is related to her degree of belief function Pr old before the learning experience by the rule of conditionalization: Pr new (·) = Pr old (·/E), where the conditional probability Pr(Y/X) is defined by Pr(Y&X)/Pr(X) when Pr(X) ≠ 0.48 If Pr old reflects previously acquired knowledge K, that is, Pr old (·) = Pr oldold (·/K), then Pr new (·) = Pr oldold (·/K&E). From here on I will drop the temporal subscripts on probabilities. The temporal aspect continues to be reflected in the evidence statements that appear to the right end p.26 of the slash in the conditional probability. Although the rule of conditionalization is not looked upon by all Bayesians of being on a par with the probability axioms as a condition sine qua non for rationality, it seems to me fair to apply it to Hume.49 What is now called Bayes' theorem shows how the acquisition of new knowledge impacts on the agent's degrees of belief: • (1) • Given the definition of conditional probability, (1) is a trivial consequence, but one with profound implications. In applications, it is helpful to think of H as the hypothesis at issue, K the background knowledge, and E as the new evidence. Pr(H/K&E) and Pr(H/K) are called, respectively, the posterior and prior probability of H.50 Pr(E/K&H) is called the likelihood of H; it is a measure of how well H explains E. Pr(E/K) is variously called the prior likelihood or the expectancy of E; it is a measure of how surprising the new evidence E is. Using the principle of total probability (see Appendix), (1) can be recast in a form that is useful in many applications: • (2) • For Bayesians, the explanation of the truisms of confirmation and induction are most often to be traced back to an application of (1) and (2).51 Even if Hume had read Bayes' essay, he would not have found Bayes' theorem there, for the theorem that bears Bayes' name was the invention of later writers. What Hume would have found was the recognition of the importance of prior probabilities for inductive reasoning. And here we reach a divide in Bayesianism: the subjectivists, who take the position that there are no constraints on priors, other than the axioms of probability vs. the objectivists who hold that there are additional constraints. Bayes belonged to the latter camp, at least for the particular type of inductive inference studied in his essay. Consider a repeatable process (such as coin flipping) that is characterized by a fixed objective chance p, 0 ≤ p ≤ 1, of yielding an outcome with a property B on each trial. (The set up corresponds to what modern statisticians call independent and identically distributed [IID] trials. To match up with the previous discussion, take the property A to be that of being an outcome of this IID process.) The problem Bayes set himself then is this: Given that in n trials m of the outcomes are B (denote this evidence by E(m, n)), what is the rational degree of belief that p lies between given limits? The answer is fixed if, and only if, the prior (degree of belief) probability distribution over the objective chance parameter p end p.27 is given. Bayes supplied an ingenious argument for the conclusion that in the absence of any further background information about the process, other than that it yields IID trials (K), the prior distribution over p should be uniform. The answer to Bayes question is then • (3) • The reader who is unfamiliar with the integral calculus should not be dismayed because what will concern us here is not (3) itself but an application. This application is reached by asking another question. Suppose that n trials are run, all of which yield B outcomes (E(n, n)). What is the probability that the next r trials will all yield B outcomes (H(r)), given the evidence of the previous outcomes? It follows from (3) that • (4) • which is commonly called Laplace's rule of succession. Neither Bayes nor Price derived (4). But in his Appendix to Bayes' essay, Price did work out an instance of (3) that was surely intended to be a response to Hume's skeptical attack on induction. Here is Price's description of the problem and his solution: Let us imagine to ourselves the case of a person just brought forth into this world, and left to collect from his observations of the order and course of events what powers and causes take place in it. The Sun would, probably, be the first object that would engage his attention: but after losing it the first night he would be entirely ignorant whether he would ever see it again. He would therefore be in the condition of a person making a first experiment about an event entirely unknown to him. But let him see a second appearance or one return of the Sun, and an expectation would be raised in him of a second return, and he might know that there was an odds of 3 to 1 for some probability of this. (Bayes 1763, 312–313) On Price's way of analyzing this situation, there is only one relevant trial (m = n = 1) since the first observation is needed to acquaint the observer with the sun. If we take “some probability” to mean that p ≥ 0.5, then (3) yields the value of 3/4 or, as Price said, odds of 3 to 1. Bayes' prior probability assignment is open to challenges, but I will not be concerned with them here.52 What I do want to call attention to is the curious blend of inductivism and anti-inductivism that flows from Bayes' analysis. From (4) it follows that if all of the first n trials have yielded Bs, then the probability that the next trial will also yield a B is (n + 1)/(n + 2). So as n → ∞, the probability that the next instance will be a B approaches 1—inductivism at work. But, as will be seen in the next section, it follows from Bayes' assignment of priors that the probability end p.28 Hume's sin—which goes in the other direction—was much worse. His straight rule of induction is both descriptively inadequate to actual scientific practice, and it is stultifying to scientific inquiry. Among the zillions of protons observed by particle physicists, none has been verified to decay. But particle physicists do not assign a probability of 1 to the proposition that the next proton to be observed will not decay, and they certainly do not think that they have adequate inductive grounds for probabilistic certainty with respect to the general proposition that no proton ever decays—otherwise the expenditure of time and money on experiments to detect proton decay would be inexplicable on the standard expected utility model of decision making. The general situation is this. If constant and uniform experience E speaks in favor of the lawlike generalization L, then by Hume's straight rule Pr(L/E& K) = 1. Thus, if M express an exception to L, Pr(M/E& K) = 0. It follows that for any further evidence E′, eyewitness or other, that intuitively should count in favor of M, either Pr(M/E′& E& K) = 0 or else Pr(M/E′& E& K) is not defined, in which case Pr(E′/E& K) = 0. In either case further inquiry into events that would undermine L is useless,54 for any potential positive evidence against L would either be rejected as probabilistically impossible or else would not help to raise the credibility of an exception to L above zero.55 Is this a result that Hume intended? Strictly speaking, the question is meaningless since Hume does not explicitly use the language of conditional probability. Nevertheless, there is both positive and negative evidence about whether Hume intended a consequence like this one. On the positive side, there is Hume's discussion in Part 2 of “Of Miracles” of the hypothetical story of Queen Elizabeth's resurrection (see section 18), Cardinal de Retz's story of the recovery of a leg by rubbing holy water on it, and of the Jansenist miracle stories. Hume praises Cardinal de Retz for giving no credence to the story he related: He considered justly, that it was not requisite, in order to reject a fact of this nature, to be able accurately to disprove the testimony, and to trace its falsehood, through all of the circumstances of knavery and credulity that produced it. . . . He therefore concluded, like a just reasoner, that such evidence carried falsehood on the very face of it, and that a miracle supported by any human testimony, was more properly a subject of derision than of argument. (E 124; 149) end p.31 And about numerous corroborative witnesses to the Jansenist miracles, he writes: “And what have we to oppose to such clouds of witnesses, but the absolute impossibility or miraculous nature of the events, which they relate? And this surely, in the eyes of all reasonable people, will alone be regarded as a sufficient refutation” (E 125: 149). On the negative side, there is the fact that maintaining such a position appears dogmatic. And not surprisingly, Hume does try to distance himself from such dogmatism. When uniform experience supports a law statement L that is contradicted by testimony. Hume speaks of putting “proof against proof, of which the strongest must prevail, but still with a diminution of its force, in proportion to that of its antagonist” (E 114: 143). This idea is reiterated in the letter to Blair quoted above in section 9. After claiming to provide a proof against miracles that “implies no doubt,” he adds: “[B]ut there are degrees of this species [of proof], and when a weaker proof is opposed to a stronger, it is overcome” (L, Vol. 1. 350). But if the weighing of proof against proof is to be done within the ambit of the probability calculus and the rule of conditionalization,56 then Hume's straight rule has to be dropped—his proof in favor of L by uniform experience cannot be taken to mean probability 1 but at most a high probability that is short of 1. Consequently, uniform experience does not furnish a proof against a miracle in the sense of making the conditional probability of its occurrence flatly zero, although this probability may be very, very tiny. Such a concession is far from tiny since it would mean that the distinction between a (Hume) miracle and a marvel is a matter of degree rather than of kind. And once the concession is granted, it is natural to wonder how it can be that testimonial evidence can ground belief in marvels but not in (Hume) miracles. One response to this challenge involves a partial retreat: grant that for a miracle statement M, Pr(M/E&K) can be greater than zero and that testimonial evidence t(M) to M can suffice to make Pr(M/t(M)&E&K) > 0.5, at least for some cases of secular (Hume) miracles; but maintain that, because of the special features of cases of (Hume) miracles with alleged religious significance, testimonial evidence can never suffice to make Pr(M/t(M)&E&K) > 0.5. In section 16. I will present the evidence that Hume opted for this position in Part 2 of his essay. But before turning to that matter, it is worth examining a case that many of Hume's critics have taken as a vivid illustration of how the account of induction underlying Hume's “proof” against miracles serves to stultify empirical enquiry. I refer to the Indian prince. end p.32 14 The Indian Prince John Earman Hume's critics have found innumerable ways to underscore Richard Price's point (see FD 405ff; 163) that unless testimonial evidence is allowed to overcome prior improbabilities, there is no way to underwrite the sorts of inferences made in everyday life and in science. We would not give much credence to a newspaper report of the number of the winning ticket in a fair lottery with odds of millions to one; we would not, as Richard Whately noted in his delightful satire “Historical Doubts Relative to Napoleon Bonaparte” (1819), give credence to the reality of a figure whose career is marked by so many fantastical adventures, etc. Hume apologists tend to respond by citing the miracle vs. marvel distinction and by claiming that there is no problem here since the examples in question fall on the marvel side of the cut. That is fair enough. In his History of England (1754– 1762) Hume wrote: “It is the business of history to distinguish between the miraculous and the marvelous; to reject the first in all narrations merely profane and human; to doubt the second; and when obliged by unquestionable testimony . . . to admit something extraordinary, to receive as little of it as is consistent with the known facts and circumstances” (128). What is not fair is the hocus pocus that apologists and Hume himself have used in an attempt to deal with examples that certainly appear to fall on the (Hume) miracle side of the cut. Just such a case arises for the Indian prince. Hume's Indian prince, who had never experienced a cold climate and refused to believe reports of the effects of frost, is undoubtedly an indirect reference to Locke's story of the king of Siam.57 But the example and the point it raises is hardly original to Locke. A good part of St. Thomas More's Dialogue Concerning Heresies (1557) is devoted to combating the notion that reports of miracles are to be dismissed because they seem to be contrary to nature and reason.58 Not surprisingly, India turns up in one of his illustrations: If there were a man of Inde y1 neuer cam out of his country nor neuer had sene any whyte man or woman in his lyfe & syth he seeth innumerable peple blak he mygt wene that it were agaynst the nature of man to be whyte. Nowe yf he shall bycause nature semeth to shewe hym so byleue therfore that all the worlde lyed yf they wolde say the contrary who were in the wronge he that byleueth his reason and nature or they y1 agaynst his of reason and nature shall tell hym as it is of trouthe? (65) Here then is the challenge for Hume: if there is a principled objection to allowing testimony to count in favor of a resurrection, will not the end p.33 same objection also lead to the (absurd?) result that the Indian prince was rational in not allowing testimony to count in favor of the claim that water can become so hard as to bear up the weight of an elephant? Since the challenge is so obvious and since there were so many variants in the literature of the time, it is surprising that Hume did not take it up in the first edition of the Enquiry.59 Hume's silence in the face of this well-known challenge was criticized by implication in Skelton's Ophiomaches (1749), which Hume had read in manuscript form.60 Thus, it can hardly be a coincidence that in the 1750 edition of the Enquiry Hume's Indian prince makes an appearance. Hume obviously did not think that the extra paragraph he added to the 1750 edition sufficed because he later penned a note that was printed on the last page of the new edition along with the explanation that “The distance of the Author from the Press is the Cause, why the following Passage arriv'd not in time to be inserted in its proper place.” In subsequent editions this note is printed as a footnote. It is difficult to tell whether haste or deliberate obfuscation was responsible for the resulting mess. Hume begins by saying that the prince, “who refused to believe the first relations [i.e., reports] concerning the effects of frost, reasoned justly” (E 113; 143). How so? The prince was right to be suspicious of reports of a solid form of water. But Hume's account of induction seems to imply not just suspicion but outright rejection. Hume does say that “it naturally required very strong testimony to engage his [i.e., the prince's] assent to facts, that arose from a state of nature, with which he was unacquainted, and which bore so little analogy to events, of which he had constant and uniform experience” (E 113– 114; 143). How Hume thinks that further testimony can justly win the assent of the Indian prince but cannot justly win assent in cases of religious miracles will be discussed in due course. Here I am concerned with Hume's attempt to muddy the waters of the Indian prince. Hume's first move is to distance himself from Locke, on whose analysis the Dutch ambassador related facts that were “contrary” to the experience of the king of Siam (recall section 7). Hume says that the similar facts related to the Indian prince, “though they were not contrary to his experience, they were not conformable to it” (E 114; 143). This is a distinction which many commentators from Campbell (1762) on down have found sophistical. And understandably so: Why isn't the passing of water from a liquid to a solid state just as contrary to the prince's experience as the springing to life of a dead more sensible suggestion is that the inductive leap should be made less daring by modifying the original straight rule to require not only that the number of instances be sufficiently large but also that they come from a variety of circumstances and/or that they constitute a representative sample of the entire reference class. That would indeed be an improvement, but improvements of this kind do not avoid the Indian prince embarrassment. That embarrassment will always resurface in more complicated examples as long as the rule of induction yields a probability-one conclusion for a universal generalization from finite data. On the other hand, if Hume's straight rule of induction is modified so as to escape this embarrassment by assigning a probability less than 1, then Hume no longer has a “proof” against miracles, nor a principled distinction between miracles and marvels, and the way is opened for testimonies to establish the credibility of resurrections and the like. Commentators seem unable to appreciate this basic point. A good example is found in John Stuart Mill's attempted rescue of Hume in System of Logic (Bk. III. ch. 25) from the Indian prince embarrassment. When Hume says that the stories the Indian prince found marvelous were “not contrary to his experience,” Mill takes him to mean that the facts related are not contrary to any “law of causation” known to the prince. Mill himself employs a straight rule of induction for establishing that A causes B. To be sure, his rule is more complicated than Hume's since the uniform experience needed to instantiate Mill's rule must support the generalizations that correspond to Mill's Methods of Agreement. Difference, Residues, and Concomitant Variation. But when the uniform experience in favor of these generalizations is weighty enough. Mill speaks of a “complete induction” for the law of causation, and any alleged fact that contradicts a (presumptive) law of causation supported by a complete induction is “to be disbelieved totally” (System of Logic, 439). This is the same stultifying result that flows from Hume's less sophisticated straight rule. Mill did not succeed in showing how Hume's straight rule of induction can be jiggled so as to exclude the kinds of miracles Hume wanted to banish while also allowing for scientific progress. Finally, it is worth reflecting on what Hume says about analogy. In the paragraph added to the main text of the 1750 edition, Hume seems to be saying that frozen water bears some positive analogy to the states of nature with which the prince is acquainted, although the analogy is very weak. However, the appended note seems to say that there is no positive analogy: One may sometimes conjecture from analogy what may follow; but still this is conjecture. And it must be confessed, that, in the present case of freezing, the event follows contrary to the rules of analogy, and is such that a rational Indian would not look for. The operations of cold upon water are not gradual, according to the degrees of cold; but whenever it comes to the freezing point, the water passes in a moment, from the utmost liquidity to perfect hardness. (E fn 114; 153–54) end p.37 The notion of analogy is vague enough to allow such seemingly contradictory intuitions. But it seems to me that the most sensible reaction is that unless the prince was completely hidebound, he must have had experiences that furnish a positive analogy. I refer to phase changes. In India, as elsewhere, water vapor condenses as the temperature falls, and molten metal solidifies as it cools. If F is the hypothesis that water solidifies at low temperatures, E records the prince's past experiences in which water never freezes, and K records the experiences of the just mentioned phase changes, then the positive analogy suggests that Pr(F/E&K) be set above 0. If the analogy here is regarded as weak, then Pr(F/E&K) should not be set much above 0 so that, as Hume says, very strong testimony would be needed to boost the probability of F to a respectable level. All of this is interesting, but how does it help Hume? He could modify his straight rule so as to confer a probability of 1 on a presumptive (or strongly presumptive) law if and only if there is no positive analogy in favor of an exception. Call such a presumptive law a presumptive hard law, and call a violation of such a law a hard Hume miracle. Hume could then maintain that testimony to hard miracles is to be rejected while allowing that testimony may overcome doubts about the softer variety of miracles. And further, he could hold that the miracles scientists are willing to entertain—violations of conservation of energy, say—are soft miracles, whereas miracles that lie at the heart of religions—the raising of a dead man, the turning of water into wine, etc.—are hard miracles. I must admit that I find a certain appeal to this line. But I am dubious that it can lead to the kind of “proof” against religious miracles that Hume wanted. The notion of analogy is so elastic that in any moderately complex situation one can always find positive and negative analogies. If one sees a positive analogy for a solid form of water in other phase changes, why not see a positive analogy for resurrection in near death experiences, catatonic states, and the like? 15 Hume's Maxim John Earman Toward the end of Part 1, Hume announces 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 endeavours 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. (E 115–116; 144) end p.38 Hume's Maxim begs to be made precise by translating it into the language of probability theory. There should be no surprise, however, in finding that a number of inequivalent translations are possible since seemingly transparent English statements about the credibility of events turn out to be hiding ambiguities about conditional probabilities.63 But while there may be no single ‘correct’ translation of Hume's Maxim, some seem to me, for both technical and contextual reasons, to be preferable to others. At the start, I stipulate that I am mainly interested in translations that take “establish a miracle” to mean make credible rather than to make certain. The opposite reading has, as we will shortly see, certain advantages for Hume, but it also carries the major drawback of making the Maxim useless against opponents, of which there were many in the eighteenth century, who are willing to eschew certainty in favor of reasonable belief. Before dealing with modern translation attempts, it is well to see what Hume's contemporaries thought. In Four Dissertations, Price paraphrased the first part of Hume's Maxim as: “[T]hat no testimony should engage our belief, except the improbability in the falsehood of it is greater than that in the event which it attests” (FD 405: 163). In the language of conditional probability Price apparently took this paraphrase to mean either that • (P) • or else that • (P′) • That Price thought that the conditional probability of M. Pr(M/E&K), prior to testimony belongs on the left-hand side of the inequality, is clear: Let it be remembered, that the improbability of the event here mentioned, must mean the improbability which we should have seen there was of its happening independently of any evidence for it, or, previously to the evidence of testimony informing us that it has happened. No other improbability can be meant, because the whole dispute is about the improbability that remains after the evidence of testimony given for the event. (FD fn 405; 174–75) But what he thought belongs on the right-hand side is less clear, although (P) fits best with the text. He posits as an example that the “testimony informed us rightly ten times to one in which it deceived us,” and asserts that under this supposition there would be a “probability of ten to one for the reality of every fact supported by testimony” (FD 406– 407; 163). A plausible reading of this passage is that Price is using frequency data to justify setting Pr(¬ M/t(M)&E&K) = 1/11. He then goes on to claim that this case provides a counterexample to Hume's Maxim, which would make sense if (P) is taken as the translation. For assuming that Pr(M/E&K) end p.39 is low—say, one in a million—(P) fails although the testimony renders the miracle credible since in this case Pr(M/t(M)&E&K) = 10/11. The reader can easily supply an example to show that (P′) likewise fails as a necessary condition for testimony to establish the credibility of a miracle. ((P′) does come close to being a necessary condition for testimony to establish the credibility of a miracle since Pr(M/t(M)&E&K) > 0.5 implies that Pr(M/E&K) > Pr(t(M)/¬ M&E&K)× Pr(¬ M/E&K) and since Pr(¬ M/E&K) = 1 − Pr(M/E&K) will be close to 1 if M is a miracle statement.) However, it is worth noting that (P′) is a necessary condition for Pr(M/t(M)&E&K) = 1,64 so that if, contrary to my stipulation. Hume takes “establish” in this context to mean render certain rather than render credible, then (P′) would seem to be a sensible reading of the Maxim. However, we may safely assume that Pr(M/E&K) < 1—otherwise M momentous the affair is, or is esteem'd, so much more plain, and certain, should be the evidence” (RJC 63; 134). But it is risible to attribute to either Hume or Annet some deep insight. All of the parties on the opposite side from Hume in the eighteenth-century debate on miracles knew that miracle claims could not be established without the help of very strong evidence. In some cases they thought they had produced the required evidence. Perhaps they were wrong. But to show that they were wrong takes more than solemnly uttered platitudes. What additional principles or facts did Hume need to move from the platitude that forms the first part of Hume's Maxim to the conclusion that it is impossible or even difficult to establish the credibility of a miracle? That the prior Pr(M/E&K) is zero would sufficient, but I have already rejected this move. That Pr(M/E&K) is nonzero but very small does not seem sufficient, as Price himself was quick to argue. He pointed to the degree of [prior] improbability which there is against almost all the most common facts, independently of the evidence of testimony against them. In many cases of particular histories which are immediately believed upon the slightest testimony, there would have appeared to us previously to this testimony, an improbability of almost infinity to one against their reality. . . . It is then very common for the slightest testimony to overcome an almost infinite [prior] improbability. (FD 406; 163) Hume has two options here. He could challenge Price's claim in general. And in effect Hume does this with his own claim that the probative value of the evidence of testimony to an event is diminished by prior improbability of the event (see section 17). Or he could counter that although Price's claim is correct for some cases, it fails in cases of miracles with alleged religious significance because of the special features of these cases (see section 16). But before turning to these matters a few words should be said about the second half of Hume's Maxim. end p.42 The first half of the Maxim admits a probabilistic reading that makes this part of the Maxim into a correct though nearly tautologous principle. But then the second half of the Maxim appears to be nonsensical. Recall that it says that “even in that case there is a mutual destruction of arguments, and the superior only gives an assurance suitable to the degree of force, which remains, after deducting the inferior.” The italicized phrase suggests that even when the testimony is of such a kind that its falsehood would be more miraculous than the fact which it endeavours to establish there is still a further destruction of arguments. Such talk appears to involve an illicit double counting: the weighing up of the countervailing factors in t(M) and in E&K has already been done, and if the result is that Pr(M/t(M)&E&K) > 0.5, then that's the way it is, and no further subtraction is called for. Hume uses the idea of a “destruction of arguments” and the need to “deduct” or “subtract” the force of the one from the other throughout his essay. My contention is that such talk is out of place in the Maxim. It turns up again in Part 2 of the miracles essay, first, in the claim that in the case of popular religions the subtraction “amounts to an entire annihilation” (see section 16) and, second, in his contrary miracles argument (see section 23). In these instances, my contention is that the idea is appropriately but crudely applied. Commentators from Campbell (1762) onward have complained about the crudity. The only precise way to evaluate the complaints is to turn the handle on Bayes's theorem and crank out the posterior probability on the total evidence. The result is not always what Hume wants it to be.67 16 What Is Hume's Thesis? John Earman At this juncture, readers may be puzzled about what Hume's thesis is, especially if they are operating under the principle of charity which presumes that such an acute philosopher as Hume must have had some claim in mind that is interesting but not glaringly false. I am all for charity, but in this instance charity requires a real stretch. We have seen that in Part 1 of “Of Miracles” Hume claims to offer a proof against miracles that is “as entire as any argument from experience can possibly be imagined.” The proof, such as it is, applies to all miracles whether of a religious or a secular nature. Why doesn't Hume's essay end there? Why did Hume need to add a Part 2 that is twice as long as Part 1? Because the proof from experience is not the final word since it may be opposed by a proof from testimony. Part 2 is concerned with how this contest of opposing arguments plays itself out, especially in cases of alleged miracles deemed to have religious significance. What is Hume's thesis about the outcome of such contests? Throughout Part 2. Hume end p.43 bobs and weaves, shifting among several different claims against the possibility of establishing the credibility of a miracle. This shiftiness is. I think, symptomatic both of Hume's uncertainty about what he wanted to prove and also of his (perhaps unconscious) doubts about what his arguments establish. I can put my charge sharply, if somewhat unfairly, by posing a dilemma for Hume. There is a weak version of his thesis that is surely correct, but it amounts to no more than a collection of platitudes that hardly require a philosophical dissertation for support. There is a very strong version of his thesis that is far from platitudinous; indeed, it is patently false. Part 2 contains attempts to escape between the horns of platitude and patent falsity. The way is narrow. I will eventually take a path that Hume would not have found uncongenial (see section 20). But unlike Hume. I do not think that this path leads to a philosophical high ground that justifies the self-congratulatory remarks at the beginning of Hume's essay. To begin, we can read Part 2 on one level as a cautionary sermonette. Reflect, oh gentle reader, on mankind's passion for surprise and wonder; reflect on our susceptibility to deception and self-deception, which is heightened when religious enthusiasm is present; reflect on the fact that the religiously converted may be tempted to use deception to promote a holy cause; and finally, reflect on the fact that miracles abound chiefly “among ignorant and barbarous nations” (E 119; 146). Such reflections should make us think twice before accepting reports of miracles and thrice when the alleged events are thought to have religious significance. Platitudes have their uses, and it doesn't hurt to repeat this one. But Hume's repetition of it does not serve to advance the eighteenth century discussion of miracles since all parties to the debate would have readily agreed to it— indeed, even the proponents of religious miracles enunciate versions of it. The platitude under discussion can be given various useful forms by means of the probability calculus. For example, the probabilistic translation (C) of the condition for testimony to establish the credibility of a miracle can be shown to be equivalent to • (C′) • The Humean sermonette based on (C′) goes as follows. Suppose that uniform experience as codified in E is very strongly in favor of a presumptive law of which M states an exception. So as not to stultify the Bayesian version of enquiry, assume that Pr(M/E&K) is greater than o but very small (e.g., 10−20). Suppose further as part of the background knowledge K that the witness is a religious enthusiast who takes the alleged miracle in question to have religious significance. Such a person can be expected to shout it to the world if he actually observed the miraculous event, so that if the background knowledge K indicates that the witness is in a favorable position to observe the event if it occurs, then Pr(t(M)/M&E&K) end p.44 should be very close to 1. Thus, the factor [] in (C′) will be close to unity. As a consequence, (C′) will surely fail if Pr(t(M)/¬ M&E&K) is substantially greater than Pr(M/E&K) (= 10−20). And Pr(t(M)/¬ M&E&K) will be non-negligible for religious enthusiasts who have a tendency to testify to the miraculous event when it doesn't occur, either because they have been deceived or because they resort to the use of deceit to win over the unconverted. Having said all of this, we still haven't escaped the realm of the platitudinous, although the platitude has been given a useful quantitative form. Nor has anything been said to raise disagreement from Hume's opponents. For the probability calculus is perfectly compatible with values for the relevant probabilities for which (C′) does hold; and, of course. Hume's opponents will claim that the details of some actual cases of reported religious miracles makes these values reasonable. Hume certainly escaped the platitudinous when he made the very strong claim, in editions of the Enquiry prior to 1768, that “no Testimony for any kind of miracle can ever possibly amount to a Probability, much less to a Proof; and that even supposing it amounted to a Proof, 'twould be opposed by another Proof, deriv'd from the very Nature of the Fact, which it would endeavour to establish” (1748, 198–199). In this context the element of divine intervention in Hume's second definition of ‘miracle’ is irrelevant since Hume is talking about naturalistically characterized events, such as the return to life of a dead man. Under this reading Hume's very strong claim is false, or so I have argued. In the 1768 edition Hume substituted “has ever amounted to” for “can ever possibly amount to.” Was the recognition of a need for a retreat occasioned by Price's Four Dissertations (1767) and Hume's conversations with Price? The timing and Hume's complimentary remarks about Price (see section 10) might seem to suggest a positive answer. However, the situation is unclear, for, as will be seen presently, even in the original 1748 edition Since Pr(t(M)/M&D&E&K) = 0 and Pr(t(M)/M&¬ D&E&K) = 1, we have that Pr(t(M)/M&E&K) = Pr(¬ D/M&E&K). Similarly, Pr(t(M)/¬ M&E&K) = Pr(D/¬ M&E&K). So under our suppositions, (6) becomes end p.47 • (8) • For (8) to be greater than 0.5, it must be that []{} < 1. But since M contradicts a presumptive law, Pr(M/E&K) will be very small and, thus, [] will be huge. So to make []{} < 1, {} must be tiny. But in typical cases, Pr(D/M&E&K) is small (e.g., our religious enthusiast is not apt to be deceived into thinking that there is no walking on water when actually presented with such a phenomenon), so that the denominator of {} is close to 1. So unless Pr(D/¬ M&E&K) is small enough to balance off the hugeness of [], Pr(M/t(M)&E&K) will not be greater than 0.5. Hume can be read as declaring that his personal probabilities are such that Pr(D/¬ M&E&K) is significantly different from zero in every case of the kind in question. He is entitled to his opinion, but then so are others who, in some cases at least, assign Pr(D/¬ M&E&K) a small enough value that Pr(M/t(M)&E&K) > 0.5. The subjectivist form of Bayesianism offers no adjudication since it appears that both assignments are consistent with the probability axioms and the rule of conditionalization. The objectivists can hold out hope of a resolution by demanding a conformity of degrees of belief to frequency data, where available. Hume's review of miracle stories in Part 2 can be seen as an attempt to gather such data; but if so, the attempt is crude since not enough information is given to determine whether or not the witnesses were in fact deceived. And as with all frequency data, the reference class is crucial. It would not be very surprising to find, in concert with Hume's cynicism, that the relative frequency with which religious enthusiasts in general have been deceived into thinking that a miracle occurred when it did not is high. But the relevant reference class may be narrower than this. Imagine, for example, that K specifies that the witnesses in question hold that religious conviction should be based on faith or prudential considerations rather than miracles, and that they are determined to make sure that false miracles do not pollute the canon. It would not be surprising to find that the frequency with which this class of witnesses is deceived into thinking that a miracle has occurred when in fact it hasn't is quite low. I will have more to say on these issues in section 20, where I indicate a rare point of agreement with Hume. The best way to summarize this section is with a challenge. Commentators who wish to credit Hume with some deep insight must point to some thesis which is both philosophically interesting and which Hume has made plausible. I don't think that they will succeed. Hume has generated the illusion of deep insight by sliding back and forth between various theses, no one of which avoids both the Scylla of banality and the Charybdis of implausibility or outright falsehood. end p.48 17 Hume's Diminution Principle John Earman I have argued at some length that Hume's blunderbuss arguments against miracles are ineffective and that his ambition to provide a “proof” against miracles is based on an impoverished conception of inductive inference. But “Of Miracles” is dotted with a number of smaller arguments and less ambitious goals that are of considerable interest both in their own right as well as for their implications for their miracles debate. When testimony is offered in favor of a marvelous or a miraculous event, Hume speaks of a “contest of two opposite experiences; of which the one destroys the other as far as its force goes” (E 113; 143). The contest is supposed to be guided by what I will call Hume's diminution principle: “the evidence, resulting from the testimony, admits of a diminution, greater or less, in proportion as the fact is more or less unusual” (E 113; 142). The corollary we are invited to draw is that in the case of a miraculous event, the diminution is so great that the probative value of the testimonial evidence is lost: “I should not believe such a story were it told me by Cato: was a proverbial saying in Rome, even during the lifetime of that philosophical patriot. The incredibility of a fact, it was allowed, might invalidate so great an authority” (E 113; 143). It might seem that Hume's diminution principle is a consequence of Bayesianism. Bayes theorem shows that Pr(M/t(M)&E&K) = Pr(M/E&K)xX—that is, the posterior probability of the miracle after testimony is directly proportional to its prior probability. If Pr(M/E&K) were flatly zero, Hume's desired corollary would follow immediately, but that possibility has already been dismissed because of its unpalatable consequences. Leaving aside the intended corollary, what of the diminution principle itself? If Pr(M/E&K) is not zero, it is surely very small—just by definition of a miracle or a marvel—and since the posterior probability of M is proportional to Pr(M/E&K), does it not follow that the force of the testimonial evidence t(M) is diminished in proportion as the event reported in M is unusual? No. Nevertheless there is something correct about Hume's diminution principle. But the valid core depends not just on the prior improbability of M but also on those factors that tend to make eyewitness testimony unreliable. A good place to begin the discussion is with Price's attempt in his Four Dissertations to refute the diminution principle. Price's counterclaims are that “improbabilities as such do not lessen the capacity of testimony to report the truth” and that “the only causes of falsehood in testimony are the intention to deceive, and the danger of being deceived” (FD 413; 165). In cases where the former is absent, Price claims that the testimony “communicates its own probability” to the event, whatever its prior probability end p.49 (FD 414; 00). So for instance, if past experience shows that the witness is apt to be wrong only one times in ten, then (Price contends) the posterior probability of the event, given the testimony and the background knowledge, is 0.9, no matter how small the (nonzero) prior probability of the event. The type of case Price had in mind is that of a lottery, a case that was thoroughly analyzed by Pierre Simon, the Marquis de Laplace in his Philosophical Essay on Probabilities (1814). Tickets numbered 1 to N are put in a box, and a random mechanism is used to select one of the tickets, which is then replaced and mixed with the other tickets. After each draw, a witness reports on the number drawn. It is found that in the long run she is wrong one time in ten. Let P n be the proposition that ticket #n was drawn on some particular occasion. Suppose that on this occasion the witness announces that #79 was the winning ticket. Our job is to calculate Pr(P 79 /t(P 79 )&K). Using a by now familiar form of Bayes' theorem and setting Pr(P 79 /K) = 1/N, we have • (9) • If we want our degrees of belief to reflect the relevant frequency data, we should set Pr(t(P 79 )/P 79 &K) = 0.9. The sticking point is the numerator of the [] term in (9). Using the principle of total probability, we find that • (10) • So (9) becomes • (11) • Here we are stuck until we are given further information about the witness's tendencies in cases where she misreports. If we suppose that when she misreports, there is no tendency to report any one number among the N − 1 false numbers rather than another, then for any n ≠ 79, Pr(t(P 79 )/P n &K) = .1/(N − 1), which is the probability of misrepresenting equally divided among the N − 1 false possibilities.69 Putting this value in (11) results in Pr(P 79 /t(P 79 )&K) = 0.9, and just as Price claimed, the testimony “communicates its own probability” to the event. This result is independent of the prior probability of P 79 , Pr(P 79 /K) = 1/N, which can be made as small as you like by making N large enough. Thus, Hume's diminution principle fails in this case. However, this result does not hold if the witness has, to use Laplace's phrase, “some interest in choosing 79 among the numbers not drawn” (PEP 111; 195). If, for example, the witness made a side bet on 79 and is tempted to collect the stakes of the bet by falsely announcing 79, then the posterior probability of P 79 can be considerably reduced. Price was aware of this pitfall—recall that he was careful to specify that his claim is conditional on the assumption that, although the witness may herself be deceived, she has no motive to deceive others. witness (who may misperceive or lie) there is a story which should not be held to be more likely than not if told by that witness. But just as clearly the moral is wrong if it is taken to mean: There is a story so a priori improbable that there is no possible witness such that the story is made more likely than not by the testimony of the witness. For whatever the choice of N, as long as it is finite, there are values of p′ e and p′ ℓ different from 0 but sufficiently small that Pr(W/t(W)&E&K) > 0.5. On Hume's behalf it can be replied that mathematically possible witnesses are beside the point and that, in actual fact, the psychological profiles of religious enthusiasts make them incapable of reducing the probabilities of error and deceit to low enough values so as to balance the diminution effect and to ground the credibility of religious miracles. Hume clearly believed some proposition in the neighborhood of this one, and his recitation of the checkered history of attested miracles is supposed to provide some inductive evidence in its favor. But “Of Miracles” will be searched in vain for a convincing general argument for it.70 For the sake of completeness, I should mention an entirely different sort of diminution effect taken up by Hume in the Treatise. If testimony is transmitted down a chain of witnesses and if the force of the testimony is diminished with each successive link, then the original testimony “must in the end lose all of its force and evidence” (T 145) if the chain is long enough.71 Here Hume represents himself as defending the Christian religion against a “celebrated argument,” his counterargument being that the evidential value of the Gospel stories is not fatally compromised since in this instance the links in the chain are “all the same kind, and depend on the fidelity of Printers and Copyists” (T 146). It is not unlikely that Hume was willing to put up this defense in order to ward off what he saw as a greater danger. John Craig (1699) had used an estimate of the rate of diminution of successive links to calculate a date for the Second coming, his assumption being that Christ would appear again before the evidential value of the Gospel stories is extinguished. Hume's defense undercuts Craig's basis for expecting a Second Coming.72 18 Multiple Witnessing John Earman One way in which the diminution effect can be countered is by piling up the number of witnesses. Attempts to quantify the effects of multiple witnesses started very early. An especially interesting example is contained in an anonymous essay entitled “A Calculation of the Credibility of Human Testimony” published in the 1699 volume of the Philosophical Transactions of the Royal Society (London).73 Suppose that each of N “concurrent reporters” gives an assurance of a of the arrival of a ship or a end p.53 gift to me of £ 1200. It is asserted that together the witnesses give an “assurance” (probability) of 1 − (1 − a)N. For (the reasoning goes), the first gives an expectation of a· £ 1200, leaving (1 − a)· £ 1200 unassured. Of what is left unassured, the second witness gives an assurance of a(1 − a)· £ 1200, leaving (1 − a)(1 − a)· £ 1200 unassured, etc. In the end, £ 1200 − (1 − a)N· £ 1200 remains unassured. Dividing this expectation by £ 1220 gives a probability of 1 − (1 − a)N. On this analysis, multiple witnessing is very powerful indeed: for no matter how small a is, as long as it is greater than 0, 1 − (1 − a)N can be made as close to 1 as you like by making N large enough. Karl Pearson (1978, 467–468) approved of this result, but stated that it can be obtained more simply in the following way. Suppose for simplicity that the witnesses never misperceive but may lie. Then the event in question fails to occur just in case every one of the N witnesses lies. If the witnesses are independent, the probability of such mass cretinism is said to be (1 − a)N, and thus, by the negation principle, the probability of the event is 1 − (1 − a)N. This reasoning is seductive but potentially misleading. That each witness gives an assurance of a for the gift G presumably means that Pr(G/t i (G)&E&K) = a for i = 1, 2, . . . , N, where t i stands for the testimony of witness i. If the independence of witnesses meant that Pr(¬ G/t 1 (G)& . . . &t N (G)&E&K) = Pr(¬ G/t 1 (G)&E&K)x . . . xPr(¬ G/t N (G)&E&K), then Pearson's result would be secured. But this is an implausible way to express the assumption that the witnesses testify independently of one another. Why not say in the same spirit that the independence means that Pr(G/t 1 (G)& . . . &t N (G)&E&K) = Pr(G/t 1 (G)&E&K)x . . . xPr(G/t N (G)&E&K), reaching the contrary result that the posterior probability of G is equal to aN? There are some special circumstances under which Pearson's result holds, and Bayesianism reveals what they are. But I will leave it to the reader to reach the revelation by turning the crank on Bayes' theorem, for there is another route to revealing the power of independent witnessing that does not rely on such specialized assumptions. The effects of multiple testimonies to the same event were given a systematic Bayesian analysis by Charles Babbage in his Ninth Bridgewater Treatise (1838). The claimed upshot of his discussion is this: “[I]f independent witnesses can be found, who speak the truth more frequently than falsehood, it is ALWAYS possible to assign a number of independent witnesses, the improbability of the falsehood of whose concurring testimonies shall be greater than that of the improbability of the miracle itself” (NBT 202: 212). Here Babbage is accepting Hume's Maxim (see section 15) and using it against him. I take the form of Babbage's claim to be this. Suppose that Pr(M/E&K) = > 0, and suppose that the witnesses are independent and that each one's testimony is more likely to be true than false. Then no matter how small is (as long as it is positive), there is an N( ) such that Pr(M/t 1 (M)&t 2 (M)& . . . &t N (M)&E&K) > 0.5. And, in fact, N( ) can be chosen so that the posterior probability is as close to 1 as is desired. end p.54 This claim is still vague until the suppositions of independence and reliability of the witnesses are given precise probabilistic form. I will suppose that on the relevant occasion each of the witnesses testifies, either to the occurrence or the nonoccurrence of the event in question so that ¬ t i (M) is equivalent to t i (¬ M). I then take the independence of the testimonies to mean that • (1) • where ± Φ stands for the choice of Φ or its negation, the understanding being that the same choices must be made uniformly on the left- and right-hand sides of the equality. (Note that (I) is much weaker than the generally implausible principle that, on the basis of E&K alone, the testimonies are uncorrelated, that is. Pr(± t 1 (M)& . . . & ± t N (M)/E&K) = Pr(± t 1 (M)/E&K)x . . . xPr(± t N (M)/E&K).) For sake of simplicity I also assume that all the witnesses are equally reliable (or unreliable) in that for all i, Pr(t i (M)/M&E&K) = p and Pr(t i (M)/¬ M&E&K) = q. Bayes' theorem then gives the posterior probability of the miracle, conditional on the testimony of the cloud of witnesses: • (15) • The implications of (15) are best discussed in cases. Case (a). p = q. Then for any value of N, Pr(M/t 1 (M)& . . . &t N (M)&E&K) = Pr(M/E&K). Thus, no matter how large the cloud of witnesses, their collective testimony has no probative value. Case (b). q > p. Then as N → ∞, (q/p)N → ∞ and Pr(M/t 1 (M)& . . . &t N (M)&E&K) → 0. Piling one unreliable witness on another only serves to reduce the credibility of the event. Case (c). p > q. Then as N → ∞, (q/p)N → 0 and Pr(M/t 1 (M)& . . . &t N (M)&E&K) → 1. Here the power of independent witnessing comes into its own. What is remarkable about this power in the above set up is that the witnesses do not have to be reliable in any absolute sense; for example, it could be that they are unreliable in the absolute sense that Pr(t i (M)/¬ M&E&K) > 0.5 for each i. All that is required is that they are minimally reliable in the comparative sense that Pr(t i (M)/M&E&K) > Pr(t i (M)/¬ M&E&K). In the case where the witnesses are not equally reliable, (15) has to be replaced by • (16) • where p i = Pr(t i (M)/M&E&K) and q i = Pr(t i (M)/¬ M&E&K). Now in order to assure that the posterior probability goes to 1 as N → ∞ it is not sufficient to assume that each witness is minimally reliable in the comparative sense that p i > q i . It is also necessary that the ratio q i /p i does not approach 1 too rapidly as N increases. In the Théorie Analytique des Probabilités (1812, 463) Laplace derived a formula similar to (16). However, he seems to have assumed that q i = 1 − p i . Specializing back to the case where the p i are all equal to p, we see that under Laplace's analysis the power of multiple independent witnesses does not materialize unless the witnesses are reliable in the absolute sense that p > 0.5. If one is not careful, it is easy to fall in with Laplace's assumption, which may help to explain why there has been a general lack of recognition of the power of independent multiple witnessing. Hume made a nod to the power of independent witnessing. In the case of the hypothetical miracle of eight days of total darkness, he writes: • Thus, if it could be shown that • (19) • then it would follow, as desired, that Pr(M 1 v M 2 /t 1 (M 1 )&t 2 (M 2 )&K) is greater than either of Pr(M 1 /t 1 (M 1 )&K) or Pr(M 2 /t 2 (M 2 )&K). A long slog using (S 1 ), (S 2 ), and the conditions that Pr(M 1 /t 1 (M 1 )&K) < 1 and Pr(M 2 /t 2 (M 2 )&K) < 1, shows that (19a) holds if and only if • (20) • It is sufficient for (20) to hold that the second witness is minimally reliable (i.e., Pr(t 2 (M 2 )/M 2 &K) > Pr(t 2 (M 2 )/¬ M 2 &K)) and that M 1 is positively relevant to M 2 (i.e., Pr(M 2 /M 1 &K) > Pr(M 2 /¬ M 1 &K)). But interestingly enough it is also sufficient that the second witness is not minimally reliable while M 1 is negatively relevant to M 2 . The analysis of (19b) is similar. The upshot is that for two witnesses to different miracles, the dual testimony of both witnesses makes it more likely that some miracle has occurred than if either of the witnesses alone had testified, provided that the witnesses are independent in the sense of (S 1 ) and (S 2 ) and provided that they are both minimally reliable (respectively, not minimally reliable) and the miracles are positively (respectively, negatively) relevant to one another. With some more work, weaker sufficient conditions for the efficacy of dual witnessing can be established, but I leave this exercise in Bayesianism to the reader. I also leave it to the reader to show that the above result generalizes from two witnesses to an arbitrary finite number, and I turn to the issue of whether asymptotic certainty as to the occurrence of some miracle or other is reached as the number of independent witnesses is increased without bound. What complicates the issue is that we want to rule out the possibility that lim n→ ∞ Pr(M 1 v M 2 v . . . v M n /K) = 1, for otherwise end p.58 the asymptotic certainty would have nothing to do with the testimonial evidence. Now lim n→ ∞ Pr(M 1 v M 2 v . . . v M n /K) = 1 − lim n→ ∞ Pr(¬ M 1 &¬ M 2 & . . . &¬ M n /K). Since Pr(¬ M 1 /K), Pr(¬ M 1 &¬ M 2 /K), . . . is a monotonically decreasing series and is bounded below, it has a limit ℓ, which we want to be greater than 0. But Pr(¬ M 1 &¬ M 2 & . . . &¬ M n /K) = Pr(¬ M 1 /K)x Pr(¬ M 2 /¬ M 1 &K)x . . . x Pr(¬ M n /¬ M 1 &¬ M 2 & . . . &¬ M n−1 &K). If ℓ is to be greater than 0, it must be the case that Pr(¬ M n /¬ M 1 &¬ M 2 & . . . &¬ M n−1 &K) ¬ → 1, or equivalently, Pr(M n /¬ M 1 &¬ M 2 & . . . &¬ M n−1 &K) ¬ → 0. In this case, we can say that the Ms bear a strong asymptotic analogy to each other. Now assuming that the basic result generalizes to an arbitrary finite number of miracles. Pr(M 1 /t 1 (M 1 )&K), Pr(M 1 v M 2 /t 1 (M 1 )&t 2 (M 2 )&K), . . . , forms a monotonically increasing series. Since it is bounded from above, the limit lim n→ ∞ Pr(M 1 v M 2 v . . . v M n /t 1 (M 1 )&t 2 (M 2 )& . . . &t n (M n )&K) exists. We would like this limit to be 1, or equivalently lim n→ ∞ Pr(¬ M 1 &¬ M 2 & . . . &¬ M n /t 1 (M 1 )&t 2 (M 2 )& . . . &t n (M n )&K) = 0. By similar reasoning to the above, the latter condition holds if Pr(¬ M n /¬ M 1 &¬ M 2 & . . . &¬ M n−1 &t 1 (M 1 )&t 2 (M 2 )& . . . &t n (M n )&K) 1, or equivalently, Pr(M n /¬ M 1 &¬ M 2 & . . . &¬ M n−1 &t 1 (M 1 )&t 2 (M 2 )& . . . &t n (M n )&K) 0. By applying the appropriate generalizations of (S 1 ) and (S 2 ), this last condition is seen to be equivalent to Pr(M n /¬ M 1 &¬ M 2 & . . . &¬ M n−1 &t n (M n )&K) 0. In words, asymptotic certainty as to the occurrence of some miracle or other is reached if the testimony of the independent and minimally reliable witnesses to the different miracles is strong enough to overcome the strong asymptotic analogy among the miracles. The qualification of this result makes it much less powerful than the limit result achieved for the case of independent witnesses to the same event. 20 What Is Right About Hume's Position John Earman In 1761 Hugh Blair sent Hume a copy of the manuscript of George Campbell's Dissertation on Miracles. Hume was clearly annoyed by Campbell's attack, but out of consideration for Blair, his comments were moderate.75 There is one golden nugget worth quoting from Hume's response to Blair: “Does a man of sense run after every silly tale of witches or hobgoblins or fairies, and canvass particularly the evidence? I never knew any one, that examined and deliberated about nonsense who did not believe it before the end of his inquiries” (L 350). The point Hume is making encompasses religious miracles but applies more generally to “silly tales” of all stripes. Indeed, I venture that if Hume were writing today he would focus not on religious miracles but on such things as UFO abductions and the like. Like Hume, I do not think that a man of sense should give end p.59 much credence to such tales, although unlike Hume I do not think that there are valid principles of inductive reasoning to show that such tales are never, in principle, to be credited. But then what am I—and Hume—to do about the results of sections 18 and 19 on the power of multiple witnessing? There is no lack of witnesses to silly tales, e.g. opinion polls show that an alarmingly large percentage of the people in the United States believe that they have been alien abductees. Still I do not—and I presume Hume would not—take alien abduction reports seriously. There are only five ways out. The first is to point to some defect either in Bayesianism itself or in the Bayesian analysis of multiple witnessing. This is not an option I can choose since, for present purposes, I am a Bayesian,76 and since I think the Bayesian analysis of multiple witnessing is correct. The second out is to set the prior probability of UFO abductions (that is the conditional probability of abductions given all of the background evidence prior to receiving eyewitness testimony) to zero. This is not an option I would want to exercise since it precludes any Bayesian learning on the matter. The evidence is mounting that a nontrivial percentage of stars have planets. Presumably some nontrivial percentage of these alien planets have conditions favorable to life, and presumably on some nontrivial percentage of the hospitable planets, the processes of evolution produce higher life forms capable of interplanetary travel. Thus, I think it rash to utterly dismiss the possibly that our planet has been visited by extraterrestrials. The third out is to set the prior probability above zero but still so low that the testimony of a million witnesses would not push the posterior probability to a respectable level. This is a superficially more attractive option, but its effectiveness is ephemeral. Even if a worldwide opinion poll found hundreds of millions of witnesses to alien abductions, I would still not become a believer. (I am not completely intransigent on this matter. I would, for instance, be swayed by hard physical evidence, such as pieces from a flying saucer.) The fourth out is to deny the independence assumptions that were crucial to the positive results of sections 18 and 19. This is a much more plausible and effective option. The fact that many self-confessed alien abductees draw similar pictures of their captors and tell similar stories about invasive examinations of their bodies is to me not evidence in favor of alien abductions but rather evidence of the pervasive influence of media stories and television “documentaries.” But I would certainly admit—and argue that Hume would have to admit—that there is nothing in principle impossible about arranging circumstances where the requisite independence conditions are satisfied for witnesses to (alleged) alien abductions or for that matter to (alleged) religious miracles. (It is not hard to imagine how to arrange the external circumstances so as to prevent one witness from directly influencing another and so as to prevent the indirect influence though media stories. But it would also be necessary to rule out or take into account the possibility that humans are “hard wired” to have the sorts of experiences that get reported as alien abductions.) The fifth out is to deny the minimal reliability assumption. Hume would presumably want to follow this route. Recall that in discussing the hypothetical case of the resurrection of Queen Elizabeth he writes: “You would in vain object to me the difficulty, and almost impossibility of deceiving the world in an affair of such consequence. . . . I would still reply, that the knavery and folly of men are such common phenomena, that I should rather believe the most extraordinary events to arise from their concurrence, than to admit so signal a violation of the laws of nature” (E 128; 151). Now again I do not believe that there is any, in principle, unbreachable obstacle to satisfying the minimal reliability condition for witnesses to religious miracles or UFO abductions. But I do believe, in a way that I cannot articulate in detail, that these cases are in fact relevantly similar to the case of faith healing where there is a palpable atmosphere of collective hysteria that renders the participants unable to achieve the minimal reliability condition—indeed, one might even say that a necessary condition for being a sincere participant in a faith healing meeting is the suspension of critical faculties essential to accurate reporting. Here, finally, Hume and I are in partial agreement. But the difference between us is that I am just giving a personal opinion. Moreover, I acknowledge that the opinion is of the kind statement of this viewpoint is to be found in Of the Principles and Duties of Natural Religion (1699) by John Wilkins, Bishop of Chester and a founder of the Royal Society. 'Tis sufficient that matters of Faith and Religion be propounded in such a way, as to render them highly credible, so as an honest and teachable man may willingly and safely assent to them, and according to the rules of Prudence be justified in so doing. Nor is it either necessary or convenient, that they should be established by such cogent Evidence, as to necessitate consent. Because this would not leave any place for the virtue of Believing, or the freedom of our obedience; nor any ground for Reward and Punishment. end p.63 It would not be thank-worthy for a man to believe that which of necessity he must believe, and cannot otherwise chuse.78 (30–31) Another example is provided by Tillotson, upon whom Hume heaps ironic (?) praise at the opening of “Of Miracles”: “And for any man to urge that tho' men in temporal affairs proceed upon moral assurance, yet there is a greater assurance required to make men seek Heaven and avoid Hell, seems to me highly unreasonable” (1728, 23–24). And as a final example, in his discourse on natural religion Samuel Clarke (1705) averred that “such moral Evidence, or mixt Proofs from Circumstances and Testimony, as most Matters of Fact are only capable of, and wise and honest Men are always satisfied with, ought to be accounted sufficient for the present Case [the truth of the Christian revelation]” (ONR 600). Locke also belonged to this camp, but, in contrast to the figures named above, he was unhappy about giving up the strong sense of knowledge which implies certainty. Grant then that Hume's more sophisticated opponents were willing to settle for reasonable belief. And grant that testimonial evidence has sufficed to establish the credibility of some New Testament miracle M event, such as a resurrection—in the language of conditional probability, Pr(M/t(M)&E&K) ≥ p, where p is greater than 0.5 and, perhaps, even close to 1. Hume's admirers can still claim that it has not been shown how this credibility can be transferred to some doctrine C of Christianity, that is, Pr(C/t(M)&E&K) > 0.5. Hume himself does not explicitly pose this challenge, but he does say something relevant toward the end of Part 2 of his essay: “Though the Being to whom the miracle is ascribed, be, in this case, Almighty, it does not, upon that account, become a whit more probable; since it is impossible to know the attributes or actions of such a Being, otherwise than from the experience which we have of his productions, in the usual course of nature” (E 129; 152). Grant Hume that it is impossible for us to know from direct experience the attributes of the Almighty Being. By the same token, we cannot know by direct experience the attributes of quarks. But we can form specific hypotheses about the attributes and actions of the Almighty or of quarks, and these hypotheses can make a difference to the conditional probabilities of events we can come to know by direct experience. And because of this, testimonial evidence to these events can make a difference to the confirmation/disconfirmation of the hypotheses about the Almighty or about quarks, or so I will argue in the following section. We have yet another example of how Hume's crabbed view of induction, which he tried to turn against miracles, makes it impossible for modern science to operate. end p.64 22 Probabilifying Religious Doctrines John Earman Given some plausible assumptions, the question of how testimony to the occurrence of an event that constitutes a miracle in the sense of Hume's first definition—say, a resurrection—can serve to probabilify a theological doctrine can be divided into two sub- questions: First, how can the testimony probabilify the naturalistically characterized miracle event? And, second, how can such a miracle probabilify the doctrine?79 Using the principle of total probability, we find that • (21) • Assume, as seems plausible, that the testimony t(M) to some New Testament miracle M bears on some tenet C of Christianity only through M in the sense that • (22) • Then (21) becomes • (23) • which provides the promised division. Let us assume, for the sake of simplicity, that testimony has been very successful in establishing M beyond reasonable doubt, that is, Pr(M/t(M)&E&K) ≈ 1. Then by (23), Pr(C/t(M)&E&K) ≈ Pr(C/M&E&K). The question of how well testimonial evidence to M supports C then devolves to the question of how well M supports C. This latter question is not easy to answer, but there is something to be said that might seem to be uncontroversial. It might seem that if M is some New Testament miracle and C comprises the central tenets of Christianity, then Christians and non-Christians alike will agree that • (24) • or equivalently • (25) • It follows that • (26) • or equivalently • (27) • So from the seemingly uncontroversial (24), it follows that M incrementally confirms C. In the case where M is a logical consequence of C, we have an instance of hypothetico- deductive confirmation; the fact that such an M incrementally confirms C is then a direct consequence of Bayes' theorem, assuming that neither of Pr(C/E&K) nor Pr(M/E&K) is 0 or 1. To reach the conclusion that t(M) incrementally confirms C it is not necessary to make the simplifying assumption that testimonial evidence has been so effective in establishing M. Assume that Pr(M/t(M)&E&K) > Pr(M/E&K). Does it follow from (22) and (24) that • (?) • Applying the principle of total probability to both sides of (?) and using (22) and the negation principle, one finds that (?) holds if and only if • (28) • By our starting assumption, the [] term is positive, so that (?) holds if and only if Pr(C/M&E&K) > Pr(C/¬ M&E&K), which holds if and only (24) holds. The (?) is discharged. This has been so easy that one suspects that there must be a catch. Could the catch lie in the seemingly innocuous (24)? Suppose, for sake of illustration, that ¬ C consists of the disjunction of Zoroastrianism (Z) and Buddhism (B). Then Pr(M/¬ C&E&K) = [Pr(M/Z&E&K)× Pr(Z/E&K) + Pr(M/B&E&K)× Pr(B/E&K)]/[Pr(Z/E&K) + Pr(B/E&K)]. To simplify, assume that Pr(M/Z&E&K) = Pr(M/B&E&K) = v. Then Pr(M/¬ C&E&K) = v, which for a New Testament miracle M is presumably much less than Pr(M/C&E&K), so that (24) holds. But now suppose that ¬ C includes the possibility of a nasty deceiver god (N) who abolishes heaven and hell but arranges for the occurrence of M in order to lure the unsuspecting into lives of fruitless religious observance. Setting Pr(M/N&E&K) = 1, we now have Pr(M/¬ C&E&K) > Pr(N/E&K)/[Pr(Z/E&K) + Pr(B/E&K) + Pr(N/E&K)]. The right-hand side of this inequality may be greater than or equal to Pr(M/C&E&K) if Pr(N/E&K) is very large in comparison with (Pr(Z/E&K) + Pr(B/E&K)) and Pr(M/C&E&K) < 1, in which case (24) fails. This result may be somewhat discouraging to theists because it shows that whether or not miracles are seen as confirming a particular form of theism depends on the prior end p.68 religion disconfirm rival systems of religions and the miracles on which they rest? Here is one try: (P 1 ) Let H 1 , H 2 , . . . , H n be pairwise incompatible hypotheses. Suppose that E i , i = 1, 2, . . . , n, gives positive support to H i for each i, that is, Pr (H i /E i &K) > Pr (H i /K). Then E i gives negative support to the other hypotheses, that is, Pr (H j /E i &K) < Pr (H j /K) for j ≠ i, and the other evidence statements, that is, Pr (E j /E i &K) Pr (E j /K) for j ≠ i. This principle is false in general. For instance, even though the H i are incompatible with one another, it can happen that H i &K entails E for each i. Then if the prior probabilities of E and the H i are all strictly between 0 and 1, it is a simple exercise using Bayes' theorem to show that E incrementally confirms each of the H i . Consider another try. (P 2 ) Let H 1 , H 2 , . . . , H n be pairwise incompatible, and let E i , i = 1, 2, . . . , n be such that (a) Pr (E i /H i &K) > Pr (E i /¬ H i &K), but Pr (E i /H j &K) < Pr (E i /¬ H j &K) for j ≠ i. Then it follows that (b) Pr (H i /E i &K) > Pr (H i /K) but Pr (H j /E i &K) < Pr (H j /K) for j ≠ i, and (c) Pr (E i /E j &K) < Pr (E i /K) for j ≠ i. Further, if t i (E i ) is the testimony of witness #i to the truth of E i and if (d) Pr (E i /t i (E i )&K) > Pr (E i /K) then (e) Pr (t i (E i )/t j (E j )&K) < Pr (t i (E i )/K) for j ≠ i. Assumption (a) is plausible when the H i are contrary religious doctrines and the E i are miracle statements appropriate to the corresponding religions. (But recall the discussion of the preceding section.) Then (b) does follow so that the miracles of one religion do undermine the other religions in the sense of incremental disconfirmation. However, it does not follow without further assumptions that (c) holds for this application (i.e., that the miracles of one religion undermine the miracles of the others). The implication does hold if it is further assumed that (f) Pr (E i /H i &E j &K) = Pr (E i /H i &K) for j ≠ i, and (g) Pr (E i /¬ H i &E j &K) = Pr (E i /¬ H i &K) for j ≠ i. The assumption (f) strikes me as plausible for its intended applications; but (g) strikes me as dubious. Similarly, (e) follows from (d) only with the help of further dubious assumptions. But grant for the sake of argument that (P 2 ) does hold for the intended application to religious doctrines. What moral is Hume entitled to draw? Hume thinks that the answer is clear: “This argument may appear over subtle and refined; but it is not really different from the reasoning of a judge, who supposes, that the credit of two witnesses, maintaining a crime against any one, is destroyed by the testimony of two others, who affirm him to have been two hundred leagues distant, at the same instant when the crime is said to have been committed” (E 122; 148). But, of course, judges and juries are not always at a loss when presented with testimonies that are directly or indirectly in conflict, for they may have good reason to give high credibility to the testimony of some witnesses end p.69 and low credibility to the testimonies of others. What Hume needs to underwrite the claim of the last quotation is not (P 2 ) but (P 3 ) Let H 1 , H 2 , . . . , H n be pairwise incompatible hypotheses, and suppose that E i , i = 1, 2, . . . , n, are such that (a) each E i gives positive support to H i and negative support to H j , for j ≠ i, and (perhaps also) (b) the E i are pairwise incompatible or at least are probabilistically negatively relevant to one another, then it cannot be rational to assign probabilities such that Pr (H k /t 1 (E 1 )&t 2 (E 2 )& . . . &t n (E n )&K) is much greater for some H k than any competing H j , j ≠ k. (P 3 ) is clearly false in general. And Hume has given no reason to think that it is true for the special case where the H i are competing religious doctrines and the t i (E i ) are testimonies to their corresponding miracles. In sum, Hume's contrary miracles argument has some effect against those who take miracles to be proofs of religious doctrines. But against those who take miracles only as providing confirmation of religious doctrines, Hume's argument is not vouchsafed by any valid principles of confirmation—at least not of the Bayesian variety. Hume is thus forced to leave the high ground and descend into the trenches where, as he must have been aware, there were opponents who had considered the contrary miracles argument and were prepared to argue on the basis of contextual details for the superiority of the New Testament miracle stories over heathen miracle stories. These opponents may or may not have been right. But Hume had no good reason for avoiding an engagement with them. 24 Conclusion John Earman In “Of Miracles,” Hume pretends to stand on philosophical high ground, hurling down thunderbolts against miracle stories. The thunderbolts are supposed to issue from general principles about inductive inference and the credibility of eyewitness testimony. But when these principles are made explicit and examined under the lens of Bayesianism, they are found to be either vapid, specious, or at variance with actual scientific practice. When Hume leaves the philosophical high ground to evaluate particular miracle stories, his discussion is superficial and certainly does not do justice to the extensive and vigorous debate about miracles that had been raging for several decades in Britain. He was able to create the illusion of a powerful argument by maintaining ambiguities in his claims against miracles, by the use of forceful prose and confident pronouncements, and by liberal doses of sarcasm and irony. Early in Part , Hume warns us that “Eloquence, when at its highest pitch, leaves little room for reason and reflection; but addressing itself entirely to the fancy or the affections, captivates the willing hearers, and subdues their understanding” (E 118; 145). I find it ironic that so many readers of Hume's essay have been subdued by its eloquence. And I find it astonishing how well posterity has treated “Of Miracles,” given how completely the confection collapses under a little probing. No doubt this generous treatment stems in part from the natural assumption that someone of Hume's genius must have produced a powerful set of considerations. But I suspect that in more than a few cases it also involves the all too familiar phenomenon of endorsing an argument because the conclusion is liked. There is also the understandable, if deplorable, desire to sneer at the foibles of the less enlightened—and how more pleasurable the sneering if it is sanctioned by a set of philosophical principles! Having denigrated Hume's essay, I want to praise the man. An unmistakable mark of greatness in philosophy is the ability to identify important problems and to pose them in interesting and provocative forms. That Hume succeeded in this regard for the issue of how eyewitness testimony bears on the credibility of miracles is evident not only from the contrast with the efforts of his contemporaries (e.g., Conyers Middleton's antimiracles tract Free Inquiry [1749] is, by the standards Hume set, philosophically uninteresting and boring reading)84 but also from that fact that his essay continues to provoke a lively debate. However, his own responses to the issues he so provocatively posed were bound to fall short, driven as he was by a deep set animus toward organized religion and hampered by his own inadequate account of inductive inference and by his unfamiliarity with the probabilistic tools his contemporaries were developing. But Hume undoubtedly provoked others to produce useful quantitative analyses of the role of deception and self- deception in diminishing the force of testimony, the power of independent multiple witnesses, and so forth. How much comfort can theists take from the failure of Hume's project? Considerable comfort can be found not so much in the failure of Hume's arguments—for there could conceivably be better arguments waiting in the wings—but in the manner of their failure. Let me begin explaining what I mean by reminding the reader of a key difference between logical positivism and logical empiricism. As a representative of the latter camp, Hans Reichenbach rejected the verifiability and falsifiability criteria of meaningfulness, which would have relegated not only religion but large portions of science as well to the limbo reserved for gibberish. Instead, he opted for a confirmability criterion which required cognitively meaningful hypotheses to admit of probabilification by the evidence of observation and experiment. As a would-be realist about the unobservable entities postulated by modern science, Reichenbach saw a need for a criterion with an “overreaching” character: “The probability theory of meaning . . . allows us to maintain propositions as meaningful which end p.71 concern facts outside the domain of immediately given verifiable facts; it allows us to pass beyond the domain of given facts. This overreaching character of probability inferences is the basic method of the knowledge of nature” (1961, 127). I am in agreement here with Reichenbach, although I would substitute the degrees of belief interpretation of probability for his favored frequency interpretation. And I would note that the overreaching character of Bayesian epistemology stretches much further than Reichenbach himself might have wanted; indeed, it seems to me to extend into the religious realm. Belief formation in natural religion can proceed inductively as it does in science and everyday life on the basis of observation and eyewitness testimony. And the resulting degrees of belief are to be deemed rational as long as they satisfy the strictures of Bayesianism. Rationality of belief is one thing, objectivity quite another. There are two ways in which the latter can be achieved in natural religion. First, we saw that given some mild assumptions, which can be made plausible or at least can be motivated, results about the • (A9) • Defining conditional probability by Pr(Y/X) ≡ Pr(Y& X)/Pr(X) when Pr(X) ≠ 0, another form of total probability states that: • (A10) • Exercise for readers: show that (A4)–(A10) follow from (A1)–(A3). In some applications (A1)–(A3) need to be strengthened by the principle of countable additivity: • (A11) • 87 Suppose that in intended models universal quantification ranges over a countably infinite domain in which the individuals are named by a 1 , a 2 , . . . Then ( i)Pa i Pa i & . . . &Pa n , for all n. So Pr(( i)Pa i ) ≤ lim n → ∞ Pr(Pa 1 & . . . &Pa n ). With countable additivity, the ≤ becomes =. end p.76 Notes 1. Originally published in 1748 as Philosophical Essays Concerning Human Understanding. For simplicity, I will refer to it throughout as the Enquiry. The version reproduced in Part II is from Hume (1898); it marks the changes and additions Hume made to “Of Miracles” as the Enquiry went through various editions. Hume commentators have generally neglected the clues to Hume's intentions offered by these changes. 2. For a recounting of this history, see Hempel (1965) and Laudan (1983). 3. It is clear that many of the claims made in pseudo-scientific disciplines are genuine claims; that is, in the logical positivists' jargon, they do have cognitive and empirical significance. 4. Here I am in complete agreement with Laudan (1983). 5. Some commentators assume that Hume's apparently admiring reference to Tillotson was intended to be ironic or mocking. I do not see why the reference must be read this way even though, of course, Hume thought that he had disposed of the miracles on which Tillotson partly rested his own religious convictions. For an account of Tillotson's argument against transubstantiation, see Levine (1988). Tillotson also offers prudential arguments for believing in the existence of God in his “The Wisdom of Being Religious” (1664). Jordan (1991) suggests that this sermon is one of Hume's main targets in Dialogue XII of Dialogues Concerning Natural Religion. 6. Two especially good books are Gasking (1978) and Yandell (1990). 7. See Burns (1981). In 1751 Hume sent Gilbert Elliot a sample of his Dialogues Concerning Natural Religion: You wou'd perceive . . . that I make Cleanthes the Hero of the Dialogues. Whatever you can think of, to strengthen that Side of the Argument, will be most acceptable to me. Any Propensity you imagine I have to the other Side, crept in upon me against my Will: and tis not long ago that I burn'd an old manuscript Book, wrote before I was twenty. . . . It began with an anxious Search after Arguments, to confirm the common Opinion: Doubts stole in, dissipated, return'd, were again dissipated, return'd again; and it was a perpetual Struggle of a restless Imagination against Inclination, perhaps against Reason. (L, Vol. 1, 154) 8. Philo states the matter in the conditional mode: “If it affords no inference that affects human life” (1776, 227). But it is clear from the context that Philo (Hume?) thinks that the antecedent holds. end p.77 9. See Jordan (1991) for documentation of this two-pronged strategy in the natural religion of the eighteenth century. 10. As Robert Meyers (1997) has noted, the Treatise contains proto versions of some of the arguments that later appeared in “Of Miracles.” For example, in Bk II, Pt. 3, sec. 1, Hume writes: Shou'd a traveller, returning from a far country, tell us, that he has seen a climate in the fiftieth degree of northern latitude, where all the fruits ripen and come to perfection in the winter, and decay in the summer, after the same manner as in England they are produc'd and decay in the contrary seasons, he wou'd find few so credulous as to believe him. I am apt to think a traveller wou'd met with as little credit, who shou'd inform us of people exactly of the same character with those in Plato's Republic on the one hand, or those in Hobbes's Leviathan on the other. There is a general course of nature in human actions, as well as in the operations of the sun and climate. There are also characters peculiar to different nations and particular persons, as well as common to mankind. The knowledge of these characters is founded on the observation of an uniformity in actions, that flow from them; and this uniformity forms the very essence of necessity. (T 402–403) 11. The editors of New Letters of David Hume hypothesize that this is William Hamilton, Jacobite poet and friend of Hume. 12. Commentators differ on the most likely place to have inserted “Of Miracles” in the Treatise; see for example, Nelson (1986) and Wootton (1990). The most likely answer seems to me to be that Hume would have inserted it in a place that corresponds to its thematic location in the Enquiry—that is, after the discussion of knowledge and probability and before the discussion of skeptical philosophy. 13. For a different explanation of why Hume decided to publish the miracles essay, see Nelson (1986). 14. This view is repeated in the Ethics: “Nothing happens in nature which could be attributed to any defect in it, for nature is always and everywhere one and the same. Its virtue and its power of acting are the same—that is, the laws and rules of nature, according to which all things happen and are changed from one form to another, are always and everywhere the same” (III pref, II: 138; quoted in Curley 1969, 49). 15. Alan Donegan (1996) has noted that Spinoza's views lead to a position on eyewitness testimony which, in principle, is distinct from Hume's. Unlike Hume, Spinoza was not committed to a reflexive skepticism regarding testimony to events that apparently go against the order of nature; rather, Spinoza is committed only to the existence of a naturalistic explanation, whether or not the testimony is correct. In practice, however, Spinoza's interpretation of scripture is such that Hume could have found little with which to quarrel. For example, as regards the miracle reported in Joshua 10: 12–14, Spinoza reads the passage “the sun stood still, and the moon stayed” metaphorically—not that the sun and moon literally stopped in their tracks but only that the day was, or seemed, longer than usual, (TPT 93). As for resurrections, Spinoza held that the revival by Elisha of a boy believed to be dead (II Kings iv: 34–35) was not a genuine resurrection but merely a case of a comatose boy revived by the warmth of Elisha's body (TPT 91; 113). The alleged resurrection of Jesus is treated end p.78 the opposite way: Spinoza believed the testimony that Jesus died on the cross but not the testimony that he returned from the dead (Ep 75; Shirley 1995, 337–339). More generally, I know of no instance in which Spinoza accepts testimony to an event that contravenes the order of nature in the sense of an inductively well confirmed lawlike regularity. 16. See Harrison (1995) for references to and analyses of relevant Newtonian texts. 17. Holland (1965) offers the modern version of the coincidence conception of miracles. Locke's brief for miracles relies less on coincidence and more on what Burns (1981) dubs the “principle of context,” according to which it is reasonable to take an event as having religious significance if the circumstances are such as to make the event a suitable vehicle for revealing God's purposes and character; see Locke's Discourse of Miracles, reproduced in Pt. II. A similar view is found in Chubb (1741). 18. The message is spelled out in both English and French over Canada. 19. From the perspective of modern science, the paradigm example of miracle in the eighteenth century debate—a resurrection—is on a par with the Emuh example, at least assuming that the laws of biology must supervene on the laws of physics. For the motions of the elementary particles in the body of a dead person needed to bring her back to life would not seem to contravene any of the fundamental laws of physics, although such motions presumably have a very low probability on a par with the improbability of the motions of the water vapor molecules that spelled out the messages in the Emuh case. But I do not see that learning elementary particle physics automatically undermines the evidentiary value for Christianity of the resurrection of Jesus. Admittedly, this way of looking at miracles does not fit well with Hume's rather simplistic conception of laws of nature (see sections 6 and 9). So much the worse for Hume I say. 20. The issue of what constitutes a lawlike regularity is subject to continuing controversy in philosophy. The details of this issue will not directly affect the current discussion. 38. In Bk. I, sec. 15 of the Treatise (“Rules by which to judge of causes and effects”), Hume points to some relatively sophisticated inductive procedures designed to determine cause and effect relations. Here Hume takes a cause to be necessary as well as sufficient for is effect (“The same cause always produces the same effect, and the same effect never arises but from the same cause” [T 173]. Thus, care must be taken to weed out the nonnecessary effects: There is no phaenomenon in nature, but what is compounded and modify'd by so many different circumstances, that in order to arrive at the decisive point, we must carefully separate whatever is superfluous, and enquire by new experiments if every particular circumstance of the first experiment was essential to it. These new experiments are liable to a discussion of the same kind; so that the utmost constancy is requir'd to make us persevere in our enquiry, and the utmost sagacity to choose the right way among so many that present themselves. (T 175) end p.81 39. Some commentators have expressed puzzlement over the “fact” that Hume deals only with eyewitness testimony to miracles and does not deal with first-hand experience. If my attribution of the straight rule to Hume is correct, this puzzlement rests on a false presupposition. 40. See Klibansky and Mossner (1958, 233) 41. It is known that Hume visited Price at his home in Newington Green. It is reported that on one of these occasions Hume “cordially acknowledged that on one point Mr. Price has succeeded in convincing him that his arguments were inconclusive” (quoted in Thomas 1924, 30). Unfortunately, the subject of this discussion is not recorded. 42. The authorship of An Introduction to the Doctrine of Fluxions (1751) has been attributed to Bayes, but Bayes' election as a Fellow came in 1742. Pearson (1978) has attributed another work, Explanation of Fluxions (1741), to Bayes, and hypothesizes that this work was responsible for Bayes' election to the Royal Society. 43. More precisely, the will left £ 200 to be divided between John Boyl and Richard Price; see Barnard (1958). 44. Thus I cannot agree with Raynor's (1980) claim that Hume knew about Bayes's work as early as 1767; and it is certain that Hume did not know about “Bayes's theorem” at this date since this theorem is not in Bayes' paper (see below). 45. Gower (1990, 1991) has argued that Hume's talk of probabilities does not conform to the standard axioms of probability. For a response, see Mura (1998). 46. A brief overview of the relevant part of probability theory is given in the Appendix. 47. The Dutch book construction is not above criticism; see Maher (1993, sec. 5.1). 48. A more sophisticated rule of conditionalization has been developed by Jeffrey (1983) to cover the case of uncertain learning. Dutch book justifications for rules of conditonalizations have also been offered; see Skyrms (1987). 49. For a defense of the view that the axioms of probability, but not the rule of conditionalization, characterize the logic of inductive reasoning, see Howson (1996). 50. The prior probability Pr(H/K) of H—the probability of H prior to getting the new evidence E—need not be thought of as the a priori probability of H—the tabula rasa probability of H—since the background knowledge K may be very rich. 51. See Howson and Urbach (1993) and Earman (1992) for relevant examples. 52. Bayes' attempted justification of his prior probability assignment is discussed in Earman (1992, ch. 1). If this justification succeeded, it would provide a solution to the problem of induction. 53. See Earman (1992, ch. 4) if you are interested in the proof. 54. Broad complained that “if the testimony of others does not shake my belief in the law, there is no reason for me to think that there is anything that needs explanation or investigation. If scientists had actually proceeded in this way, some of the most important natural laws would never have been discovered” (1916–17, 87). end p.82 55. C. D. Broad made the same point without explicitly using the probability apparatus: Clearly many propositions have been accounted laws of nature because of invariable experience in their favor, then exceptions have been observed, and finally these propositions have ceased to be regarded as laws of nature. But the first reported exception was, to anyone who had not himself observed it, in precisely the same position as a story of a miracle, if Hume be right. Those, then, to whom the first exception was reported ought to have rejected it, and gone on believing in the alleged law of nature. Yet, if the first report of the first exception makes no difference to their belief in the law, their state of belief will be precisely the same when a second exception is reported as it was on the first occasion. . . . So that it would seem on Hume's theory that if, up to a certain time, I and every one else have always observed A to be followed by B, then no amount of testimony from the most trustworthy persons that they observed A not followed by B ought to have the least effect on my belief in the law. (1916–17, 87) 56. There remains the possibility of non-Bayesian learning. E.g., if Pr(L/E&K) = 1 and if evidence E′ in favor of an exception to L is acquired, then Pr is changed by some means different than conditionalization to a new Pr′ such that Pr′(L/E′&E&K) < 1. I will not discuss such possibilities here, except to say that what is sauce for the goose is sauce for the gander: if such a change is allowed in, say, the case of the (presumptive) law of the conservation of energy, why isn't it also allowed in the case of the (presumptive) law that a dead person cannot return to life? 57. See section 7. George Campbell is an example of one of Hume's contemporaries who interpreted the Indian prince this way; see his Dissertation on Miracles (CDM 32ff). 58. An unidentified source at Notre Dame called this text to my attention. 59. Versions are to be found in Sherlock (1728); Butler (1736), who speaks of “the prince who has always lived in a warm climate”; and Annet (1744a). 60. As noted by Burns (1981) and Wootton (1994). See Mossner (1954, 232). 61. Campbell (1762) accuses Hume of equivocating between these two senses of “experience.” While this charge seems to me to be unfair, I think that there is much merit in Section II (“Mr Hume charged with some fallacies in his way of managing the argument”) of Part I of Campbell's Dissertation on Miracles. 62. The notion that law statements may contain ceteris paribus clauses is criticized in Earman and Roberts (1999). 63. As Colin Howson has kindly reminded me. 64. I am grateful to Colin Howson for bringing this point to my attention. 65. This interpretation was first offered in Earman (1993). 66. It is easy to show that • Sobel (1996) shows that end p.83 • 67. Hambourger (1980) attributes to Hume the following “principle of relative likelihood”: “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 weigh 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 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 to believe that P” (590). Exercise for the reader: Let P be the proposition that ticket number so-and-so won the lottery, and let the testimony to P be in the form of report from a newspaper known for its reliable reporting. Does this example provide, as claimed by Hambourger, a counter-example to the principle of relative likelihood? See Hájek (1995). 68. Some commentators have read Hume as presenting the example of eight days of total darkness as an example of a marvel rather than a miracle. This reading does not square well with the text just quoted. Nor does it square with Hume's 1761 letter to Blair: There is no contradiction in saying, that all the testimony which ever was really given for any miracle, or ever will be given, is the subject of derision; and yet forming a fiction or supposition for a particular miracle, which might not only merit attention, but amount to a full proof of it. For instance, the absence of sun during 48 hours; but reasonable men would only conclude from this fact, that the machine of the globe was disordered during the time. (L, Vol. 1, 349–350) 69. Here I am following Sobel (1996). See also Schlesinger (1987, 1991). 70. 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The Idea of the Miraculous: The Challenge to Science and Religion. London: Macmillan. Wilson, F. 1989. “The Logic of Probabilities in Hume's Argument against Miracles,” Hume Studies 15: 255–275. end p.94 Abstract: Part II contains reprints of some of the original source material needed to understand the origins of Hume's essay on miracles together with some of the subsequent attempts to assess the probative value of eyewitness testimony. Keywords: Peter Annet, Charles Babbage, George Campbell, Samuel Clarke, George Hooper, Laplace, John Locke, Richard Price, Thomas Sherlock, Spinoza Part II The Documents John Locke, an Essay Concerning Human Understanding (1690), Book IV, Chapters 15 and 16 John Earman Chapter 15, “Of Probability” 1. As demonstration is the showing the agreement or disagreement of two ideas, by the intervention of one or more proofs, which have a constant, immutable, and visible connexion one with another; so probability is nothing but the appearance of such an agreement or disagreement, by the intervention of proofs, whose connexion is not constant and immutable, or at least is not perceived to be so, but is, or appears for the most part to be so, and is enough to induce the mind to judge the proposition to be true or false, rather than the contrary. For example: in the demonstration of it a man perceives the certain, immutable connexion there is of equality between the three angles of a triangle, and those intermediate ones which are made use of to show their equality to two right ones; and so, by an intuitive knowledge of the agreement or disagreement of the intermediate ideas in each step of the progress, the whole series is continued with an evidence, which clearly shows the agreement or disagreement of those three angles in equality to two right ones: and thus he has certain knowledge that it is so. But another man, who never took the pains to observe the demonstration, hearing a mathematician, a man of credit, affirm the three angles of a triangle to be equal to two right ones, assents to it, i.e. receives it for true: in which case the foundation of his assent is the probability of the thing; the proof being such as for the most part carries truth with it: the man on whose testimony he receives it, not being wont to affirm anything contrary to or besides his knowledge, especially in matters of this kind: so that that which causes his assent to this proposition, that the three angles of a triangle are equal to two right ones, that which makes him take these ideas to agree, without knowing them to do so, is the wonted veracity of the speaker in other cases, or his supposed veracity in this. 2. Our knowledge, as has been shown, being very narrow, and we not happy enough to find certain truth in everything which we have occasion to consider; most of the propositions we think, reason, discourse—nay, act upon, are such as we cannot have undoubted knowledge of their truth: yet some of them border so near upon certainty, that we make no doubt at all about them; but assent to them as firmly, and act, according to that assent, as resolutely as if they were infallibly demonstrated, and that our knowledge of them was perfect and certain. But there being end p.97 degrees herein, from the very neighbourhood of certainty and demonstration, quite down to improbability and unlikeness, even to the confines of impossibility; and also degrees of assent from full assurance and confidence, quite down to conjecture, doubt, and distrust: I shall come now, (having, as I think, found out the bounds of human knowledge and certainty,) in the next place, to consider the several degrees and grounds of probability, and assent or faith. 3. Probability is likeliness to be true, the very notation of the word signifying such a proposition, for which there be arguments or proofs to make it pass, or be received for true. The entertainment the mind gives this sort of propositions is called belief, assent, or opinion, which is the admitting or receiving any proposition for true, upon arguments or proofs that are found to persuade us to receive it as true, without certain knowledge that it is so. And herein lies the difference between probability and certainty, faith, and knowledge, that in all the parts of knowledge there is intuition; each immediate idea, each step has its visible and certain connexion: in belief, not so. That which makes me believe, is something extraneous to the thing I believe; something not evidently joined on both sides to, and so not manifestly showing the agreement or disagreement of those ideas that are under consideration. 4. Probability then, being to supply the defect of our knowledge, and to guide us where that fails, is always conversant about propositions whereof we have no certainty, but only some inducements to receive them for true. The grounds of it are, in short, these two following: first, the conformity of anything with our own knowledge, observation, and experience. Secondly, the testimony of others, vouching their observation and experience. In the testimony of others, is to be considered: 1. The number. 2. The integrity. 3. The skill the witnesses. 4. The design of the author, where it is a testimony out of a book cited. 5. The consistency of the parts, and circumstances of the relation. 6. Contrary testimonies. 5. Probability wanting that intuitive evidence which infallibly determines the understanding and produces certain knowledge, the mind, if it will proceed rationally, ought to examine all the grounds of probability, and see how they make more or less for or against any proposition, before it assents to or dissents from it; and, upon a due balancing the whole, reject or receive it, with a more or less firm assent, proportionably to the preponderancy of the greater grounds of probability on one side or the other. For example: If I myself see a man walk on the ice, it is past probability; it is knowledge. But if another tells me he saw a man in England, in the midst of a sharp winter, walk upon water hardened with cold, this has so great conformity with what is usually observed to happen, that I am disposed by the nature of the thing itself to assent to it; unless some manifest suspicion attend the relation of that matter of fact. But if the same thing be told to one born between the tropics, who never saw nor heard of any such thing before, there the whole probability relies on testimony: and as the relators are more in number, and of more credit, and have no end p.98 after as full and exact an inquiry as they can make, they lay up the conclusion in their memories, as a truth they have discovered; and for the future they remain satisfied with the testimony of their memories, that this is the opinion that, by the proofs they have once seen of it, deserves such a degree of their assent as they afford it. answer, and show the insufficiency of: it would, methinks, become all men to maintain peace, and the common offices of humanity, and friendship, in the diversity of opinions; since we cannot reasonably expect that any one should readily and obsequiously quit his own opinion, and embrace ours, with a blind resignation to an authority which the understanding of man acknowledges not. For however it may often mistake, it can own no other guide but reason, nor blindly submit to the will and dictates of another. If he you would bring over to your sentiments be one that examines before he assents, you must give him leave at his leisure to go over the account again. And, recalling what is out of his mind, examine all the particulars, to see on which side the advantage lies: and if he will not think our arguments of weight enough to engage him anew in so much pains, it is but what we often do ourselves in the like case; and we should take it amiss if others should prescribe to us what points we should study. And if he be one who takes his opinions upon trust, how can we imagine that he should renounce those tenets which time and custom have so settled in his mind, that he thinks them self-evident, and of an unquestionable certainty; or which he takes to be impressions he has received from God himself, or from men sent by him? How can we expect, I say, that opinions thus settled should be given up to the arguments or authority of a stranger or adversary, especially if there be any suspicion of interest or design, as there never fails to be, where men find themselves ill treated? We should do well to commiserate our mutual ignorance, and endeavour to remove it in all the gentle and fair ways of information; and not instantly treat others ill, as obstinate and perverse, because they will not renounce their own, and receive our opinions, or at least those we would force upon them, when it is more than probable that we are no less obstinate in not embracing some of theirs. For where is the man that has incontestable evidence of the truth of all that he holds, or of the falsehood of all he condemns; or can say that he has examined to the bottom all his own, or other men's opinions? The necessity of believing without knowledge, nay often upon very slight grounds, in this fleeting state of action and blindness we are in, should make us more busy and careful to inform ourselves than constrain others. At least, those who have not thoroughly examined to the bottom all their own tenets, must confess they are unfit to prescribe to others; and are unreasonable in imposing that as truth on other men's belief, which they themselves have not searched into, nor weighed the arguments of probability, on which they should receive or reject it. Those who have fairly and truly end p.101 examined, and are thereby got past doubt in all the doctrines they profess and govern themselves by, would have a juster pretence to require others to follow them: but these are so few in number, and find so little reason to be magisterial in their opinions, that nothing insolent and imperious is to be expected from them: and there is reason to think, that, if men were better instructed themselves, they would be less imposing on others. examined, and are thereby got past doubt in all the doctrines they profess and govern themselves by, would have a juster pretence to require others to follow them: but these are so few in number, and find so little reason to be magisterial in their opinions, that nothing insolent and imperious is to be expected from them: and there is reason to think, that, if men were better instructed themselves, they would be less imposing on others. 5. But to return to the grounds of assent, and the several degrees of it, we are to take notice, that the propositions we receive upon inducements of probability are of two sorts: either concerning some particular existence, or, as it is usually termed, matter of fact, which, falling under observation, is capable of human testimony; or else concerning things, which, being beyond the discovery of our senses, are not capable of any such testimony. 6. Concerning the first of these, viz. particular matter of fact. I. Where any particular thing, consonant to the constant observation of ourselves and others in the like case, comes attested by the concurrent reports of all that mention it, we receive it as easily, and build as firmly upon it, as if it were certain knowledge; and we reason and act thereupon with as little doubt as if it were perfect demonstration. Thus, if all Englishmen, who have occasion to mention it, should affirm that it froze in England the last winter, or that there were swallows seen there in the summer, I think a man could almost as little doubt of it as that seven and four are eleven. The first, therefore, and highest degree of probability, is, when the general consent of all men, in all ages, as far as it can be known, concurs with a man's constant and never-failing experience in like cases, to confirm the truth of any particular matter of fact attested by fair witnesses: such are all the stated constitutions and properties of bodies, and the regular proceedings of causes and effects in the ordinary course of nature. This we call an argument from the nature of things themselves. For what our own and other men's constant observation has found always to be after the same manner, that we with reason conclude to be the effect of steady and regular causes; though they come not within the reach of our knowledge. Thus, That fire warmed a man, made lead fluid, and changed the colour or consistency in wood or charcoal; that iron sunk in water, and swam in quicksilver: these and the like propositions about particular facts, being agreeable to our constant experience, as often as we have to do with these matters; and being generally spoke of (when mentioned by others) as things found constantly to be so, and therefore not so much as controverted by anybody—we are put past doubt that a relation affirming any such thing to have been, or any predication that it will happen again in the same manner, is very true. These probabilities rise so near to certainty, that they govern our thoughts as absolutely, and influence all our actions as fully, as the most evident demonstration; and in what concerns us we make little or no difference between them and certain knowledge. Our belief, thus grounded, rises to assurance. end p.102 7. II. The next degree of probability is, when I find by my own experience, and the agreement of all others that mention it, a thing to be for the most part so, and that the particular instance of it is attested by many and undoubted witnesses: v.g. history giving us such an account of men in all ages, and my own experience, as far as I had an opportunity to observe, confirming it, that most men prefer their private advantage to the public: if all historians that write of Tiberius, say that Tiberius did so, it is extremely probable. And in this case, our assent has a sufficient foundation to raise itself to a degree which we may call confidence. 8. III. In things that happen indifferently, as that a bird should fly this or that way; that it should thunder on a man's right or left hand, &c., when any particular matter of fact is vouched by the concurrent testimony of unsuspected witnesses, there our assent is also unavoidable. Thus: that there is such a city in Italy as Rome: that about one thousand seven hundred years ago, there lived in it a man, called Julius Caesar; that he was a general, and that he won a battle against another, called Pompey. This, though in the nature of the thing there be nothing for nor against it, yet being related by historians of credit, and contradicted by no one writer, a man cannot avoid believing it, and can as little doubt of it as he does of the being and actions of his own acquaintance, whereof he himself is a witness. 9. Thus far the matter goes easy enough. Probability upon such grounds carries so much evidence with it, that it naturally determines the judgment, and leaves us as little liberty to believe or disbelieve, as a demonstration does, whether we will know, or be ignorant. The difficulty is, when testimonies contradict common experience, and the reports of history and witnesses clash with the ordinary course of nature, or with one another; there it is, where diligence, attention, and exactness are required, to form a right judgment, and to proportion the assent to the different evidence and probability of the thing: which rises and falls, according as those two foundations of credibility, viz. common observation in like cases, and particular testimonies in that particular instance, favour or contradict it. These are liable to so great variety of contrary observations, circumstances, reports, different qualifications, tempers, designs, oversights, &c., of the reporters, that it is impossible to reduce to precise rules the various degrees wherein men give their assent. This only may be said in general, That as the arguments and proofs pro and con, upon due examination, nicely weighing every particular circumstance, shall to any one appear, upon the whole matter, in a greater or less degree to preponderate on either side; so they are fitted to produce in the mind such different entertainments, as we call belief, conjecture, guess, doubt, wavering, distrust, disbelief, &c. 10. This is what concerns assent in matters wherein testimony is made use of: concerning which, I think, it may not be amiss to take notice of a rule observed in the law of England; which is, That though the attested copy of a record be good proof, yet the copy of a copy, ever so well end p.103 This sort of probability, which is the best conduct of rational experiments, and the rise of hypothesis, has also its use and influence; and a wary reasoning from analogy leads us often into the discovery of truths and useful productions, which would otherwise lie concealed. 13. Though the common experience and the ordinary course of things have justly a mighty influence on the minds of men, to make them give or refuse credit to anything proposed to their belief; yet there is one case, wherein the strangeness of the fact lessens not the assent to a fair testimony given of it. For where such supernatural events are suitable to ends aimed at by Him who has the power to change the course of nature, there, under such circumstances, that may be the fitter to procure belief, by how much the more they are beyond or contrary to ordinary observation. This is the proper case of miracles, which, well attested, do not only find credit themselves, but give it also to other truths, which need such confirmation. 14. Besides those we have hitherto mentioned, there is one sort of propositions that challenge the highest degree of our assent, upon bare testimony, whether the thing proposed agree or disagree with common experience, and the ordinary course of things, or no. The reason whereof is, because the testimony is of such an one as cannot deceive nor be deceived: and that is of God himself. This carries with it an assurance, beyond doubt, evidence beyond exception. This is called by a peculiar name, revelation, and our assent to it, faith, which [as absolutely determines our minds, and as perfectly excludes all wavering,] as our knowledge itself; and we may as well doubt of our own being, as we can whether any revelation from God be true. So that faith is a settled and sure principle of assent and assurance, and leaves no manner of room for doubt or hesitation. Only we must be sure that it be a divine revelation and that we understand it right: else we shall expose ourselves to all the extravagancy of enthusiasm, and all the error of wrong principles, if we have faith and assurance in what is not divine revelation. And therefore, in those cases, our assent can be rationally no higher than the evidence of its being a revelation, and that this is the meaning of the expressions it is delivered in. If the evidence of its being a revelation, or that this is its true sense, be only on probable proofs, our assent can reach no higher than an assurance or diffidence, arising from the more or less apparent probability of the proofs. But of faith, and the precedency it ought to have end p.106 before other arguments of persuasion. I shall speak more hereafter; where I treat of it as it is ordinarily placed, in contradistinction to reason: though in truth it be nothing else but an assent founded on the highest reason. Benedict De Spinoza, a Theologico-Political Treatise (1670), Chapter 6 John Earman Chapter 6, “Of Miracles” As men are accustomed to call Divine the knowledge which transcends human understanding, so also do they style Divine, or the work of God, anything of which the cause is not generally known: for the masses think that the power and providence of God are most clearly displayed by events that are extraordinary and contrary to the conception they have formed of nature, especially if such events bring them any profit or convenience: they think that the clearest possible proof of God's existence is afforded when nature, as they suppose, breaks her accustomed order, and consequently they believe that those who explain or endeavour to understand phenomena or miracles through their natural causes are doing away with God and His providence. They suppose, forsooth, that God is inactive so long as nature works in her accustomed order, and vice versa, that the power of nature and natural causes are idle so long as God is acting: thus they imagine two powers distinct one from the other, the power of God and the power of nature, though the latter is in a sense determined by God, or (as most people believe now) created by Him. What they mean by either, and what they understand by God and nature they do not know, except that they imagine the power of God to be like that of some royal potentate, and nature's power to consist in force and energy. The masses then style unusual phenomena “miracles,” and partly from piety, partly for the sake of opposing the students of science, prefer to remain in ignorance of natural causes, and only to hear of those things which they know least, and consequently admire most. In fact, the common people can only adore God, and refer all things to His power by removing natural causes, and conceiving things happening out of their due course, and only admires the power of God when the power of nature is conceived of as in subjection to it. This idea seems to have taken its rise among the early Jews who saw the Gentiles round them worshipping visible gods such as the sun, the moon, the earth, water, air, &c., and in order to inspire the conviction that such divinities were weak and inconstant, or changeable, told how they themselves were under the sway of an invisible God, and narrated their miracles, trying further to show that the God whom they worshipped arranged the whole of nature for their sole benefit: this idea was end p.107 so pleasing to humanity that men go on to this day imagining miracles, so that they may believe themselves God's favourites, and the final cause for which God created and directs all things. What pretension will not people in their folly advance! They have no single sound idea concerning either God or nature, they confound God's decrees with human decrees, they conceive nature as so limited that they believe man to be its chief part! I have spent enough space in setting forth these common ideas and prejudices concerning nature and miracles, but in order to afford a regular demonstration I will show— I. That nature cannot be contravened, but that she preserves a fixed and immutable order, and at the same time I will explain what is meant by a miracle. II. That God's nature and existence, and consequently His providence cannot be known I. That nature cannot be contravened, but that she preserves a fixed and immutable order, and at the same time I will explain what is meant by a miracle. from miracles, but that they can all be much better perceived from the fixed and immutable order of nature. III. That by the decrees and volitions, and consequently the providence of God, Scripture (as I will prove by Scriptural examples) means nothing but nature's order following necessarily from her eternal laws. IV. Lastly, I will treat of the method of interpreting Scriptural miracles, and the chief points to be noted concerning the narratives of them. Such are the principal subjects which will be discussed in this chapter, and which will serve, I think, not a little to further the object of this treatise. Our first point is easily proved from what we showed in Chap. IV. about Divine law— namely, that all that God wishes or determines involves eternal necessity and truth, for we demonstrated that God's understanding is identical with His will, and that it is the same thing to say that God wills a thing, as to say that He understands it; hence, as it follows necessarily from the Divine nature and perfection that God understands a thing as it is, it follows no less necessarily that He wills it as it is. Now, as nothing is necessarily true save only by Divine decree, it is plain that the universal laws of nature are decrees of God following from the necessity and perfection of the Divine nature. Hence, any event happening in nature which contravened nature's universal laws, would necessarily also contravene the Divine decree, nature, and understanding; or if anyone asserted that God acts in contravention to the laws of nature, he, ipso facto, would be compelled to assert that God acted against His own nature—an evident absurdity. One might easily show from the same premises that the power and efficiency of nature are in themselves the Divine power and efficiency, and that the Divine power is the very essence of God, but this I gladly pass over for the present. Nothing, then, comes to pass in nature1 in contravention to her universal laws, nay, everything agrees with them and follows from them, for whatsoever comes to pass, comes to pass by the will and eternal decree of God; that is, as we have just pointed out, whatever comes to pass, comes to pass according to laws and rules which involve eternal necessity and truth; nature, therefore, always observes laws and rules which involve end p.108 eternal necessity and truth, although they may not all be known to us, and therefore she keeps a fixed and immutable order. Nor is there any sound reason for limiting the power and efficacy of nature, and asserting that her laws are fit for certain purposes, but not for all; for as the efficacy and power of nature, are the very efficacy and power of God, and as the laws and rules of nature are the decrees of God, it is in every way to be believed that the power of nature is infinite, and that her laws are broad enough to embrace everything conceived by the Divine intellect; the only alternative is to assert that God has created nature so weak, and has ordained for her laws so barren, that He is repeatedly compelled to come afresh to her aid if He wishes that she should be preserved, and that things should happen as He desires: a conclusion, in my opinion, very far removed from reason. Further, as nothing happens in nature which does not follow from her laws, and as her laws embrace everything conceived by the Divine intellect, and lastly, as nature