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

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

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

In lieu of an abstract, here is a brief excerpt of the content:Fogelin on Hume on Miracles Antony Flew I.Introduction In "What Hume Actually Said About Miracles"1 Robert Fogelin maintains that two contentions are essential to what, following Dorothy Coleman, he calls the "traditional interpretation" ofSection X ofthe first Enquiry. The first is that "Hume did not put forward an a priori argument intended to show that miracles are not possible"; the second, that "Hume did put forward an a priori (...) argument intended to show that testimony, however strong, could never make it reasonable to believe that a miracle had occurred." Fogelin further sees me as "virtually alone in challenging the traditional interpretation, arguing, in particular, that... Hume's argument was intended to do no more than place a 'check' on arguments put forward to establish... miracles on the basis oftestimony." Fogelin concludes his statement of what he wants to refute by quoting from my Hume's Philosophy ofBelief: What he is trying to demonstrate a priori in Part I is: not that, as a matter offact, miracles do not happen; but that, from the very nature of the concept—'from the very nature of the fact'—there must be a conflict of evidence required to show that they do. Fogelin's own contrary conclusion is agreeably forthright and decisive: "the traditional readingofHume's essay on miracles is wrong, and Flew, in rejecting the aspect ofthe traditional interpretation that is correct, is doubly wrong." II.What, indisputably, Hume did not say About all this the first thing which we need to recall is that Hume certainly does not present, and in consistency could not present, what is the most obvious a priori argument to show that miracles, defined as supernatural overridings ofthe order ofnature, must be (naturally and) physically impossible. That obvious a prior argument takes off from the semantic observation that to assert that a law of nature obtains is to assert, among other things, that the occurrence ofevents the occurrence of which would be inconsistent with the truth of that lawis (naturally and) physically impossible. Forit is only and precisely inasmuch as the assertion ofsuch laws embraces assertions ofphysical Volume XVI Number 2 141 ANTONYFLEW impossibility that it becomes logically possible to deduce contrary to fact implications from nomological propositions. It therefore follows immediately that miracles, thus defined, must be (naturally and) physically impossible. The key word 'miracle'has to be construed in this way since Hume is here concerned, primarily albeit not exclusively, with the possibility of proving the occurrence of a miracle "so as to be the foundation of a system of religion. I have taken care regularly to insert the parenthetic qualification "(naturally and)" in order to make it quite clear that no one is trying to rule out the occurrence of such Supernatural overridings as, by definition, fogically impossible. Being unable to discover any antecedent impression from which the idea of physical necessity could be derived, Hume disqualifies himself from appealing thus openly and directly to the necessary physical impossibility ofthe miraculous. But, even ifhe had to his own satisfaction succeededinlegitimatingthat crucial concept, it would still have been pointless here to point to the (natural and) physical impossibility of the miraculous—as if this was a reason for thinking that there have not in fact been and could not conceivably have been or be Supernatural overridings of the natural order. Had Fogelin noticed that Hume certainly did not present that obvious yet irrelevant a prior argument, he could not have concluded, not at least without emphatic qualification, "that this consensus on the first part of the traditional interpretation is unfounded."??. Proofs against proofs are no proofs In arguing about the interpretation of"the first part ofSection X ofthe Enquiry Concerning Human Understanding" Fogelin insists upon attending only to what Hume wrote in that one part ofone section. But suppose we refuse to follow him in imposing this curiously unscholarly self-denying ordinance upon ourselves. Then we find, in the very first sentence of Part II of that same Section X, that Hume is at pains to warnreaders that we are to construe the previous Part I: not as offering "an apriori argument... to show that testimony, however strong, could never make it reasonable to... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:An Intervention into the Flew/Fogelin Debate Kenneth G. Ferguson Under an aggressive title, Robert FogeUn has recently undertaken to reveal "What Hume Actually Said About Miracles."1 He felt this necessary to correct whathe considers a serious misreading ofHume's essay "OfMiracles" (sec. 10 ofthe Enquiries2), a reading which infers that Hume did not argue thatmiracles are impossible a priori (Fogelin, 81). One writer at least regards this reading so common (...) that she has dubbed it the "traditional interpretation" of Hume's account of miracles.3 At any rate, it finds a strong advocate in Anthony Flew,4 against whom the majority ofFogelin's comments are directed. What I find fascinating about this debate is that both Flew and FogeUn appear to be right. On the one hand, Hume does have the textual resources to marshall a fully deductive argument against miracles, at least, once a strict definition of miracles is admitted. On the other hand, while exploiting these resources, Hume somewhat clumsily mingles in vestiges ofa not-fully consistent inductive argument against miracles which he bases on the balancing of probabilities. I will attempt to identify these two skeins ofargument, in the anticipation that this will help to temper the debate between Flew and Fogelin. Hume opens section 10by promisingan argument that will furnish "an everlasting check to all kinds of superstitious delusion" (E 110). Moreover, he claims that "there is here a direct and full proof... against the existence of any miracle" (E 115), a quote which Fogelin repeats seven times (toextractits full flavour). C. S. Peirce, wholate inlife took an interest in Hume's argument, conjectured that Hume hoped to provide a general disproof of all miracles that would not require "a minute analysis of each story"; such a procedure was in fact popular amongthe miracle debunkers ofHume's day, forexample, Rev. Thomas Woolston, whose books were extremely popular.5 Hume's boast of "a direct and full proof might be assumed, offhand, to augur an a priori argumentbased on the comparison ofideas; butitmust notbe forgotten that back in the Treatise (for which the essay "Of Miracles" was originally drafted6) Hume defines a "proof" as an argument "deriv'd from the relation of cause and effect."7 There he contrasts "proofs" explicitly with the type of assured knowledge that comes "from the comparison ofideas" (T 124). Still, Hume requires that proofs, despite their empirical origin, must nonetheless be "entirely free from doubt Volume XVII Number 2 105 KENNETH G. FERGUSON and uncertainty" (T 124); proofs, then, must be superior to ordinary causal arguments that are able to offer only a degree of probability (T 124). By his own examples, namely, that "the sun will rise to-morrow" and "all men must dye" (T 124), likewise from the essay "Of Miracles" itself, that "lead cannot, of itself, remain suspended in the air" and that "fire consumes wood" (E 114), Hume makes it clear that "proofs" are simply to be causal arguments uniformly confirmed by a great wealth of past experience: empirical conclusions so sound that any who deny them "wou'd appear ridiculous" (T 124). Taking Hume's definition of "proof" to heart, we might infer that his "direct and full proof against miracles is not then to be an a priori or deductive conclusion, but instead merely a fully convincing induction, along the Unes of"all men must dye." This,would appear to dispel Fogelin's hope to portray the argument as a priori; but the logic ofHume's special proofagainst miracles is somewhat complicated. As Hume's own selection of examples verify, a proof, at least ordinarily, issues in the confirmation of a law of nature. This contrasts with the special proof against miracles where the object is, of course, not to defend a law of nature, but rather to exploit reasoning about the formation of such laws to prove a result regarding the occurrence of miracles. The proof against miracles, consequently, concerns causes, but is not necessarily a causal argument in the ordinary sense. Indeed, it might be properly thought ofas a "meta-causal" argument, if such a term is allowed. And such an argument may potentially have, as Fogelin proposes, an a priori... (shrink)