Too Much Evidence

Lachlan J. Gunn et alia argue in a paper, “Too good to be true: when overwhelming evidence fails to convince,” that in some situations, as you apparently gather evidence in favor of a theory, it becomes less and less likely to be true:

In this paper, for the first time, we perform a Bayesian mathematical analysis to explore the question of multiple confirmatory measurements or observations for showing when they can—surprisingly—disimprove confidence in the final outcome. We choose the striking example that increasing confirmatory identifications in a police line-up or identity parade can, under certain conditions, reduce our confidence that a perpetrator has been correctly identified.

Imagine that as a court case drags on, witness after witness is called. Let us suppose thirteen witnesses have testified to having seen the defendant commit the crime. Witnesses may be notoriously unreliable, but the sheer magnitude of the testimony is apparently overwhelming. Anyone can make a misidentification but intuition tells us that, with each additional witness in agreement, the chance of them all being incorrect will approach zero. Thus one might naïvely believe that the weight of as many as thirteen unanimous confirmations leaves us beyond reasonable doubt.

However, this is not necessarily the case and more confirmations can surprisingly disimprove our confidence that the defendant has been correctly identified as the perpetrator. This type of possibility was recognised intuitively in ancient times. Under ancient Jewish law, one could not be unanimously convicted of a capital crime—it was held that the absence of even one dissenting opinion among the judges indicated that there must remain some form of undiscovered exculpatory evidence.

This is an interesting situation, and someone might suppose that it is one where the evidence changes sides.

But this does not follow. The reality is a bit different. Suppose you flip a coin thirty times, and get heads every time. Each time you get heads, you receive evidence in favor of the hypothesis, “I am having a really lucky streak.” But each time you also receive evidence, and stronger evidence, in favor of the hypothesis, “This coin is biased.” After flipping it thirty times, you thus are likely to become very convinced of the latter hypothesis, and thus convinced that the former is mistaken. But this did not happen because at some point the evidence went from one side to the other, but because the evidence supported two different theories, and one more than the other.

However, regardless of exactly how we describe the situation here, this does have important consequences for the evaluation of multiple instances of testing the same thing. In the case of the police line-up discussed in the article, we know from experience that people are far from infallible in their identification. So if you have a large number of people who identify the same person, without any exception, that is strong evidence that the process is biased; perhaps the police encouraged the people to identify a particular person, for example. Likewise, eyewitness testimony tends not to be perfectly accurate. Consequently, if we take the testimony of many eyewitnesses to the same complex events, and there is not the slightest discrepancy, this is good evidence that their testimony is biased. Perhaps someone created a story and instructed them not to deviate from it, for example. And on the other hand, minor discrepancies in such accounts do not weaken their testimony, but strengthen it (although not to the discrepant point itself), by making it less likely that they are biased in such a way.

 

Miracles and Multiple Witnesses

A fairly frequent claim, often in connection with the alleged Marian apparitions at Medjugorje, although not only in that connection, is the claim that rosary chains have changed to gold, or become golden plated. Thus for example Fr. Francis Marsden makes this claim in a letter published in the Tablet on May 26, 1990:

Leaving for Medjugorje after Easter 1989, I decided I would take my own ordination pair of rosary beads (received from the Vatican in 1984). I had seldom used them but kept them as a memento. As I put them in a little cloth bag in my trouser pocket, I checked that they were silver. “If it does happen, I’d like it to happen to this pair”, I thought.

They remained in my pocket untouched down to Heathrow, and out to Zagreb, Split and Medjugorje, from Saturday night through to Monday lunchtime. Five of us priests were on top of Krizevac, the Hill of the Cross. I took out the rosary to say the Glorious Mysteries. To my shock and near-disbelief, the links by the medal glittered gold in the sunshine. Inspecting further, I found that all the links touching either a bead or the crucifix were now golden. “My God, it’s happened”, I thought, much moved.

The extra links separating the decades remained silver. The message for me was, “It is prayer which changes things”.

Later I checked the inside of the little cloth bag. The lining was clean. There were no signs of any metal having rubbed off. I also asked a priest friend with an identical Vatican silver rosary to try rubbing off the silver. He told me that after a long time scraping with a coin, he began to get a very slight dull bronze tinge to the silver. That degree of abrasion was impossible in my pocket.

Fr. Francis is here giving reasons for supposing that the change was not natural. Continuing in the same vein, he says:

So Mr. Falkiner’s theory fails to explain all the observed facts. Undoubtedly he is correct in some cases in suggesting that prolonged, sweaty use will cause tarnishing. But in my case and many others there has been no “hard use”. Nor has the trans-coloration been over all the links, but selectively and with a beautiful subtlety. I have seen several other patterns to the transformation.

Does air travel at 30,000 ft produce the change? Do some Medjugorje locals steal pilgrims’ rosaries from their pockets at night and spray them? Is it psychological wish-fulfilment? If so, please instruct me how to harness this power and, like Midas, I will try it out on some of our silver chalices and patens.

One Jesuit priest told me how he actually saw his rosary change colour. He and a friend were walking up Krizevac, joking about the phenomenon. taking 10p and 20p coins out of their pockets: “Has this one changed yet, Bernard?” “No, let’s have a look at this one . . .”. And as he was holding his rosary in his hand, he saw the golden colour come over it.

He has given some reasons for supposing that the change was not natural, but one could object that there is no external proof of the change. But in various cases people say that they experienced such a change, and confirmed it later by external testing. For example, William Simon says in his autobiography, A Time for Reflection,

After our first Mass at Medjugorje, I remember telling my son Billy, “That is the closest I’ve ever felt to heaven on earth.” I then pulled out the old, inexpensive rosary beads that I had bought about ten years earlier, and noticed that the chain was glittering in the sun. That was strange. The chain was just some cheap, dull alloy, yet it suddenly appeared radiant and golden and vibrant and remained so. I wasn’t quite sure what to make of it, and upon my return brought the rosary to a jeweler for an appraisal. He confirmed that the chain, inexplicably, had turned to solid gold. I can’t explain the transformation, either of the rosary  or of my own life, except as a sign of divine intervention, and accept it as such.

The total number of people who have claimed to have observed such cases is probably at least many hundreds, or more likely many thousands. I have seen one such rosary myself and can confirm that it appeared a golden color when I saw it. And while most people do not appear to have had any specific tests done, a number did do this, like William Simon in the above quotation.

Like reports of meteorites in the 18th century, these reports should be taken seriously. However, note that although we have multiple witnesses, the witnesses are not all to the same event, but to different events, and this can make a significant difference.

Suppose we took one such rosary, and passed it from person to person, each of them taking it and having it tested, and each confirmed that the metal of the chain had actually changed. If several dozen people confirmed this without exception, without bias in the selection of persons, including persons that had no interest in such a miracle, such as Jews and atheists, there would be no reason to doubt that the rosary chain was now gold or golden plated. It would be quite wrong to follow Hume’s advice and to dismiss this as risible rather than a matter of argument.

However, the argument in reality is much weaker because in fact these witnesses are testifying to separate events. If we have the situation described above, where dozens of witnesses confirm the same event, without a bias in the selection of witnesses, then if they are all wrong, something very unlikely has taken place: either they are all lying, their tests were all mistaken, or some combination of these things. This would be very unlikely indeed, in the situation described, and could easily be made more unlikely to whatever degree one desired, by renewed testing.

But suppose that in the actual case of multiple witnesses attesting to multiple events, no rosary chain has actually undergone such a change. This still implies that all of our witnesses are mistaken or lying. But it does not imply anything extremely improbable: there may have been people who tested their rosaries, and confirmed that nothing had changed, but there was no reason for them to publish the matter. Instead, only those published who were willing to lie, were mistaken, or who received mistaken results from their jewelers or chemists.

Thus it is very possible that the latter situation is the actual truth, and it would be a mistake to reject this possibility simply on the grounds that it is distrustful of human testimony.

But it is also possible that some of these chains have in fact changed to gold or become gold plated.

Hume’s Error on Miracles

After his comparison with the idea of the Real Presence, Hume continues by saying that we should proportion our beliefs to the evidence for them:

Though experience be our only guide in reasoning concerning matters of fact; it must be acknowledged, that this guide is not altogether infallible, but in some cases is apt to lead us into errors. One, who in our climate, should expect better weather in any week of June than in one of December, would reason justly, and conformably to experience; but it is certain, that he may happen, in the event, to find himself mistaken. However, we may observe, that, in such a case, he would have no cause to complain of experience; because it commonly informs us beforehand of the uncertainty, by that contrariety of events, which we may learn from a diligent observation. All effects follow not with like certainty from their supposed causes. Some events are found, in all countries and all ages, to have been constantly conjoined together: Others are found to have been more variable, and sometimes to disappoint our expectations; so that, in our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence.
A wise man, therefore, proportions his belief to the evidence. In such conclusions as are founded on an infallible experience, he expects the event with the last degree of assurance, and regards his past experience as a full proof of the future existence of that event. In other cases, he proceeds with more caution: he weighs the opposite experiments: he considers which side is supported by the greater number of experiments: to that side he inclines, with doubt and hesitation; and when at last he fixes his judgement, the evidence exceeds not what we properly call probability. 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. A hundred instances or experiments on one side, and fifty on another, afford a doubtful expectation of any event; though a hundred uniform experiments, with only one that is contradictory, reasonably beget a pretty strong degree of assurance. In all cases, we must balance the opposite experiments, where they are opposite, and deduct the smaller number from the greater, in order to know the exact force of the superior evidence.

While Hume is right to say that convictions should in some way be proportionate to the evidence for them, we can already see here the cause of a serious error. As I have pointed out elsewhere, Hume does not have a developed mathematical theory of probability. Hence his talk of how one should “deduct the smaller number from the greater, in order to know the exact force of the superior evidence.” If one takes this literally, this would suggest that something with no experiments supporting it has a force of 0; something with 35 experiments supporting it and nothing against has a force of 35; something with 40 experiments supporting it and 5 against has the same force; and so on. All of this, of course, is evidently absurd.

He then brings up the example of the testimony of witnesses:

To apply these principles to a particular instance; we may observe, that there is no species of reasoning more common, more useful, and even necessary to human life, than that which is derived from the testimony of men, and the reports of eye-witnesses and spectators. This species of reasoning, perhaps, one may deny to be founded on the relation of cause and effect. I shall not dispute about a word. It will be sufficient to observe that our assurance in any argument of this kind is derived from no other principle than our observation of the veracity of human testimony, and of the usual conformity of facts to the reports of witnesses. It being a general maxim, that no objects have any discoverable connexion together, and that all the inferences, which we can draw from one to another, are founded merely on our experience of their constant and regular conjunction; it is evident, that we ought not to make an exception to this maxim in favour of human testimony, whose connexion with any event seems, in itself, as little necessary as any other. Were not the memory tenacious to a certain degree; had not men commonly an inclination to truth and a principle of probity; were they not sensible to shame, when detected in a falsehood: were not these, I say, discovered by experience to be qualities, inherent in human nature, we should never repose the least confidence in human testimony. A man delirious, or noted for falsehood and villainy, has no manner of authority with us.
And as the evidence, derived from witnesses and human testimony, is founded on past experience, so it varies with the experience, and 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. There are a number of circumstances to be taken into consideration in all judgements of this kind; and the ultimate standard, by which we determine all disputes, that may arise concerning them, is always derived from experience and observation. Where this experience is not entirely uniform on any side, it is attended with an unavoidable contrariety in our judgements, and with the same opposition and mutual destruction of argument as in every other kind of evidence. We frequently hesitate concerning the reports of others. We balance the opposite circumstances, which cause any doubt or uncertainty; and when we discover a superiority on any side, we incline to it; but still with a diminution of assurance, in proportion to the force of its antagonist.
This contrariety of evidence, in the present case, may be derived from several different causes; from the opposition of contrary testimony; from the character or number of the witnesses; from the manner of their delivering their testimony; or from the union of all these circumstances. We entertain a suspicion concerning any matter of fact, when the witnesses contradict each other; when they are but few, or of a doubtful character; when they have an interest in what they affirm; when they deliver their testimony with hesitation, or on the contrary, with too violent asseverations. There are many other particulars of the same kind, which may diminish or destroy the force of any argument, derived from human testimony.
Suppose, for instance, that the fact, which the testimony endeavours to establish, partakes of the extraordinary and the marvellous; in that case, the evidence, resulting from the testimony, admits of a diminution, greater or less, in proportion as the fact is more or less unusual. The reason why we place any credit in witnesses and historians, is not derived from any connexion, which we perceive à priori, between testimony and reality, but because we are accustomed to find a conformity between them. But when the fact attested is such a one as has seldom fallen under our observation, here 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. The very same principle of experience, which gives us a certain degree of assurance in the testimony of witnesses, gives us also, in this case, another degree of assurance against the fact, which they endeavour to establish; from which contradiction there necessarily arises a counterpoize, and mutual destruction of belief and authority.
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.
The Indian prince, who refused to believe the first relations concerning the effects of frost, reasoned justly; and it naturally required very strong testimony to engage his assent to facts, that arose from a state of nature, with which he was unacquainted, and which bore so little analogy to those events, of which he had had constant and uniform experience. Though they were not contrary to his experience, they were not conformable to it.

While we might disagree that someone would be reasonable in refusing to accept testimony concerning the effects of frost, Hume’s general points here are fairly reasonable.

But when he attempts to apply to this miracles, he basically attempts to reason from the invalid mathematical points in the previous text:

But in order to increase the probability against the testimony of witnesses, let us suppose, that the fact, which they affirm, instead of being only marvellous, is really miraculous; and suppose also, that the testimony considered apart and in itself, amounts to an entire proof; in that case, there is proof against proof, of which the strongest must prevail, but still with a diminution of its force, in proportion to that of its antagonist.
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. 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, and there is required a violation of these laws, or in other words, a miracle to prevent them? Nothing is esteemed a miracle, if it ever happen in the common course of nature. It is no miracle that a man, seemingly in good health, should die on a sudden: because such a kind of death, though more unusual than any other, has yet been frequently observed to happen. But it is a miracle, that a dead man should come to life; because that has never been observed in any age or country. There must, therefore, be a 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 and full proof, from the nature of the fact, against the existence of any miracle; nor can such a proof be destroyed, or the miracle rendered credible, but by an opposite proof, which is superior.
The plain consequence is (and it is a general maxim worthy of our attention), ‘that no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish; and even in that case there is a mutual destruction of arguments, and the superior only gives us an assurance suitable to that degree of force, which remains, after deducting the inferior.’ 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. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle. 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.

There are various ways to read this, but each way leads to problems. Hume has told himself that he believes that he has found a conclusive proof that accounts of miracles should never be accepted; and this implies that he must be saying that his condition, that the testimony should “be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish,” can never be satisfied.

But there is no reasonable understanding where this condition can never be satisfied. Hume seems to be equating “more miraculous” with “less probable,” but there is no degree of probability that could not be established by witnesses in principle. Even if each witness has only a small chance of telling the truth, multiple independent witnesses could in principle establish any degree of probability whatsoever.

The basic problem here seems to be Hume’s mathematically incorrect understanding of probability. If something has never been seen to happen, he says, this is a full proof that it cannot happen. Thus he seems to imply that there is a 0% chance of it happening. But this is evidently unreasonable. In reality, of course, we often see particular things happen which never happened before. And similarly, it is simply not true that a miracle is only called a miracle because it “has never been observed in any age or country.” There have been many reports, in many ages and many countries, of dead people coming to life again. So the only way Hume could say that a dead person coming to life is a miracle in this sense, is by assuming that all of these reports are false. This is simply to assume what he is trying to prove, and in any case we think that resurrection is a miracle whether or not these reports are true. In other words, to say that resurrection is a miracle is not to say that these reports are false, but that if they are true, they are reports of miracles.

Taken in another way, Hume seems to be saying, “A miracle requires a suspension of natural laws. But false testimony does not. Therefore if we have the choice of believing that there was a miracle or of believing that there was false testimony, we should always choose to believe that there was false testimony.” The problem is that, again, if you evaluate this in terms of probabilities, the suspension of natural laws might well be more probable than a particular possibility which does not suspend natural laws. If someone predicts the result of a coin flip 100,000 times in a row, it does not violate natural laws to think that this happened by chance, with a fair coin. But it is much more probable that natural laws were violated, than that this happened by chance with a fair coin.

While it would only relate to Hume personally, we might also note that according to Hume, induction cannot even establish a probability, let alone a necessity.  So according to his position, the experience of dead people remaining dead does not make it improbable that one would rise, let alone excluding it as impossible.

Hume himself seems to sense that there is something wrong with his position, even if he cannot quite work out what it is, again probably on account of the lack of a mathematical theory of probability. Consequently he adds a number of arguments:

For first, there is not to be found, in all history, any miracle attested by a sufficient number of men, of such unquestioned good sense, education, and learning, as to secure us against all delusion in themselves; of such undoubted integrity, as to place them beyond all suspicion of any design to deceive others; of such credit and reputation in the eyes of mankind, as to have a great deal to lose in case of their being detected in any falsehood; and at the same time, attesting facts performed in such a public manner and in so celebrated a part of the world, as to render the detection unavoidable: all which circumstances are requisite to give us a full assurance in the testimony of men.
Secondly. We may observe in human nature a principle which, if strictly examined, will be found to diminish extremely the assurance, which we might, from human testimony, have in any kind of prodigy. The maxim, by which we commonly conduct ourselves in our reasonings, is, that the objects, of which we have no experience, resembles those, of which we have; that what we have found to be most usual is always most probable; and that where there is an opposition of arguments, we ought to give the preference to such as are founded on the greatest number of past observations. But though, in proceeding by this rule, we readily reject any fact which is unusual and incredible in an ordinary degree; yet in advancing farther, the mind observes not always the same rule; but when anything is affirmed utterly absurd and miraculous, it rather the more readily admits of such a fact, upon account of that very circumstance, which ought to destroy all its authority. The passion of surprise and wonder, arising from miracles, being an agreeable emotion, gives a sensible tendency towards the belief of those events, from which it is derived. And this goes so far, that even those who cannot enjoy this pleasure immediately, nor can believe those miraculous events, of which they are informed, yet love to partake of the satisfaction at second-hand or by rebound, and place a pride and delight in exciting the admiration of others.
With what greediness are the miraculous accounts of travellers received, their descriptions of sea and land monsters, their relations of wonderful adventures, strange men, and uncouth manners? But if the spirit of religion join itself to the love of wonder, there is an end of common sense; and human testimony, in these circumstances, loses all pretensions to authority. A religionist may be an enthusiast, and imagine he sees what has no reality: he may know his narrative to be false, and yet persevere in it, with the best intentions in the world, for the sake of promoting so holy a cause: or even where this delusion has not place, vanity, excited by so strong a temptation, operates on him more powerfully than on the rest of mankind in any other circumstances; and self-interest with equal force. His auditors may not have, and commonly have not, sufficient judgement to canvass his evidence: what judgement they have, they renounce by principle, in these sublime and mysterious subjects: or if they were ever so willing to employ it, passion and a heated imagination disturb the regularity of its operations, their credulity increases his impudence: and his impudence overpowers their credulity.
Eloquence, when at its highest pitch, leaves little room for reason or reflection; but addressing itself entirely to the fancy or the affections, captivates the willing hearers, and subdues their understanding. Happily, this pitch is seldom attains. But what a Tully or a Demosthenes could scarcely effect over a Roman or Athenian audience, every Capuchin, every itinerant or stationary teacher can perform over the generality of mankind, and in a higher degree, by touching such gross and vulgar passions.
The many instances of forged miracles, and prophecies, and supernatural events, which, in all ages, have either been detected by contrary evidence, or which detect themselves by their absurdity, prove sufficiently the strong propensity of mankind to the extraordinary and the marvellous, and ought reasonably to beget a suspicion against all relations of this kind. This is our natural way of thinking, even with regard to the most common and most credible events. For instance: There is no kind of report which rises so easily, and spreads so quickly, especially in country places and provincial towns, as those concerning marriages; insomuch that two young persons of equal condition never see each other twice, but the whole neighbourhood immediately join them together. The pleasure of telling a piece of news so interesting, of propagating it, and of being the first reporters of it, spreads the intelligence. And this is so well known, that no man of sense gives attention to these reports, till he find them confirmed by some greater evidence. Do not the same passions, and others still stronger, incline the generality of mankind to believe and report, with the greatest vehemence and assurance, all religious miracles?
Thirdly. It forms a strong presumption against all supernatural and miraculous relations, that they are observed chiefly to abound among ignorant and barbarous nations; or if a civilized people has ever given admission to any of them, that people will be found to have received them from ignorant and barbarous ancestors, who transmitted them with that inviolable sanction and authority, which always attend received opinions. When we peruse the first histories of all nations, we are apt to imagine ourselves transported into some new world; where the whole frame of nature is disjointed, and every element performs its operations in a different manner, from what it does at present. Battles, revolutions, pestilence, famine and death, are never the effect of those natural causes, which we experience. Prodigies, omens, oracles, judgements, quite obscure the few natural events, that are intermingled with them. But as the former grow thinner every page, in proportion as we advance nearer the enlightened ages, we soon learn, that there is nothing mysterious or supernatural in the case, but that all proceeds from the usual propensity of mankind towards the marvellous, and that, though this inclination may at intervals receive a check from sense and learning, it can never be thoroughly extirpated from human nature.
It is strange, a judicious reader is apt to say, upon the perusal of these wonderful historians, that such prodigious events never happen in our days. But it is nothing strange, I hope, that men should lie in all ages. You must surely have seen instances enough of that frailty. You have yourself heard many such marvellous relations started, which, being treated with scorn by all the wise and judicious, have at last been abandoned even by the vulgar. Be assured, that those renowned lies, which have spread and flourished to such a monstrous height, arose from like beginnings; but being sown in a more proper soil, shot up at last into prodigies almost equal to those which they relate.

Hume is making some reasonable points here. But note that all of these things are contingent. They could have been otherwise in general, and they might well be otherwise in particular cases, even actual ones. Consequently they cannot possibly amount to a full proof that miraculous accounts should not be accepted. The fact that Hume feels the need to point to these contingent facts shows that at some level he is aware of the fact that his argument is not conclusive, although he wishes it to be.

In the end, Hume’s argument does not establish anything, but only expresses his own incredulity, as in this example:

There is also a memorable story related by Cardinal de Retz, which may well deserve our consideration. When that intriguing politician fled into Spain, to avoid the persecution of his enemies, he passed through Saragossa, the capital of Arragon, where he was shewn, in the cathedral, a man, who had served seven years as a doorkeeper, and was well known to every body in town, that had ever paid his devotions at that church. He had been seen, for so long a time, wanting a leg; but recovered that limb by the rubbing of holy oil upon the stump; and the cardinal assures us that he saw him with two legs. This miracle was vouched by all the canons of the church; and the whole company in town were appealed to for a confirmation of the fact; whom the cardinal found, by their zealous devotion, to be thorough believers of the miracle. Here the relater was also contemporary to the supposed prodigy, of an incredulous and libertine character, as well as of great genius; the miracle of so singular a nature as could scarcely admit of a counterfeit, and the witnesses very numerous, and all of them, in a manner, spectators of the fact, to which they gave their testimony. And what adds mightily to the force of the evidence, and may double our surprise on this occasion, is, that the cardinal himself, who relates the story, seems not to give any credit to it, and consequently cannot be suspected of any concurrence in the holy fraud. 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 the circumstances of knavery and credulity which produced it. He knew, that, as this was commonly altogether impossible at any small distance of time and place; so was it extremely difficult, even where one was immediately present, by reason of the bigotry, ignorance, cunning, and roguery of a great part of mankind. He therefore concluded, like a just reasoner, that such an evidence carried falsehood upon the very face of it, and that a miracle, supported by any human testimony, was more properly a subject of derision than of argument.

This is a distorted account of the miracle of Calanda. Ironically, Hume’s position is actually supported to some extent by the errors contained in his own account of the miracle: we cannot “trace its falsehood,” in the sense that we cannot determine whether the account has been distorted by Hume himself, by the Cardinal, by the residents of Zaragoza, or by others, or some combination of these, but it is easy enough to determine the fact that it has been so distorted. Nevertheless, Hume is not proving anything here, but simply asserting that he would not believe in a miracle no matter how good the testimony brought in its favor.

This is not a reasonable attitude, but sheer stubbornness.