Science in Christian Perspective




Miracles and David Hume

John A. Cramer
Physics Department
Oglethorpe University

From : PSCF 40 (September 1988) 131-137.

David Hume believed he had found an "everlasting check" against belief in miracles, "useful as long as the world endures." Indeed, Hume's proof has been a major skeptical influence. Careful consideration, however, uncovers a number of serious flaws in the proof which render it useless. In particular, Hume's confidence that a miraculous explanation is always less probable than a naturalistic one turns out to be misplaced.

In the introduction to his Everlasting Man, G. K. Chesterton remarked that many people "live in the shadow of the faith and have lost the light of the faith. "1 This sad state is not, I think, unrelated to the fact that the Christian faith itself has necessarily lived in shadows since the Enlightenment. There was unbelief before that time, but not until the Enlightenment was that unbelief intellectually respectable. A major contributor to this change was David Hume. Known more in his own time for his writings on English history, Hume is best known today as the greatest of skeptics.

It is not primarily his skeptical view of human knowledge that has damaged people's view of theology. Undoubtedly, the longest shadow Hume cast over theology came from his devastating critique of miracles. Almost single-handedly, he deprived the theology of the supernatural of its status as an intellectually respectable category of thought.

Hume's attack on miracles appears as a chapter in his primary exposition of skepticism, An Enquiry Concerning Human Understanding, published in 1748. Although this work is strongly associated with his skepticism, it is quite separable from it. In fact, in ways it is in conflict with both his empiricism and his skepticism, as we shall see.

Hume's Argument Against Miracles

Hume's argument, which he judged would be "an everlasting check to all kinds of superstitious delusion ... useful as long as the world endures,"2  can be briefly summarized: A miracle is necessarily less probable than any alternative explanation, so the alternative is preferred to the miracle. He concluded:

Upon the whole, then, it appears, that no testimony for any kind of miracle has ever amounted to a probability, much less to a proof; and that, even supposing it amounted to a proof, it would be opposed by another proof; derived from the very nature of the fact, which it would endeavor to establish. It is experience only, which gives authority to human testimony; and it is the same experience, which assures us of the laws of nature. When, therefore, these two kinds of experience are contrary, we have nothing to do but subtract the one from the other, and embrace an opinion, either on one side or the other, with that assurance which arises from the remainder. But according to the principle here explained, this subtraction, with regard to all popular religions, amounts to an entire annihilation; and therefore we may establish it as a maxim, that no human testimony can have such force as to prove a miracle, and make it a just foundation for any such system of religion.3

Hume's argument depends on the definition of a miracle as "a violation of the laws of nature," but these laws are established by "a firm and unalterable experience" against the occurrence of such violations. As he said:

... 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.... 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 be relates; then, and not till then, can he pretend to command my belief or opinion.4

Men of the eighteenth and nineteenth centuries shared Hume's post-Newtonian view of the "laws of nature," so his critique of miracles appeared unanswerable. Certainly no response to his arguments from those centuries has had an enduring influence. Anti-supernaturalism, both in and out of theology, flourished.

It was C.S. Lewis who first responded adequately to Hume. In his book Miracles, Lewis uncovered several serious defects in Hume's argument. The first is question-begging:

The question, "Do miracles occur?" and the question, "Is the course of Nature absolutely uniform?" are the same question asked in two different ways. Hume, by sleight of hand, treats them as two different questions. He first answers, "Yes," to the question whether Nature is absolutely uniform: and then uses this "Yes" as a ground for answering, "No," to the question, "Do miracles occur?" The single real question which he set out to answer is never discussed at all. He gets the answer to one form of the question by assuming the answer to the other form of the same question."5

To be fair, whether or not Hume himself understood the implications of his procedure, there is nothing wrong with answering a difficult question by recasting it into a form more easily answered. Possibly Hume would defend himself by claiming to have been following such a plan. Lewis' complaint is, however, that the answer to the "easier" question is assumed so that, in effect, the answer to the more difficult question is also assumed rather than discovered by reasoning.

Hume's reason for "assuming" that the laws of nature are absolutely uniform was that "a firm and unalterable experience has established these laws."6 In other words, experience confirms that the laws of nature are absolutely uniform. The laws of nature are absolutely uniform because, otherwise, they would never have been discovered as laws of nature. The process of determining what is and what is not a law of nature includes this absolute uniformity as a criterion.

The Laws of Nature & the Possibility of Miracles

These serious deficiencies of this post-Newtonian view of the laws of nature were overlooked by Hume. On the philosophical side, this is an inductive view of the laws of nature. Suppose, for example, we have never observed a swan that is not white. Therefore, we conclude by induction that all swans are white. Induction, however, is never sufficient to establish a generalization absolutely. It is always possible that, after a string of thirteen thousand fifty-one white swans, the thirteen thousand fifty-second swan examined will not be white. Laws of nature produced in the manner envisioned by Hume can never be determined to be absolutely uniform. All one can say is they have proven uniform to date. That is hardly the absolute uniformity required for Hume's "proof."

The irony of the situation is that Hume knew very well that there was a problem with inductive thinking.

Lewis noted, "The odd thing is that no man knew this better than Hume. His Essay on Miracles is quite inconsistent with the more radical, and honorable, scepticism of his main work."7 For example, commenting on the problems of human understanding, Hume said:

For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future. . . 8

Thus, Hume's empiricism conflicted with his view of the laws of nature. If past experience cannot be an absolute guide to the future, then no laws of nature derived from our experience of nature can be absolute. That he retained an absolutist view of the laws of nature in defiance of his own empiricism and skepticism is probably not so much evidence that he was truly a naturalist (rather than an empiricist) at heart, as it is evidence that he was an anti-supernaturalist at heart.

The scientific side of the deficiencies of Hume's view of natural law is not entirely his fault (though, here again, following his own skepticism should have restrained him from this error). Scientists of his time did nothing to discourage (indeed, many actively encouraged) the belief in absolute laws of nature. Nonetheless, even a student of introductory physics who has tried the experimental confirmation of Newton's second law of motion should be suspicious of absolutist formulations of the laws of nature. Certainly research scientists who have been actively involved in the discovery of laws of nature should know how difficult it can be to verify those statements we call the "laws of nature."

For example, in order to conclude that all swans are white, we will need to examine and classify swans. Getting down to the details immediately embroils us in unexpected difficulties. Here is a group of rather dingy gray swans. Do we classify them as white or gray swans? No, we wash them all. Most of them turn out quite white, but a few persist in their grayness and a few turn out yellowish. Now what should we do? Classify them all as white and assume the off-colors are due to some contaminant that cannot be washed off? Is the law of white swans absolute? Not on this showing, and Hume, the skeptic, should have anticipated it.

How relevant is the requirement that the laws of nature be absolute? Cannot Hume's proof be reformulated without absolute laws of nature? Essentially, that has been done by Antony Flew, a modern-day disciple of Hume. An immediate result of relaxing the requirement of absolute laws is that if the laws of nature are not uniformly and absolutely opposed to the occurrence of Miracles, one cannot claim that miracles never happen. However, Hume's revised argument now deprives anyone of the intellectual right to believe any putative miracle has happened because any other explanation is still more probable than a miraculous one.

The revision of Hume's argument costs the naturalist little for the difference between an absolute prohibition on miracles, and an absolute prohibition against believing in miracles is a small cost. The consequences are still disastrous for the supernaturalist who remains deprived of any intellectual right to exist.

Fortunately, some of the deficiencies of Hume's argument remain to be uncovered. In particular, attention needs to be focused on Hume's use of probabilities.

Scientists of his time did nothing to discourage (indeed many actively encouraged) the belief in absolute laws of nature.

Again, it was Lewis who first complained that Hume used probabilities just at the point where they necessarily break down.

Probabilities of the kind Hume is concerned with hold inside the framework of an assumed Uniformity of Nature. When the question of miracles is raised we are asking about the validity or perfection of the frame itself. No study of probabilities inside a given frame can ever tell us how probable it is that the frame itself can be violated. Granted a school time-table with French on Tuesday morning at ten o'clock, it is really probable that Jones, who always skimps his French preparation, will be in trouble next Tuesday, and that he was in trouble on any previous Tuesday. But what does this tell us about the probability of the time-table's being altered? To find that out you must eavesdrop in the master's common-room. It is no use studying the time-table.9

Lewis is actually reformulating Hume's own remarks in this complaint. We have already noted Hume's observation that, "If there be any suspicion that the course of nature may change ... all experience becomes useless, and can give rise to no inference or conclusion. "10 Once again, Hume's anti-supernaturalism overcomes his skepticism. Lewis' criticism is devastating, coming, as it does, almost from Hume's own mouth. The original prohibition against miracles, weakened into a prohibition against believing in miracles, has slipped yet further. In Hume's own words, the situation gives "rise to no inference or conclusion."

Nevertheless, we have reached a still very unsatisfactory state of affairs. The possibility of miracles cannot be denied but neither can it be affirmed. The supernaturalist has been allowed elbow-room at least, but the space allotted is airless and cannot sustain life. The naturalist is not much better of f (though after his

An immediate result Of relaxing the requirement of absolute laws is that if the laws of nature are not uniformly and absolutely opposed to the occurrence of miracles, one cannot claim that miracles never happen.

attempted murder of the supernaturalist his sadly reduced estate may not distress us overly much). There are other unsatisfactory features. As Lewis noted, "we cannot say that uniformity is either probable or improbable.... This result is equally disastrous for the scientist and the theologian; but along Hume's lines there is nothing whatever to be done about it. "11

Despite this unsatisfactory situation, Lewis considerably improved the logical status of miracles. Hume's 11 everlasting check to all kinds of superstitious delusion, " once regarded as the devastating and final argument against miracles, is palpably in error. We are not, however, quite back to where we started from before Hume. The doubts unleashed by the "proof" are not easily recalled. After all, even though the "proof" has turned out to be less than airtight, aren't miracles really very improbable? Isn't there some sense to the thought that explanations which avoid supernaturalism are always more probable than those that have recourse to the supernatural?

There are several things to be said in response to these doubts. The first is that, as has already been said, the probability of a miracle cannot be calculated because miracles are not a category amenable to such calculations. Hence, any argument which even estimates the probability of a miracle (an infinitely or very improbable event) is incoherent on the grounds that it is attempting to apply a procedure beyond its natural limits. Our calculations of probabilities are based on experience of natural events, but such experience cannot be applied with any confidence to supernatural events.

While strictly fair and proper, this response is likely to sound much like special pleading. It would appear we are establishing a favored category of explanations immune to the ordinary criteria by which we judge events. For example, while it might be emotionally satisfying to call the ordinary birth of a normal child a "miracle," doesn't this response reinforce a supernaturalistic account of childbirth (if one were foolish enough to advance one)?

In my opinion, this response does indeed offer reinforcement of such an improvident claim. That, however, is not a measure of its foolishness or weakness but of its strength. Only a very strong position can overcome the deficiencies of a weak idea. That is not to say that a supernaturalistic account of childbirth is true; it can be ruled out on other grounds related to the nature of miracles, rather than because it is improbable.

The force of the first response is so great that it might appear we need proceed no further, but there are good reasons for continuing. It is by no means clear yet that we have any respectable reason for believing miracles have occurred. So far we have only prevented the enforced conclusion that we cannot call anything a

There is simply no way to estimatethe probability of a supernaturalevent.

miracle. Also, the right to believe in a general uniformity of nature has not yet been established.

Examination of a Miracle

The right to believe in the uniformity of nature is important to me, as a physicist, but I will not pursue it here. Rather, I want to take a closer look at the problem of whether or not one can ever conclude a miracle has occurred. Considering the revised form of Hume's argument where the laws of nature cannot be regarded as absolutely uniform, and-for the hope of eventually improving the stalemate we have reached-setting aside the first response that the probability of a miracle can never be properly calculated, what happens when we examine a particular putative miracle?

Hume's proposal was, supposedly, to calculate the probabilities, compare them, and make a decision in favor of the more probable event. In actual fact, no such calculation has ever been attempted (to my knowledge). The results have always been assumed without substantiation. Why not try to carry out Hume's full program once just to see what happens? Since no event is more crucial to Christianity, I suggest we look at the Resurrection event and, as the alternative explanations, we take the orthodox, miraculous explanation and the explanation that the disciples and witnesses simply lied.

 We must calculate the probabilities of the two explanations being true. The probability of drawing the red

The probability of a miraculous explanation is not certainly smaller than the probability of a naturalistic explanation for an event. Hume was wrong.

marble from a bag containing one red marble and forty-nine white marbles is 1:50 (one out of fifty). This probability was found by assuming that the one outcome has occurred and dividing that number (1) by the number of possible outcomes (50 different marbles might have been drawn). To find the probability that a man has come back from the dead, we assign that one event the value (1) and divide that number by the number of possible outcomes. Now, what is the number of possible outcomes? This was just Lewis' point: that number is inherently indeterminant because we have no other events or other experiences to draw on in constructing the number of possible outcomes.

We have, however, decided to set aside Lewis' perfectly valid complaint. The only experiences to which we can then compare the Resurrection must be all other human deaths. Demographers say that the number of people alive today is equal to half of all the people who have ever lived. Thus, the number of human deaths since the world began is about the same as the number of people presently alive, say, about 5 x 109deaths. Hence, the probability of the Resurrection is 1:5 x 109 a small but certainly not infinitely small probability.

Quite likely someone will wish to complain, at this point, that the probability I have deduced is far too large. This probability is about one one-thousandth of the probability of winning the Readers' Digest Sweepstakes! The Resurrection is surely an extremely improbable event. Wouldn't 1:l0100 be closer to the mark? As I have said before, there is simply no way to estimate the probability of a supernatural event. The probability that a natural event will be unique is similarly incalculable (though every natural event is unique in some way). All that can be done, then, is to try to find a class of similar events that can correspond to the drawing of individual marbles from the bag. There are no set rules for this procedure. All I can say is that this seems a reasonable way of handling this particular event as a natural event. If a critic finds it unsatisfactory we can argue about it, but it is unlikely we will ever reach complete agreement. The stalemate is Hume's fault, not mine. It was his idea to calculate the probabilities.

As to the other explanation, there are five primary sources for the Resurrection: the four Evangelists and St. Paul. What is the probability that all these sources lied? First, we calculate the probability that one lied, and then we make a proper combination of five probabilities for the final result. How shall we find the probability that one source lied? Presumably, the ratio we want is 1 divided by the number of possible outcomes-but what outcomes should we count? Do we want the number of times witnesses lie when the lie will cost them their lives? Perhaps we should use the number of times pathological liars occur among normal people? Should we be looking for the frequency at which lies appear in legal testimony?

In fact, there is no clear way to proceed. Nothing in Hume's program guides us in this matter. Obviously, Hume never worried about the problem because he never seriously intended to do real calculations. We have seen that Hume's program is incoherent because it requires the use of a procedure beyond its proper limits. Now we find that the program cannot be carried out unambiguously; hence, it is additionally incoherent in the sense that one can never be certain just how the program is to be followed.

This new defect is serious, but, in any particular case, we may be able to get agreement on a range of probabilities. Suppose we find in a range between 1: 100 and 1:10,000 the probability that one of the sources lied (numbers I regard as very generous to Hume). When we now ask how we are to combine the five probabilities to get a total, further uncertainties arise. If the five accounts are independent, the proper procedure is to just multiply the five probabilities together. If they are not independent, we will need to know more of the nature of their relationship before we can proceed. Between the naturalist and the supernaturalist, it is unlikely we can even get agreement on which way to turn here and, again, Hume's program gives no guidance whatsoever.

Since the four Gospels all actually disagree in several details, I regard them as four independent sources, but possibly the naturalist, recognizing an advantage when he sees one, will insist on only two independent traditions. Also, is the Pauline information independent of Luke? If we decide Luke and Paul are not independent, then Mark and Matthew each form at least one other independent tradition. Thus, we have three to five independent sources. In the case of five independent sources, the total probability ranges from 1: 1010 to 1:1020. For only three independent traditions, a rough calculation gives the range 1:106 to 1:1012 . Hence, we

The concept of probability cannot apply to miracles because the use of probability requires a context (of repeated events) which does not characterize miracles.

have the 1:5 x 109 probability of a miracle, compared with a final estimate for the probability that all five sources lied ranging from 1:106 to 1:1020. It is, of course, a very broad range. That breadth is a reflection of the deficiencies of Hume's program.

In fact, it is hard to see how meaningful numbers can ever be generated for probabilities such as Hume claimed to consider. Anyone familiar with the calculation of probabilities for real events-for example, an accident at a nuclear power plant or (as Lewis suggested) the whole history of the Earth-should have been able to anticipate this difficulty. Hume lived before the development of most probability theory, so he could not have attempted this calculation (though that does not explain how he could attach such importance to an idea he only vaguely understood).

The final comparison is inconclusive. The probability of the Resurrection fits pretty much into the middl@ of the range of probabilities on the other side. Beyond further demonstration of the failings of Hume's program, the final calculations allow one last moral: The probability of a miraculous explanation is not cert@inly smaller than the probability of a naturalistic explanation for an event. Hume was wrong.


Taking stock of our progress thus far, we have found four serious flaws in Hume's proof that miracles do not occur. The first was that the proof begs the question by assuming the answer to the question in one form in order to get the answer to the question in another form. Contributing to the confusion here was a false idea of the laws of nature. If the proof is recast, using a better concept of natural law, it is reduced in force to a prohibition against believing miracles occur. A second flaw, that of using experience in one category to estimate probabilities of events proper to another category, undermined that proof, leaving us unable to say anything at all about the probability of a miracle.

On closer examination, we found that the entire program of calculating probabilities of the truth of explanations of an event is ambiguous and cannot be carried out coherently for two reasons. Firstly, the concept of probability cannot apply to miracles because the use of probability requires a context (of repeated events) which does not characterize miracles. Secondly, even treating miracles as part of a class of nonsupernatural events does not lead to an unambiguous, disagreement-free conclusion, because there is no certain way to estimate the probabilities of many of the relevant natural events. Lastly, we found that it simply is not true that the probability of a miracle will surely be less than of any naturalistic alternative account of an event. In fact, we found a number of possible estimates (remember, all these numbers are very uncertain) in which a miraculous Resurrection proved considerably more likely than reasonable, naturalistic alternatives.

Natural laws just don't seem to be absolute, and nothing can be done about that.

Thus, Hume's "proof" is so reduced in power that it is no longer the "everlasting check ... useful as long as the world endures," which its originator expected it would be.

It will do not good to respond, as I imagine someone may be tempted to do, that "you can prove anything with numbers." The complaint really rebounds to rather damage Hume's case. If the charge is correct, it shows that Hume made a poor choice of the terrain over which to mount an assault. Whether the response is valid or not, raising the issue at all is surely poor sportsmanship. Hume and his followers have crafted an argument, using probabilities, in a way they thought guaranteed them a win. It is hardly reasonable to complain of the rules after having lost at a game you invented.

Further Problems With Hume's Logic

There is a problem with Hume's argument that is quite unrelated to miracles. In Flew's revised form, it seems to me that the argument can be used to prevent a scientist from believing another scientist who announces a major discovery where a break with previous thinking is involved.

The recent announcement of high temperature superconductivity was received with great astonishment by the physics community. Indeed, the discoverers themselves reacted with considerable caution. The important point is that the announcement was not greeted with rejection and disbelief, although all that we know suggested at the time that the phenomenon was impossible. Even as I write, no explanation has been found.

If physicists still took Hume seriously, we would have no logical right to react as we did. Hume's logic would compel us to disbelieve the announcement because it claimed a wildly improbable thing really occurred. Scientists have been mistaken many times, and the new superconductivity claim was incredible. Therefore, Hume's argument implies, it would be illogical to believe the announcement because it is much more likely that a mistake had been made.

I think, based on my own reactions and speculating on the reactions of others, that the response was due to two things. First, we really believe and trust other physicists. That is, our estimation of the probability that a physicist would lie or be mistaken about such an important thing is very low. We judge it highly or even extremely improbable. Second, we judge our current wisdom and understanding of the laws of nature as tentative and incomplete. That is, we judge something that is wildly improbable by current understanding, not certain to be wildly improbable forever. In a sense, then, we physicists do follow Hume's advice.

It is not safe to try to draw incontrovertible conclusions from the behavior of scientists in these matters. It does seem fair to say, however, that the behavior of scientists can hardly be interpreted as supporting the drift of Hume's argument. The hidden agendas of Hume and Flew, a willingness to call others fools or liars and a wish to establish skepticism about claims for highly unlikely occurrences, are simply not generally shared by scientists. Physicists have a fairly well deserved reputation for hardheadedness and rationalism. Thus, it would seem that the route Hume and Flew advocated is not the only one deserving intellectual respect.

One final problem grows out of Hume's argument. Antony Flew noted that weakening the claim that natural law is absolute has repercussions for apologeties. Specifically, attempts to argue that miracles, like the Resurrection, "prove" that Christianity is true, are jeopardized.

It is only and precisely in so far as it [a miracle] must involve an overriding from outside and above-an event which, so to speak, Nature by herself must be unable to contrive-that such an event would force the conclusion that a transcendent Power is revealing itself.

This being so, it will get the apologist nowhere fast to urge that such a notion of the miraculous [as Hume's] is somehow quite unsound. He is the one who needs it, if, that is, the occurrence of a miracle is to serve as the credentials of his candidate revelation.12

Flew's point is that, if natural laws are absolute, a violation of natural law is an absolute sign of transcendence. if, however, natural laws are not absolute, as Hume's empiricism and the history of science indicate, then miracles cannot become invincible or absolute proofs of anything. I don't think we have much choice here. Natural laws just don't seem to be absolute, and nothing can be done about that. Flew, of course, wants apologists to retain absolute law so that he may further badger and flummox them. There is no reason to oblige him.

The point is significant, nonetheless. Miracles simply cannot be used as an absolute proof; a sort of cudgel with which to bludgeon infidels into silence, if not into belief. It never has been possible to use them so. The chief priests and Pharisees witnessed the natural consequences of the Resurrection and did not believe. The Athenians, hearing the preaching of Paul, were not absolutely compelled either into belief or disbelief.

Miracles are evidence for the truth of Christianity. They are not absolute evidence, but that is really nothing new. The early Church got along well without absolute evidence. This later Church, set in a culture more sophisticated about logical distinctions, will need to be more sophisticated too, but for all that, I see no reason it should not get along well without absolute evidence. At least, we do not have to contend with Hume's "proof." It is as dead as its author.


John A. Cramer is a physicist by training, with degrees in physics from Wheaton College (B.S.), Ohio University (M.S.) and Texas A & M University (Ph.D.). His areas of specialization have been low temperature solid state physics and the kinetic theory of gases. Dr. Cramer has taught at Wheaton College and The King's College, and is currently Associate Professor of Physics at Oglethorpe University in Atlanta, Georgia.


1G.K. Chesterton, The Everlasting Man. (Garden City, NY: image Books, 1955), p. 11.

2David Hume, An Enquiry Concerning Human Understanding. (LaSalle, IL: The Open Court Pub. Co., 1963), p. 121.

3Ibid., pp. 140,141.

4Ibid., pp. 127,128.

5C.S. Lewis, Miraclm, a Preliminary Study. (New York: MacMillan, 1947), p. 106.

6Hume, op. cit., p. 126.

7Lewis, op. cit., p. 106.

8Hume, op. cit., p. 39.

9Lewis, op. cit., p. 106.

10Hume, op. cit., p. 39.

11Lewis, op. cit., p. 107.

12Antony Flew, God and Philmophy. (New York: Dell, 1967), p. 148.