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The Presumption of Naturalism and the Probability of Miracles: A Reply to Keith Parsons


In “The Will to Believe” William James passed along an unorthodox definition of faith attributed to an anonymous schoolboy: “Faith is when you believe something that you know ain’t true.”[1] James himself considered this humorous concept symptomatic of a more serious if misguided conviction that whenever “sufficient evidence” for a religious claim is lacking, fear of its being false is somehow inherently more rational than hope of its being true. For the pragmatic James, faith operates by a risk-reward principle that at least offers the prospect of hope, if no guarantees; whereas skepticism is always a losing proposition because by it nothing can be gained. A little less than a century later, Carl Sagan advised a more cautiously empirical approach: “Extraordinary claims,” he said, “require extraordinary evidence.” In our scientifically enlightened culture, Sagan’s view has found the more receptive audience. Whether it be the resurrection of Christ or the healing of an amputee, in many circles a miracle claim seems hard to believe indeed apart from some unusually powerful evidence in support of it.
The popular sentiment that extraordinary claims require extraordinary evidence has since been revised by Keith Parsons as part of a sophisticated argument for naturalism. In Chapter Four of Science, Confirmation, and the Theistic Hypothesis, Parsons presents a general critique of miracle claims with the stated purpose of defending naturalism as a rational operating philosophy against potential defeaters.[2]

In this article I will try to answer what appears to be Parsons’ overriding contention—that belief in miracles simply has no legitimate place within a modernized, scientific society. Or as he puts it: “Supernatural interruptions into the natural order are not easily countenanced by the prevailing notions of scientific rationality.” Along the way I will address various claims by Parsons and suggest three broad counterclaims:

  1. For any currently unexplained phenomenon, the burden of proof falls equally upon naturalists and supernaturalists, whose respective explanations should be evaluated in proportion to the reasons and evidence offered for them.
  2. The repudiation of all miracle claims on the presumption of naturalism can only be maintained at the price of implicitly making naturalism unfalsifiable, which would disqualify naturalistic appeals to science against the miraculous in principle.[3]
  3. The element of subjectivity inherent in estimating the prior probability of miracles leaves open the prospect of confirming specific miraculous claims on the basis of historical evidence and eyewitness testimony.

The Presumption of Naturalism and The Burden of Proof

In laying out the historical context for these issues, Parsons alleges that miracle claims, having once enjoyed widespread acceptance in a bygone era of human naïvety and prevalent supernatural belief, are now “something of a stumbling-block.” It should be noted that many Christian apologists acknowledge the same. Kenneth D. Boa and Robert Bowman Jr., for instance, write: “To those who do not believe in God and are resistant to the idea of a miracle-working God, miracles are a major type of stumbling block to faith.”[4] This secular-scientific mindset has led many biblical scholars to adopt Rudolf Bultmann’s “demythologizing” exegetical methodology, which is premised on the idea that miracle claims are simply unnecessary embellishments to the historical and even theological core of the gospel message. Parsons is right to argue (in my opinion) that such a capitulation to modernist suppositions amounts to “just a rather disingenuous species of secular humanism.” A meaningful and robust theism must make room for the power of the deity to perform miracles.

According to Parsons, there are basically two kinds of apologetic rationale for permitting legitimate explanatory powers to the miraculous. The hard-line approach seeks to undercut the philosophical foundation of skepticism about miracles—naturalism—either by showing it to be self-defeating, or by providing incontrovertible evidence for a miracle. The soft-line approach treats judgments about whether miracles occur alongside judgments about beauty—in the “eye of the beholder” of unexplained phenomena. That is, the soft-line rationale takes the fideistic or subjective standpoint that belief in miracles is perfectly rational, at least for a believer. In that case the apologist must be content with making no inroads against naturalism.

Parsons contends that the hard-line argument against the coherence of naturalism fails on the grounds that its strongest presentation—by C. S. Lewis in his 1947 book Miracles—”has been ably and completely refuted elsewhere.” I am unmoved by such assurances, even when accompanied by a reference to an entire book dedicated to proving the point. If there is anything to be learned from the ongoing give and take among philosophers and theologians, it is that scarcely any major proposition is ever “ably and completely refuted”—that is, settled to the satisfaction of a broad cross section of observers from all sides of the issue. But suffice it to say that for the purposes of this paper, debate about the coherence of naturalism is best left for another discussion.

That leaves us with the question of the confirmation of miracles themselves via the hard-line approach; specifically, whether any proposed miracle claim can, in principle, be presented so convincingly that it leaves no wiggle room for naturalistic explanations whatsoever. Parsons answers in the negative, in part because formerly inexplicable phenomena have historically turned out to be easily explained by future scientific discoveries. So diseases, for example, are now understood to be caused by pathogens rather than by evil spirits. Implicitly Parsons’ argument seems to be that scientific discoveries have progressively confirmed naturalism while simultaneously discrediting supernaturalism in general and theism in particular. Thus the burden of proof for any miracle claim must, according to Parsons, extend beyond appeals to the current state of scientific knowledge and, in addition, preclude any conceivably rational naturalistic alternative explanation: “Hence, a miracle must be partially defined as an event that is in principle incapable of receiving a naturalistic explanation.”

While at first glance it may seem to be a great strength of the naturalist’s position, the implicit refusal to accept burden of proof may signal a great weakness. For it is difficult to imagine any event in space and time—no matter how clearly or completely at variance with the observable, regular operations of the physical world—which naturalists could not manage to ascribe to “nature.” To the extent that naturalists make this maneuver the presumption of naturalism appears suspect as a rational default position.

Mere conceivability of an alternate explanation for a claim should not be considered a legitimate defeater for that claim. Otherwise the claim that a flying orb appeared above the Dome of the Rock in Jerusalem and was filmed by scattered eyewitnesses (as reported by major news networks earlier this year[5]) could be handily defeated by merely imagining that the eyewitnesses were all involved in an elaborate hoax. But then a skeptic’s counterclaim that flying orbs do not exist, or at least do not appear above major landmarks in large cities, could just as easily be defeated by merely imagining that the flying orb accounts are true after all. At issue, then, are two claims rather than one. The theist proposes on the basis of some ordinary form of evidence that a miracle has occurred. The naturalist counters that no ordinary form of evidence could confirm a miracle, because—presumably—the evidence required to confirm a miraculous event would have to be as extraordinary as the event itself. But not all observers would agree to such a presumption of naturalism from the outset. Therefore each party bears a burden of proof commensurate with its particular claims. This is not to say that these burdens themselves are equal—the miracle claimant bears the heavier burden for the more extraordinary claim—but that the naturalist should not simply “win by default” wherever claims on unexplained phenomena have not yet been confirmed.

Now in a culture given to “prevailing notions of scientific rationality,” to even question the presumption of naturalism may seem… presumptuous. Parsons cites Antony Flew’s suggestion that establishing a reliable criterion for identifying a scientifically inexplicable event (a potential miracle) is impossible. Flew rejects the prospect of limiting the powers of nature to explain pretty much anything, writing: “[O]ur evidence about the powers of nature in general, and of man in particular, is precisely and only everything that things and people do.”[6] Flew’s seemingly innocuous statement actually strikes at the heart of supernaturalistic positions like miracle-affirming theism. If everything that happens necessarily owes to “the powers of nature” by definition, then admittedly naturalism must be true and miracle claims must be false. The question at hand, however, is whether evidence could ever support the occurrence of miracles on an evidential rather than stipulative formulation of naturalism. Flew’s stipulative formulation of naturalism simply begs that question.

Moreover, when the viability of his form of naturalism is at issue, Flew appears to abandon the strict criterion of potential falsification that he demands of theism. In his famous essay “Theology and Falsification” Flew compares belief in God to belief in an invisible gardener responsible for a plot of flowers and weeds discovered in a clearing surrounded by jungle. To the objections of a skeptic, a believer in the gardener concedes that no gardener is ever seen, nor sensed in any way, and that the “garden” appears suspiciously unkempt. Nonetheless, he maintains his belief, partly because no one can prove that his gardener does not exist. For Flew, such a belief is so loaded with ad hoc explanations and assumptions that it dies “the death by a thousand qualifications.” He closes with a question: “What would have to occur or to have occurred to constitute for you a disproof of the love of, or the existence of, God?”[7] I would call such an occurrence an antimiracle, a disproof so overwhelming that no theistic explanation could stand before it.

Flew’s question is sensible enough, but for the sake of consistency something similar should be asked of the naturalist: “What would have to occur to constitute for you a disproof of naturalism?” Both Parsons and Flew imply that no conceivable form of evidence can invalidate the presumption of naturalism; but if so, then the presumption of naturalism is itself incapable of falsification.[8] Does it then die a death by a thousand qualifications? Imagine Flew’s invisible gardener scenario, except with a garden that bears all the marks of diligent upkeep: Seeds are buried just below the soil, in straight rows equally spaced across the plot; wood stakes are placed upright, again arranged just so, upon which tomato and cucumber plants climb toward the sun; there is clear evidence of pruning; no weeds can be seen; and none of the ripened vegetables are ever found to have simply dropped to the ground, left to whither. In light of such cumulative evidence of conscious gardening activity, the bare fact that no gardener is directly visible may not be sufficient grounds for maintaining that impersonal natural causes were responsible instead.

It would seem, then, that a given scientific mystery or historical anomaly cannot be solved by simply replacing one metaphysical stopgap explanation—”God did it”—with an alternative metaphysical stopgap explanation—”Nature did it.” Yet among some naturalists this appears to be standard operating procedure. If such a strategy is justified, it ought to be conceded at the outset that miracles can never be confirmed because the sheer possibility of a naturalistic alternative explanation cannot be strictly falsified. But is that standard fair, or even reasonable? In light of their evident admiration for science and the scientific method, naturalists such as Parsons would not be expected to embrace an in principle irrefutable form of naturalism as a defense against any and all miracle claims.

One of the more useful functions of science is to separate the scientifically explicable from the purely metaphysical at the point of verifiability, or minimally at the point of falsifiability per Karl Popper’s philosophy of science. But Parsons seems to hold to a metaphysical (if not mystical) notion that with nature (as otherwise with God) “All things are possible.” That may be so, but in terms of testability this would leave little meaningful difference between God and nature. God is said to have created the universe with transcendent, supernatural power. Nature, on the other hand, is said to have brought forth the universe by undisclosed means at a mysterious initial point of almost unimaginable heat and density where two of the best-supported scientific theories of our time—general relativity and quantum mechanics—become irreconcilable. We may not all be comfortable depending on “faith” or “belief” to make sense of the universe, but in many respects the universe continues to leave us little choice.

Hume’s Argument and Bayes’ Theorem

Naturalism draws much of its strength from the notion of natural laws, unfailing regularities of the physical world that in principle can be observed and measured. In evident agreement with theistic philosopher Richard Swinburne on this point, Parsons notes that “a law of nature is not a mere description of observational results, but is a generalization or formula extrapolated from those results.” Isaac Newton’s F = ma (force equals mass times acceleration) is one example that comes to mind. That seems fair enough as a definition of a law of nature. Naturalism itself, however, requires a number of unverifiable assumptions—not only that nature is all that exists (at least on its most common formulation), but that nature has within itself the wherewithal to establish and manage these regularities so remarkably efficiently that no deviations from them have ever occurred in the entire history of the universe, and despite numerous appearances and reports to the contrary. If Parsons is correct, it is the latter assumption (or something much like it)—what could be rightly termed hard-line naturalism—that the hard-line apologist for miracles must overcome.

Parsons accordingly defines miracles as “events which we have every reason to believe are physically impossible; i.e., our best-confirmed natural laws must tell us that events of this sort cannot occur.” Taken to mean something like “Physical agents cannot cause physically impossible events,” such a definition would be unobjectionable: Only a supernatural agent could cause an event that is precluded by any form of natural causation. Otherwise, the definition of a miracle as an impossibility would be too far-reaching. According to John DePoe, “Only if one assumes that miracles must occur by natural means or that all events are natural events can one assign an infinitesimal probability to an event on the grounds that it is a ‘natural impossibility.'”[9] On one point at least there is no dispute: Events which strictly cannot occur are impossible indeed. David Hume began what most readers consider a sophisticated critique of miracles with a similar assertion: “There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appellation.”[10] Hume went on to argue that this same “uniform experience” disallows the very possibility of a reliable miracle account. That argument holds so long as uniformity stands as a given. To the contrary, answers C. S. Lewis, because such knowledge cannot be verified, it cannot be forwarded as a premise:

Now of course we must agree with Hume that if there is absolutely ‘uniform experience’ against miracles, if in other words they have never happened, why then they never have. Unfortunately we know the experience against them to be uniform only if we know all the reports of them to be false. And we can know all the reports to be false only if we know already that miracles have never occurred. In fact, we are arguing in a circle.[11]

Nonetheless, Hume’s procedure highlights, as Parsons notes, a conflict of evidence inherent in miracle testimony: the evidence of those claiming the miracle versus the evidence of nature suggesting that miracles do not happen. This observation led Hume to adopt a “general maxim” against miracle claims: “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.”[12] Even if a miracle were to occur, Hume seems to suggest, we would still have no justifiable basis for believing the extraordinary testimony of biased and fallible human beings making the claim against the accumulated weight of experiences and observations to the contrary; and therefore we would have no reliable means of inferring that a miracle had actually occurred. Given human nature, a reported angelic visitation would be most readily explained in terms of ordinary human realities—exaggeration, delusion, or hallucination—rather than a genuine interaction with the supernatural. The burden of proof for miracle claims in general would, it appears, always be too unwieldy for any particular miracle claim to manage. All this leads Parsons to the central question regarding extraordinary claims and corresponding evidence, “whether any evidence would be strong enough to establish that such events had taken place.”

Here the argument takes a statistical turn based on the axioms of probability. Conditional probability defines the probability of one event given the probability of another when the former is statistically dependent upon the latter. For example, suppose I place a Friday order with my favorite supplier for various production materials, including a box of widgets, due to arrive at my plant the following week, but I decide to order the widgets with the new polished finish instead of the usual standard finish. I know from industry insiders that my supplier has shipped 978 of 1000 widget orders complete, so the company’s fill rate (the probability of shipping an order complete) is roughly 98% for widgets. But then I discover that of the 25 orders placed for polished widgets in particular, only 18 have shipped complete. Given that the widgets are polished, the probability of an order of them shipping complete should be revised downward to 18/25, or 72%.

Now suppose that I don’t know anything about the fill rate for polished widgets. While I may have tremendous confidence that my supplier has shipped the order complete, based on personal experience of 100% filled orders going back as far as I can remember, my confidence may be shaken if I receive an advanced shipping notice which reads “Shipped – 0” on the polished widgets line item. It is of course conceivable—but not likely—that the advanced shipping notice is simply in error and my order shipped complete after all. But the introduction of this evidence will typically cause me to revise my initial probability estimate to account for the new information. If my supplier then calls me to apologize for failing to ship the polished widgets, my growing suspicion that the order did not ship complete has been all but confirmed. Conversely, the hypothesis that my supplier always ships orders complete has been essentially disconfirmed. (Depending on the strength of my prior belief, I may nonetheless continue to withhold skepticism until the order arrives and I inspect its contents personally.) Although I still don’t know the fill rate for polished widgets, I have taken into consideration the perceived strength of new evidence to revise my probability of receiving complete shipments somewhat downward. This “inverse” inference method is known as belief updating, the process used to derive a more accurate probability for an otherwise subjective initial estimate.[13]

More formally, Bayes’ theorem states that for a hypothesis with an unknown prior probability and evidence given for it, a revised or posterior probability p(h/e&k) will equal

---------   x   p(h/k)

where p(e/h&k) is the probability of our having the evidence if the hypothesis (h) is true, given our background knowledge (k); p(e/k) is the probability of our having the evidence itself, again given background knowledge; and p(h/k) is the prior probability of the hypothesis. When this prior probability is multiplied by a ratio estimating likelihood, or the degree to which the hypothesis predicts the evidence, the result is a more reliable posterior probability.

Incorporating the logic of Bayes’ theorem into his argument, Parsons explains why it should be considered statistically implausible that the weight of testimonial evidence in support of the hypothesis that a miracle has occurred will ever overcome the probability that a miracle has not occurred (~h) in light of background knowledge. A consequence of Bayes’ theorem is that the probability that the miracle hypothesis is true is greater than the probability that it is false, if and only if

p(e/h&k)       p(~h/k)
----------  >  ---------
p(e/~h&k)      p(h/k)

As Parsons says, p(e/~h&k) refers to the probability that we would have the evidence even had a miracle not occurred. The probability that a miracle occurred given only background knowledge is again represented as p(h/k), and the probability that no miracle occurred given background knowledge is represented as p(~h/k). Against this backdrop, Parsons proceeds to the core of the argument:

We have seen that a miracle, in order to do the job hard-liners require of it, must be a physically impossible event; otherwise it will be rational to regard it as scientifically inexplicable. A physically impossible event will, by definition, be as unlikely a priori as any contingent event could be. Hence, p(h/k) will be extremely low and, since p(~h/k) = 1 – p(h/k), p(~h/k) will be extremely high, p(~h/k)/p(h/k) will therefore be enormous indeed.

By these premises, the probability against a miracle in light of our present state of knowledge is extremely high, mainly because the a priori probability of a miracle is extremely low by definition. The hard-line apologist in that case faces the task of producing evidence for a miracle of such quantity and quality that it boosts the probability of that miracle beyond the already extremely high number represented by p(~h/k)/p(h/k). “The problem,” says Parsons, “arises with p(e/~h&k). Given what we know about human frailties and weaknesses, it seems quite likely that we would have the given testimonial evidence even if the miracle testified to had not occurred.”

In other words, even if plenty of admissible evidence is offered for a particular miracle, the probability for a miracle in light of that evidence must somehow overcome the impressive probability against, represented by a body of background knowledge that includes not only a well-documented progressive record of scientific discovery, but a general history of “human mendacity, gullibility, and superstitiousness.” Because of this basic untrustworthiness of human testimony, the value of p(e/~h&k) will be substantial regardless of whether a miracle has actually occurred. That leaves a ratio of p(e/h&k)/p(e/~h&k) that will in every conceivable instance be much lower than it must be to confirm the miracle. Or so Parsons argues.

Human Nature and Ockham’s Razor

The hard-line apologist can meet this challenge first by pointing out that human frailties and weaknesses are common to all humans. Presumably mendacity, gullibility, and superstitiousness do not confine themselves to religious people but apply to scientists and naturalists as well. This is not to deny that the institution of science has contributed immeasurably to advancements in medicine, technology, and human knowledge in general. Those successes are attributable largely to the scientific method and self-correcting mechanisms such as peer review. Yet despite a commendable determination to carefully track observations, test hypotheses with rigorous experimental designs, analyze results systematically, and so forth, scientists often maintain an evident confirmation bias in practice.

Examples of scientists clinging to a theory in the face of clear and mounting contrary evidence abound. The Piltdown Man hoax was foisted successfully on both the scientific community and the general public for over forty years.[14] Albert Einstein initially refused to acknowledge that his own theorem implied an expanding universe, and Arthur Eddington subsequently rejected the same proposition as “preposterous.”[15] More recently, after four years in the Stanford University biochemistry labs psychologist Kevin Dunbar observed a pattern in researchers’ behavior in response to unexpected findings: They would first fault the method, then retest; then if an anomaly remained, they would ignore it or make a note of it and file it away. “The scientists had discovered a new fact,” reported Dunbar, “but they called it a failure.”[16]

Untold instances of similar “failures” with respect to data bearing on the question of miracles would skew the perceived value of p(~h/k) upward—if, for instance, naturalists refused to acknowledge the testimony of their own senses, or even suppressed evidence for a bona fide miracle for no other reason than to maintain the presumption of naturalism. On that account p(~h/k) has been overestimated by scientists and naturalists, and thus it would not take a monumental increase of p(h/k) to reach a point where, with enough good evidence, a miracle claim would provide the most likely explanation for certain historical events in the context of Bayesian confirmation theory.

The hard-line apologist can also maintain that whether miracles occur is not at bottom a matter of probability in the first place, so Bayesian probabilistic considerations cannot be used to support a naturalistic defense against miracle claims. Such a defense would have to be found elsewhere. Indeed, Parsons’ appeal to statistical procedures does not involve the calculation of any actual probabilities, as none have been provided. They arguably cannot be provided, for the values assigned to the variables within the theorem largely depend on subjective perceptions of experience. Bayesian confirmation theory thus rests in part on the notion of confirmational relativity: “Evidential relationships must be relativized to individuals and their degrees of belief.”[17] Using the hypothetical example of the occurrence of a miraculous healing from cancer in light of prior experience and the evidence of a sudden unexplained recovery, Francis Collins comments accordingly: “To evaluate that question in the Bayesian sense will require you to postulate what the ‘prior’ is of a miraculous cure of cancer occurring in the first place…. This is, of course, where reasonable people will disagree, sometimes noisily.”[18]

“The problem,” according to Victor Reppert, “is that experience does not come to us in clean-cut pieces of uninterpreted fact. Rather, what we call experience is interpreted in terms of already-existing theoretical constructs.”[19] It was none other than David Hume who demonstrated the futility of appealing to probability without first acknowledging, explicitly or implicitly, the assumptions inherent in these theoretical constructs: “Probability is founded on the presumption of a resemblance between those objects of which we have had experience and those of which we have had none; and therefore it is impossible that this presumption can arise from probability.”[20] Put differently, the assumption of uniformity at the heart of Hume’s argument against miracles cannot be derived through probability, for probability depends on the assumption of uniformity. “And clearly,” adds Lewis, “the assumption which you have to make before there is any such thing as probability cannot itself be probable.”[21] Bayes’ theorem typically falls under the heading of “subjective probability,” and for good reason. That subjectivity only intensifies when the matter at hand invokes metaphysical notions such as an eternal, all-powerful God or a self-existent and self-regulating system of nature.

Some Bayesians would object that certain tools are available for settling upon an objective—or at least not purely subjective—prior probability for drawing a reliable statistical inference even with incomplete information. Ockham’s razor, for example, has often been cited as a general methodological rule for arriving at the simplest or most “compressed” hypothesis that explains the evidence. As attributed to medieval philosopher and theologian William of Ockham, Ockham’s razor maintains that “entities should not be multiplied beyond necessity” or “plurality should not be assumed without necessity.” So if p(e/h1) = p(e/h2), then the hypothesis containing the fewest explanatory elements should be chosen. The idea is that extraneous explanatory elements only serve to weaken or obscure explanations. If the doors creak in a house known to be drafty, we need not invoke the presence of ghosts to explain the noise. So in principle there may be a way to “objectivize” priors.

However, this appeal to parsimony appears to lead right back to the original problem. Supposing that one commits to apply the principle of parsimony before deciding upon priors, one would still have to decide which explanation is most parsimonious; and as the question at hand involves foundational metaphysical assumptions about reality, that decision would still have to be subjective, or belief-driven. It is not, after all, self-evident that a seemingly complicated or contrived “naturalistic” explanation necessarily multiplies entities less than a miracle claim which happens to accord well with the evidence in a theological-historical context. Some skeptics have suggested that theism is necessarily less parsimonious than naturalism if only because it adds a divine element on top of any competing natural explanation. But the respective explanations don’t always match up so neatly. There doesn’t seem to be anything especially parsimonious about postulating quantum fluctuations in a false vacuum as a precursor to the Big Bang, for example, to counter a theistic claim that the universe must have been caused. Nor is it particularly parsimonious, at least on its face, to introduce an infinity (or near infinity) of separate universes to dilute the probability of theism suggested by fine-tuning arguments. For his part, Ockham believed that the only truly necessary entity is God, for he is the only self-existent, hence noncontingent, being.[22] Though it is clear that naturalists would disagree with Ockham about what constitutes a truly necessary entity, that observation supports my point about the subjectivity of prior beliefs.

Given the subjectivity of one’s metaphysical presuppositions, Parsons’ appeal to probability—like that of Hume before him—becomes almost irrelevant. For if a God with power over nature exists and decides to perform a miracle, the probability for a miracle is precisely 1; but if neither God nor any other nature-transcending power exists, then nature is all that exists and the probability for a miracle is 0. There are no meaningful probabilities to be calculated in between the two poles of certainty and impossibility that could help us decide, on a priori grounds, the plausibility of miracles generally. That is, the a priori probability of miracles depends ultimately on the existence of an entity with nature-transcending power and a determination to perform a miracle, all of which amounts, arguably, to a theological proposition not subject to statistical analysis.[23]

With no way to derive a meaningful estimate of the prior probability of the existence of God, we would be left with no means to settle upon a general posterior probability of miracle claims. Perhaps Ockham’s razor could still prove useful, as we could set aside the question of priors altogether and simply consider for each case whether p(e/h) > p(e/~h). If so, then the miracle hypothesis might turn out to be more likely than not given the evidence bearing on the case. Some would consider this less a matter of induction or probability than of abductive reasoning, or inference to the best explanation. Such a procedure would demand careful investigative skills, familiarity with both qualitative and quantitative research methods, and the ability to sift through reams of related philosophical, theological, scientific, and historical information.

History, Science and the Miraculous

Of course, miracles would still have to be regarded as highly “improbable” according to a frequency interpretation of probability, for by definition they do not happen very often. But in principle individual miracle claims could be validated on the basis of their surrounding historical evidence, just as singularly improbable historical events have been, such as Henry V’s victory over the French at Agincourt in 1415, Bob Beamon’s record-shattering long jump in Mexico City in 1968, or the destruction of the World Trade Center in New York City by international terrorists using domestic airliners as missiles in 2001. Nassim Taleb dubs certain unlikely occurrences black swans (after the creatures unexpectedly discovered in Australia in 1697), namely high-impact events that take place precisely because they are improbable: “Think of the terrorist attack of September 11, 2001: had the risk been reasonably conceivable on September 10, it would not have happened.”[24] History, then, would suggest that the best explanation for a historical claim is not necessarily the most probable in Bayesian terms, but the most consonant with the prima facie evidence relevant to the case.

To clarify, the ultimate source of a given phenomenon, historical or otherwise, need not be identified to assess the strength of a specific claim relative to the evidence cited in support of it. That distinction applies even to evidence for the laws of nature themselves. For example, the attraction between bodies with mass in inverse proportion to the square of the distances between them might be due to nothing more than the efficient self-governance of nature. Or it may be that innumerable angels are assigned to regulate the complex gravitational attractions between and among innumerable bodies with mass. Alternatively, perhaps at creation the deity established an intricate system of initial conditions and defining parameters within which gravitational forces would operate necessarily and consistently.

“Gravity” would be an appropriate designation for the invisible force governing the observable interactions of massive bodies regardless of whether nature, the direct activity of God, or the indirect activity of God were its ultimate cause. “The point to note here,” the logician Irving Copi writes, “is that from the point of view of observability and direct verifiability there is no great difference between modern scientific theories and the unscientific doctrines of mythology or theology. One can no more see or touch a Newtonian ‘particle,’ an atom, or electron, than an ‘intelligence’ or a ‘gremlin.'”[25] It should go without saying that if God is either the direct or indirect cause of gravity, then God has the power and authority to override gravitational forces at his discretion. On the question of ultimate cause Newton himself remarked, “Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers.”[26]

The metaphysical identity of gravity’s own cause therefore remains a mystery no matter how precisely and consistently we are able to predict the behaviors between and among massive bodies. That being the case, theism and naturalism remain equally unaffected by the ongoing success of science—at least with respect to gravity.

With no direct evidence available to confirm one ultimate cause rather than another, the laws of nature would seem to be descriptive rather than prescriptive. Hume may be summoned as a surprise witness for the defense of miracle claims, at least on this point. On the assumed necessary relation of cause and effect at work in nature, widely acknowledged to be the foundation for the scientific method and belief in natural laws, Hume was famously skeptical. Following a carefully reasoned case demonstrating that no logically necessary connection can be established between any proposed set of causes and effects, he concluded:

‘Tis therefore by EXPERIENCE only, that we can infer the existence of one object from that of another. The nature of experience is this. We remember to have had frequent instances of the existence of one species of objects; and also remember, that the individuals of another species of objects have always attended them…. Thus we remember to have seen that species of object we call flame, and to have felt that species of sensation we call heat. We likewise call to mind their constant conjunction in all past instances. Without any further ceremony, we call the one cause and the other effect, and infer the existence of the one from that of the other.[27]

If Hume is correct then what we call a law of nature is little more than an interpretation of ordinary human experience, which by definition does not include extraordinary experience. Textbook presentations of the laws of nature typically have cleaned up messy details—like experimental anomalies, statistical outliers, and fiercely opposing opinions among researchers—arguably due to extraordinary experience. The inductive method discloses mainly what selected pools of data have confirmed so far in respect to a specific theory, not what can and cannot happen in the grand scheme of things. Philosophers like Peter Strawson have addressed this problem by saying that induction is such a pervasive part of human reasoning that it ought to be accepted as intrinsically valid, like the axioms of logic or mathematics. “But,” says Samir Okasha, “most people agree that it is very hard to see how there could be a satisfactory justification for induction.”[28]

The naturalist’s appeal to scientific progress arguably fares no better than the principle of induction in explaining evidence for miracles. That is, if the accumulation of scientific data never actually closes the “gaps” in our knowledge but simply creates new ones, it may be that the gaps will never close. It could be said that the flip side of ongoing scientific progress is enduring scientific ignorance. At first blush this may seem a radically postmodern notion, which perhaps explains why those who hold it are often called antirealists. Appropriately enough, one of the most common rejoinders raised against the antirealism position is known as the “no miracles” argument. Okasha explains:

According to this argument, it would be an extraordinary coincidence if a theory that talks about electrons and atoms made accurate predictions about the observable world—unless electrons and atoms actually exist…. On this view, being an anti-realist is akin to believing in miracles. Since it is obviously better not to believe in miracles if a non-miraculous alternative is available, we should be realists not anti-realists.[29]

But in the history of science certain popular and empirically successful theories, such as the phlogiston theory of combustion and the wave theory of light, have subsequently turned out to be false. “Once we pay due attention to the history of science, argue the antirealists, we see that the inference from empirical success to theoretical truth is a very shaky one.”[30] This historical pattern leads to a paradox for naturalists who see superstition in errors of the past but fail to appreciate that their own theories could eventually succumb to the same fate. If the realists are correct to say that falsification of an empirically successful theory is akin to a miracle, then the history of science itself suggests that belief in something akin to miracles is quite warranted.

Any given miracle claim ought to be evaluated on the basis of the evidence offered in support of it in a religious-historical context, then, not on its perceived compatibility with currently accepted but likely soon to be displaced (or at least substantially modified) scientific theories. Hume himself offered what may appear at first glance to be a similar plea: “A wise man … proportions his belief to the evidence.”[31] Assessing the evidence for a particular claim in a relevant historical context, however, is just what Hume’s generalized inductive approach does not do. As Norman Geisler objects, Hume’s dictum confuses the concepts of evidence and probability: “What Hume overlooks is that the wise people base their beliefs on facts, not on odds. Sometimes the ‘odds’ against an event are high (based on past observation), but the evidence for the event is very good (based on contemporary observation or testimony).”[32]

Given that a metaphysical belief—whether belief in God or belief in a closed system of nature—ought to be regarded as unverifiable, a proposed correspondence between a certain miracle claim and the objective evidence supporting it should decide whether or not that particular miracle has actually occurred.[33] Here the naturalist’s demand for extraordinary evidence is understandable, for in principle it would not take many well-confirmed miracles to completely discredit naturalism. Miracles would falsify naturalism in the same way that disconfirming evidence would falsify a scientific theory. Appeals to science, then, cannot rescue naturalism from miracles. At issue is precisely the possibility of a temporary break in the natural order, so that the issue cannot be decided simply on the basis of assuming an unbroken natural order underlying the scientific method. Moreover, in-principle falsifiability lies at the heart of the scientific method. If any given law of science should be regarded as subject to potential falsification at any time, then the laws of science cannot be cited as evidence against the potential falsification of naturalism in the form of a miracle.

Still, the nature of the evidence for miracles, and the character of those advancing miracle claims, remain important questions. According to Parsons, “All our evidence for the laws of nature arises from observation,” and because observation is verifiable, it is inherently more reliable than eyewitness testimony of a singular past event. Though certainly valid to a point, this dichotomy should not be overstated. Testimony itself, after all, arises from observation. Our knowledge of history, from the Peloponnesian War to the Peace of Westphalia, depends at least in part on the testimony of eyewitnesses. Much if not most of what passes for reliable information even in our scientifically minded society can be found in what may be loosely called “testimony”—of writers, researchers, and instructors, often communicated through little more than the pages of a textbook.

Miracles in Context

At this point let us revisit what the miracle claimant actually says about miracles. What is the nature of the claim itself? The Bible consistently denotes miracles as “signs and wonders,” conspicuously marvelous happenings designed to glorify God and encourage faith. From a theological standpoint miracles should not be defined as scientifically inexplicable or physically impossible arbitrary events, but as divinely ordained interruptions into perceived patterns of predictable, seemingly hopeless regularity. Miracles thus require a theological or religious context. As Geisler puts it:

From the scientific, observational viewpoint [a miracle] might appear to be simply an anomaly of nature, i.e., a natural event that has not yet been shown to fit a lawful pattern. But, in the case of a miracle, there would be a context of theistic claims to give it intelligibility.”[34]

The significance of the purported Easter miracle, for example, is not just that a man who was dead now appears to be alive, but that this man claimed to be the Son of God, preached eternal life, predicted his own death and resurrection, and subsequently appeared to his disciples to instill hope in their hearts that his message was the truth. William Dembski adds that the sign of the resurrection was not arbitrary or irrational, but specifiable: “Jesus, in predicting his resurrection, clearly specifies it as a sign. The resurrection is therefore not simply some incredibly unusual event that hits us out of the blue. Instead it is a specified event.”[35] If this theological understanding of miracles seems overly permissive to hard-line naturalists, perhaps they have misinterpreted their own experiences of regularity as indicative of strictly inviolable natural laws, the limits of which define the realm of impossibility. But the realm of possibility almost certainly extends beyond what has been revealed to human experience. Hume realized as much, again in the context of dismantling any deductive a priori basis for cause and effect:

Our foregoing method of reasoning will easily convince us, that there can be no demonstrative arguments to prove, that those instances, of which we have had no experience, resemble those, of which we have had experience. We can at least conceive a change in the course of nature; which sufficiently proves, that such a change is not absolutely impossible. To form a clear idea of anything, is an undeniable argument for its possibility, and is alone a refutation of any pretended argument against it.[36]

In Hume’s parlance, there are no demonstrative (deductive or logically conclusive) arguments to prove the impossibility of instances of which we have had no experience—a category which necessarily includes miracles for those who have not personally witnessed them. Moreover, since we can at least conceive (postulate or conceptualize) a break in the natural order, there is nothing intrinsically impossible about the occurrence of a miracle.

Adding to the theme found in Hume and Sagan that eyewitness testimony is generally unreliable and that even honest and sincere people are susceptible to deception, Parsons goes on to maintain that “it can be fairly concluded that the stronger a set of beliefs are, the more they will tend to distort perception.” Here Parsons seems to mean that because religious beliefs are especially strong, the religious context in which miracles are said to take place is itself a liability for the miracle claimant. This implied bias on the part of believers may not apply so well in the case of Jesus’ own disciples, whom the Gospels describe consistently as fearful, of little faith, and “slow of heart to believe.” According to accounts like those involving “doubting Thomas,” the disciples were convinced of the resurrection only on the strength of extraordinary evidence. Besides, Parsons is not a neutral observer in this sense. The issue again does not concern one belief system with claims on the evidence, but two—theism and naturalism—and therefore two drastically different sets of beliefs are both subject to such distortion.

Missing this point risks committing the genetic fallacy by maintaining that religious explanations are suspect for no other reason than that the people who advance them are religious. Still, the temptation to expose the presumably superstitious psychological roots of supernaturalism may be too great for a naturalist eager to debunk all miracle claims in one stroke. Reiterating the point introduced by Hume, Parsons alleges that “primitive cultures, as a rule, are much more credulous with respect to miracle-claims than scientific ones.” If miracles could be rightly defined as scientifically inexplicable phenomena, then perhaps that statement would pass muster. However, as Parsons has gone to some lengths to demonstrate, naturalists rather uncritically believe coherent naturalistic explanations to be forthcoming even for realities not currently explicable in scientific terms. In other words, naturalists are, not surprisingly, quite credulous when it comes to naturalistic interpretations of even the most seemingly improbable events.

For example, I have never witnessed an origin of life event. To my knowledge, neither have naturalists or anyone else. In one sense (one notably used by Hume) that makes the origin of life an inarguably improbable event. Nonetheless, all of us are faced with indisputable evidence—being alive—that life actually originated one way or another despite whatever slim probabilities ought to be assigned to origin of life events on the basis of human experience or scientific observation. Where Christian theists interpret this actualized improbability as evidence of divine creation, naturalists posit various theories of abiogenesis. The point here is not that the origin of life was necessarily a miracle, but that a tremendously improbable event nevertheless must have taken place. Tremendous improbability, then, cannot serve as a valid justification for summarily rejecting miracle claims.


I have aimed to show that Parsons’ naturalistic defense against hard-line miracle claims depends on an unreasonable presumption of naturalism. However, this presumption is neither a verifiable fact nor a self-evident truth and thus cannot serve as reliable background knowledge that would statistically defeat any proposed miracle claim. As Dembski observes, “Naturalism is a metaphysical position, not a scientific theory based on evidence.”[37] If there remains no prima facie justification for the presumption of naturalism, there remains no corresponding hard-line burden of proof for miracle claimants. This leaves the veracity of miracle claims an open question where any particular miracle claim may be subject to confirmation. John DePoe agrees: “Since miracles cannot be given an infinitesimally low probability, then it remains possible in principle to accumulate enough finite evidence to confirm a miracle.”[38] To determine the relative likelihood of particular miracle claims, each claim would have to be evaluated on the quality and quantity of the reasons and evidence cited in support of it. Apologists such as William Lane Craig, Gary Habermas, and J. P. Moreland maintain that the resurrection of Christ, for example, can be proven beyond a reasonable doubt not with probabilities derived from statistical theorems, but with “cumulative case” arguments—qualitative appeals to the perceived cumulative weight of historical evidence for the resurrection against any proposed alternative theory.

On one point Christian theists would agree with Parsons: “It is … unquestionably true that if the physical resurrection of Jesus can be shown to have occurred, this would lend strong support to the claim that Christianity is the one true religion.” Although Parsons mentions this in the context of comparative-religious miracle claims, which may be played against one another by the skeptic, his statement is telling. In the context of assessing the plausibility of miracle claims in general, confirmation of the resurrection of Jesus would demonstrate that at least one genuine miracle had indeed taken place.

At any rate, nothing in probability or statistics seems to preclude one from reasonably concluding that Jesus rose from the dead in light of the facts of the case. According to Christian philosophers Peter Kreeft and Ronald Tacelli, those facts include “the existence of the Gospels, the origin of the Christian faith, the failure of Christ’s enemies to produce his corpse, the empty tomb, the rolled-away stone [and] the accounts of the post-resurrection appearances.”[39] I have already mentioned the origin of life as a case of seemingly extreme improbability actualized by unknown means. I would suggest that the resurrection of Christ belongs in the same category. At minimum, the resurrection should qualify as a serious candidate for historical confirmation of a miracle. Others, of course, would disagree. To those who disagree on the basis of Bayesian confirmation theory and prior scientific knowledge, I refer once more to Hume’s own skepticism of induction. As he objected quite reasonably, “Your appeal to past experience decides nothing in the present case.”[40]


[1] William James, The Will to Believe and Other Essays in Popular Philosophy (New York, NY: Longmans Green and Co., 1907), p. 29.

[2] Keith M. Parsons, Science, Confirmation, and the Theistic Hypothesis (Ph.D. Dissertation, Queen’s University, 1986), Ch. 4 (“Miracles, Confirmation, and Apologetics“). From here on out all Parsons quotations will refer to this source without further citation.

[3] By ‘naturalism’ I mean the metaphysical position rather than the methodological principle; and by ‘presumption of naturalism’ I mean the implication that naturalism ought to be presumed true until proven false. Naturalism may be broadly defined as the belief that nature is all that exists, but can also refer to the narrower view that nature is a closed system in the sense that nothing that is outside of nature can affect anything inside of it. (Either version would effectively exclude miracles.) For example, see Keith Augustine, “A Defense of Naturalism” (Master’s thesis, University of Maryland, College Park, 2001) and Paul Draper, “Natural Selection and the Problem of Evil” in God or Blind Nature? Philosophers Debate the Evidence, ed. Paul Draper (The Secular Web, 2007-2008).

[4] Kenneth D. Boa & Robert Bowman Jr., Faith Has Its Reasons: An Integrative Approach to Defending Christianity (Waynesboro, GA: Paternoster, 2006), p. 507.

[5] See for example Michael Wuebben, “UFO Sighted Over Jerusalem,” CBS News, February 3, 2011. Retrieved from

[6] Antony Flew, “Miracles” in The Encyclopedia of Philosophy ed. Paul Edwards (New York, NY: MacMillan, 1967), pp. 348-349. Before Flew passed away in April 2010, he publicly announced that he had abandoned atheism for a sort of deism in 2004. Though this surprising announcement was met with mixed reviews, atheists and theists alike largely agree that Flew wrote his most influential work when he was an atheist and commentator on David Hume’s skeptical empiricist philosophy. Flew’s “The Presumption of Atheism”—a chapter of his God, Freedom and Immortality: A Critical Analysis (Buffalo, NY: Prometheus Books, 1984)—famously argued that theists rather than skeptics bear the burden of proof for their position because theists affirm their position while skeptics merely refrain from affirming the theistic position. Since Flew understands atheism here as mere lack of commitment to theism, his presumption of atheism is not analogous to what I am calling the “presumption of naturalism,” for naturalism (however it is characterized) entails distinct metaphysical claims of its own.

[7] Antony Flew, “Theology and Falsification,” University, 1950-51. Reprinted in Joel Feinberg (ed.), Reason and Responsibility: Readings in Some Basic Problems of Philosophy (Belmont, CA: Dickenson Publishing, 1968), pp. 48-49.

[8] Parsons does admit the sheer possibility of scientifically inexplicable phenomena: “Perhaps if all the galaxies in the Virgo cluster were instantly rearranged so that when viewed from earth they spelled out ‘PREPARE TO MEET THY GOD’ this would be a good candidate for the scientifically inexplicable.” But even for such a clear-cut case of divine intervention, he adds, “we do not have, and have little prospect of getting, an adequate criterion for distinguishing the inexplicable from the merely extraordinary.” The idea here seems to be that if supernatural claims are inexplicable by definition, they are also epistemologically problematic: One cannot say just where “extraordinary but explicable in principle” ends and “inexplicable” begins. Even so, the upshot is that for some naturalists even an evident instance of God going to extraordinary lengths to make himself known would not constitute an irreversible falsification of every possible scientific explanation, and therefore would not necessarily defeat naturalism.

[9] John DePoe, “Vindicating a Bayesian Approach to Confirming Miracles: A Response to Jordan Howard Sobel’s Reading of Hume,” Philosophia Christi, Vol. 10, No. 1 (2008): 229-238, p. 235.

[10] David Hume, An Enquiry Concerning Human Understanding (New York, NY: Barnes & Noble, 2005), p. 88. Originally published 1772.

[11] C. S. Lewis, Miracles (New York, NY: HarperCollins, 2001), p. 162. Originally published 1947.

[12] David Hume, Enquiry, p. 89.

[13] Yang Xiang, Probabilistic Reasoning in Multiagent Systems: A Graphical Models Approach (New York, NY: Cambridge University Press, 2002), p. 17.

[14] For a historical review of the Piltdown scandal from an anthropologist critic of “mainstream neo-Darwinism,” see Jeffrey H. Schwartz, Sudden Origins: Fossils, Genes, and the Emergence of Species (New York, NY: Wiley & Sons, 1999), pp. 107-114.

[15] Norman Geisler, Miracles and Modern Thought (Grand Rapids, MI: Zondervan, 1982), pp. 19-20.

[16] Jonah Lehrer, “Accept Defeat: The Neuroscience of Screwing Up,” Wired, December 21, 2009. Accessed from .

[17] James Joyce, “Bayes’ Theorem,” Stanford Encyclopedia of Philosophy (2003 Edition). Accessed from https://plato.stanford.edu/entries/bayes-theorem/.

[18] Francis Collins, The Language of God: A Scientist Presents Evidence for Belief (New York, NY: The Free Press), p. 50.

[19] Victor Reppert, “Hume on Miracles, Frequencies, and Prior Probabilities,” The Secular Web, 1998. Accessed from https://infidels.org/library/modern/hume-on-miracles-frequencies-and-prior-probabilities/.

[20] David Hume, A Treatise of Human Nature (New York, NY: Barnes & Noble, 2005), p. 73. Originally published 1739.

[21] C. S. Lewis, Miracles, p. 163.

[22] See Paul Vincent Spade, “William of Ockham,” Stanford Encyclopedia of Philosophy (2006 Edition). Accessed from https://plato.stanford.edu/entries/ockham/. Spade writes: “For Ockham, the only truly necessary entity is God; everything else, the whole of creation, is radically contingent through and through.

[23] It should be noted that evidential Christian apologists such as Richard Swinburne argue that theism itself (as distinct from specific miracle claims) is in fact amenable to Bayesian confirmation, even as atheologians variously argue not only that Swinburne’s argument fails, but that a Bayesian analysis of evil disconfirms theism.

[24] Nassim Nicholas Taleb, “The Black Swan: The Impact of the Highly Improbable,” New York Times, April 22, 2007. Accessed from .

[25] Irving Copi, Introduction to Logic, 5th ed. (New York, NY: MacMillan, 1978), p. 463.

[26] Cited in Peter Ackroyd, Newton (New York, NY: Doubleday, 2006), p. 88.

[274] David Hume, Treatise, p. 71.

[28] Samir Okasha, Philosophy of Science: A Very Short Introduction (New York, NY: Oxford University Press, 2002), p. 28.

[29] Samir Okasha, Philosophy of Science, p. 63.

[30] Samir Okasha, Philosophy of Science, p. 64.

[31] David Hume, Enquiry, p. 85.

[32] Norman Geisler, Miracles and Modern Thought, p. 31.

[33] Though it would fall short of verifying the existence of God, confirmation of a miracle would provide strong evidence for theism as a metaphysical belief.

[34] Norman Geisler, Miracles and Modern Thought, p. 123.

[35] William A. Dembski, Intelligent Design: The Bridge Between Science and Theology (Downers Grove, IL: InterVarsity Press, 1999), p. 41.

[36] David Hume, Treatise, p. 73. An anonymous reviewer has pointed out that, strictly speaking, Hume is mistaken here. One may entertain a “clear idea” of an actually existent hobgoblin, for example, but if no hobgoblin actually exists, then it is impossible for there to be an actually existent hobgoblin. Philosophers like David Chalmers also dispute the notion that conceivability necessarily translates to metaphysical possibility—for example that there must be a possible world where light travels at a billion meters per second or water consists of elements other than hydrogen and oxygen. If they are right, then Hume may have spoken too soon. But logical conceivability at least clears the first hurdle toward metaphysical possibility.

[37] William A. Dembski, Intelligent Design, p. 142.

[38] John DePoe, “Vindicating a Bayesian Approach to Confirming Miracles,” p. 238.

[39] Peter Kreeft and Ronald Tacelli, Handbook of Christian Apologetics (Downers Grove, IL: InterVarsity Press, 1994), p. 195.

[40] David Hume, Treatise, p. 74.

I would like to thank Secular Web editor Keith Augustine, along with two anonymous referees, for reviewing this article and offering critical suggestions to improve it.

Copyright ©2011 Don McIntosh. The electronic version is copyright ©2011 by Internet Infidels, Inc. with the written permission of Don McIntosh. All rights reserved.

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