The Empirical Confirmation of Miracle Claims

Is the empirical confirmation of miracles possible, in principle? Hume has often been interpreted as denying the possibility. However, Hume does say that it is conceivable that there could be testimony for a miraculous event that is so unlikely to be false that it would be a “greater miracle” for the testimony to be false than the occurrence of the event. Presumably, he means that, in principle, the likelihood of the provision of particular testimony T, given the non-occurrence of the Miracle M, P(T |~M & K),might be so low that it outweighs the prior improbability of the miracle, P(M | K), making the occurrence of the miracle given the particular testimony and background knowledge, P(M | T & K), greater, perhaps very slightly greater, than .5.

If we interpret Hume as making this concession, it makes understandable, what some commentators have found unfathomable, that Hume would add his Part II to his miracles essay, where Part II examined the actual historical circumstances of miracle claims. If the confirmation of miracle claims has already been shown impossible, why continue with the discussion? On the other hand, if we interpret Hume as making the “in principle” concession in Part I, then we can see why he devoted so much space to the “in practice” problems he raises in Part II. The upshot is that, though it is possible in principle for testimony to confirm a miracle, in practice, i.e. given the actual historical circumstances that have surrounded miracle claims, it is most unlikely that testimony could establish the occurrence of a historical miracle with such assurance as to, in Hume’s words, “so as to be the foundation of a system of religion.”

Hume restricted himself to the evidence for past miracles based upon human testimony, but, if our topic is the more general one of whether empirical evidence could support a miracle-claim there is no reason to accept such restrictions. We might consider a spectacular public demonstration of a miracle, one that might be witnessed by thousands in person and many millions more via electronic media. One possibly sticky point would be how “miracle” is to be defined. To avoid spending too much time on tedious matters of definition, I will stipulate that a miracle is a physically impossible event caused by a supernatural agent. By a “supernatural agent” I mean a being with nonphysical causal powers such as those supposedly wielded by God when, in the Book of Genesis, he says “Let there be,” and it comes to be. Another example would be the psychokinetic power of souls to influence physical bodies alleged by Cartesian dualists.

By “physically impossible event” I mean one that, while logically possible (i.e. the proposition asserting its occurrence does not entail a contradiction), is not realizable in the physical universe given what we know about the capacities and limitations of physical entities and forces. A physically impossible event would therefore be one like the ones featured in an old Monty Python skit. In this skit, a sleazy conman exploits a pathetic lunatic by claiming that the deranged individual can perform such feats as leaping the English Channel, devouring a cathedral, and digging to Java with a shovel. Clearly, given everything that we know about human capacities and limitations, it is physically impossible for a human being to leap across the English Channel, devour a cathedral, or tunnel to Java with a shovel. Yes, we may playfully imagine such events, but they just cannot be done.

So, I will propose a scenario for the public performance of an ostensibly physically impossible event claimed to be caused by the Christian God, and then ask how the witnesses might reasonably respond to such an event. I will argue that the conclusion that the occurrence was in fact a physically impossible event caused by the Christian God is one, but only one, of several possible conclusions that might reasonably be drawn by witnesses. However, if it is one reasonable conclusion, and perhaps even the most reasonable conclusion, that the event was a physically impossible event caused by the Christian God, then this indicates that, conceivably, there could be empirical evidence for a genuine miracle. There might even be empirical evidence for a miracle such that it would support the claim that the Christian God is the true God.

(Note: In the history of science it has, of course, occurred that an event previously thought to be physically impossible was shown to occur or possibly occur, thereby changing scientists’ views on what is physically possible. For instance, some eminent physicists asserted that it was impossible that heavy nuclei could be split in such a way as to cause a runaway chain reaction permitting a nuclear weapon. The Trinity Test of July 16, 1945 proved them wrong. What I am considering here is something different, namely, whether we can witness an event thought to be physically impossible, and still reasonably regard it as physically impossible after its occurrence.)


Imagine a scenario like the famous Mt. Carmel “contest” between Elijah and the priests of Baal, recounted in I Kings, Chapter 18. This is about as good an instance as one can imagine of an experimentum crucis. To prove that Yahweh is the true god and not Baal, Elijah prepares two sacrifices and challenges the priests of Baal to call fire down from heaven to consume their sacrifice. The priests cry out all day to no effect. At the end of the day, exhausted and roundly mocked by a scornful Elijah, the priests collapse in defeat. Elijah, to heighten the dramatic effect, has his sacrifice thoroughly soaked with water. He then steps back to a safe distance, and calls upon The Lord, and a massive column of fire descends from the sky and utterly consumes the sacrifice. The assembled people proclaim Yahweh to be The Lord, and, led by Elijah, piously massacre the priests of Baal.

Imagine a similar event (Without the culminating massacres, one hopes.), in which a modern day prophet claims that the Christian God exists, and that he will demonstrate this God’s existence to all doubters, scoffers, and infidels by calling upon God to perform a spectacular miracle. He proposes that materials for a large bonfire be collected, and, to safeguard against trickery, the entire process is conducted by a select group of unbelievers, including a sizable contingent of skeptical stage magicians such as James Randi. Thousands gather around, and the proceedings are broadcast internationally. Richard Dawkins, Sam Harris, officials of the Center for Inquiry, the American Humanist Association, the Freedom from Religion Foundation, and assorted atheist philosophers and scientists are all seated on the front row. The prophet, until now carefully sequestered from the scene, is brought forth and led to a microphone stand. He prays for a demonstration of God’s power in Jesus’ name, and WHOOSH! In a display worthy of Steven Spielberg, a great column of brilliant fire falls from a cloudless sky and consumes the flammable materials with such an ardent heat that the eyebrows and beards of the closest witnesses are singed.


So, how does one react after witnessing such a remarkable event? What do we think we have seen? The following sorts of hypotheses seem possible:

H1: The event was a physically impossible event caused by the Christian God.

H2: The event was a physically impossible event caused by an agent other than the Christian God.

H3: The event occurred, but was not physically impossible, and has a mundane explanation. Perhaps, despite all of our extremely careful precautions against trickery, there was trickery after all, and what we saw was merely an elaborate piece of stage magic.

H4: The event occurred, but was not physically impossible, and has an extraordinary but physical cause. It turns out that our scientific beliefs about what is physically impossible are incorrect. Perhaps the event was brought about by highly advanced extraterrestrials who are millions of years ahead of us in scientific knowledge, and who therefore possess technologies that appear to us to have miraculous powers.

H5: The event did not occur. No fire fell from the sky. We were all victims of a mass hallucination or some other sensory delusion so that fire only appeared to fall from the sky.

I think 1-5 exhaust all of the possibilities, and so constitute a set of jointly exhaustive and mutually exclusive hypotheses. Which, if any, is the most reasonable hypothesis? We would assess the strength of any of these five hypotheses, Hj, using the general form of Bayes’ Rule, where i takes the values of 1 through 5:

P(Hj) × P(E | Hj)

P(Hj | E) = —————————–

∑ [P(Hi) × P(E | Hi)]

So, a defender of H1, the hypothesis that the event was physically impossible and was caused by the Christian God, would seek to show that the background probability, P(Hi), for each of the other hypotheses was very low and/or that the likelihood of the evidence E—the spectacular event that we witnessed—P(E | Hi), was very low given each other hypothesis. Let’s consider how this argument would be made with respect to each of the alternate hypotheses.

Clearly, H5 is the weakest of the hypotheses. If such an event can be a hallucination, then everything is a hallucination. Further, we may suppose that the event was recorded by numerous inanimate devices, which are not subject to hallucination. Finally, we may examine the aftermath; something consumed the pile of stuff we had gathered.

H2 would seem to have a significantly higher background probability than H1. After all, there are indefinitely many other putative supernatural agents other than the Christian God that might have caused the event. Further, prima facie, there is no reason to think that the event would have been less likely given some other such agent. After all, such an agent might have as much motivation to communicate its existence to us as the Christian God.

The defender of H1 would reply by noting that the event occurred specifically upon the invocation of the Christian God, with a prayer “In Jesus’ name.” If further experiments showed that such events occurred only when the Christian God was specifically invoked, and never when any other God was called upon, then this would be strong evidence for H1 over H2.

The background probability of H3 would seem to be rather high. As the wise saying has it, “When you hear hoofbeats in the distance, think ‘horses,’ not ‘unicorns.'” That is, we should always initially expect a mundane explanation, and not turn to extraordinary explanations until we have exhausted every attempt at an ordinary one. On the other hand, the likelihood of the event given H3 might be quite low, if we have a great deal of confidence in the expertise, honesty, and thoroughness of our precautions against trickery. The reason why we required a corps of skeptical stage magicians, who presumably would make independent evaluations, is to make it as sure as possible that no trickery was involved. If we have high confidence in those precautions, we will judge P(E | H3) to be quite low.

H4 would be the option for many. After all, modern science is only 400 years old, and can we have any assurance that a scientific civilization millions of years older would not have vastly more scientific knowledge than we do? Also, as another wise saying (from Arthur C. Clarke) puts it, “Any sufficiently advanced technology is indistinguishable from magic.” So, extremely advanced beings might wield technologies that would have apparently miraculous effects to us. Further, given the vastness and age of the universe, it does not seem too improbable that there might be other civilizations far more scientifically advanced than we are.

H4 seems to me to be a reasonable alternative, but the defender of H1 might still have arguments against it. He could note once again that the events only occur when the Christian God is specifically invoked. This leaves it a complete mystery why the putative aliens would only produce their spectacular effects when the Christian God was invoked. What interest could they possibly have in inculcating belief in such a deity? Why the deception? Any suggestion here would seem to be ad hoc, given that we have no independent knowledge of such aliens or their intentions.

Further, though we clearly do not know nearly everything about the nature of the universe, we do really seem to know some things. There seems to be no good reason to think that everything we think we know will turn out to be wrong. Even the most pessimistic meta-induction from the history of science would still seem to leave us with some reliable knowledge of what natural things exist and their capacities and limitations. Therefore, we do seem to have a basis for saying that some things really are just impossible, and that millions of years from now they will still be impossible. If columns of fire materializing from a clear sky are indeed conceivable given what we now know about physics, it should be possible to imagine other events that would not be. Perhaps if tonight all the galaxies in the Virgo Cluster were instantly rearranged—across millions of light years of space—to spell out “Prepare to meet thy God!” that would do it.

The upshot is that the defender of H1 would seem to have arguments, of varying degrees of cogency, against all the other hypotheses 2-5. Could he win out over the disjunction of them, which he would need to do to show that P(H1 | E) > .5? I do not know, but it seems clear that the basic point I wanted to establish has been shown, namely that there could, in principle, be empirical evidence for a miracle and even empirical evidence for the truth of Christianity from the occurrence of a seemingly physically impossible event.


To show that something is “in principle” possible is a pretty weak conclusion. It is something else entirely to show that it has really been done or even realistically could be done. My take on the confirmation of miracle claims is the same as Hume’s in my reading of him, namely, that it is possible in principle but devilishly difficult in practice. We now know far more than Hume did about how false claims can become accepted as true (The recent presidential election in the U.S. was a veritable laboratory for the study of the emergence and spread of false claims.). We know a great deal about the psychology of hallucinations (see the late, great Oliver Sacks’ book), and a great deal about how false memories are formed (e.g. the research of Elizabeth Loftus). We know that many things can produce as sense of the numinous (for me, Bruckner’s Eighth does it every time) or a sense of a divine presence. We understand the many foibles of eyewitness testimony, and how easy it is to “see” what we want to see rather than what is there. Further, studies of folklore show how easily tales can arise and spread far faster than any critical evaluation can catch up.

Personally, I would love for a Christian apologist to set up an experiment like the one I imagine in my above scenario. Don’t hold your breath. They aren’t going to do it, and you do not have to be too much of a a cynic to suspect why. I suspect that they know as well as I do that they would have the same success as the priests of Baal in I Kings. What? Am I being arrogant and presumptuous? OK. Prove me wrong. Do the experiment.

The one distinct advantage for atheist in conceding that there could, in principle, be empirical evidence for a miracle and even for one supporting Christianity, is that it gives us a reply to a standard rhetorical gambit. In debate, atheists are often asked what it would take to make them abandon their atheism. Antony Flew’s famous falsification challenge is thrown back at the atheist (William Lane Craig asked me this in our first debate.). In answer, the atheist can cite instances like the one imagined in my scenario. Do something like that, and I will be sitting on the front pew of the church of my choice next Sunday. Until then, I will continue to plan to spend my Sunday mornings in my La-Z-Boy chair, with the Sunday paper, and mugs of excellent coffee.