The Problem with Miracles and the Shaky Groundwork of Corduan and Purtill (1999, 2005)
[Part 3A of a larger Review of In Defense of Miracles.]
Purtill defines a miracle as “an event brought about by the power of God that is a temporary exception to the ordinary course of nature for the purpose of showing that God has acted in history” (72). The primary problem with his definition is that it makes recognizing an actual miracle as a miracle almost impossible. As an empirical hypothesis, using Purtill’s definition, the statement “x is a miracle” requires that we establish, with empirical evidence, a causal connection between the event x and this God, which in turn requires that we establish, with empirical evidence, that this God exists. That is a tough task. Moreover, we must establish, again with empirical evidence, that God caused x for a specific purpose, which in turn requires us to be able to examine and demonstrate the intentions of God in that specific case. That can sometimes be done without interviewing the agent–we can infer intent from the nature and context of an action, and we often engage in such reasoning in law courts, but it often isn’t easy. Finally, we must be able to establish that x could not have happened in “the ordinary course of nature.” In other words, we must show that God is a necessary, not just a sufficient, cause of x. So Purtill has set the bar almost too high for anyone, in the present world as we know it, to ever recognize a miracle. Even if a miracle happened right in front of us, we would almost never be able to establish that it was a miracle, and this difficulty only becomes exponentially greater when the miracle happened to someone else a long time ago.
As an example, according to Purtill, the resurrection of Lazarus was a miracle, because “it was Lazarus’s nature to die in the circumstances of his illness” and so “his resurrection was, in the strict sense, supernatural, going beyond what was natural for him” (63). On the other hand, “if…we find that some apparently wonderful event can be accounted for by some power less than the power of God” then it is not a miracle (64). He gives no example here, yet he should give us a contrafactual about Lazarus to show us he is seriously considering the problems with his definition. We are left to wonder just what evidence or argument would suffice to convince him that the resurrection of Lazarus could be accounted for by some power less than that of God. Certainly we can account for Lazarus’s resurrection as a result of natural causes, and are only prevented from proving this by our inability to access any evidence, lacking a time machine or any records, such as those of a doctor overseeing the care and burial of Lazarus.
But Purtill is equally unable to show that Lazarus’s resurrection went “beyond” what was natural for him. He does not know what illness Lazarus had or whether he was really clinically dead, and so he does not what was natural for Lazarus, and almost certainly never will. Yet both he and I know there could be a plausible natural explanation for the report we have, for history and science afford us ample evidence that this sort of thing can happen. Do we have anywhere near as much evidence that there is a god who can explain it? We do not. And even if we had better proof that God exists, then we could only offer God as a possible explanation for Lazarus’s revival. Of course, at present I honestly can’t even do that, having no reason at all to believe there is such a god. Yet even if I had that proof, I would still only have God as a possible explanation, not a necessary one. In other words, even if I believed God exists, I would still not have enough evidence at hand to say that God raised Lazarus from the dead even if he did. That is because it is not enough to show that God could be a sufficient cause of this event. We must prove that God is a necessary cause, which, given the present state of the evidence, we can never do. This is a serious problem for Purtill. Later in the book Winfried Corduan attempts but fails to solve it.
Are there Any Recognizable Miracles?
However, I must make one thing clear: Purtill’s definition at least allows that it may be possible, in some circumstance, to prove–even scientifically–that a miracle has occurred. But the circumstances required would be so unusual that this is of little use to Christians, since the resurrection of Jesus, for instance, does not meet these vital circumstances and thus cannot be shown to be a miracle by Purtill’s definition. We simply have no evidence that will allow us to demonstrate that God is a necessary cause of the reported resurrection of Jesus. But since I expect it of Purtill, I will offer my own contrafactual to show that I am serious about my position:
I can imagine my pet fish suddenly speaking to me, telling me that God gave it the power to tell me that He loves me. As a rational person, my first hypotheses would be either that I am being tricked by someone, or that I am suffering from hallucinations–either from a brain disorder or chemical influence. Indeed, I would be running through my memory to recall if I drank anything that someone might have dropped a tab of acid in. I would then test all those hypotheses. Can others hear the fish talk? Can the fish tell me anything that I could not have learned any other way–like the name and location of a lost child? Is the sound unmistakably coming from the fish–even when I move it, and change its bowl? Can others confirm all of this? Can doctors confirm that I have no drugs in my system and no obvious brain disorder? Under these conditions, I believe I would have enough proof to call this a miracle under Purtill’s definition (this example is borrowed from my article “A Fish Did Not Write This Essay”).
Now, someone might say that even this is not enough, because this phenomenon could still conceivably be caused by demons or aliens or psychics or something equally bizarre (or an even more elaborate natural explanation, such as an extraordinarily sophisticated delusion). In other words, I still would not have enough to be certain that God was a necessary cause of the fish’s ability to talk, but given what the fish is saying and what I am learning from it, and all the other details, I would have enough evidence to reasonably believe that it is God doing it, and for the requisite purpose (since the effect–the things said by the fish–allows us to infer this, even if we happen to be wrong). In such a case I would indeed convert at least to the teachings of my fish, so long as, upon interrogation, the fish’s wisdom proved to be morally good and the fish could adequately prove all its assertions–and did not expect me to believe what it could not prove (since it is immoral to demand blind obedience), and so long as this theory is not refuted in the future. But all this evidence is totally lacking in every other miracle account in history. Thus, although Purtill’s definition at least makes it possible for the “argument from miracles” to convert me to theism, I know of no real case which meets these requirements. This is, in fact, a major reason why I am an atheist.
This means that Purtill’s chapter fails to support the rest of the book’s argument. None of the following chapters presents sufficient proof that God has ever been a necessary cause of any event in history. Most of the chapters do a good job of showing that God can be a sufficient cause of certain events, but that fails to show the existence of any miracle by Purtill’s definition, and this renders the book as little more than a philosophical exercise, with no useful application to reality. Of course, if a God really existed, we would see miracles all the time, and then Purtill’s definition would be immensely useful–it might even become a scientific principle. The fact that it is not useful, because there happen to be no miracles that can be identified, makes a good case for atheism, or at least for the lack of miracle-working in the behavior of any god, neither of which is a conclusion that these authors want us to reach.
Corduan to the Rescue…or Not
Nevertheless, the editors tried to salvage this disaster by recruiting Winfried Corduan to clean up the mess. His attempt is an embarrassment. Consider what he claims to have established by the end of his essay: “the recognition of a miracle is initially the prerogative of believers” who can sway unbelievers only by arguing for “prima facie presumptions” that only “sometimes favor” the hypothesis that God has acted in history (111). Think about that. Believers can realize things we unbelievers can’t. Why? Because they follow certain unproven assumptions (that is what a “prima facie presumption” is) that might support the belief that God did something. I’m not joking. This is Corduan’s argument: in a nut shell, miracles can only be recognized if we first assume, among other things, that God exists and acts in history! This is as vacuous as arguments get. It fails to show that any event in history actually can be recognized as a miracle, at least by Purtill’s definition, and thus the entire book fails to show that any miracle has ever occurred. All Corduan can tell us is that miracles can only be identified by believers, and not because they know anything we don’t, and not because they have some special sense or source of data that we lack, but simply because they assume their worldview is true, a worldview which comes ready-supplied with officially-identified miraculous events, like the resurrection of Jesus. “Miracles exist because miracles exist.” Tautology galore!
Defining Natural and Supernatural
How Corduan talks himself into this ridiculous circle is worth examining, because many skeptics stumble over the same block. His chapter begins by outlining the usual objections to recognizing a miracle, all of which boil down to what I call “the naturalist fallacy,” which he gives in various forms, citing various naturalists who often parrot this mistaken argument: “if new observations conflict with present theories, the scientist needs to revise his or her theories, not blame the event on something supernatural” (100), or in other words “a scientist may never consider the possibility of a natural cause to have been eliminated” (101) and thus can never consider a supernatural theory. This is a fallacy, which is believed valid only because people do not define the distinction between “natural” and “supernatural,” and do not recognize that it is only valid as a rule of thumb, not as a logical principle (as I will explain in the end). Corduan sees it is fallacious, but fails to correctly identify why, and that is where he slips. For when this distinction is carefully made, it becomes apparent that the “naturalist fallacy” is not always true because it can pointlessly eliminate possible theories. Eliminating theories is a valid enterprise, but you must have a reason for it, and there is no reason which will allow a blanket elimination of some category of theories called “supernatural” if this category is entirely arbitrary. And is there any objective way to distinguish the natural from the supernatural?
Consider psi, the undefined power which would explain ESP and telekinesis, among other things. We would all readily call that supernatural. But why? If there was a lawful, regular feature of the universe which allowed ESP and telekinesis to exist, then wouldn’t psi be natural, not supernatural? What makes something supernatural anyway? We can levitate and move an entire train with magnetism, and transmit thoughts by radio, two powers that the ancients of Paul’s day would certainly have called supernatural. Even God could be entirely natural, for if he existed he would be a regular feature of the universe, every bit as much as you or I. The attempt to draw a line between God and nature will always be somewhat arbitrary. “Nature is created” the theists will say, “God is not.” But does that mean if we discovered the universe was not created, we would have to conclude that nature does not exist? That would be a silly thing to say. Nature is what exists: we look at the world, learn how it works, discover its inhabitants and rules, and call that nature. Consequently, God, miracles, psionics, angels, ghosts, flying saucers, would all be a part of nature if they existed.
Even if we ignored this simple observation, and chose to draw lines at whim between natural and supernatural things, this would never give us the right to absolutely exclude one of those categories from all possibility of investigation. The only category of theories that can legitimately be excluded from investigation is the category of all untestable theories. If we can test a theory, then it cannot be excluded from investigation. But it will not suffice to make “supernatural” and “untestable” into equivalent categories, since human convention is already set against such an equivalence. Why this is so is important, and I will address that in the end.
For example, the theory that Julius Caesar shaved every day of his life is untestable, but it is hardly supernatural by anyone’s use of the word. Likewise, it is impossible to test the theory that there are other universes that are a lot like this one but that will never influence this universe in any way. Yet this is not a supernatural theory, either–it is in fact a scientific theory called the “multiverse hypothesis.” Thus, it should be clear that the “naturalist fallacy” is indeed a fallacy. Consequently, a scientist can consider miracle theories if he wants to, so long as the theory of miracles is testable, as Purtill’s definition allows. Miracles are only closed to scientific investigation when they are untestable–and if they are untestable, then even the theist is forced to admit that he cannot know if any such theory is true, any more than he knows whether, for example, it is true that Julius Caesar shaved every day of his life.
From the Naturalist Fallacy to the Theist Fallacy
This is where Corduan goes wrong: in order to escape the “naturalist fallacy” he rightly enters the point of view of “someone who is open to the supernatural” in order to see if it is possible “to recognize a miracle” (102). But he steps immediately not into an open mind, but into a theist’s mind: he only considers the point of view of a “believer” who specifically and only accepts that some “miracles” may have happened. But that still excludes every other “supernatural” theory, such as psi. So Corduan moves from a naturalist fallacy into a theist fallacy, and thus has made no progress. If he had genuinely stepped into an open mind, he would no doubt have realized that miracles cannot be recognized as miracles because there are so many competing theories that cannot be eliminated, such as psi, or demons, or aliens, or the features of Buddhist and Hindu worldviews which also allow the incredible to happen. At the very least, he would have been forced to deal with this problem, and might have escaped the vicious circle that his chapter ends up circumscribing.
Post Hoc Reasoning
But instead, Corduan offers fallacies as if they justified the “believer” in his belief in particular miracles. In other words, he address the problem of recognition by proposing that adopting a fallacious inference allows us to distinguish miracles from coincidences. Consider his first example of how a believer can “recognize” a miracle: he tells a story whereby a man loses a job application and prays to god to help him, and by an incredible stream of natural events the application ends up at its destination anyway. This example is textbook in the way it shows how superstitious thinking arises from shallow analysis: Corduan argues that the man is justified in regarding it as a miracle because it is what he prayed for. This is called a post hoc fallacy, and it is a primary cause of superstition, as Stuart Vyse demonstrates at length in Believing in Magic: The Psychology of Superstition (1997), especially in chapter 3, which begins with the following true case:
Bjorn Borg, five-time Wimbleton champion, was playing in the French Open while his grandfather listened by radio as he was fishing. His grandfather “spat in the water and at just that instant Bjorn won a point.” Believing it was no coincidence, “he continued to spit throughout the match, going home with a sore throat. Borg won in four sets” (59-60). Bjorn’s grandfather falsely reasoned that because spitting was followed by his son’s success, he was entitled to believe that spitting was responsible for it, and thus continued spitting, and his son’s continued victories only reinforced his belief. This is post hoc reasoning, which is short for post hoc ergo propter hoc, “after this, therefore because of this,” the assumption that a sequence of events entails causation. Humans are actually inherently designed to make this mistake, because our brain is built to “see” causes by the only data available: sequence. Moreover, Vyse surveys scientific studies showing that post hoc superstitions are more likely to persist when they are set-up by a prior belief in their truth, and even more so when reinforced by social approval–the very conditions which cause Corduan’s “man” to think his prayer was answered by God (i.e. religious socialization and prior commitment to the efficacy of prayer).
Corduan’s example is an excellent example of this post hoc reasoning. Consider: the man’s job application was already ready to be mailed–it was addressed and stamped–when it was lost. Thus, the odds of it arriving at its destination were from the outset fairly good–it could have been found by anyone at any stage on its journey and been placed in the mail. This compares with the fact that Bjorn was a champion–the odds of his winning a set were already fairly good (though not too good, since he was playing another champion at the time). Likewise, how often do we think Corduan’s hypothetical man prays for God’s help? Almost certainly, he does so on a regular basis, just as Bjorn’s grandfather’s spitting in the water while fishing was probably not an unusual event. Thus the prior odds of a prayer coinciding with any coincidence in the hypothetical man’s life are also very good. This means that the odds of a match between a prayed-for-result and a coincidental outcome are going to be good enough that at least one match can be expected in a man’s lifetime, if not several, even though these matches will be entirely accidental. Appealing to a “prior assumption” that God answers prayers is exactly like Bjorn’s grandfather appealing to a “prior assumption” that spitting can influence a distant tennis match: it is not a justification, but an error. Yet Corduan thinks otherwise, and he implies that R. F. Holland and Norman Geisler also think so, too (105).
The Regrown Hand
Corduan’s second example of how a believer can “recognize” a miracle goes like this: “a believer might claim that a miracle has occurred if her hand had been severed in an accident, she prayed, and a new hand ‘grew back’ instantaneously” (105). First of all, note that he chooses a good example–an example better than any other healing miracle in the Bible. The actual miracles reported in the New Testament are not this clear-cut. Unlike the regrowing of a severed limb, never once reported of Jesus, the actual healings attributed to Christ can easily be explained as psychosomatic. It is no accident that these hypothetical examples that Corduan uses to make an argument are always better than any real examples. For example, he posits a holy man whom skeptics would have a hard time denying was a miracle-worker, since he “heals people of various diseases, including some that are irreversibly degenerative” (109) [emphasis added]. But this last phrase entails the existence of evidence not available in any of the cases of healing reported in the Bible. How curious that even he thinks we need stronger evidence than that found in the gospels before we can really believe in miracles. Now, reports of regrown limbs appear in the middle ages, and it is also interesting that these authors never mention any of these medieval accounts. I suspect that since these are not essential to their evangelical mission of conversion, these miracles can “safely” be dismissed as delusions, exaggerations, mistakes, or pious frauds, even though they stand on the very same quality of evidence.
But let us move back to the original problem: in this regrown-hand example he has moved from one closed mind to another, and thus fails to see that the evidence is not sufficient to recognize this as a miracle. The woman can just as easily conclude that she psychically healed her hand herself, the prayer merely focusing her desire to heal, or being a coincidence (since she no doubt always prays when hurt), or that reality can be changed by changing one’s perception if the desire is strong enough (and a prayer would likely coincide with a powerful desire), or that demons answered her prayer, or that she has a genetic mutation which gives her an extraordinary healing ability, and so on. Before she can conclude that the cause really was God, she must eliminate other plausible explanations like these, in order to establish God as a necessary cause. Certainly, the theory that her body healed her hand by the same means as every other human, which we normally call the “natural explanation,” can be ruled out here, but Corduan is mistaken in thinking that this allows one to immediately adopt God as the best explanation. There is more to proving a theory than merely eliminating one competitor. You must have positive evidence for it.
Are Believers Skilled Miracle-Recognizers?
Corduan moves from these examples by trying to argue that “believers do not have a definite recognition formula at their disposal” (106) yet “it is quite possible that believers are more expert when it comes to recognizing miracles” because their worldview prepares them for it (107). His analogies are telling:
- Identifying the symptoms of diabetes: he says a doctor will recognize this more readily than a layman, thus his expertise is to be trusted.
- Recognizing the aurora borealis: a says a meteorologist will recognize this more readily than a layman, thus his expertise is to be trusted.
- Seeing that a certain syllogism is invalid: he says a logician will recognize this more readily than a layman, thus his expertise is to be trusted.
But these are all false analogies. The doctor, meteorologist, and especially the logician, actually have criteria. Not only that, but they can explain those criteria to a layman. On the other hand, when the doctor depends on skill and intuition in an uncertain case, it does not follow that he has recognized diabetes. He only intuits that the given symptoms may signify diabetes, and consequently he will order tests to check his hypothesis. Being honest, he would say “I suspect diabetes in this case.” He would not say, “You have diabetes,” unless the criteria were met so clearly that even a layman would agree with the conclusion, once the evidence was pointed out and explained. In the same fashion, if a light in the sky was so vague that only an expert meteorologist might suspect it was an aurora, it is still quite likely that he could be mistaken, and he would admit as much, unless he really could exclude other explanations to the satisfaction of a layman. And in the case of a logician, there is absolutely no tolerance for intuition in his enterprise. He would actually have to prove a syllogism invalid before he could say it was, and that proof would be just as visible to a layman once identified. Experts cannot simply claim they are right because they are experts. Being an expert only means that you know how to test and prove a claim, it does not excuse you from doing the testing and proving. Thus, we should expect the same from theists. Instead, Corduan argues that a theist’s “expertise” is alone sufficient to justify belief in a miracle–sans any kind of explicable tests or proof. We hardly need point out what is wrong with that thesis.
Prima Facie Presumptions vs. The Lessons of History
The next step Corduan engages is to identify the necessary “prima facie presumption” that a believer needs in order to identify miracles. The presumption is this: it is a miracle if “as-yet-to-be-discovered scientific laws” must be resorted to as an explanation, since this “appeals to something we do not have while we do have something else, namely a cogent supernatural explanation” (109). But this rationale does not work. By this reasoning we would never have made any scientific progress. In the 1st century we had no idea what caused lightning, but we had a cogent supernatural explanation in divine or demonic agency, ranging from the anger of Zeus to the combats of evil spirits in the clouds. Is Corduan saying that pagans successfully recognized lightning as a miracle? That can’t be, because we now know it was not a miracle. As this shows, his method clearly fails, for it justifies every superstitious explanation, so long as it is “cogent.” On the other hand, scientists of the 1st century proposed that lightning was caused by friction between colliding clouds, by analogy with colliding flint stones. It should not be lost on us that this explanation is actually closer to the truth. It only lacks the “as-yet-to-be-discovered scientific laws” of electricity, laws which a man like Corduan would have said were too bizarre and implausible even to investigate, and sufficiently so that he would be justified in attributing lightning to Zeus instead.
This is where Corduan’s underlying assumption is exploded: he assumes that a Christian’s worldview better prepares him to recognize miracles, but never shows that a Christian’s worldview is likely to correspond to reality. Yet he must do this first before he can appeal to that worldview as a justification for any belief about reality, including the existence and nature of miracles. On the other hand, ancient scientists had found that what we call “natural” explanations kept working: contrary to “cogent supernatural explanations,” the stars and planets actually followed predictable laws that had nothing to do with human events, tested drugs cured the sick more often than spells, agriculture flourished under scientific care but floundered under prayers and magic. Then they found that atomic and other “naturalistic” explanations for all phenomena had a much wider explanatory power than divine theories, predicting more things, more successfully. Thus, they correctly guessed that they were on to something, and stopped accepting “supernatural” explanations because they constantly failed, and instead they pursued “natural” theories. Thus, they got very close to the truth, articulating explanations for sound, light, evolution, weather phenomena, poison, disease, and certainly getting far closer than any theologian ever came.
Unfortunately, this brilliant discovery was thwarted by the rise of Christianity, which put science on hold for 1000 years, relying instead on Corduan’s “cogent supernatural explanations.” It was not until the Renaissance, when pagan science was rediscovered, that the bias in favor of what we now call the “natural” was taken up again, and lo and behold, every century since has seen unprecedented progress. Here is the lesson: we have come to call this bias “natural” precisely because it has so often and so successfully corresponded with success. In other words, we developed a bias for what worked, having proven over a thousand years what didn’t work, and then divided these two into the “natural” and the “supernatural.” There is thus some merit to the naturalist fallacy (discussed above): it is indeed valid as a rule of thumb, which is more likely to produce success, even though it is not valid as an absolute law. Its utility as a rule of thumb is entirely dependent on the fact that all reliable evidence of any kind supports the rule, and so far offers no support for breaking it. So uniform and massive is this body of evidence that it has even led moderns into assuming that the “supernatural” was so useless that it could never be true, hence the naturalist fallacy. This is why the naturalist worldview is a more reasonable model of reality than Christian theism, and why Corduan cannot appeal to the latter to support the existence and identification of miracles.
Lack of Evidence is the Final Straw
In order to overcome the overwhelming evidence against him, Corduan must present good positive evidence for the theory that any particular event is a miracle, otherwise it is never going to be reasonable. It is simply an undeniable fact that, given two options with equal evidence–a plausible natural explanation (“he has an as-yet-unexplained immunity to asp poison”) and a supernatural alternative (“God rewards his faith with an immunity to asp poison”)–we are simply smarter to bet on the former. The natural type of theory is like a horse from a trainer whose numerous horses have run a million races and none of them has ever lost. What idiot would bet against one of his horses in the next race? Corduan’s argument is this: since all the races aren’t finished, and we have not seen this specific horse run yet, we are not entitled to believe that this horse will win. That is hardly a sound argument, given the evidence of the past. Sure, it is possible the horse will lose, but is it reasonable to expect it? Even still, scientific thinkers wisely follow Corduan’s advice, but they reserve judgment until we actually watch the horse run, and don’t even stop there, but wait until we’ve seen it in a dozen races before trusting its infallibility, and even then we allow that it might yet fail. That is science. Corduan’s alternative is to never let the horse run a race, and on the “evidence” that it has not won a race, pronounce it lame.
In the end, Corduan has utterly failed to explain how theists are to distinguish a miracle from something else, and thus it stands, as far as I can see, that this can never be done, except in the most unusual of circumstances, which have never been met in any real case. This destroys the entire mission of the book. Corduan says it all with the following posit: “when the evidence for the occurrence of an event is beyond reasonable doubt and there is no other plausible explanation available” then we just might have a miracle. Of course, think of what this would have done for the ancient explanation of lightning, and you will see the flaw in his reasoning: “not having a proven explanation” is not the same as having a falsified one, nor the same as having evidence for any alternative. He wants us to think that “lack of an explanation” is actually proof of an explanation. It does not work that way. But in the end even this is moot, because we must ask: has there ever been a case where there is no other plausible explanation available? I cannot think of any, and Corduan has presented none–even his hypothetical examples fail this test. He has thus failed to show us how to recognize a miracle, even if miracles do in fact happen.
Return to this review’s Table of Contents to read more detailed critiques of specific chapters in In Defense of Miracles.
 I think I know what Corduan was thinking. There is one sense in which pure expertise can create knowledge without criteria: acting on learned reflexes, e.g. riding a bike, carving a statue from stone, distinguishing variations in color or sound, etc. These things differ from identifying miracles in that although I can ride a bike without knowing the criteria for every correct action, the statement “when I trust my intuition, I can ride a bike” is itself a criteria-based empirical hypothesis: you don’t need to know how to ride a bike to know from observation whether I can. The knowledge involved in riding a bike is noncognitive and thus differs categorically from propositional knowledge (like “I can ride a bike”). A statement like “this is a miracle” is propositional, not noncognitive, and therefore requires criteria. In fact, these criteria are entailed automatically by the meaning of the sentence itself.
Michael Polanyi’s Personal Knowledge: Towards a Post-Critical Philosophy (1958) gives a good account of noncognitive knowledge, although I think his views must be tempered in light of A.J. Ayer’s Language, Truth, and Logic, 2nd ed. (1946), which explains why verbal sentences automatically entail criteria for their own verification or falsification. I discuss my own epistemology as it relates to such issues in Richard Carrier, Sense and Goodness without God: A Defense of Metaphysical Naturalism (2005).
Even our ability to make distinctions in sensory data or patterns is not without describable criteria: someone can learn to identify middle-C without knowing what length of string or surface (and hence what audio-frequency) would confirm their judgment, but this is “trained intuition,” where the brain is trained to automatically employ certain criteria. This is not the absence of criteria, for the statement “this sound is middle-C” must still have verifiable truth conditions which would allow anyone to confirm it, otherwise it would have no meaning as a statement. As with all definitions, the criterion in this case is whether the judgment conforms to human convention (what English-speakers have chosen to call “middle-C”), but even without such a convention, the criterion would be sensory distinctiveness from all non-middle-C sounds. Since miracles involve theories of causation, not just mere sensory distinctions, much less mere coherence to arbitrary human naming conventions, expertise cannot be a substitute for criteria in their case.
Finally, intuitive expertise must be learned from repeated cases of success, i.e. actual training. Thus, for intuitive expertise to aid in recognizing miracles, we would have to have extensive experience observing genuine miracles that we could confirm as such independently. After all, we could not identify them with intuitive experience we don’t yet have, and so without criteria we could not know whether we were learning to identify actual miracles or something else.
 See Richard Packham’s The Man With No Heart for a good example of a hypothetical “well-attested” miracle. On how numerous problems arise when we start combing the actual historical record for “good examples,” see my discussion of Beckwith’s Chapter.
 Although it should be noted: the argument that there are no plausible explanations for certain events (except the explanation of “miracle”) is attempted by Craig and Habermas, and Geivett and Newman.