History, Probability, and Miracles

One of the most common misconceptions about history is the idea that history *is* our past. This misconception is understandable, since when we are taught “history” in high school or even in college the courses provide an overview and summary of different periods in humankind’s past on Earth. The historiographical method, however, which enables us to discover what happened in the past, interpret what it means, and choose how to represent it in a narrative, is often discussed only briefly or not at all. Just as science *is not* the same thing as nature, but the method that we use to investigate nature, history *is not* the same thing as the past, but rather a method that we use in the present to investigate the past.

Herodotus of Halicarnassus, who is considered to be the “father of history,” had been told many stories about past events in the Greek and Persian world. Being the first historian, however, Herodotus wanted to figure out which of these stories were true, which were false, how do we know these stories, and what really happened in these past events. In the opening of his historical work (1.1.0), Herodotus tells his readers that he is performing a ἱστορία (“inquiry”) into human events. His goal was, just as when one investigates nature through scientific observation, to investigate the past by gathering evidence, traveling to different lands, interviewing witnesses, inspecting inscriptions and remains, and ultimately getting to the bottom of what had really taken place.

One of the major differences between history and many of the hypotheses tested in the natural sciences, however, is that the past is not repeatable and cannot be directly observed. You cannot repeat the exact event of Julius Caesar crossing the Rubicon in 49 BCE, in the same way that you can repeat an experiment in a laboratory. Instead, historians often have to rely on second-hand reports in ancient texts to know about certain events. This does not mean, however, that history and science should be considered incongruous in their methodology. Good historians do not simply accept whatever is recorded in ancient sources without any consideration for science.

As I explain in my article “History and the Paranormal,” historians assume scientific background knowledge about the natural world when they investigate ancient historical claims. The acceleration rate of gravity on Earth in the 1st century CE was 9.8 m/s/s, regardless of the fact that no ancient source wrote about it. This is not historical knowledge, but scientific knowledge, and historians assume such scientific knowledge regularly when analyzing claims about the past.

Scientific background knowledge is particularly important for evaluating certain types of historical claims — such as the ancient historian Tacitus’ (Ann. 6.28) claim that a phoenix visited Egypt in 34 CE — which involve paranormal phenomena that have not been confirmed by scientific evidence. When historians are confronted with paranormal claims in ancient texts, they do not simply accept such reports at face value in the same way that they accept reports for ordinary events, such as Caesar crossing the Rubicon. The latter example involves no controversial unscientific assumptions (namely, that a human being is capable of crossing a river on a horse), whereas the example of Tacitus’ phoenix does involve controversial unscientific assumptions (namely, that birds like phoenixes even exist and appear in certain places). Historians take into account the lack of scientific evidence for phoenixes when they assess Tacitus’ claim that a particular phoenix visited Egypt in the year 34 CE. This lack of scientific evidence plays a major role in why virtually all Classicists doubt that this event literary happened.

History also has major differences with forensic science, which is a subcategory of science that can more often be used to test unrepeatable events (e.g. the crime scene of a murder). The main difference between ancient history, in particular, and forensic science is the distance from the event being investigated and the types of evidence available. Forensic science is often able to use far more rigorous forms of evidence and testing, such as fingerprints, DNA, materials testing, and so on. Such evidence, however, is typically only available for a limited window of time after the event. When it comes to ancient historical events, from which we are distanced by more than two millennia, such forms of evidence are usually no longer available. There are a few forms of ancient evidence that can still be subjected to (limited) scientific testing — such as archeological evidence with Carbon-14 dating — but the fact is that most events in the ancient world did not leave behind any such physical evidence.

Instead, our knowledge for many historical events in the ancient world relies solely on the reports found in ancient texts. Ancient texts, however, cannot be scrutinized as thoroughly as the evidence studied in forensic science, and thus using ancient texts as a form of evidence for knowing about the past is often far more speculative and less certain (especially when such texts are highly literary or symbolic in their composition). Frequently, the ancient sources that a historian consults will be biased, vague, misinformed, speculative, or simply outright liars (see Bart Ehrman’s Forged: Writing in the Name of God). In short: ancient texts suck as a method for knowing about the past. If we could go back in time and instead test these events through direct observation or forensic science, that method would beat ancient texts in a heartbeat. But sometimes ancient texts are the only evidence that we have for certain historical claims.

As I discuss in my article “When Do Contemporary or Early Sources Matter in Ancient History,” all of our knowledge of the historical Jesus (including the reports of his resurrection) comes down through ancient texts. There is absolutely no archeological evidence at all for Jesus. None of the evidence for Jesus’ resurrection can be tested by the methods of forensic science (though, a similar event could still hypothetically be recorded by forensic science today, despite there being no evidence of such a thing). Furthermore, we have no eyewitness sources for Jesus of any kind (discussed here) and all of the textual sources that discuss his resurrection are not historical in their genre (discussed here). Instead, all we have for investigating Jesus’ resurrection is religious scripture (particularly biased Christian scriptures), which is far from our most reliable kind of evidence. Likewise, as is shown with the example of Tacitus’ phoenix above, historians cannot take paranormal reports in such ancient texts at face value, without consideration of broader scientific background knowledge.

Instead, a method is needed that can situate these claims within our broader background knowledge of the world, in order to determine the likelihood of whether such events could have really taken place within it. 

Bayes’ Theorem

Because history is a method, we need to refine that method if we are to have any hope of ever reaching the truth. When the past can no longer be directly observed, but can only be known through ancient texts, a historian must analyze the evidence available and then construct a hypothesis, based on that evidence, of what probably took place. Different historians looking at the same evidence, however, often form conflicting hypotheses arguing for different versions of what had happened. How do we determine which version is the most likely? How can I argue that my theory about the past is more credible than yours?

Historians have different methods for investigating history, some of which I have discussed before in my blog “Methodological Approaches to Ancient History.” Since history relies on the most probable explanation of the data, however, all historical reasoning that seeks to provide an argument of probability must have a basic introduction to probability theory. Historiographers such as Aviezer Tucker in Our Knowledge of the Past and Richard Carrier in Proving History argue that all of historical reasoning is reducible to Bayesian probability. Thomas Bayes’ theorem is first described by Richard Price in the late 18th century, who wrote to his friend John Canton a letter which explained that Bayes’ goal was “to find a method by which we might judge the probability that an event has to happen, in given circumstances, upon the supposition that we know nothing concerning it but that, under the same circumstances, it has happened a certain number of times, and failed a certain number of times.”

Bayes’ Theorem offers a formula that estimates the probability of a hypothesis about an unobservable event by multiplying the prior probability of the hypothesis by the likelihood of the expected evidence if the hypothesis is true. The hypothesis is further divided by its own probability in addition to the probability of alternative hypotheses, which measures the original hypothesis’ likelihood not in isolation, but in comparison to alternative hypotheses about the event. The last part of this process, which measures the likelihood of alternative hypotheses, is particularly important, since it requires that a hypothesis not only be plausible, but also be the most probable explanation in comparison to alternative explanations.

This is all rather complicated to explain in prose, so I will first provide the formula below, along with Carrier’s simplified explanation of the variables:

Pic 1

P = probability, h = hypothesis, ~h = alternative hypothesis, e = evidence, and b = background knowledge. Here is Carrier’s far more simplified explanation:

Pic 2

Prior Probability = (How typical our explanation is)

Expected Evidence = (How expected the evidence is if our explanation is true)

Why the Prior Probability Is Really Important

Now that a summary of Bayes’ Theorem has been laid out above, allow me to give an example to illustrate how the prior probability can increase or decrease the probability of a particular hypothesis compared to an alternative hypothesis that has equal expected evidence.

Suppose that I am walking across a beach twenty minutes from my home in Southern California and I see hoof prints in the sand. I can tell that some four-footed, hoofed animal ran through, but I cannot tell the exact animal that it was. Suppose then that a friend of mine, who religiously believes in unicorns, argues that these hoof prints are good evidence that a unicorn ran through here and thus unicorns exist. It is true that if a unicorn had ran through that it would have left this kind of evidence, but why am I skeptical of my friend’s claim? The answer is that because the explanation of a unicorn has a much lower prior probability.

Let’s lay out three hypotheses to explain the hoof prints:

H1 = Unicorn

H2 = Zebra

H3 = Horse

The expected evidence of hoof prints in the sand is equal for all three of these hypotheses:

Unicorn (Expected Evidence) = Zebra (Expected Evidence) = Horse (Expected Evidence)

The reason that I can tell that my friend’s explanation is unlikely is because the other two hypotheses have a much higher prior probability in Southern California. When considering the prior probability for these hypotheses the likelihoods are:

Unicorn (Prior Probability) < Zebra (Prior Probability) < Horse (Prior Probability)

In this situation, despite equal expected evidence for each hypothesis, the intrinsic likelihood of a horse being the cause of hoof prints in Southern California drastically increases the probability that a horse had ran through rather than a zebra, and a zebra has a higher probability than a unicorn running through. Even if one does not consciously use Bayes’ Theorem in coming to this conclusion, most of us subconsciously use this intuition when being skeptical of the unicorn hypothesis. Fleshing out how this logic works, however, helps us refine our estimates about an otherwise unobserved event.

Why the Expected Evidence Is Really Important

The example above illustrates that extraordinary claims are less likely than ordinary ones. Does this mean that extraordinary events cannot ever be the most probable hypothesis? Not at all. This is why it is important to also consider the expected evidence when assessing the probabilities of competing hypotheses.

Let’s use another example to illustrate how the expected evidence can support the probability of a hypotheses even when it has a low prior probability.

Suppose that I purchased a ticket in a 1/1,000,000 odds lottery from a state vendor. The lottery only has two options:

H1 = Winner

H2 = Loser

The prior probability that I will win the lottery is vastly lower than the prior probability that I will lose:

Winner (prior probability) < Loser (prior probability)

Suppose then when the winning numbers are announced, the numbers on my ticket match them and I win the lottery. The ticket further contains all of the marks and signs of a valid lottery ticket. I return to the vendor to collect my winnings. The vendor carefully inspects the ticket and finds no signs of tampering or forgery. We have all of the evidence we would expect if I had genuinely won the lottery and none of the evidence we would expect if I lost the lottery:

Winner (expected evidence) > Loser (expected evidence)

The prior probability that I would win is 1/1,000,000, and the prior probability that I would lose is 999,999/1,000,000. But let’s say that the expected evidence that I have a genuine lottery ticket is 999,999,999/1,000,000,000 versus the probability that I had managed to perfectly forge a winning ticket and cheat the system being 1/1,000,000,000. Our Bayes’ formula for the probability of me genuinely winning the would be:

Pic 3

In this example, despite a very low prior probability for winning the lottery, the expected evidence is so strong as to yield a 99.9% chance that I am a genuine winner. Accordingly, a low prior probability does not entail that an unlikely event can never happen. To the contrary, so long as an event with a low prior has strong expected evidence, and the alternative hypotheses have a lower percentage value when you times their prior probability by their expected evidence, unlikely hypotheses can still be the most probable explanation for an event.

The Meaning of Historical Statements

Historians do not always need to assign precise numerical values to the probability of events, as I did above. In fact, most historical judgements will not be so precise. This does not mean, however, that a historian is not using Bayesian logic when assessing the probability of historical claims. Good historians when they argue for the greater probability of a certain historical theory — even if they do not assign precise numerical values — are still evaluating their hypothesis through considerations of its prior probability, expected evidence, and the probability of alternative hypotheses.

When we make historical statements about likelihood, even if we do not spell out their percentage values, we still imply them. The phrases below (roughly) correspond to the different degrees of probability that we are assessing:

“The event almost certainly did not happen” = 1%

“The event very likely did not happen” = 10%

“It is more likely that the event did not happen” = < 50%

“It is uncertain whether the event happened” = 50%

“It is more likely that the event did happen” = > 50%

“The event very likely did happen” = 90%

“The event almost certainly did happen” = 99%

Natural Events That Probably Did Not Happen in the Past

Now that we have laid out the methodology above, I will provide an example of a natural (i.e. non-miraculous) hypothesis advanced by ancient historians that I do not believe is credible.

When I was in the first year of my Classics M.A. program, I wrote a paper about the Roman emperor Tiberius’ execution of his Praetorian prefect Sejanus in the year 31 CE (around the same time as Jesus’ execution). All of the historical sources who write about this event — such as Philo of Alexandria, Josephus, Tacitus, Suetonius, and Cassius Dio — agree that Sejanus was leading a conspiracy to usurp Tiberius. Without going into all of the details of this “conspiracy,” here is the basic sequence of events that the historians report: Sejanus had seduced the wife of Tiberius’ son and heir Drusus, he had used Drusus’ wife — Livilla — to poison Drusus (who died in 23 CE, though poison was not suspected at the time of his death), he had convinced Tiberius to retire from Rome so that he could cultivate his own power as Tiberius’ representative in the city (Tiberius retired to the island of Capri in 26 CE), he was controlling all the letter correspondence to Tiberius, he was working schemes to execute Tiberius’ remaining nephews and heirs, and he was either rallying the Praetorian Guard and the Senate to declare him emperor, or was at least working to deceptively convince Tiberius to adopt him as his heir.

Each of these historians provides good evidence for what you would expect if there had been a genuine conspiracy. The conspiracy makes less sense, however, when you analyze the details. First, Sejanus was born an equestrian, not of the senatorial class, and it is very unlikely that the Roman Senate — even if Sejanus had managed either to kill Tiberius or to convince Tiberius to declare him his heir — would have been willing to declare an equestrian emperor. This would be completely unprecedented and unheard of in the historical context of the Roman Empire during the 1st century CE [1]. In short, the prior probability that such a conspiracy could succeed was extremely low. Sejanus was no fool, so it would be odd that he would undergo such a dastardly plan. Furthermore, some of the expected evidence for the conspiracy seems less strong when scrutinized. The accusation that Sejanus had engineered the poisoning of Tiberius’ son Drusus through his wife Livilla, for example, was only made after Sejanus had died, and it was put forth by an enemy of Livilla (Sejanus’ ex-wife Apicata) in order to get her executed. Furthermore, the supposed motive for Livilla in the conspiracy was to be the wife of the new emperor by marrying Sejanus, but she was already married to Tiberius’ son Drusus and in line to become the new empress before the alleged poisoning. The theory of the conspiracy is both intrinsically unlikely and questionable in some of its evidence.

So what happened? As a historian I had to formulate a hypothesis that went against the evidence of all the ancient sources to document this event. This required a certain degree of ad hocness on my part. I postulated that perhaps Drusus had died of natural causes (not uncommon in those days, especially since poison had not been expected at the time Drusus’ death, and there are even a few indications in ancient sources that he had poor health). I also consulted Classicist Robin Seager’s Tiberius, in which he too doubts that Sejanus had been attempting to usurp Tiberius, and instead postulates a theory that, after Drusus’ death, Sejanus was not trying to overthrow Tiberius, but rather working to marry Drusus’ former wife Livilla, in order to become the guardian of her young son Gemellus. Gemellus was Tiberius’ grandson but he was too young to rule on his own, and if Sejanus could convince Tiberius to execute the other family heirs in line before Gemellus (he succeeded in killing two of them), then Gemellus would come to power and Sejanus could rule through him as guardian, in the place of being emperor himself. Unfortunately for Sejanus, however, Tiberius expected foul play and favored the heir in line right in front of Gemellus — Gaius Caligula. Although close to getting Gemellus in power, Sejanus fell short by one heir and was executed.

The theory advanced above is not spelled out by any ancient historian. It further requires that one tweak their interpretations of the data in order to suit an alternative thesis. In this case there is less expected evidence for theory outlined above than the theory of a conspiracy, which has an abundance of ancient evidence. Nevertheless, the prior probability of this theory is stronger than the prior probability of Sejanus leading a conspiracy. Furthermore, some of the expected evidence can be tweaked a little to explain ad hoc assumptions and alternative interpretations of events. Likewise, none of these ad hoc assumptions were of an extraordinary or unscientific character. It is well known that people can try to gain political influence by being appointed the guardians of young royalty, and making such an assumption is nothing like assuming the existence of phoenixes or immortal resurrections. As such, I had a perfectly plausible thesis, and one that I still think is most probable.

In short, in the paper I doubted multiple credible ancient historians about an event. The event had good evidence: multiple attestation, early witnesses, and a detailed explanation of what took place. Nevertheless, I do not believe that this evidence was strong enough to overcome the low prior probability of many of the details, and an alternative hypothesis, even if not attested by any other source to document this period, seems more credible. I am still not completely certain that this theory is correct, but I would assign a low probability to the conspiracy hypothesis (maybe 20% or so), compared to the alternative hypothesis that Sejanus was attempting to become a guardian, as Seager argues. Bear in mind that my ordinary modus operandi in evaluating ancient texts is not to doubt every claim that they report, but in situations where the authors relate inherently implausible, unlikely, or suspicious events, it behooves the modern historian to be more critical and to at least consider alternative explanations. It is fair to say that there are certain types of historical claims that demand more skepticism than others.

If I can doubt multiple credible and independent historians about the likelihood of a natural event, how can I not doubt four anonymous and textually dependent hagiographies like the Gospels in their claims about the supernatural resurrection of Jesus? I underwent all of the steps above in doubting a natural hypothesis that apologists claim skeptics only use in singling out and doubting the miracles of Jesus. If I can doubt a much, much more probable hypothesis like Sejanus’ conspiracy, however, I can certainly doubt a highly extraordinary hypothesis such as Jesus’ immortal resurrection.

Miracles and Probability

First off, something should be said about the meaning of the term “miracle.” The Cambridge Introduction to the Philosophy of Religion (pg. 208) defines a “miracle” as follows:

“An event (ultimately) caused by God that cannot be accounted for by the natural powers of natural substances alone. Conceived of this way, miracles don’t violate the laws of nature but rather involve the occurrence of events which cannot be explained by the powers of nature alone. When dead bodies come back to life it is a miracle because the molecules that make up the corpse lack the powers necessary to generate life.”

In other words, miracles involve supernatural intervention from outside of the physical order to effect events that are not causally possible through physical explanations alone. Jesus resurrecting from the dead after three days of brain-death, due to the supernatural intervention of the Judeo-Christian God, is thus a miracle. So far so good.

Sometimes apologists claim that the existence of miracles is purely a “philosophical” question that cannot be tested through science. However, nothing could be further from the truth. Science is a method that is above all empirical. Miracles like resurrections from the dead or turning water into wine would involve demonstrable, empirical change. Scientists could thus test them with scientific methods. Forensic expert Richard Packham discusses the exact sort of evidence that scientists and medical experts could use to prove a miracle in his article “The Man with No Heart: Miracles and Evidence.” It just so happens that there is no evidence — peer reviewed by forensic scientists, medical experts, or parapsychologists — that exists for the occurrence of such miraculous phenomena in modern times. But nevertheless, the existence of miracles is still a scientific question.

If there is no scientific evidence for the existence of miracles, such as Jesus’ resurrection, then this needs to be factored into our background knowledge in the exact same way that the lack of the scientific evidence for phoenixes, discussed above, is factored into our evaluation of Tacitus'(Ann. 6.28) claim that a phoenix had visited Egypt in 34 CE. We do not simply treat the initial probability of all historical claims as equal because of the consideration of prior probability. Events with low priors are less intrinsically likely to occur and, as such, they require greater expected evidence to be rendered more probable. The more extraordinary or unlikely the prior is, the more extraordinary the evidence needs to be.

Often times apologists use false analogies when discussing the probability of miracles with Bayes’ Theorem. William Lane Craig, for example, has argued that winning the lottery may be an extremely unlikely event, but this does not mean that a historian cannot say that someone won the lottery in the past when there is good evidence (like the example I gave above). However, this completely misrepresents the nature of a miracle. Someone winning the lottery is not as unlikely of an event as a miracle. If a million people entered a 1/1,000,000 chance lottery, I would not at all be surprised if one person won it. In fact, if ten million people entered a 1/1,000,000 lottery, and then nobody won, I would be rather surprised. Miracles are not at all like this, however.

We have evidence that lottery wins occasionally occur, but we have no such evidence for miracles. Professional parapsychologists investigate claims about the supernatural all the time, and yet not one has ever passed scientific peer review. There are simply no “bench mark” miracles that we can use as a reference for assessing other miracle claims [2]. Furthermore, there are other extraordinary aspects of Jesus’ resurrection, in particular, that make its occurrence highly unlikely, given our background knowledge of the world we live in. Sometimes apologists appeal to people resuscitating from the dead under extraordinary circumstances (e.g. a person being declared dead for a couple of hours, before resuscitating) as proof that resurrections from the dead are possible. However, this entirely misses the metaphysical character of Jesus’ resurrection. As theologian William Craig (Knowing the Truth about the Resurrection, pg. 15) explains about the nature of Jesus’ resurrection:

“Resurrection is not resuscitation. The mere restoration of life to a corpse is not a resurrection. A person who has resuscitated returns only to this earthly life and will die again.”

Instead, Craig (pg. 127) explains that the actual transformation that is entailed by the Christian claim that Jesus rose from the dead:

“Jesus rose to eternal life in a radically transformed body that can be described as immortal, glorious, powerful, and supernatural. In this new mode of existence, he was not bound by the physical limitations of the universe, but possessed superhuman powers.”

Here, we should immediately think about prior probabilities. Thomas Bayes set out to find a formula “to find a method by which we might judge the probability that an event has to happen, in given circumstances, upon the supposition that we know nothing concerning it but that, under the same circumstances, it has happened a certain number of times, and failed a certain number of times.”

Resuscitations from the dead are known to occur under certain circumstances. Their prior probability is thus not that extraordinarily low. But how many people have immortally resurrected into an imperishable body and never died again? Well, none. As Bayesian expert Robert Cavin (slide 108) explains, the likelihood that Jesus would immortally resurrect, based only on the consideration of how often people immortally resurrect or do not resurrect under the same given circumstance of dying (ignoring other considerations that might further reduce the prior probability of the resurrection), can be computed through a simple statistical syllogism:

  1. 99%+ of Xs are Ys
  2. A is an X
  3. Therefore, A is probably a Y

In the case of Jesus’ resurrection, Cavin computes the prior probability using “The Anti-Resurrection Prior Probability Statistical Syllogism”:

  1. 99.999…999% of the dead are not supernaturally interfered with by God, and, thus, not raised by Him.
  2. Jesus was dead.
  3. Therefore, it is 99.999…999% probable that Jesus was not supernaturally interfered with by God, and, thus, not raised by Him.

As this syllogism shows, the prior probability for the resurrection of Jesus must be, at the very least, extremely low. So low that alternative explanations, when they are not so intrinsically improbably and can explain the same data, greatly outweigh the probability of the resurrection. I lay out such alternative explanations in my article “Knocking Out the Pillars of the Minimal Facts Apologetic.” Remember, as was discussed above, historians do not analyze individual hypotheses in isolation, but also take into account alternative hypotheses that can explain the same data. When such alternative explanations involve far less intrinsic implausibilities and can still explain the same data, they will always tend to be more probable than extraordinary or paranormal explanations.

Recognizing that the initial likelihood of Jesus’ resurrection is extremely low, apologists often try to argue that the prior probability can be increased, if one takes into consideration the religious context behind the resurrection. For example, apologist William Craig argues:

“That Jesus rose naturally from the dead is fantastically improbable. But I see no reason whatsoever to think that it is improbable that God raised Jesus from the dead.”

But here apologists are assuming far more than is given by the historical evidence. Remember that the evidence is not that God wants to raise Jesus from the dead. As I explain in my article “History and the Divine Sphere,” historians do not have access to God’s will and cannot assume theological premises when engaging in “historical” analysis. As Bayesian expert Robert Cavin (slide 347) explains, things like “religious context” are not bona fide part of the historical evidence. Apologists, for example, often argue that considerations such as Jesus being the “Son of God,” or a fulfillment of biblical prophecies, or having moral perfection, increase the likelihood that God would raise him from the dead. But these are nothing more than religious dogmas, not historical facts. They thus cannot be assumed as sound premises when evaluating the historicity of Jesus’ resurrection, especially when apologists try to use “minimal facts” arguments to try to prove the resurrection. It *is not* a “minimal fact” that God even exists nor that he would want to raise Jesus from the dead. Instead, the only data that the historian needs to explain is why there are *ancient texts* claiming that Jesus rose from the dead.

As historical philosopher Aviezer Tucker (Our Knowledge of the Past, pg. 99) explains, the real question to ask about ancient texts that report miracles is:

“‘What is the best explanation of this set of documents that tells of a miracle of a certain kind?’ The center of research is the explanation of the evidence, not whether or not a literal interpretation of the evidence corresponds with what took place.”

The historian thus only needs to provide a hypothesis for what causes could have produced the ancient texts reporting a miracle. Such causes do not need to entail the actual occurrence of the miracle reported, since reports of miracles can have other causes — such as lies, rumors, misinterpretations of natural phenomena, legendary development, and so on. As I explain in my rebuttal to the minimal facts apologetic, secular historians have identified a number of natural causes that can explain the origins of Christianity and the texts in the New Testament that claim Jesus rose from the dead, without the actual occurrence of a miracle. Likewise, these natural causes do not have the same problems with low prior probabilities. False rumors of resurrections and post-mortem sightings have been known to happen. Actual resurrections have never been confirmed.

Just how low, then, is the prior probability of a miracle like the resurrection of Jesus? Here I argue the such priors are not static. They are being updated all the time by the evidence that scientists, medical experts, and parapsychologists find about the world. If peer reviewed evidence were presented of an immortal resurrection that occurred tomorrow, then the prior probability of Jesus’ resurrection would dramatically increase. The problem is, however, that no such evidence exists. As scientists and other experts continue to accumulate data that shows no signs of such phenomena, their prior probability gradually becomes lower and lower. Moreover, when there are numerous reports of miracles that are later proven to be false under investigation, this data likewise reduces the prior probability of a genuine miracle taking place.

To be fair, the prior probability for any inductive hypothesis can never strictly be 0. However, given infinite time and an infinite number of events, if we continue to take in data that only ever indicates a purely natural world with no miracles, then the prior probability of a miracle will gradually approach 0. Such an asymptotical trend is similar to the following mathematical limit [3]:

Pic 4

This asymptotical trend provides a cumulative case for assigning a low prior probability to miracle claims, as well as other paranormal and extraordinary events. Eventually, enough data is accumulated to render the prior probability of a miracle as statistically insignificant to historical analysis [4]. Now, low priors can be offset by strong expected evidence. But that is the very problem that we have with ancient texts: they will almost never produce extraordinary evidence. Literature that was produced in the ancient world was written in an age before forensics, scientific testing, journalism, internet access, or even common literacy. Ancient literature is thus simply far less reliable than many other forms of evidence that are capable of being produced today.

Something should be said at this point about what is meant by the term “extraordinary.” As forensic expert Richard Packham (“The Man with No Heart: Miracles and Evidence”) explains, the term “extraordinary” does not mean that the type of evidence itself has to be remarkable. Video tapes, x-rays, medical records, and so on are all part of ordinary life experience. What is meant by “extraordinary” in this case is that the evidence in question cannot be equally explained by a wide range of causes, but is only rendered probable under a very specific hypothesis.

Suppose there is a man who has been hit by a vehicle that has broken nearly every bone in his body. He is brought to the hospital, inspected by doctors, and x-rayed. The man dies not long after being brought in. Suppose then that the man is attached to heart and brain monitors for three days showing no activity. Then, on the third day, suppose that the man rises suddenly and walks away from the morgue. The doctors, being amazed, perform another x-ray of the man’s body and find not a single bone broken. The man’s heart and brain are found to be fully functional and healthy. Now, how many alternative hypotheses can explain this kind of data — namely, the doctors’ testimony, x-rays taken before and after the event, heart and brain monitors recording activity throughout multiple days — without the man actually being miraculously cured and raised? Not many. It is not easy to falsify such records, so that the range of alternative explanations that can account for them is quite small. This kind of evidence is thus extraordinary.

The problem with many of the claims in ancient literary texts is that they can be explained by a much wider range of alternative explanations. Suppose that an anonymous author in an ancient text wrote a narrative that cited none of his sources about a man, who lived 40 years in the past in a distant land, having broken nearly every bone in his body, being breathless for three days, and then suddenly rising and walking away perfectly unscathed. Such an event is equally miraculous as the one discussed above. However, the evidence is not extraordinary. All we have is an unknown author writing about the alleged event long after it happened. But we know that authors can write about things for other causes than the event being true. The author may have lied, only reported a rumor, wrote what he had only imagined to be true, been speaking allegorically, and so on. If we know very little about how the evidence in the text was produced (which is the case for the vast majority of ancient texts, including the Gospels), we cannot exclude alternative explanations that are more mundane. It is very easy to falsify such records. They are thus not extraordinary.

Now, we can trust such fallible texts for ordinary claims that do not involve extraordinarily low prior probabilities. When ancient authors wrote about Caesar crossing the Rubicon during a time of war, we know that wars are common events in human history. So, even if an ancient text claiming that a war occurred may have hypothetically been falsely produced, we know that these kinds of events have been confirmed and are not commonly lied about. Their prior probability is much higher and thus can be confirmed with only a moderate amount of expected evidence. No extraordinary evidence is needed for such ordinary claims. But, when it comes to events with extraordinarily low prior probabilities — such as immortal resurrections after multiple days of brain death — historians are justified in exercising greater skepticism, especially when alternative explanations can account for the same data that are less intrinsically improbable.

For example, Tacitus’ (Ann. 6.28) claim of a phoenix visiting Egypt in 34 CE was discussed above. Not only do we have no evidence whatsoever from biologists, zoologists, or ornithologists that phoenixes actually exist, but we also know that reports of such creatures can be caused by purely natural causes — such as lies, rumors, misinterpretations of natural phenomena, legendary development, and so on. In such a circumstance, the probability of Tacitus’ claim being literally correct is so small as to be statistically negligible. It doesn’t even matter that he was an ancient historian (unlike the authors of the Gospels). Ancient historical texts, even when written by the best historians, will virtually never be so extraordinary as to offset the low prior probability of a phoenix actually visiting Egypt. That is why Classicists do not even seriously entertain such a hypothesis, but universally reject it after the briefest consideration. In order to change this assessment, one would need to first give scientific evidence that phoenixes actually exist. Only then would the prior probability of a genuine phoenix appearance in 34 CE be raised to the point of being worth serious historical consideration.

The same exact reasoning can be applied to miracles, such as the resurrection of Jesus. No matter how insistent the report of a miracle in an ancient text may be, and no matter how many ancient sources claim it happened, the extremely low prior probability of such extraordinary occurrences still drags down their overall likelihood to the point of being statistically insignificant, when ancient texts are the only form of expected evidence that we can rely on. At the very least, professional historians usually bracket such miracle claims as being beyond the scope of ordinary historical analysis, both due their intrinsic improbability, and because their underlying theological and metaphysical assumptions are not part of the available historical evidence. Remember that all it took for an author in antiquity to falsely report such claims was merely writing about them in ancient texts. Because such evidence can so easily be falsely produced, it will virtually never be extraordinary enough to offset the low priors of such paranormal claims (especially when there are alternative explanations with higher priors that can explain the same evidence).

In contrast, peer reviewed evidence among scientists, medical experts, and parapsychology cannot so easily be falsely fabricated. These forms of evidence thus have a far greater potential to provide extraordinary evidence and to actually confirm a miracle. And yet these far more reliable methods have never shown that the types of miracles reported in ancient texts ever occur under similar circumstances, when rigorous documentation and investigation is available. Given such cumulative data, virtually any non-miraculous hypothesis that is intrinsically more probable — even if it is less unattested in ancient sources  will still be more probable than a miracle reported in an ancient text actually being genuine. At the very least, the prior probability of a miracle is low enough to render it as too statistically problematic to almost ever be the best explanation in historical analysis, especially when only weak forms of evidence, such as ancient texts, are the only data to consider. 

An apologist might now object that I have “presupposed” naturalism and have axiomatically ruled out any possibility of a miracle happening. This, however, could not be further from the truth. The asymptotical trend, argued above, only states that prior the probability of a miracle will approach 0, if n -> ∞ with no evidence of miracles. All that would be required to change this trend is the confirmed occurrence of just one miracle event. Forensic scientists, medical experts, and parapsychologists have the means to investigate such claims. If peer reviewed evidence for miracles can be offered by such authorities, I will accept it. The burden is on the apologist to provide such evidence. They cannot shortcut the peer review process by simply appealing to a miracle claim in an ancient text, and then claiming that it is a “philosophical” matter that science cannot investigate. Apologists can, in principle, provide the evidence that is need. It just so happens that everyone who has attempted to do so thus far has failed, so that n -> ∞ is still on its current course. But that is simply a matter of where the evidence leads, not apologists being axiomatically ruled out from ever being able to prove such claims.

Miracles That Almost Certainly Did Not Happen in the Past

Rather than singling in on only doubting Jesus’ resurrection, as apologists claim we skeptics do, I will instead compare the evidence for this miracle claim to another supernatural claim about the past that I also do not believe took place. There are countless reports of ancient miracles throughout Pagan literature: Aesculapius healing hundreds of named witnesses (see here), statues moving in front of whole crowds of people (Plutarch’s Coriolanus 38), fish resurrecting from the dead in front of whole towns (Herodotus 9.120). I doubt all of these miracles, and yet I am criticized for doubting the resurrection of one itinerant Jewish prophet from the 1st century CE.

Why do we get these stories? The ancients lived in a world of poor literacy, no cameras, no internet, very little scientific method, no journalism, and extreme superstition. As time has progressed and we have improved in all of these categories, miracle stories have decreased and those that have surfaced have all been discredited when direct examination is possible.

One miracle that I believe has relatively better evidence in antiquity than the resurrection of Jesus (or at least equal evidence) is a miracle that the emperor Vespasian is said to have performed in Alexandria between 69-70 CE. At least three independent historians — Tacitus (Hist. 4.81), Suetonius (Vesp. 7.2), and Cassius Dio (65.8) — record this miracle in which Vespasian, through the aid of the god Serapis, is said to have cured a blind man by spitting in his eyes before a whole crowd of people, in addition to curing a crippled man. Every piece of evidence we have for Vespasian’s miracle can be compared to the resurrection of Jesus.

  • Date of Earliest Source: Tacitus records Vespasian’s miracle in his Histories (written c. 105 CE), which places his testimony approximately 35 years from the event. The earliest source that we have for Jesus’ resurrection is the apostle Paul, writing about 20-30 years from the event. However, both of these authors had earlier sources. As I have shown in my paper “The Propaganda of Accession of the Roman Emperor Galba,” many of the claims made by the ancient historians who record the Roman civil war of 69 CE (which is the time in which Vespasian’s miracle is recorded to have taken place) have corroborating evidence and independent attestation, which show that the reports they relate must must have dated to much earlier. In fact, since this story is found in both Tacitus and Suetonius, who are likely independent of each other (as discussed by Tristan Power in “Suetonius’ Tacitus”), we can tell that the report about Vespasian’s miracle must have predated both of their works. NT scholar Eric Eve in “Spit in Your Eye: The Blind Man of Bethsaida and the Blind Man of Alexandria” finds evidence for Vespasian’s miracle being alluded to in Mark 8:22-25. Since the Gospel of Mark dates to 70-75 CE in its composition, this could provide very early evidence for the story of Vespasian’s miracle, showing that it was circulating within a year or so of the event’s alleged occurrence. Likewise, the apostle Paul alludes to creeds about the resurrection of Jesus that predate his epistles. In 1 Cor. 15:3-7 Paul relates a creed that discusses the resurrection of Jesus, which most scholars date to 2-5 years after Jesus’ death (I discuss this creed and its relevance further here). Both miracle reports, therefore, probably date to within years of their alleged occurrence.
  • Fullness of the Account: The problem with these earliest sources is that they do not provide many substantive details for the event. While stories of Vespasian healing the blind were circulating well before Tacitus, he is still our earliest source to provide a substantive account of what allegedly took place. Likewise, the apostle Paul’s testimony does not describe the circumstantial details of Jesus’ resurrection (at least as they are later reported in the Gospels). For example, Paul says nothing about an empty tomb being found by women or Jesus appearing to his disciples in an earthly setting for 40 days, or anything like that. Instead, all Paul relates is that Jesus had died and then ὤφθη (“appeared”) to a number of his followers, without specifying any location, time, or even whether these appearances were physical, as opposed to spiritual revelations. This sparse information, therefore, only tells us that the belief in Jesus’ resurrection dated to the time of the creeds that Paul relates. To get any specific details or substantive narrative of what allegedly took place, we must consult later sources. For Vespasian’s miracle, we have full reports from both Tacitus and Suetonius, respectively 35 and 50 years after the event had allegedly taken place. Cassius Dio also corroborates the event much later in the 3rd century CE. For Jesus’ resurrection, the first substantive narratives that we possess for the event are the canonical Gospels, which date to 40-60 years after its alleged occurrence.
  • Independent Attestation: Tacitus, Suetonius, and Cassius Dio are all very different sources (Dio, writing in Greek, even uses a different language than the earlier Latin authors). Tacitus is writing about a historical span of a few decades in his year-by-year annalistic narrative, Suetonius is writing a historical biography of Vespasian’s life, and Dio is writing a universal history of Rome that only small part of which covers Vespasian’s reign. Nevertheless, despite being highly independent, they all corroborate Vespasian’s miracle. In contrast, the Gospels are not independent sources. Matthew copies 80% of Mark’s material, Luke copies about 65% of Mark, and John, although more loosely, probably followed Mark’s basic skeleton or was at least aware of the earlier narratives (as show by Ruprecht in This Tragic Gospel). Accordingly, while we have three independent sources for Vespasian’s miracle, we have highly dependent sources for Jesus’ resurrection via the empty tomb. This is important when assessing the evidence for each event, since independent corroboration is a major criterion that historians consider when assessing probability.
  • Genre of Writing: Tacitus, Suetonius, and Cassius Dio are all authors of historical prose. They have lengthy programmatic statements about their historical methodology, they often cite where they obtained their material, their narratives align with what we know about the historical context of the time, and they are writing to a critical and educated audience. In contrast, the authors of the Gospels wrote religious hagiographies intended to serve as theological scripture, they embellish details, they invent completely unrealistic events — such as the Sun going out for three hours and all the saints breaking forth from their tombs and resurrecting along with Jesus — and they ultimate provide legendary, rather than historical accounts. For a further comparison of the genre of the Gospels with the actual historical writing from the same time and period, see my article “Ancient Historical Writing Compared to the Gospels of the New Testament.”
  • Known Authors: The authorial traditions of Tacitus, Suetonius, and Cassius Dio are not disputed by any major scholars, and from what we know of these authors’ biographies, they would have had access to a variety of sources and evidence in constructing their histories. In contrast, the dubious authorial traditions of the Gospels are disputed by the large majority of mainstream NT scholars and we have little knowledge of their anonymous authors’ backgrounds and what information may have been available to them. For a further explanation of why scholars doubt the traditional authors of the Gospels, see my article “Why Scholars Doubt the Traditional Authors of the Gospels.”
  • Directly Observed Miracle vs. Circumstantial Miracle: Notice also how Vespasian performed a miracle in front of an entire audience. Jesus’ resurrection via the empty tomb is not a directly observed miracle but a circumstantial one. Nobody actually saw Jesus rise from the dead; instead, the Gospel legends claim that an empty tomb was found and that Jesus later appeared to people. Because the resurrection itself was not observed, this leaves open other possible explanations for the circumstances, which weakens the case for Jesus’ miracle.
  • Verification of Condition: In Tacitus’ account of Vespasian’s miracle, physicians are present who verify the condition of the blind and crippled man. In contrast, no physician checks Jesus’ vitals in the Gospels to confirm his death. This leaves open possibilities like the swoon theory (i.e. Jesus only fainted on the cross), which I do not believe are very likely (though still plausible), but this is just another example of how the Gospels’ evidence is weaker than the strength as the physicians’ testimony in Tacitus.

Ultimately, the historical evidence for Vespasian’s miracle is either stronger or at least equal to the evidence for Jesus’ resurrection in every category that has been considered. And yet, I do not believe in Vespasian’s miracle either.

The prior probability that Vespasian miraculously cured the blind and crippled man, as I discussed above, follows an asymptotical trend similar to the mathematical limit lim[n->∞](1/n) = 0. Until we have evidence of such miraculous curings today (so that n does not approach ∞ with only natural events occurring), alternative natural hypotheses will tend to have a stronger probability, due to their higher prior probability, even if there is worse expected evidence. This is because the evidence for Vespasian’s miracle can all plausibly be explained as the result of natural causes, and the ancient texts that report the miracle are not strong enough to offset its low prior probability.

Perhaps Vespasian staged the event, perhaps the man only falsely said he had been cured of his blindness, perhaps the saliva did temporarily help his eyes, but did not fully cure his blindness. Despite these possibilities, Tacitus (Hist. 4.81) counters all of them by stating: “Both facts [the curing of the blind man and the crippled man] are told by eye-witnesses even now when falsehood brings no reward.” Nevertheless, we must dismiss Tacitus’ claim, despite having no other ancient source who refutes him or the independent authors who corroborate the event. We likewise have no ancient sources that say that Vespasian staged this event. Every piece of ancient evidence that we have says that this miracle was genuine. But at the end of the day, we only have ancient texts, which are not a reliable form of evidence for proving such extraordinary claims. The probability that something natural occurred, especially when there are alternative natural explanations with higher prior probabilities that can explain the same evidence, will always tend to be more probable.

As discussed above, apologists often claim that the prior probability of Jesus’ resurrection is only low if one ignores the religious context. But in the case of Vespasian’s miracle, our historians tell us that he performed the miracle with the aid of the Egyptian god Serapis. Using the same logic, then there is considerable religious context that, by the apologists’ own reasoning, should raise the prior probability of Vespasian’s miracle occurring. Yet I see no better evidence that Serapis exists than that the Abrahamic god Elohim exists. The role of neither is a relevant factor in assessing probability. As discussed above, we cannot consider such theological premises as bona fide part of the historical evidence.

Why Jesus’ Resurrection Almost Certainly Did Not Happen in the Past

I have laid out in this discussion how history is not the same thing as the past, but a method that we use to investigate the past. Lacking the ability to forensically investigate either Vespasian’s or Jesus’ miracles, historian must rely on ancient texts to construct a hypothesis of the most probable explanation of the data. The best explanation of that data, however, must not only take into account the expected evidence of the hypothesis, but also the prior probability. As I have discussed above, absent of any peer reviewed scientific, medical, or parapsychological evidence, we have no “bench mark” miracle to establish that miracles even occur in the world to begin with. As such, the prior probability of a miracle will follow an asymptotical trend similar to the limit lim[n->∞](1/n) = 0, until such evidence is provided. Lacking such evidence, the prior probability will continue to approach 0 as n -> ∞, when only evidence of a natural world is ever found. In light of this, almost any natural explanation will tend to be more likely than a miraculous one.

In the case of Jesus’ resurrection via the empty tomb, there are numerous natural explanations that can explain the same data without relying on premises with extraordinarily low prior probabilities. I spell of these alternative explanations in my article “Knocking Out the Pillars of the Minimal Facts Apologetic.” When it comes to assessing these different alternative hypotheses, one furthermore does not need to favor any pet theory. Part of using Bayes’ Theorem is recognizing that there can be multiple hypotheses to explain the same set of data. Since there are multiple possible theories, a combination of alternative hypotheses in addition to a particular hypothesis will always be more probable than that individual hypothesis on its own. When you combine multiple natural theories — such as Jesus’ empty tomb being invented, the disciples hallucinating, the body being moved or stolen, the women going to the wrong tomb, the swoon theory, and so on — even if an individual theory may have a low probability on its own (e.g. the swoon theory), the combined probability of multiple theories is much greater. In this way, we do no need to specifically know, for example, that Jesus’ body was stolen, when we can know with greater certainty the more general claim that something other than the resurrection happened in the case of Jesus, whether the body was stolen or something else had occurred. Based on the cumulative evidence against miracles and the analysis above, I would argue that the combined probability of something other than the resurrection of Jesus occurring at Christianity’s origins is well over +99%.

Now, none of this means that one cannot believe in the resurrection on the basis of faith. The story of doubting Thomas in the Gospels makes clear that the resurrection was supposed to be based on faith: “Because you have seen me, you have believed; blessed are those who have not seen and yet have believed” (John 20:29). I have only written this article because professional apologists — such as William Craig, Gary Habermas, and Mike Licona — claim that they can “historically” prove the resurrection using ancient texts. But this rhetoric is born solely out of the desire to evangelize. A proper understanding of historical methodology, and of how to formulate theories based on the most probable explanation of the data, which includes consideration of our broader scientific knowledge about the world, shows that such miracle claims will virtually never be the most probable explanation of the data. Natural explanations that account for the same evidence are simply far more probable.

I undertake writing these extensive blogs in order to prevent my own discipline of Classics and Greco-Roman history from being hijacked by religious fundamentalists. That I should have to single in on refuting apologetic agendas to “prove” miracles exclusive to only their religion, such as Jesus’ resurrection, while these very apologists ignore the countless Pagan miracles that are likewise confirmed by their same “historical” methodology, shows that such apologists are not really concerned with abstractly proving miracles. They are concerned primarily with proving the miracles exclusive to their religious faith. I, in contrast, doubt both Pagan and Christian miracles, along with many other paranormal claims found in ancient texts, on the exact same logical grounds. Skepticism towards all miracles is consistent, but only seeking to prove miracles exclusive to one’s religious faith, while denying others, is a case of special pleading.

-Matthew Ferguson

[1] The idea of an equestrian becoming Roman emperor was rather unthinkable in the early Roman Empire (27 BCE – 192 CE), during which time every emperor to ascend to power came from senatorial families. In the later Roman Empire, the imperial system became disrupted by civil war which broke down the old senatorial power dynamics, and likewise the equestrians rose in public prominence. It was not until the 3rd century CE that Rome had an equestrian emperor, when Macrinus usurped the emperor Caracalla. Like Sejanus, Macrinus was a Praetorian prefect, but he dated to almost two centuries later and gained power under very different political conditions. A usurpation like Macrinus’ would have been much less plausible in the 1st century CE, not only because Macrinus was Punic (which no Roman emperor had been up until that point), but also because every emperor during the early 1st century CE was related by blood or marriage to the house of Julius Caesar. That Sejanus, therefore, could have pulled off a conspiracy like Macrinus’ during this period is highly unlikely. Instead, adoption was the far more realistic pathway to power, but Sejanus was of too low of rank to have been adopted by Tiberius. As such, this article favors historian Robin Seager’s hypothesis in Tiberius that Sejanus had more realistically been seeking to become the guardian of Tiberius’ grandson Gemellus, in order to rule indirectly through the young prince. There is a 1st century CE precedent for this type of power dynamic, since the philosopher Seneca was appointed to a similar position over the young emperor Nero. However, Sejanus’ original plan was probably embellished by later historians, owing to his infamous downfall and negative reputation, which caused him to be depicted as directly planning to overthrow Tiberius.

[2] Apologists often appeal to Craig Keener’s volume Miracles: The Credibility of the New Testament Accounts in order to claim that there is modern evidence indicating that miracles actually do occur in the modern world. It is true that Keener has cataloged a large number of miracle claims that still spread throughout multiple regions of the globe; however, even Keener (pg. 1) discusses in the book that he lacks the time and resources to fully investigate the miracles that he records: “With a research grant and a year or two to travel, I could have easily have collected hundreds of further stories … Some circles whose reports I was exploring invited me to witness their experiences first hand; while this deeper investigation would have been ideal, my academic schedule and other factors have precluded my plans to do so.” More importantly, none of Keener’s evidence has passed any peer review by scientists, medical experts, or parapsychologists. If it had, Keener would have no doubt won the Nobel Prize in Medicine by now. Instead, Keener has merely cataloged a bunch of miracle claims without subjecting them to necessary scrutiny. This does not provide any evidence for a “bench mark” confirmed miracle, making Keener irrelevant to the analysis above. Instead, what Keener’s evidence really shows is that a large number of miracle claims still circulate in the world, but that, when they are not disproven, they are simply incapable of being adequately investigated. If they could be adequately investigated, we would have peer reviewed evidence by now (instead of only an apologetics book from Evangelical Christian publisher Baker Publishing Group, written by a NT scholar — rather than a scientist, medical doctor, or parapsychologist — who works at a faith-based seminary with a doctrinal statement affirming the inerrancy of the Bible and the truth of the resurrection). Finally, Keener does not record any miracles that are of a similar character as Jesus’ resurrection. For example, he discusses a number of cases in which people resuscitate under extreme circumstances (pp. 536-579), but, as is discussed above, resuscitations are not at all the same as immortal resurrections. Keener records nothing like people rising into immortal and imperishable bodies, so that even the unconfirmed lesser miracles that he reports are really just a case of comparing apples with oranges. Here is a critical review of Miracles, which raised many good additional points, and I likewise discuss further problems with Keener’s evidence here.

[3] The mathematical limit lim[n->∞](1/n) = 0 is, of course, technically a different equation than the Bayesian equation, and is not to be understood as a precise calculation of prior probability. Rather, what the limit represents is the asymptotical effect that occurs when repeated evidence and events, given infinite time, continually speak against or provide no instances of a particular kind of phenomenon, such as Sasquatch sighting, psychic predictions, or miracles. As such data is a accumulated, the prior probability of these phenomena actually occurring gradually drops. However, the prior probability can never technically be 0, and hence what occurs instead is an asymptotical trend in which the prior gradually approaches 0, eventually reaching a point where the likelihood of such events actually occurring is statistically insignificant, unless there is extraordinary evidence to offset the extremely low prior. This asymptotical trend is represented, in more simplified form, by the mathematical limit lim[n->∞](1/n) = 0, but the Bayesian equation follows a similar asymptotical trend as well.

[4] An apologist might object to this approach by arguing that such an asymptotical trend towards 0 for the prior probability of a miracle, based on the cumulative inductive data of no genuine miracles ever occurring and miracle claims being repeatedly falsified, places too much emphasis on modern observation, and does not consider the possibility that a resurrection event, such as Jesus rising from the dead, may only occur once in human history, and thus cannot ever be repeated and reliably documented. Indeed, even as far back as Augustine, many Christians have claimed that the past was an “age of miracles,” which has come and gone, so that a lack of present/future miracles does not falsify God’s past involvement in the world. There are two major problems with this response:

i. To begin with, this kind of rationalization plays easily into the argument from locality. The argument from locality observes that religious experiences, particularly miracles and revelations, tend to be culturally isolated and specific to certain times and regions. This is very odd if there really is one true God, who transcends all time periods and who wishes to make his presence known in the world. Instead, locality suggests that there is no universal force driving religious experience, but rather that human culture is completely relative on the question of religion, which in turn suggests that no one religion is ultimately correct. If God, therefore, only performed miracles like raising Jesus from the dead in a sealed-off time period in the past and only within specific regions (conventionally in times and regions that lacked modern recording and documentation technology), it makes little sense that such a deity would use such isolated evidence to make his presence known in the world. So, even if you perfectly gerrymander the “age of miracles” to have only occurred when Jesus was on Earth, and to have only occurred in front of the first generation of Christians, it is difficult to see what evidence should convince an outsider to raise his or her prior probability of a genuine miracle occurring, given that the only evidence presented is suspiciously so temporarily, regionally, and culturally specific.

ii. But furthermore, even if you gerrymander your hypothesis of miracles, so that miracles only occurred on Earth conveniently during the time of Jesus, to argue that a lack of present/future miracles can in no way falsify the assumption that miracles occurred in the past, this kind of rationalization still drastically lowers the prior probability of a genuine miracle. The reason why has to do with a Bayesian fallacy of gerrymandering one’s hypothesis to perfectly explain consequent probability, without considering the effect of such gerrymandering on prior probability. As Richard Carrier explains in “Two Bayesian Fallacies”:

“Hypotheses can always be gerrymandered so that the probability of the evidence is 1, but that would not mean P(e|h) is always 1, but only that it can always be forced to equal 1 with some elaboration (thus, only with the elaboration can it do so). And even then, such a tactic cannot ignore the mathematical consequences of such gerrymandering to the prior probability. The more you gerrymander a theory to raise its consequent probability, the more you lower that theory’s prior probability, often to no net gain. This is the basic logic of Ockham’s Razor … In essence, you can’t gerrymander P(e|h) to equal 1 without ‘paying for it’ with a reduction in P(h|b). So you would just be moving probabilities around in the equation and not actually getting any better result.”

So, indeed, if one’s pet theory of miracles is that the only miracle that ever has or will occur is Jesus rising from the dead in the 1st century CE and appearing to his followers in the exact way that the Gospels describe, then, indeed, the consequent probability of this hypothesis would be 1, given the evidence in the New Testament. However, as Carrier explains, you cannot get away with this kind of rationalization without “paying for it.” It is extremely ad hoc to assume that such an ultra-specific and conveniently unfalsifiable hypothesis is correct. As such, even if you argue that a lack of present/future miracles in no way lowers the prior probability of a miracle like this occurring in a past “age of miracles,” you still cannot get around the fact that such a gerrymandered theory likewise dramatically lowers the prior probability due to its ad hocness. So, no matter how you slice it, the prior probability of a miracle like Jesus’ resurrection is still extremely low.

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14 Responses to History, Probability, and Miracles

  1. Tito says:

    Amazingly well done write-up. Thanks for taking the time to lay this out so well. I will refer others to this for certain.

    • Thanks Tito. I wrote this as an expansion upon Hume’s argument against miracles. The proper application of Bayes’ Theorem answers all of the apologists’ objections to Hume, while making his argument more moderate on the skeptical side. Basically, I don’t think that Hume’s objection would always be true (certainly not true if we lived in a world that was actually like the Old Testament), but given the background knowledge of the world we do live in, Hume is spot on about disregarding fantastical miracle claims. Apologists want to argue that a lack of belief in miracles is purely an a priori prejudice, but then I make it quite clear that they could change that skepticism by updating our background knowledge. This is the step, however, that they desperately want to avoid, since they have no evidence to demonstrate that miracles are really more probable than we think.

  2. Nate says:

    Excellent article! Very glad I came across it 🙂

  3. Dj says:

    ‘Regardless, one does not even need to favor any pet theory. Any natural explanation, even if it is unlikely on its own, is more likely than a miraculous resurrection.’ Why not just write this? The rest of the article is redundant. All the Bayesian probability is just a cover for what you believe by faith. And I do not buy for a moment your miracle cited is more likely – it was done by a Roman Emperor – can’t you see a certain amount of coersion must be present!

    • Dear DJ,

      “And I do not buy for a moment your miracle cited is more likely – it was done by a Roman Emperor – can’t you see a certain amount of coersion must be present!”

      Did you even read Tacitus’ account of this miracle? Here is what Tacitus (a historian who is elsewhere critical of Roman emperors and who is writing after both Vespasian and the Flavian Dynasty) records about Vespasian’s miracle:

      “So Vespasian, believing that his good fortune was capable of anything and that nothing was any longer incredible, with a smiling countenance, and amid intense excitement on the part of the bystanders, did as he was asked to do. The hand was instantly restored to use, and the day again shone for the blind man. Both facts are told by eye-witnesses even now when falsehood brings no reward.”

      This means that Tacitus was not only aware of eye-witnesses, but also knew of some who still attested to the truth of this miracle, even later when there was no reward or coercion in place. Therefore, we even have an ancient historian who explicitly states that the coercion you claim is behind this miracle report never took place.

      I am surprised that you would be so quick to dismiss this miracle and yet scoff when I doubt the miracles attributed to Jesus. No ancient sources say that this miracle of Vespasian *did not* take place. There would have been religious context (a divine power sanctioning a new emperor), and there are multiple historians who record this event.

      If you believe that miracles actually occur in the world and that ancient historical texts can be used to confirm them, what grounds do you have for doubting Tacitus, Suetonius, and Dio when they independently record this event?

      “The rest of the article is redundant. All the Bayesian probability is just a cover for what you believe by faith.”

      I, in contrast, have written a lengthy analysis explaining how we have a cumulative inductive case for doubting that any miracles occur in the world, and I have also written elsewhere about the methodological problems involved in trying to use ancient texts to try to prove past miracle claims.

      The inductive analysis in this article is based on the cumulative fact that no genuine miracle has ever been confirmed by parapsychologists, medical experts, or forensic scientists, and the fact that virtually all previous miracle reports, when they are capable of being fully investigated by such experts, have been falsified or shown to have a natural explanation when a full investigation is performed. This cumulative information provides us with background knowledge suggesting that ancient miracles were probably falsified or had a natural explanation as well. We can, at the very least, say that such miracle reports are overwhelmingly more likely to be false than genuine. I use this approach to doubt both the miracles of Vespasian and Jesus.

      If you have evidence to the contrary, showing that miracles actually do occur in the world, please submit this evidence to a parapsychology, medical, or scientific journal, have it peer reviewed by experts, and then I am sure that you will receive the Nobel Prize.

      Short of that, I do not think that we can prove *any* past miracles with good probability using ancient texts. This applies equally to the miracles of Vespasian and Jesus. I am thus methodologically consistent in doubting both of them.

      You seek to deny one, while believing in the other, when both are attested among ancient sources (and, IMO, much better sources in the case of Vespasian, since his miracle is recorded by actual historians). I do not, therefore, see a methodologically consistent grounds for you to accept the miracles of Jesus on the basis of ancient texts, and yet to deny the miracles of Vespasian that are also recorded in ancient texts. Lacking such a consistent methodological basis, one is instead engaging in special pleading.

  4. Dj says:

    Did you even read Tacitus’ account of this miracle? Here is what Tacitus (a historian who is elsewhere critical of Roman emperors and who is writing after both Vespasian and the Flavian Dynasty) records about Vespasian’s miracle:
    “So Vespasian, believing that his good fortune was capable of anything and that nothing was any longer incredible, with a smiling countenance, and amid intense excitement on the part of the bystanders, did as he was asked to do. The hand was instantly restored to use, and the day again shone for the blind man. Both facts are told by eye-witnesses even now when falsehood brings no reward.”>>

    I don’t know what Tacitus means here. Were these men threatened with death unless they recanted like the apostles were? I doubt it. Why would they change their story and be made out as liars? As for the ‘prior probability’ of a miracle claim being made by an emperor, given that they were considered Gods, I would say highly probable. Maybe Vespasian was inspired to do this by another ‘son of God’ who did impressive similar miracles and were making the emperor’s claims to divinity look suspect? If you can’t see the contrived nature of this story and how this is different from the miracles of Jesus – most scholars agree he was at least regarded by his contemporaries as a healer and exorcist – I don’t believe you are thinking it through.

    I agree that due the amount of independent attestation this event certainly happened. Was it a miracle? Why would anyone believe that as opposed to my simple hypothesis above? For more on this http://proecclesia.net/wp-content/uploads/2014/03/Evaluating-the-Healing-Miracles-of-Vespasian-and-Jesus-Garet-Robinson.pdf


    I don’t know any absolutely watertight cases so I will have to pass on your offer of the Nobel Prize but I do know there is plenty of belief out there. This tells me in most people’s life there is at least some experience of the supernatural. Maybe where there is smoke there is fire? This book deals with this near universal human experience. http://www.amazon.com/Miracles-Credibility-Testament-Accounts-Volume/dp/0801039525 . Why a priori dismiss them as you definitely do in your article? It seem intellectually dishonest. You points on Bayesian probability is disingenuous. You use this complex equation but then substitute in 0 into it – and anyone with even a passing understanding of mathematics knows what will happen – it will spit out 0 as an answer. Why not let the evidence speak for its self rather than crafting your own philosophically derived answer?


    Most scholars who are experts in the field believe that
    1. Jesus existed
    2. He was crucified
    3. He was buried in the tomb of Joseph of Arimathea
    4. Women found the tomb empty on the morning of the resurrection
    5. Many disciples came to believe that they had seen him alive soon afterwards and became so absolutely convinced of this that they were able to convince others even in the face of persecution, torture and death.

    If you have a naturalistic hypothesis that explains these five facts (not just one) then you’ve done better that virtually every expert in the field.

    • DJ,

      Literally every question and apologetic talking point that you have responded with I have already thought about, analyzed, and responded to elsewhere in my previous writings.

      “I don’t know what Tacitus means here. Were these men threatened with death unless they recanted like the apostles were? I doubt it.”

      Tacitus is stating that people still affirmed this miracle, even when there was no reward or coercion motivating them. You tried to immediately dismiss this miracle in your first comment by saying that the witnesses were coerced (despite Tacitus’ explicit statement to the contrary). Rather than admit that you were wrong in this hasty assumption, you have instead tried to change the subject by talking about the apostles’ alleged martrydoms.

      Here is an article where I discuss the sources behind the death of every single apostle and show how they are almost all legendary and unreliable:


      I also discuss how Christians, in the actual context of the 1st century CE, would not have been killed for believing in the resurrection (both the Romans and Jews tolerated many diverse views about the afterlife), but on other charges. The Jews persecuted Christians for allegedly teaching a heretical view of the Law (e.g. Stephen). Nero persecuted Christians on charges of arson after the Great Fire of 64 CE. When Christians were (occasionally) persecuted, therefore, historians cannot assume that they died specifically for belief in the resurrection, rather than as the result of other social, religious, and political charges.

      “As for the ‘prior probability’ of a miracle claim being made by an emperor, given that they were considered Gods, I would say highly probable. Maybe Vespasian was inspired to do this by another ‘son of God’ who did impressive similar miracles and were making the emperor’s claims to divinity look suspect? If you can’t see the contrived nature of this story and how this is different from the miracles of Jesus – most scholars agree he was at least regarded by his contemporaries as a healer and exorcist – I don’t believe you are thinking it through.”

      Scholars also agree that contemporaries regarded Vespasian as a healer. Once more, you are engaging in special pleading. You may actually have it backwards about the stories of Vespasian’s miracles being caused by challanges from another “Son of God.” Here is an article by NT scholar Eric Eve that argues that Jesus’ alleged curing of the blind man of Bethsaida (Mk. 8:22-25) was actually invented and constructed in response to Vespasian’s miracle claim (meaning that Christians were actually the ones worried about impressive, similar miracles being performed by others):


      As for the prior probability of false miracle claims circulating around Vespasian, because Roman emperors were thought of as gods, I agree! That is why we factor in background knowledge when evaluating these ancient claims and do not just naively accept them at face value.

      It is also true that post-mortem sighting of other dead people (e.g. Elvis, Nero, Apollonius of Tyana, Anastasia, and Michael Jackson) virtually always turn out to be false rumors when fully investigated. This background knowledge provides a basis for likewise thinking that Jesus’ post-mortem sightings were probably false and based on rumors.

      Likewise, there is a background precedent for other failed Jewish Messiahs being exalted by their followers after their death, who have awaited their second coming. Here is an article that discusses similarities in the early Christians’ belief in Jesus’ resurrection and the cognitive dissonance rationalizations of other failed Messianic movements, such as those of Sabbatai Zevi and Mendel Schneerson:


      “I agree that due the amount of independent attestation this event certainly happened. Was it a miracle? Why would anyone believe that as opposed to my simple hypothesis above? For more on this http://proecclesia.net/wp-content/uploads/2014/03/Evaluating-the-Healing-Miracles-of-Vespasian-and-Jesus-Garet-Robinson.pdf

      You’ve only provided a link to an article (written by a Baptist minister in TX) that you yourself haven’t written. I, in contrast, have analyzed the relevant passages above and evaluated them according to historical criteria drawing from my experience as a PhD student in Classics. You have not responded to any of my arguments but only posted a link. I am not going to do your work for you, and see my Comment Policy about why commenters should not just post links to other sites on this blog without any original contribution of their own. Your tone has also not been particularly respectful so far, with ad hominem jabs like “All the Bayesian probability is just a cover for what you believe by faith.” In all future comments you will desist from such arrogant and condescending remarks, or your comments will not be approved. Consider that a warning.

      “I don’t know any absolutely watertight cases so I will have to pass on your offer of the Nobel Prize but I do know there is plenty of belief out there. This tells me in most people’s life there is at least some experience of the supernatural. Maybe where there is smoke there is fire? This book deals with this near universal human experience. http://www.amazon.com/Miracles-Credibility-Testament-Accounts-Volume/dp/0801039525 .”

      Ah, yes, Craig Keener. I knew he was coming. I said to submit evidence of miracles to a parapsychology, medical, or scientific journal, have it peer reviewed by experts, and then I will accept it. Keener hasn’t done that. His book hasn’t been peer reviewed by any medical or scientific experts. In fact, Keener even says in that book that he doesn’t have the money or resources to investigate the claims that he has compiled. Instead, Keener has only proven that a lot of miracle *claims* still circulate in the world, but he hasn’t proven that any of them are genuine. This actually supports the reasoning in this article that miracle reports virtually always turn out to be either uninvestigable or false when investigated. Since you just posted a link in response to my analysis about Vespasian, here is a link critiquing Keener’s arguments and evidence:


      Likewise, I just ILL’d a copy of Keener’s two volumes from my university library, and I am planning to write a further critical review of my own sometime in the future (when I get around to it with my graduate work).

      “Why a priori dismiss them as you definitely do in your article? It seem intellectually dishonest. You points on Bayesian probability is disingenuous. You use this complex equation but then substitute in 0 into it – and anyone with even a passing understanding of mathematics knows what will happen – it will spit out 0 as an answer. Why not let the evidence speak for its self rather than crafting your own philosophically derived answer?”

      This is an intellectually dishonest representation of what I have said. I have specifically said that the prior probability is not 0! Instead, I have set up a *mathematical limit* for how the prior gradually approaches 0 as there is more and more inductive evidence accumulated against a certain sort of phenomena. I have simplified this asymptotical effect through the equation lim[n->∞](1/n) = 0, but the Bayesian equation produces a similar asymptotical trend as well. The prior would only be 0, if n = ∞, which of course can’t happen. I am, thus, not arguing that the prior is 0, but that it is very low and getting lower as more evidence against miracles is accumulated. This provides justification for a very low prior probability of genuine miracles (which I have reached by letting the evidence of the natural world speak for itself, along with an unprecedented record of no confirmed miracles and the continual disconfirmation of miracle reports, as explained above), without it strictly being 0, even if it will approach 0 as more counter evidence is accumulated.

      “Most scholars who are experts in the field believe that
      1. Jesus existed
      2. He was crucified
      3. He was buried in the tomb of Joseph of Arimathea
      4. Women found the tomb empty on the morning of the resurrection
      5. Many disciples came to believe that they had seen him alive soon afterwards and became so absolutely convinced of this that they were able to convince others even in the face of persecution, torture and death.

      If you have a naturalistic hypothesis that explains these five facts (not just one) then you’ve done better that virtually every expert in the field.”

      I have already written a full article explaining how all of the “facts” that you have listed can be explained – top to bottom – in fully natural terms, without the need of magic or miracles:


      I also discuss in the article how apologists William Craig and Gary Habermas (whom you are simply copying this argument from, without attribution) have misrepresented a lot of the scholarly consensus for some of these “facts.” Likewise, there are plenty of NT scholars who, contrary to your assertions, have fully explained all of these facts far better than apologists. Bart Ehrman just recently in How Jesus Became God has developed a theory that goes all the way from the historical Jesus’ teachings, to his death, to the belief in his resurrection, and to Jesus’ deification as God without the need of magic or a miracle. And there are plenty of other scholars. Even Christian scholar Dale Allison in Resurrecting Jesus acknowledges that there are natural explanations that can account for the origins of Christianity.

      Frankly, I find it is rather disingenuous that you have tried to saddle me with questions like this at the end of your comment, without providing any alternative explanation of your own, beyond a god-of-the-gaps assumption. You probably thought that you could catch me off guard and that I had never thought of these issues before, so that I would be stumped by your “5 facts.” When, in reality, I have already written extensively on how they can all be naturally explained. I will also be developing my counter arguments against the “minimal facts” apologetic even further in a book project I am working on that I will be submitting to an academic publisher.

      Despite your repeated (ad hominem) assertions that I am not “thinking it through,” I have actually thought about these issues a lot, as someone who studies ancient history at the PhD level, and I find the arguments of apologists like Craig and Habermas to be highly unpersuasive.

      Frankly, most apologetic arguments come off as after-the-fact rationalizations targeted towards a lay, built-in audience of already believing Christians. They are not even remotely persuasive to critical outsiders, who are informed on these issues. I know apologists teach you guys to parrot their specious talking points, but the reality is that all of them have been answered by serious scholars who work in real universities, rather than at faith-based Christian universities with doctrinal statements already affirming the truth of Christianity, such as where career apologists like Craig and Habermas work.

  5. Ronald Slaton says:

    Your work is so very well explained and researched. It’s difficult to say how much I appreciate your charity and generosity in sharing this material. I find it helpful in forging solid responses to much of the nonsensical rhetoric oozing from today’s apologists.

  6. sheila0405 says:

    Reblogged this on …..temporary…. and commented:
    Just in time for Easter, I discovered this amazing blog post!

  7. I enjoyed this post, but I’m uncertain of how much use it is as an anti-apologetic argument. It seems to me that if I believed in miracles, I’d have to agree with you that they have very low prior probability — if they didn’t, they wouldn’t be miracles. Maybe I’d even agree that the posterior probability is very low. But we could still part ways at the step, “If X has very low posterior probability, then I shouldn’t believe in X”. On the contrary, I might say “the Resurrection has very low posterior probability after weighing all historical evidence, and as a matter of religious faith I believe in it anyway, and even view the smallness of the posterior probability as a positive demonstration of the power of God.” Obviously, deciding not to believe in things with very low posterior probability is a basic part of the scientific mindset, but it’s still a decision, and it seems quite plausible that a religious person could just differ with a skeptic on how to properly arrive at beliefs. This is what “faith” means, as far as I understand it.

    Note that this response also allows the religious Christian to, for example, believe in the Resurrection and the miracles of Jesus but not in the Buddhist miracle traditions. They agree that the prior probability is very low in all cases, but have faith in the former rather than the latter.

    I don’t think this is the end of the discussion, but it does mean that an argument about probability alone isn’t going to suffice — you have to do the harder work of convincing the person that, for whatever reason, it’s worth it to abandon the religious mindset for the scientific one. (I haven’t really looked at their arguments, but I have to say that it surprises me that William Lane Craig etc. are trying to argue for a high probability of the Resurrection, rather than taking this tack.)

    • Celsus says:

      Hi Paul,

      Thanks for your thoughts. I am insanely busy working on an academic paper right now. I’ll get back to this comment in a couple weeks.

    • Celsus says:

      Hi Paul,

      I think at the heart of your comment is a differentiation between a faith-based approach to religion, versus an evidence-based approach. Apologetics is primarily concerned with the latter, as is this blog. I really don’t try to argue people out of a faith-based approach, since I am more concerned with protecting academia from religious-based agendas (particularly those derived from schools with doctrinal statements that do not adhere to the freedom of speech in academia).

      Apologists like William Craig and Mike Licona argue that Jesus’ resurrection can be proven with high probability. Interacting with scholars like Robert Cavin and Aviezer Tucker, I have made a case for why that is not true, and based on both a very flawed approach to historical evidence, as well as a very flawed approach to calculating the probability of a given individual resurrecting from brain death into an immortal body (along with the other details that are entailed by the resurrection event).

      Surprisingly, where I think we actually disagree is that I don’t think that miracles have to be improbable. I do not define miracles as inherently improbable events, but as interventions by God (or by other entities external to the physical world) into the physical world, to perform acts that violate normal patterns of physical cause and effect. Hypothetically, such events could happen all the time. God could part the Red Sea quite frequently, miraculously intervene in multiple wars (in obvious ways) to favor a certain nation, and immediately respond to prayers to perfectly heal amputees. All of the things I described above could also be empirically observed (and even be studied by science).

      If such things happened on a common (or even rare, but not “never once”) basis, then their prior probability would not be too low at all, actually. And, indeed, even with a low prior, if Jesus came back to Earth today, and started performing miracles in front of scientists with instruments in the streets of New York, we would still have a good posterior case for a miracle.

      So, in principle, the kinds of miracles that Craig and Licona are trying to prove could be quite provable. But a handful of ancient letters and anonymous novelistic biographies–written thousands of years ago, reconstructed from copies of copies, that we are no longer able to corroborate or investigate with any forms of forensic evidence today–are an extremely weak form of evidence. When we place that in a context where there were multiple resurrection narratives in the ancient world, people even today claiming to see dead people still alive, in a world that abounds in hearsay about miracles, Craig and Licona’s case seems quite weak. In such a circumstance, alternative explanations seem to outweigh the probability for the resurrection.

      One might have faith in the resurrection, but an evidence-based approach seems to be weak at best, disingenuous at worst, especially when targeted toward a lay audience.

  8. S.k says:

    You and Matt Dillahunty should team up and participate in a debate with others. This is one of the best articles I’ve read after reading Richard Carrier’s work on probabilities. I think Matt’s pet peeve is prior probability because in his debate with Blake Giunta he chose to respond(paraphrasing), this is why I don’t like Bayes’ theorem because anyone can increase the prior probability of something and… voilà.

    He might have changed his mind on this because he is good at researching but I hoped he gets to read this article. It only makes him better at debunking some claims.

    Another great point, as you mentioned, is that many have still not realized that there is no escaping from using the theorem or probabilities. It’s just that people and historians do it implicitly and often without great care, resulting in 1000 different positions on an issue that could be easily solved by assigning probabilities to the h and considering the evidence.

    Great work, thank you.

  9. Pingback: Vridar » How to Improve Bart Ehrman’s Argument Against the Resurrection of Jesus

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