Miracles and Probability III


We discussed the challenges of accepting a miracle as true because it contradicts how we know the world works. We then proceeded to ask the question: well, what happens if we have good evidence for the miracle? The solution to that problem was to translate our hypothesis, evidence, and background knowledge into terms of degrees of certainty and inputting that into our logically valid formula developed by Thomas Bayes. We could always resort to informal argumentation, but using Bayes’ theorem gives us special insight by breaking the problem down into components – hypothesis, prior knowledge, new evidence, etc. — and preventing us from falling victim to confirmation bias. This bias is reduced because we are given the opportunity to consider alternate hypotheses in the theorem, which are often ignored through “armchair” arguments. In this post, we will try to show that extraordinary claims do indeed require extraordinary evidence. The hypothesis we will be testing is whether or not Jesus was raised from the dead by a supernatural agent. The formula will be given again below for reference.

P(h|e,b) = P(h|b) * P(e|h,b) / [ ( P(h|b) * P(e|h,b) ) + P(~h|b) * P(e|~h,b)]

P(h|e,b) = probability that the hypothesis is true: Epistemic probability or Posterior probability
P(e|h,b) = how expected the evidence is if our explanation is true: Explanatory probability or Consequent probability
P(e|~h,b) = how expected the evidence is if our explanation is false
P(h|b) = how typical our explanation (hypothesis) is: Prior probability or Intrinsic probability
P(~h|b) = how atypical our explanation is: (1 – prior probability)

It’s helpful to see this formula in terms of an argument to the best explanation, which is often used by historians, especially apologists. It is a type of abductive reasoning. You can think of prior probability as being how plausible your hypothesis is when combined with ad hocness. Plausibility has to do with how typical our explanation is – that is, how much is it in accord with how we know the world works (background knowledge).  If you try to develop excuses (ad hoc) for your evidence in order to make it fit your hypothesis, then you lower the prior probability, P(h|b).  The other components in ABE, or argument to the best explanation, are the ones that affect the probability of the evidence explaining the hypothesis, P(e|h,b) and P(e|~h,b). The first one is explanatory power which asks if the hypothesis has a higher probability of being true than competing hypotheses, and it should account for the facts without forcing it. Increasing your explanatory power will increase P(e|h,b). Explanatory scope, on the other hand, is about explaining a wider range of evidence better than the competing hypotheses. Increasing explanatory scope lowers P(e|~h,b) relative to competing hypotheses, and if ~h has a greater scope, then P(e|h,b) drops. Lastly, explanatory fitness can’t contradict any well-established beliefs, and it functions like explanatory power in terms of probabilities affected.

Getting back to priors, an example of ad hocness could be making the assumption that at least one person can defy gravity and fly into the sky without using any special technology [Matthew Ferguson]. We would have to make this assumption or excuse in order to make the hypothesis that Jesus was raised, by natural means, into the sky plausible. Now of course if we said, b, our background knowledge includes the assumptions of metaphysical theism, then God can do anything, and it wouldn’t be ad hoc. However, if we accept that premise, then we are at the mercy of God’s will and whims. And I have yet to be convinced that a theistic God or any other god is at work behind the scenes. Even if you have the hypothesis that God interferes in everyday life, you can’t derive any reliable predictions from it. God is not like a subatomic particle that we can’t see because, as in the case of the particle, we can make predictions as to how it behaves but not so with God. We are at a loss when it comes to modeling God, for God is knowable and incomprehensible at the same time. Moreover, as theistic Christianity defines him, he’s a philosophical construct, not a scientific one. But, to be fair, we didn’t even assume naturalism in our reference class. We actually relaxed our constraints and claimed that we’ll consider all cases of god raising purported persons from the dead.

Quality of Evidence

Now, before we continue, it’s worthwhile to acknowledge that we will all interpret evidence in different ways based on our presuppositions or how skeptical we are or are not. For example, if we assume miracles are impossible to begin with, then we will underestimate the likelihood of P(h|b) and P(h|b,e). Likewise, if we assume that miracles occur all the time, then we will overestimate the likelihood of P(h|b) and P(h|b,e). We did see how we could reduce these biases in the determination of P(h|b) by keeping the reference class as narrow as possible and by being conservative on our estimates. But how do we reduce the chances of inaccurately predicting P(e|h,b)? To be candid, at this point of my investigation, I have yet to find a systematic way of determining the probability of consequent probabilities. And thus there will be an amount of subjectivity involved, which is true in general of epistemic probabilities, which come as ‘degrees of belief’ when assessing the uncertainty of a particular situation [wikipedia]. The best way to minimize bias would be to be as charitable as possible when ascertaining our probabilities.  We will be relying chiefly on Matthew Ferguson’s analysis of the evidence in addition to Richard Carrier’s, while contrasting it against Mike Licona’s and William Lane Craig’s.

Here’s the evidence we have for the fantastical claim that Jesus rose from the dead by God. Why is this claim essential to the Christian faith? Well, because the apostle Paul aptly declared, “If Christ has not been raised, then our preaching is vain, and your faith is vain” (1 Corinthians 15:14).

  • Jesus was crucified.
  • Jesus was buried by Joseph of Arimathea in a tomb.
  • An empty tomb was found by the women.
  • Postmortem appearances to Peter, Paul, James, apostles, disciples, and the “500”.
  • The disciples, James and St. Paul’s belief in the resurrection.

It’s important that we consider the quality of the evidence. The above evidence comes from the Gospels, written forty to fifty years after Jesus’ death, and the Epistles, written twenty years after Jesus’ death, all contained within the New Testament.  So, first, we have evidence decades after the fact. Keep in mind also that the above claims are not necessarily facts. After all, some of these are elements in stories contained in hagiographies (i.e. the Gospels) that are mainly used as propaganda to promote a theology or movement. We have already concluded that the genre of the Gospels are legendary biographies, meaning that the author’s chief objective was to proselytize a message about Jesus Christ and not to teach us history.  The sources also don’t have independent attestation since I consider the Gospels as dependent on one another, with the exception of, maybe, John; the Gospels may or may not have had access to the Epistles, but we will grant independency.  But it’s not until the second century do we get extra-biblical (outside of the bible) evidence of the crucifixion of Jesus Christ.  Moreover, the Gospels are all anonymous, surely not based on eyewitness testimony, and are most likely a combination of literary creations and oral tradition.  And, lastly, although we don’t know with certainty, it’s a reasonable assumption to make that superstition and the belief of gods, demons and spirits were more accepted by the population than would be now, probably because the Bronze age did not have the luxury of experiencing the Enlightenment era. The following paragraph underscores the type of evidence we have, by Matthew Ferguson.

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).


So how do we approach the analysis of the evidence – what’s our methodology? Do we take the authors’ – that are often anonymous – word for it, for example, when they say that Jesus Christ’s empty tomb was discovered by women, or do we take the skeptical stance since we don’t know who the authors were, the authors had an agenda, and no extra-biblical corroboration exists near the event? The assumptions and skepticism one exercises affect the outcome, so this is very important. So important that it (skepticism) drives Matthew Ferguson and Richard Carrier to conclude that the resurrection is very improbable while Mike Licona and William Lane Craig conclude that it’s very probable because they take the evidence at face value. Given the kind of evidence we have described in the previous paragraphs and knowing human nature and the era of that period in history, I find no reason other than to approach the evidence with skepticism, giving credence to evidence that is independently corroborated by disinterested sources and discounting that which is not.  This may not seem fair since we really don’t have any disinterested sources and the absence of evidence is not evidence for absence.  However, this presumption – that of taking a skeptical stance – is one that most reasonable people would adhere to if they were assessing others’ faith. It’s also important to acknowledge, justifying my stance, that we have better evidence for other supernatural events; for example, the Salem Witch Trials, and we don’t accept those as true.  As another good example, see Why the Resurrection is Unbelievable by Richard Carrier, where he discusses if we don’t believe Herodotus’ accounts why would we believe the Gospels or Paul’s account?  Before we get into the analysis of the evidence, I believe this excerpt by Richard Carrier in “Proving History” illustrates that we always have to be mindful of our background knowledge since P(e|h,b) is conditioned on that:

     The smell test is a common methodological principle in the study of legend, myth and hagiography.  This tests can be most simply states as if it sounds unbelievable, it probably is.”  When we hear tales of talking dogs and flying wizards, we don’t take them seriously, even for a moment.  We immediately rule them out as fabrications.  We usually don’t investigate.  We don’t wait until we can find evidence against the claim.  We know right from the start the tale is bogus.  Yet the only basis for this judgment is the smell test.  Is that test valid?
     It is certainly ubiquitously accepted by historians in every field.  It is suspiciously only rejected by religious believers, and then only when it’s applied to amazing claims they prefer to believe.  They ground this rejection in the claim that we shouldn’t be biased against the supernatural, and God can do anything.  Yet if they honestly believed in those principles they would be compelled to concede the miracle claims of every religion because “you shouldn’t be biased against the supernatural, and God can do anything.”  This includes all the pagan miracles (incredible apparitions of goddesses, mass resurrections of cooked fish, wondrous healing, and teleportation), Muslim miracles (splitting moons, wailing trees, flights to outer space), Buddhist miracles (bilocation, levitation, creating golden ladders with a mere thought), and indeed every and any amazing claim whatever.  Tales “proving” reincaration?  We can’t reject them – because God can do anything.  Ghosts confirming to the living that heaven is run by a Chinese magnate and his staff?  We can’t rule it out.  That would be bias against the supernatural.
     Honestly living that way would be impossible.  You would believe everything you read … In other words, our bias against the supernatural is warranted, just as our bias against the honesty of politics warranted: we’ve caught them being dishonest so many times it would be foolish to impolitely trust anyone in politics.  Likewise, amazing tales: we’ve caught them being fabricated so many times it would be foolish to implicitly trust any of them.
     The smell test thus represents an intuitive recognition of the low prior probability of the events described (i.e., P(h|b) << 0.5); the ease with which the evidence could be fabricated (i.e., P(e|h,b) is always high, unless we have sufficient evidence to the contrary), in fact often the ease with which such an even if real would produce or entail much better evidence (i.e., P(e|h,b) is often low); how typically miracle claims are deliberately positioned in places and times  where a reliable verification is impossible, which fact alone makes them all inherently suspicious; and sometimes the similarity of a  medical story to other tales told in the same time and culture is additionally suspect, like the odd frequency with which gods in the ancient West rose from the dead, transformed water into wine, or resurrected dead fish, oddities that curiously never occur anymore, and which are so culturally specific as to suggest more obvious origins in storytelling.


[1] Boyd, Gregory A.. The Jesus Legend: A Case for the Historical Reliability of the Synoptic Jesus Tradition . Baker Book Group.

[2] Byas, Jared. Genesis for Normal People (Study Guide Edition): A Guide to the Most Controversial, Misunderstood, and Abused Book of the Bible . Patheos Press.

[3] Carrier, Richard. Not the Impossible Faith: Why Christianity Didn’t Need a Miracle to Succeed.

[4] Carrier, Richard. On the Historicity of Jesus: Why We Might Have Reason for Doubt. Sheffield Phoenix Press.

[5] Carrier, Richard. Why I Am Not a Christian: Four Conclusive Reasons to Reject the Faith. Philosophy Press.

[6] Copan, Paul. That’s Just Your Interpretation. Baker Publishing Group.

[7] Harrison, Guy. Simple Questions for Every Christian. Prometheus Books.

[8] Keller, Timothy. The Reason for God: Belief in an Age of Skepticism . Penguin Publishing Group.

[9] Loftus, John W.. God or Godless?: One Atheist. One Christian. Twenty Controversial Questions. Baker Publishing Group.

[10] Loftus, John W. The Outsider Test for Faith: How to Know Which Religion Is True . Prometheus Books.

[11] Michael R. Licona. The Resurrection of Jesus: A New Historiographical Approach.

[12] Bruno A. Olshausen. Probabilistic Models of the Brain: Perception and Neural Function (Neural Information Processing). A Bradford Book.

[13] Price, Robert M.. Evolving out of Eden. Tellectual Press.

[14] Robert M. Price. Incredible Shrinking Son of Man: How Reliable Is the Gospel Tradition?.

[15] Templeton, Charles. Farewell to God: My Reasons for Rejecting the Christian Faith . McClelland & Stewart.

[16] Thomson, J. Anderson. Why We Believe in God(s): A Concise Guide to the Science of Faith . BookMasters.

[17] Unwin, Dr Stephen D.. The Probability of God. The Crown Publishing Group.

[18] John H. Walton. The Lost World of Genesis One: Ancient Cosmology and the Origins Debate.


  1. publicola says

    These “miracle” stories are just fiction. Made up. So-called “miracles ‘ probably start out as some event, perhaps unusual, perhaps not. As the tale moves from teller to teller, it grows taller and taller until, with enough time and distance, it has become a “miracle”. This is a common phenomenon among humans, often referred to as “fish stories”. The other possibility is that the miracles were made up from whole cloth, deliberate lies to perpetuate a myth that was so necessary for Jesus’ followers that they simply refused to believe anything else, and so concocted fables to fit their need to believe. It’s really the simplest explanation. You can’t use anything written in the Bible as evidence for these very reasons, and so you are left with no evidence. Skepticism is always good.

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