Is the resurrection probable? Let me check my math.

Many of us in the Science and Religion program have recently been examining miracles in our course on science and scripture, and today we took on the resurrection of Jesus. As you might imagine, this is a formidable topic, and one can come at it from all kinds of directions. One of the more inventive approaches we discussed comes from philosopher of religion Richard Swinburne in his book The Resurrection of God Incarnate. Swinburne begins with the hypothesis that Jesus was God incarnate and that he was resurrected, and he attempts to convince his readers using Bayesian reasoning that the likelihood of this hypothesis being true is overwhelmingly high. In fact, he comes up with a specific number: according to Swinburne’s analysis, there is a 97% probability that his hypothesis is true.

How on earth does Swinburne justify such a calculation? I’ll spare you the gory details and refer you to Wikipedia for more on Bayes’ Theorem. Suffice it to say that everything comes down to our confidence about a handful of scenarios. For instance, given the evidence of natural theology, how confident are we that a “traditional” God exists? Assuming God exists, what is the likelihood that God would become incarnate? How probable is it that the specific circumstances of Jesus’ life would come to pass if he was in fact God incarnate? Swinburne chooses values for the probability of each scenario in rather arbitrary fashion, applies the theorem, and voilà – mathematical proof that belief in the incarnation and resurrection is highly rational.

On the other hand, philosopher Larry Shapiro has a recent piece on miracles in which he wields probability to more skeptical ends. Instead of attempting to assign probabilities to theological claims surrounding the resurrection, he focuses on the reliability of human witnesses, the most direct evidence available to us. His result:

The base rate for the resurrection is (let’s say) one in 1 billion. The witnesses go wrong only one time in 100,000. One billion divided by 100,000 is 10,000. So, even granting the existence of extraordinary witnesses, the chance that they were right about the resurrection is only one in 10,000; hardly the basis for a justified belief.

Why do two approaches that use such similar methods yield such different results? I think the answer becomes clear when we examine the type of event that each author emphasizes. Swinburne attempts to quantify theological propositions that have deep implications for the nature of reality, while Shapiro turns his attention to measurable human behavior – a far more appropriate domain in which to apply statistical methods. Even as a believer, I think Shapiro’s skepticism rings more true. My natural instinct is to be suspicious of any model that claims to mathematically prove a theological proposition beyond all reasonable doubt; such a model trivializes faith. It seems fitting to me that a numerical analysis of the resurrection should yield a low probability because that result confirms my instinct.

What do you think? Are either of these approaches convincing? Can we plausibly estimate the numbers we need for this calculation? And of course, the question that’s been in the back of your mind this whole time: is there any theological value in applying mathematical methods to the resurrection, or are we wasting our time?

12 thoughts on “Is the resurrection probable? Let me check my math.

  1. The theory assumes a non-zero probability for ressurection to start with – “The base rate for the resurrection is (let’s say) one in 1 billion.”

    It’s akin to arguing that IF aliens have visited Earth then x% of UFO sightings are real. That’s a huge assumption to make about something for which may have never happened.

    • Hi Geoff, thanks for chiming in. You make a good point, but I think Shapiro is thinking about probability in a slightly different way than you are. If you define a “base rate” by the percentage of times an event has been measured, then you’re perfectly right that we should be giving resurrection a base rate of 0. But just because something hasn’t happened doesn’t mean that it’s impossible for it to happen, even if it’s a very unlikely event (contact with extraterrestrial life is actually a great example). So I think Shapiro is using this base rate to reflect the potential that resurrection could occur, even though there are no proven instances of it.

  2. I read through the Shapiro article and here are some of my thoughts:

    Firstly, it is a little unclear where he gets 1/100,000 witness reliability percentage. Is that the percentage of a single witness being incorrect in their account? If so, it disregards the number of witness for an event, in particular the Resurrection. If it is the percentage of a group of witnesses, how was such a ratio derived for the Resurrection?

    Second, his thoughts on the false negative cancer test seem to leave out an important real world result, that of multiple testings. His point seems valid, but one would suggest that if someone received a positive result from a cancer test they would undergo the test a second time, because the likelihood for two false positives is quite small. Analogously, this would seem to suggest that the greater number of witnesses (each reliable witness being a separate test) that yield a corroborating description of an event increase the reliability of such a description.

    Third, this is an activity that I do with most arguments. To apply the argument(s) to a similar, but more understood event. I thought to apply his argument to nearly all historical events, of which there are only a couple (Punic wars) of perhaps singular in occurrence (William conquering England). Given their rarity, the argument would conclude that it is unsound to believe in their occurrence, despite widespread belief. The rebuttal here would be something along the lines of having many witnesses or tangible results that are seen to propagate through other historical events, both of which are avoided in the article.

    A final thought, what about the miracles that necessarily must have occurred, such as the beginning of the Universe? Science suggests that such an event occurred approximately 14 billion years ago, though cannot account for how such an event can occur naturally. Again, using the article’s argument as it was presented, we do not have enough evidence to rationally believe such an event ever occurred, despite the necessity of its occurrence.

    For thoughts on the idea of miracles from a reputable source, take a look at this snippet of “I don’t have enough faith to be an atheist” by Norman Geisler and Frank Turek:

    Hope things are going well in the UK.


  3. I think I’m always a bit skeptical about trying to assign any sort of statistics to anything with a sample size of one! And in the case of Christ’s resurrection it is an event from a long time ago for which we have no indisputable data with which to constrain our probabilities. I think the diversity of answers to the question of the Resurrection probably says something far more (and interestingly so) about people attempting to assign a mathematical answer to this very unusual event.

    It is a bit like the Drake Equation in astrobiology. We can’t really assign proper data to the various parts of the equation, so we guesstimate them and lo and behold get out what we need/want it to tell us.

    • Thanks for your comment, Gavin. I couldn’t agree more with your comparison of these models to the Drake Equation. They’re great for generating conversation and new ways of thinking about the events they address, but you have to take the numbers with a grain of salt.

  4. “Most missing bodies don’t go missing because they rose from the dead” (Carrier). True, but Craig responds, “What [is] the best explanation [of the facts]? Here Richard says, ‘Well most bodies that disappear aren’t raised and therefore it means the resurrection is improbable’. Look, all that shows is that resurrection is improbable relative to our general background evidence. But it doesn’t show that it’s improbable relative to the evidence of the empty tomb, the post-mortem appearances, and the origin of the Christian faith. Relative to that evidence I think the resurrection is highly probable, indeed more probable than all of these naturalistic explanations that Richard has attempted to offer tonight.” (2009 William Lane Craig vs. Richard Carrier debate, Did Jesus Rise from the Dead?)

    • Hi David, thanks for that quotation – obviously very relevant! I think the evidence that Craig highlights here is exactly what Swinburne and Shapiro are grappling with in their models.

      I would offer one criticism: Craig is assuming that a naturalistic explanation is incompatible with the theological importance of the resurrection – that EITHER some highly improbable but scientifically explainable event occurred (or that the body was simply stolen), OR that God supernaturally raised Jesus. It’s not clear to me that this is the case – my view of miracles in general is that they need not be supernatural in order to be a sign of God’s acting in the world, and I think the same reasoning could apply here.

  5. Jenna,

    Thank you for posting an article about the resurrection of Jesus Christ from a mathematical perspective! I’m not sure that it is a waste of time to apply mathematical methods to such an important topic of theological value as the resurrection.

    What I would say, however, is that perhaps a more balanced approach would be to combine numerical analysis from probability theory along with the known laws of quantum mechanics, in particular quantum tunneling. I think that quantum tunneling of particles such as electrons/protons through potential barriers with greater energy than the energy of the electron/proton or other elementary particles, such as in nuclear fusion in the Sun, and other instances in biochemistry in our bodies in electron transport across long chains of molecules, could serve as a springboard for looking at the resurrection.

    So, most certainly, mathematics is essential to this, but it could be bolstered by using quantum mechanics (which of course, at root is very mathematical) to bring further meaning to this quest.

    Christian Luca

    • Thanks for the comment, Christian. I think you’re absolutely right that we’d have to start at the quantum level if we wanted to calculate the a priori probability of bodily resurrection (a fundamentally different task from these authors, since they’re accounting for evidence, a posterior consideration). Of course, the number you’d get from such calculation would be so infinitesimally close to zero that I don’t think it would be much use in persuading anyone that Jesus’ resurrection is probable, as Swinburne wants to do.

      • Just for fun, I did a back-of-the-envelope calculation to show just how miniscule a probability you get. There are about 10^14 cells in the human body (thanks WolframAlpha), but let’s assume we’re talking about a body 1000 times smaller than a human. Let’s also assume that the probability of any given cell in this dead body returning to its pre-death state due to quantum tunneling is 99% (obviously I’m being really generous here). Then the probability that this would happen in every cell is 0.99^(10^11) – in other words, the probability of resurrection in this case is 10^(-43,6480,541). And that’s just a very generous upper bound!

  6. Great post, Jenna!

    I think you are right to be suspicious of mathematical proofs for theological claims, especially ones that our instincts tell us should be incredibly improbable. As Giuseppe would probably say, it’s supposed to be hard to believe, not easy.

    Glad you are doing well across the pond!

  7. Jenna, great topic! I have been thinking about this a lot recently and am in the process of applying to the M.St. program at Edinburgh to work on this issue as much as I can. As you know, Hume weighed the probability of a miracle against the probability of reliable testimony. I think it is right to bring epistemology of testimony into the conversation. For example, the question of whether default belief in testimony is epistemically justified a priori or perhaps a posteriori -could have implications for this discussion. One way of asking this question is whether we should trust others as we trust ourselves. After all, if we would believe a miracle based on direct observation (I think most would), then why assume we are more reliable than our neighbor? On the reductionist side, does lifelong experience tip the balance strongly in favor of trusting others? Also, what complex probabilistic processes are going on in our brains that we do not have conscious access to? Beyond all of this, is probability the right way to go? If we already know, when we approach the question of a miracle, that the probability is ridiculously low -then can a predominantly probabilistic method even discover a miracle? I think perhaps we need to approach the issue differently and ask how we normally go about discovering highly improbable events. Is there an epistemic vehicle designed for transporting that kind of information? I think there is -credible testimony. Very simply, that is what credible testimony is for. Therefore, we can’t just attack the credibility of others because what they report seems unlikely. Prior probabilities might be irrelevant in cases like these. All that matters is determining whether, under ordinary circumstances, we would accept or reject the credibility of the witnesses. I suspect that is the key to unlocking this issue.

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