🧮 Bayes’ Theorem and the Resurrection

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What if I told you that a simple mathematical formula could change the way we think about the most pivotal event in human history? Imagine you’ve been tested for an incredibly rare disease—so rare that it’s practically unheard of, like 1 in a trillion. You’re skeptical about whether it even exists. But you’ve got a test that’s not perfect, but it’s reliable—let’s say it’s 70% accurate. You take the test once, and it comes back positive. Intuitively, you might not be too worried; after all, the disease is so rare that even a positive result probably just means a false alarm. But now, let’s say you take the test again. And again. And again. Ten times in total. Each time, the result comes back positive. What’s the probability that you actually have this disease now?

This is where Bayes’ Theorem comes in. At first, the chance seems minuscule because of how rare the disease is. But Bayes’ allows us to constantly update our beliefs in light of repeated evidence. With each new test result, the probability that you have the disease increases, even though the disease is so rare. If you take the test 10 more times, and all 10 times it comes back positive again, the probability of having this disease skyrockets. Even though the disease is exceedingly rare, the consistent evidence you’ve gathered forces you to reconsider your assumptions. Bayes’ Theorem allows you to adjust your thinking and make conclusions based on the overwhelming weight of independent evidence, even when that evidence initially seems to defy what you would expect.

Now, imagine applying that same principle to one of the most consequential events in human history: the Resurrection of Jesus Christ. The resurrection is considered, by many, to be highly improbable—just like the rare disease. But what if the evidence for it came from not one, not two, but many independent eyewitnesses, each with credible testimony about what they saw? Using Bayes’ Theorem, we can adjust our belief about the resurrection based on this accumulated, independent testimony, the same way we adjust our beliefs about the disease as we gather more test results.

This essay will explore how Bayes’ Theorem was actually developed to defend the historicity of Jesus’ Resurrection—not as a mathematical curiosity, but as a powerful tool in Christian apologetics. Through Bayes’ formula, we’ll see how a consistent, evidence-based approach can lead us to the conclusion that, in light of repeated, independent eyewitness testimony, belief in Jesus’ resurrection is not only reasonable, but the most rational conclusion.

How Bayes’ Theorem came about

Bayes’ Theorem is a cornerstone of probability theory, widely used in fields ranging from medical research to artificial intelligence. It provides a systematic way to update our beliefs based on new evidence, making it as foundational to modern science as basic arithmetic is to mathematics. Whether diagnosing diseases or training AI models, Bayes’ Theorem powers much of the innovation that shapes our daily lives. However, what many people don’t realise—even those who apply it routinely—is that the theorem was originally developed to defend one of the most significant events in human history: the resurrection of Jesus Christ.

In 1748, philosopher David Hume wrote an essay that shook the intellectual world of his time. His essay “Of Miracles” argued that no miracle can be credibly attested, as the evidence for such events is always outweighed by the probability of natural explanations. While it sounds sophisticated, the essay presents little more than a sweeping dismissal of the supernatural, asserting that no testimony can ever be sufficient to outweigh the improbability of miraculous events, without offering substantial reasoning or addressing how new evidence might adjust our initial beliefs.

Perhaps because no one before Hume had dared to publicly voice such radical views, the impact of the essay was profound. Many in the intellectual and atheist circles hailed it as a bold, honest challenge to the entrenched powers of the day (for Britain in 1748 was very much a Christian nation). Others, however, took deep offence at the way Hume used scientific language to mask what they saw as a materialistic and elitist dismissal of religion—encapsulating the intellectual hubris of the time. Reverend Thomas Bayes, an ordained Presbyterian minister in England, was one of those who could not remain silent. He felt compelled to address what he saw as a grave error and set to work.

Bayes aimed to show that even if we initially think the chances of a supernatural event happening are very low, these initial beliefs should be adjusted when we have credible eyewitness accounts. Specifically, in the case of Jesus’ bodily resurrection, the wealth of independent and reliable testimonies should compel one to reassess the probabilities. Bayes’ Theorem provided the mathematical framework to do just that—shifting beyond initial skepticism to consider the “posterior probability” informed by all the evidence. In 1763, Bayes’ work was published posthumously, with the help of his friend Richard Price, ensuring that the powerful logic of updating priors would eventually be available for future generations. Some 74 years later (via Laplace’s Théorie Analytique des Probabilities), someone would build upon this apologetic effort: remarkably, it was Charles Babbage—the father of modern computing—who continued Bayes’ work by calculating the likelihood of the Resurrection with explicit numerical assumptions in his Ninth Bridgewater Treatise (1837).

High-Level Summary of the Mathematical Calculation.

Please see here to go through the main Bayesian calculation for Jesus’ resurrection. Even if you’re not mathematically inclined, I encourage you to go through the exercise at least once: you will better appreciate how we can update our prior beliefs in light of new evidence. But to summarise the main ideas and key takeaways:

The Importance of Keeping an Open Mind (Non-zero Priors)

We must avoid setting the prior probability of the resurrection to zero. To do so would be to dismiss any possibility of a miracle outright, which contradicts both reason and modern scientific understanding. Quantum theory, for instance, teaches that nothing is strictly “impossible”—just “improbable.” By acknowledging the possibility of miracles, even with a very small prior, we leave room for credible evidence to update our beliefs, in alignment with both science and reason.

The Flaw in Hume’s Approach

Hume’s approach in Of Miracles effectively set the prior probability of miracles to zero, dismissing the supernatural as impossible. By refusing to allow a non-zero prior, people like Hume (or modern atheists like Richard Dawkins) close the door to new evidence and contradict basic principles of scientific inquiry. In contrast, a non-zero prior allows evidence—like credible eyewitness testimony—to shift our beliefs, aligning us with both reason and scientific principles.

The Exponential Power of Independent Eyewitnesses

Just like repeatedly testing for a rare disease with the same positive result strengthens our belief, multiple independent eyewitness testimonies have an exponentially powerful effect on the probability of the resurrection. But what do we mean by “exponential” here? Imagine ten independent witnesses, each with reliable testimony—and let’s say that they collectively increases the prior probability by a factor of 30×. Adding another set of ten witnesses doesn’t just double the 30× factor (30× + 30× → 60×)—rather, it multiplies the prior by 30× again, leading to an exponential increase (30× × 30× → 900×).

The Impressive Results of Bayesian Calculation

When we apply conservative assumptions, such as an average eyewitness trustworthiness value of 2 and the 500 witnesses mentioned in 1 Corinthians 15:6, the probability of the resurrection becomes virtually certain, even with an initially extremely low prior probability (e.g., 10^-100). After using Bayesian reasoning, we arrive at a 99.999…% certainty (with 64 nines following the decimal). Even with the most conservative assumptions, Bayes’ Theorem doesn’t just suggest belief in the resurrection; it makes it mathematically inevitable.

Conclusion

The martyrdom of the Apostles is an incredibly powerful testament to the trustworthiness of their testimony. These men—who each faced gruesome deaths for proclaiming the resurrection of Jesus—were all eyewitnesses to the resurrection of their Lord and Saviour Jesus Christ. The fact that all of them clung to their witness, even unto death, strongly suggests that they genuinely encountered the risen Jesus, rather than fabricating their stories. From Peter’s crucifixion upside down to Thomas’ brutal spear-wound in India, these apostles were not willing to recant or lie about what they had seen. Moreover, if you include Paul’s radical transformation after his encounter on the road to Damascus, the number of independent eyewitnesses expands far beyond the 500 reported in Scripture—it extends to over a billion Christians today, each one claiming a personal encounter with the risen Christ. The sheer weight of this testimony, backed by the martyrdom of the apostles and the millions who have claimed a personal encounter with the risen Christ, drives the probability of the resurrection to near certainty. This isn’t just a historical claim; it’s a global, ongoing witness.

In conclusion, just as repeated positive test results for a rare disease shift our belief in the likelihood of having the disease, the overwhelming testimonies of over 500 eyewitnesses—plus the countless millions who have encountered the risen Christ—transform doubt about Jesus’ resurrection into near certainty. By updating our beliefs based on the weight of consistent, independent evidence, we see that the prior improbability of a supernatural event is entirely overshadowed. With open minds, logical reasoning, and moral integrity, belief in miracles like the Resurrection becomes not just reasonable but the most rational conclusion we can draw from the evidence. The resurrection is not merely a historical claim—it’s a mathematical certainty!

Bayes’ Theorem and The Second Coming

If we apply the same Bayesian reasoning to the prior probability of the Scriptures containing prophecies about the timing of Jesus’ Second Coming—though not the specific day or hour, but rather the broader year and season—then the evidence of current events becomes incredibly significant. Just as the resurrection becomes near certain when you account for the overwhelming testimony of the apostles, so too does the nearness of Christ’s return become undeniable when we examine the unfolding of global events in light of biblical prophecy. When we consider prophecies regarding the rebuilding of Jerusalem and the rise of certain world powers, the regathering of Israel, the increase in apostasy, and other signs outlined in Scripture, the evidence suggests that we are living at the end of the end of the End Times. If we maintain a nonzero prior—that is, if we accept that Scripture does indeed point to a specific season for Christ’s return—then, given the mounting evidence in world events, a logical and consistent update to our beliefs is inevitable. This isn’t a speculative theory; it’s a conclusion that follows from the facts. The imminency of the Rapture and the Second Coming is not just a distant theological hope, but a near certainty based on the observable alignment of Scripture and the world around us.