Bayesian Analysis and Miracles: Academic Critique

Shared by user (iandol) via Discord, 2026-05-10

You have hit the nail on the head. Your intuition that this is an egregious misuse of Bayesian analysis is widely shared across the fields of philosophy, historiography, and even among many theistic scholars.

While Bayesian epistemology is a highly respected framework in the philosophy of science for evaluating natural phenomena and scientific theories, its application to supernatural or miraculous claims is heavily scrutinized.

Here is an overview of the academic consensus and the primary philosophical critiques regarding the use of Bayes’ Theorem to “prove” historical or theological events.

The Target: Bayesian Apologetics

The most famous modern attempt to use Bayes’ Theorem for apologetics comes from philosopher Richard Swinburne. In his book The Resurrection of God Incarnate, Swinburne plugs historical data and natural theology into the theorem to conclude there is a 97% probability that Jesus was God incarnate and rose from the dead.

Other scholars, such as William Lane Craig, use similar (though less strictly mathematical) probabilistic and inductive frameworks. Conversely, mythicists like Richard Carrier have used Bayes’ Theorem to argue the exact opposite—that the historical Jesus likely never existed at all. The fact that the same mathematical formula can be used to “prove” diametrically opposed historical extremes highlights the core criticisms of the method.

The Core Philosophical Critiques

1. The Subjectivity of Priors (Garbage In, Garbage Out) To calculate the posterior probability of a hypothesis given the evidence, P(H|E), one must first establish the prior probability of the hypothesis, P(H), and the likelihood of the evidence assuming the hypothesis is true, P(E|H). Critics point out that when H represents a supernatural entity (God), assigning numerical values to these variables is entirely speculative. Swinburne, for instance, assigns a high prior probability to the idea that if God exists, He would want to become incarnate, suffer, and provide atonement. Critics argue that you cannot statistically model the psychology, intentions, or behaviors of a divine being. Because the inputs are based on subjective theological assumptions rather than empirical data, the output—no matter how rigorous the math appears—is ultimately meaningless.

2. Historical Methodology vs. Miracles Historians, such as Bart Ehrman, argue that there is a fundamental epistemological clash between historical methodology and probabilistic arguments for miracles. The historical method is designed to determine what most likely happened in the past based on surviving evidence. A miracle, by definition, is a suspension or violation of natural law—making it inherently the least probable event to occur. Consequently, historians argue that probability and historiography simply do not have the tools to validate an event that defies the very laws of probability.

3. The Problem of Dwindling Probabilities Even within Christian philosophy, the Bayesian approach has faced harsh pushback. The renowned Christian epistemologist Alvin Plantinga critiqued Swinburne’s historical-probabilistic arguments by pointing out the “principle of dwindling probabilities.” A historical argument for the resurrection requires a chain of connected hypotheses (e.g., God exists, God wanted to become incarnate, Jesus was that incarnation, the tomb was empty, the post-mortem appearances were physical, etc.). In probability calculus, when you multiply the probabilities of multiple events together, the overall probability drastically drops. Plantinga noted that this mathematical reality makes it nearly impossible to arrive at a high posterior probability for complex, multi-layered historical-theological claims.

4. Hume’s Epistemological Barrier Most modern critiques echo the arguments laid out by David Hume in his 1748 essay Of Miracles. Hume essentially formulated an early, conceptual version of Bayesian reasoning. He argued that the evidence against a miracle (our uniform, unalterable experience of the laws of nature) will always outweigh the evidence for it (human testimony). In a Bayesian framework, the probability that human testimony is flawed, fabricated, or mistaken—P(E|~H)—is practically always higher than the probability that the laws of physics were suspended.

The Academic Consensus

There is no academic consensus supporting the use of Bayes’ Theorem to prove historical miracles or the existence of God. In fact, the consensus points in the opposite direction:

• Among Historians: It is largely dismissed as a category error. Math cannot rescue historical claims that lack empirical, contemporary corroboration.
• Among Secular Philosophers: It is viewed as mathematical theater—dressing up subjective theological biases in the authoritative language of statistics.
• Among Theistic Philosophers: Many prefer “Reformed Epistemology” (arguing that belief in God can be rational without strict empirical or mathematical proof) and view Bayesian attempts to quantify faith as misguided, reductive, and ultimately damaging to their own cause.