Bayes’ Theorem, a mathematical formula used to update probabilities based on new evidence, has increasingly been applied in historical analysis to assess the likelihood of past events. By quantifying historical probabilities, historians and scholars can provide a more rigorous evaluation of events where direct evidence is scarce. However, while the method offers significant benefits, it is not without criticisms. This blog post explores how Bayes’ Theorem is used in historical studies and some of the key objections to its application.

Understanding Bayes’ Theorem

Bayes’ Theorem is a formula in probability theory that calculates the likelihood of an event occurring based on prior knowledge and new evidence. The formula is as follows:

Where:

• P(A|B) is the probability of event A occurring given evidence B.
• P(B|A) is the probability of evidence B occurring if A is true.
• P(A) is the prior probability of A occurring.
• P(B) is the overall probability of B occurring.

In historical analysis, this theorem can help scholars evaluate competing hypotheses by assigning prior probabilities based on available evidence and adjusting them as new data emerges.

Applying Bayes’ Theorem to Historical Events

Historians and scholars have used Bayes’ Theorem in various ways, including:

• Assessing the historicity of Jesus – Richard Carrier and other scholars have applied Bayesian reasoning to evaluate the likelihood that Jesus of Nazareth was a historical figure versus a mythological construct.
• Evaluating textual reliability – Bayesian methods help analyze how likely ancient manuscripts reflect actual events versus later interpolations or fabrications.
• Assessing eyewitness testimony – Historians use Bayes’ Theorem to weigh the reliability of different sources, particularly when they conflict or contain biases.

By assigning probability values to different factors—such as the reliability of sources, the likelihood of bias, and the consistency of reports—Bayesian analysis allows for a structured and repeatable approach to historical inquiry.

Criticisms of Using Bayes’ Theorem in History

Despite its usefulness, several criticisms challenge the application of Bayes’ Theorem in historical studies:

1. Difficulties in Assigning Prior Probabilities
   One of the main issues is the challenge of assigning reasonable prior probabilities. In scientific studies, probabilities are often based on large data sets, but in history, we are often dealing with unique, one-time events with little comparative data.
2. Subjectivity in Probability Estimates
   Because many historical events lack quantifiable data, assigning probability values often relies on subjective judgment. This subjectivity can lead to widely differing conclusions based on the assumptions made by different scholars.
3. Complexity and Accessibility
   Many historians are not trained in advanced mathematics, and applying Bayesian analysis can be intimidating. This limits its accessibility as a standard historical tool.
4. Dependence on Available Evidence
   Bayes’ Theorem is only as strong as the evidence used in its calculations. If key evidence is missing, overlooked, or misinterpreted, the conclusions drawn from Bayesian analysis may be flawed.
5. Over-Reliance on Quantification
   Some critics argue that history is a discipline that deals with human actions, social contexts, and subjective experiences—factors that are difficult to reduce to mathematical probabilities.

Criticisms of Richard Carrier’s Use of Bayes’ Theorem

Richard Carrier’s application of Bayes’ Theorem in arguing against the historicity of Jesus has received notable criticism from both historians and scholars in related fields. Some key objections include:

1. Excessive Subjectivity in Assigning Probabilities
   Critics argue that Carrier assigns prior probabilities in ways that reflect his own biases rather than objective historical consensus. Since many of the inputs for Bayes’ calculations in historical studies are subjective, small changes in prior probability assumptions can dramatically alter the final outcome.
2. Misinterpretation of Historical Methodology
   Many historians maintain that history is a qualitative discipline that cannot be fully reduced to numerical probabilities. Carrier’s strict application of mathematical modeling may oversimplify the nuances of textual and archaeological evidence.
3. Lack of Scholarly Consensus
   Carrier’s conclusions are highly controversial, with most biblical scholars rejecting his mythicist position. Even among those who find Bayesian reasoning useful, his specific application of the theorem has been questioned as overly rigid and not in line with mainstream historical analysis.
4. Questionable Use of Data Sets
   Carrier often compares Jesus to mythological figures from different cultural contexts, such as Osiris or Romulus, and assigns numerical probabilities based on these comparisons. Critics argue that these analogies are misleading and ignore key differences in the sources and contexts of these figures.
5. Circular Reasoning in Probability Assignments
   Some critics claim that Carrier’s model sometimes assumes what it sets out to prove. By assigning low prior probabilities to Jesus’ historicity at the outset, the final calculations may be skewed toward confirming his mythicist position.

Conclusion

Bayes’ Theorem provides a structured and systematic way to assess historical probabilities, offering valuable insights into debates over the historicity of certain events. However, its effectiveness depends on the quality of the evidence, the fairness of probability assignments, and the willingness of historians to engage with mathematical reasoning.

Richard Carrier’s use of Bayes’ Theorem to argue against Jesus’ historicity has been widely debated, with many scholars questioning his probability assignments, data comparisons, and underlying assumptions. While Bayesian analysis remains a valuable tool, its application in historical studies must be handled carefully to avoid misrepresentation of historical evidence. The debate over its usefulness in historical inquiry is far from settled, but it continues to be an intriguing methodological approach in the field of history.