Rigorous Critique of the Essay

The essay criticizes the use of Bayesian statistics by mythicists who claim Jesus of Nazareth never existed as a historical figure. While it attempts to expose flaws in the mythicists’ application of Bayesian analysis, it itself demonstrates several significant misunderstandings and misapplications of Bayesian statistics. Below is a rigorous critique, highlighting and explaining these flaws in detail.

---

1. Misapplication of Bayes’ Theorem

Incorrect Formula Usage:

The essay presents Bayes’ theorem as:

It then simplifies this to multiplying the prior probability by the likelihoods of individual pieces of evidence, ignoring proper normalization. This is a fundamental misapplication of Bayes’ theorem.

Proper Application:

Bayes’ theorem should be applied as:

Where:

• is the posterior probability of the hypothesis given the data .
• is the prior probability of .
• is the likelihood of observing data given that is true.
• is the marginal probability of observing data , calculated as:

The denominator ensures that the posterior probabilities are properly normalized, summing to 1.

---

2. Mathematical Errors in Calculations

Incorrect Multiplication:

The essay calculates the posterior probabilities as:

• For a conservative prior :

For a liberal prior :

However, these calculations are incorrect:

• For the conservative prior:

For the liberal prior:

These results are far from the stated 53% and 73%, indicating a computational error.

Omission of the Denominator:

The essay fails to calculate the denominator , leading to posterior probabilities that are not normalized. Without this, the probabilities cannot be interpreted correctly.

---

3. Misunderstanding of Prior Probabilities

Labels of “Conservative” and “Liberal”:

The essay assigns:

• A “conservative” prior of (20%)
• A “liberal” prior of (50%)

This labeling is counterintuitive. Typically, a “conservative” estimate would favor the more widely accepted view (that Jesus existed) and thus have a higher prior probability, not a lower one.

Arbitrary Assignment:

The priors are assigned without clear justification. In Bayesian analysis, priors should be based on existing knowledge or evidence. For historical analysis, they might be informed by scholarly consensus or other credible sources.

---

4. Unjustified Likelihood Assignments

The likelihoods for each piece of evidence are assigned numerical values without explaining how these values were derived. For example:

• Josephus’ Testimonium Flavianum:
  • Likelihood (Jesus existed):
  • Likelihood (Jesus didn’t exist):

There is no methodological basis provided for these numbers. In rigorous Bayesian analysis, likelihoods should be based on statistical models, empirical data, or systematic reasoning, not subjective estimates.

---

5. Incorrect Interpretation of Bayesian Analysis

Dependence on Input Data:

The essay concludes:

“In essence your statistic is combination of things that require data you put into. Depending on what you put into it, it will give you the outcome you may want.”

This reflects a misunderstanding of Bayesian statistics. While Bayesian analysis depends on priors and likelihoods, its purpose is to update beliefs in a principled way based on evidence. When properly applied, it does not simply produce the outcome one desires.

Misrepresentation of Bayesian Inference:

The statement:

“If you start with fringe data, you will get fringe data with Bayesian.”

This is misleading. Bayesian methods are designed to systematically incorporate evidence into prior beliefs. If the data is robust and the model is properly specified, Bayesian analysis can yield meaningful insights, even if the priors are uncertain.

---

6. Lack of Consideration for the Denominator

The denominator represents the total probability of observing the data under all possible hypotheses. It ensures proper normalization of probabilities. Ignoring leads to invalid posterior probabilities that cannot be interpreted meaningfully.

---

7. Ignoring Dependency Between Pieces of Evidence

The essay treats each piece of evidence as independent, multiplying their likelihoods together. However, historical evidences are often correlated. For instance, Tacitus and Josephus may have drawn from common sources or influenced each other. Ignoring these dependencies skews the results.

---

8. Oversimplification of Historical Analysis

The essay oversimplifies the complexities of historical scholarship. Quantifying historical events and figures with precise probabilities requires substantial assumptions and careful modeling of uncertainties. This is not adequately addressed in the essay.

---

9. Criticism Based on Misunderstandings

By misapplying Bayesian statistics, the essay inadvertently demonstrates the very issues it attributes to mythicists. A valid critique requires an accurate understanding and application of Bayesian methods.

---

Conclusion

The essay contains several fundamental flaws in its understanding and application of Bayesian statistics. It incorrectly applies Bayes’ theorem, makes computational errors, unjustifiably assigns probabilities, and misunderstands Bayesian inference. A proper Bayesian analysis requires careful consideration of priors, likelihoods, dependencies, and normalization. To validly critique the use of Bayesian statistics in historical debates, one must first accurately understand and apply the methodology.

---

Richard Carrier’s Critique

To critically assess Richard Carrier’s analysis of Matt Kovacs’ arguments and methodology, the following key areas will be addressed: Carrier’s substantive points, his methodology in countering Kovacs’ arguments, and his rhetorical approach.

---

1. Substantive Points

Carrier raises valid critiques of Kovacs’ methodology and understanding of Bayesian statistics. These critiques include:

1.1 Misrepresentation of Bayesian Analysis

Carrier highlights that Kovacs fundamentally misunderstands how Bayesian reasoning works. Specifically:

• Kovacs appears to conflate the components of Bayes’ theorem, such as interpreting (the posterior probability) as “hypothesis multiplied by data.”
• He ignores the denominator , which is critical for proper normalization of probabilities.
• His failure to apply likelihood ratios correctly renders his calculations meaningless, as the ratios he uses lack empirical or theoretical justification.

1.2 Incorrect Calculations

Carrier effectively demonstrates that Kovacs’ arithmetic is flawed, pointing out that:

• Kovacs’ conservative calculation of yielding “53%” is an egregious error (the actual result being ).
• This basic mathematical mistake undermines Kovacs’ credibility and reflects a lack of numeracy required for engaging in Bayesian analysis.

1.3 Lack of Empirical Justification

Carrier critiques Kovacs for inventing his inputs:

• Likelihoods such as for the Gospels and for Tacitus lack any empirical or evidential foundation.
• Kovacs fails to account for error margins, a critical feature in Bayesian reasoning, especially when dealing with uncertain historical data.

1.4 Conflation of Consensus and Evidence

Carrier rightly challenges Kovacs’ reliance on “scholarly consensus,” pointing out:

• No proper poll exists to establish that “80-85% of scholars” agree with Kovacs’ likelihoods.
• Scholarly consensus on Jesus’ historicity often reflects biases (e.g., the predominance of Christian scholars in the field) and does not necessarily equate to robust empirical analysis.

1.5 Dependence on Dubious Evidence

Carrier highlights Kovacs’ mischaracterization of evidence, such as:

• Assigning strong likelihoods to sources like Tacitus and Josephus, despite their known problems (e.g., potential Christian interpolation and dependence on earlier Christian traditions).
• Misattributing archaeological evidence to support Jesus’ historicity when no such evidence exists.

---

2. Methodological Approach

Carrier’s critique is methodical, addressing both the technical and logical deficiencies in Kovacs’ argument.

2.1 Demonstrating Errors

Carrier meticulously walks through Kovacs’ mathematical errors and provides a corrected Bayesian calculation. This approach underscores:

• The necessity of proper normalization using the denominator .
• How Kovacs’ fabricated likelihoods skew the results, rendering his conclusions unreliable.

2.2 Addressing Misunderstandings

Carrier explains the proper application of Bayesian analysis, emphasizing:

• The role of error margins in capturing uncertainty.
• The importance of empirically justified inputs for prior probabilities and likelihoods.

2.3 Comparative Rigor

Carrier contrasts his peer-reviewed work with Kovacs’ amateurish approach. By highlighting his own reliance on empirical data and formal methods, Carrier reinforces the validity of his Bayesian analysis compared to Kovacs’ ad hoc reasoning.

---

3. Rhetorical Approach

Carrier’s rhetoric, while passionate, is often polemical and dismissive. This could alienate readers who might otherwise engage with his arguments. Notable rhetorical features include:

3.1 Dismissive Language

Carrier uses terms like “amateur,” “incompetent,” and “oblivious,” which may detract from his substantive points by appearing unnecessarily combative.

3.2 Ad Hominem Accusations

Carrier accuses Kovacs of engaging in ad hominem attacks, yet he himself frequently attacks Kovacs’ competence rather than solely critiquing his methodology.

3.3 Overgeneralizations

Carrier extrapolates Kovacs’ errors to the broader field of historical Jesus studies, suggesting that all critics of mythicism exhibit similar flaws. While there is merit to some of these observations, this broad-brush approach risks oversimplifying the diversity of scholarly opinions.

---

4. Strengths of Carrier’s Analysis

4.1 Technical Precision

Carrier’s explanation of Bayesian reasoning and his correction of Kovacs’ errors provide a clear and accessible tutorial on how Bayesian analysis should be applied to historical questions.

4.2 Focus on Evidence-Based Reasoning

Carrier’s insistence on empirically grounded inputs and rigorous methodology exemplifies critical thinking in historical scholarship.

4.3 Defense of Peer-Reviewed Work

Carrier effectively defends his peer-reviewed studies against misrepresentations, underscoring the importance of engaging with the actual arguments presented in scholarly research.

---

5. Weaknesses of Carrier’s Analysis

5.1 Tone and Accessibility

Carrier’s polemical tone may alienate readers unfamiliar with the topic or those sympathetic to Kovacs’ perspective. A more measured approach might better convey the strength of his arguments.

5.2 Overemphasis on Kovacs’ Errors

While Carrier thoroughly critiques Kovacs’ methodology, he spends less time addressing broader implications for the historicity debate, potentially limiting the relevance of his critique to a narrow audience.

---

Conclusion

Richard Carrier’s analysis effectively dismantles Matt Kovacs’ arguments, exposing fundamental flaws in Kovacs’ understanding of Bayesian statistics and historical reasoning. Carrier’s critique highlights the importance of empirical justification, mathematical rigor, and proper engagement with peer-reviewed scholarship. However, Carrier’s polemical tone and tendency to generalize Kovacs’ errors to all critics of mythicism may limit the broader impact of his critique. Nonetheless, his defense of Bayesian reasoning as a tool for historical analysis remains a compelling contribution to the ongoing debate over the historicity of Jesus.