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2 responses to “✓ The Missing Probability”

1. 

   Steve H

   May 7, 2025

   Phil, my understanding of the Bayesian analysis of Jesus’ resurrection is based on the Odds Form of Bayes’ Theorem. That form incorporates both the Prior Probabilities (ie. background evidence; knowledge of natural vs supernatural causes) and the Likelihood Probabilities (ie. likelihood of the truth vs falsity of the claim/hypothesis/resurrection in light of having vs not having evidence of empty tomb, post-mortem appearances, origin of disciples’ beliefs).

   That is, the Likelihood Probabilities (LP) calculation can far outweigh the Prior Probabilities (PP) calculation given the existence of evidence which would not otherwise exist if the claim were false. More specifically, the denominator of the LP (probability of existence of evidence if claim is false) is extremely small compared to the LP numerator (probability of existence of evidence if claim is true), which results in a very large LP calculation, which in turn can outweigh the PP.

   Thus, extraordinary claims, if true, require a higher probability of *ordinary* evidence, which can support the resurrection hypothesis as the best explanation over natural hypotheses.

   Your thoughts?

   Reply
2. 

   Phil Stilwell

   May 8, 2025

   Steve, thanks for jumping in. You’re absolutely right to bring up the odds form of Bayes’ Theorem—it’s a valid and powerful tool. But the issue isn’t with the formula. It’s with the missing input. Specifically: apologists often never assign a resurrection probability at all. That’s not a small oversight—it’s a dealbreaker.

   1. Bayes Requires a Resurrection Prior—But It’s Always Missing

   You point out that likelihoods can outweigh priors. True—but only after the priors are defined. What is the actual prior probability of a resurrection? If that value isn’t explicitly stated and justified, then saying the resurrection is “the most probable explanation” is meaningless. The engine can’t run if a critical variable is left blank.

   2. Inflating the Likelihood Ratio Doesn’t Excuse a Missing Prior

   You highlight that the evidence (empty tomb, postmortem appearances, etc.) is far more likely under the resurrection hypothesis than under naturalistic ones. Even if we grant that—and it’s a big if—it still doesn’t salvage the argument unless the prior is specified. You can’t multiply a likelihood by an undefined prior and pretend it yields a reliable result.

   3. The Resurrection Is Often Given an Implied Default of 1% or More—Without Justification

   In practice, many apologists treat the resurrection hypothesis as though it starts with a reasonable prior—1%, 5%, sometimes more. But nothing in our background knowledge of the world justifies assigning such numbers. This is where the asymmetry becomes stark: naturalistic explanations, even when assigned extremely low priors (e.g. 0.1% each), are still actually assigned values and summed disjunctively. The resurrection hypothesis often gets a rhetorical pass.

   4. The Burden of Quantification Is on the Extraordinary Claim

   Bayesian reasoning isn’t magic. It can’t rescue a claim whose prior hasn’t been defended. Until apologists are willing to say what they think the prior probability of a resurrection is—and why—then all downstream comparisons are epistemically hollow. They’re trying to win a probability contest without submitting a number.

   Bottom Line: No Prior = No Probability Claim

   If someone claims “the resurrection is the most probable explanation,” they are making a comparative assertion. And no comparative claim is valid if one of the terms is left undefined. Until the resurrection’s prior is named, supported, and compared against the disjunction of natural alternatives, the argument doesn’t merely fall short—it never begins.

   I appreciate your attempt to incorporate Bayesian reasoning here. But your central claim—that the “likelihood can outweigh the prior”—only holds after a prior is actually specified. Right now, that key term is being left blank, and without it, any posterior probability is floating in the void.

   You’re essentially saying:

   “Even if the resurrection is unlikely to begin with, the specific evidence is so much more expected if the resurrection happened than if it didn’t, that this makes the resurrection probable overall.”

   That can work in Bayesian reasoning—but only when all the terms are assigned values.

   Let me ask directly:
   What do you assign as the prior probability of a resurrection?
   If you don’t provide that, there’s no way to judge whether the likelihood ratio “outweighs” it.

   More importantly, even if the evidence (e.g., empty tomb, postmortem experiences) is very unlikely under individual natural explanations, the combined disjunction of all natural alternatives—even at small individual probabilities—can still easily exceed the resurrection hypothesis, especially if no coherent prior is given for it.

   So yes, LP can shift things—but only if PP is present in the equation. Right now, resurrection arguments often assume the LP speaks for itself and quietly smuggle in a favorable prior without ever justifying it. That’s not Bayesian reasoning. That’s Bayesian aesthetics.

   Reply