Christian Theology and Apologetics

A Historical Approach to the Resurrection of Jesus: Part 5 Bayes Theorem

Part 5

Bayes Theorem

In the first four parts to this series the evidence pertinent to Jesus’ crucifixion and entombment was examined and deemed historical credible; no serious scholar denies this. Moreover, those scholars that attempt to do so must come from a place of silence; there are no texts stating Jesus survived the crucifixion or any other concocted theory—there is no explanatory scope for the skeptical conjectures. Crossan, dismissed the narratives describing Jesus’ entombment on the basis of argumentum ex silentio. Thus, Crossan and others like him give more credence to silence than to the narratives themselves; this highlights philosophical assumptions exported onto the texts, which is to say, they presuppose what they wish to be true, despite many evidences to the contrary. Thus, the problem is not in the evidence—it stands on its own—the problem is the evidence leads to an undesirable conclusion. This is why some discard the evidence and form contentions based on silence.

In the earlier parts to this series the evidence was sifted through to uncover many salient facts regarding Jesus’ death, burial, and resurrection. It is now my intention to build a cumulative case for the probability that (R) Resurrection is higher than (~R) Resurrection alternatives. In order to express the significance of any single piece of evidence against the hypothesis (R) or (~R) I will let (F) be representative of any pertinent fact to each hypothesis. Thus, this formula asks two questions: (1) how probable is (F) on the hypothesis that (R) is true; and (2)how probable is (F) on the hypothesis that (R) is false.

This is expressed as follows:


The above is called a Bayes Factor, which provides a convenient process for representing the importance of a certain fact F given R. What Bayes factor will demonstrate is that (R) becomes more plausible when a fact (F) that is more to be expected if (R) is true than if (R) is false. Just to make the factor more clear I will break the factor down a little more to demonstrate what is going on.

 P(R|F)       P(R)     P(F|R)

——— = ————  x ———

P(~R|F)   P(~R)     P(F|~R)

If the facts (F) can be adequately accounted for on the hypothesis of (R) but not, without great unlikelihood, on the assumption of ~R, then they provide significant evidence in favor of R. Stated more colloquially, The probability of R (Resurrection) is higher than the probability of ~R (Resurrection alternatives) if and only if, F (facts) can be readily account for given R and not without great difficulty given ~R.

Now we move onto to the pertinent facts discussed in parts 1-4 of this series on Jesus’ resurrection. It is most useful to take each line of evidence independently and then craft a cumulative argument under the assumption of independence. Permit W, D, P, and J respectively stand for the testimony of the women regarding the empty tomb and Christ’s resurrection, the testimony of the disciples, conversion of Paul, and the conversion of James. These lines of evidence can be combined as follows:


P(R|F1 & . . . & FN)     P(R)   P(W|R)     P(D|R)   P(P|R)     P(J|R)

——————— ——  = —— x ——— —x ——— x ———   x ———

P(~R|F1 & . . . & FN     P(~R)   P(W|~R)   P(D|~R) P(P|~R)   P(J|~R)

The product of the last four terms (Bayes factors for W, D, P, and J) will give the bearing of these pieces of evidence on the odds under the assumption that they are independent.

Testimony of the Women. Timothy McGrew states, “There is no difficulty accounting for W if the resurrection had in fact occurred.”[1] This is prima facie true, if the women did see the empty tomb and resurrected Christ, this adequately accounts for their testimony. Now if the resurrection hadn’t occurred and the women didn’t see Christ resurrected, what could possibly have prompted them to report the resurrection? The women perceived Jesus using their senses; the text states that they saw, heard, and felt Christ when he met with them. Additionally, the notion that the women manufactured the story has a rather low probability; they were women, in Jewish society their word wasn’t considered worthy of testimony and in fact Jesus’ own disciples did dismiss their testimony (Lk 24:11). Moreover, what would be the motive for concocting such a story: which was more probable, that they would profit from the report or was it more likely they would lose their lives over the claim? It must be said that there was no motive for creating such a claim. The witnesses lack of credibility in the first century is reason enough to regard the witnesses as credible in the twenty-first century.[2] The appearance to the women after the resurrection is multiply attested to (Mk 28:1; 8-10; Jn 20:11-18; Mk 16:9-11). Moreover, the men in these narratives are not the type of leaders that instills confidence in church members. Thus, there is a double-edge sort of criterion of embarrassment; the women discover the empty tomb and Jesus, while the men do not believe their report. If one were to invent this story, surely he would place more confidence in the church leadership and not paint such a negative light on them. It seems more likely that if one were to fabricate the story of the resurrection that more important witnesses would have been used; witnesses like Joseph of Arimathea or Nicodemus would have carried more weight with audiences than lowly Jewish women who had great standing in the community.

Another resurrection alternative some have suggested is that the women experienced hallucinations of Jesus. It must be said that the women did not expect the resurrection of Jesus; they weren’t expecting Jesus to be resurrected apart from the general resurrection everyone would experience at the end of the age. McGrew states, “The prior probability for a group hallucination under these circumstances is prohibitively low, not in the sense that it is strictly zero but in the sense that it is nowhere near the magnitude of P(W|R) and therefore cannot significantly affect the strength of the argument from W for R.”[3] Anyone claiming the women saw the same hallucination bears the burden of proof for this theory and to this date the explanatory scope of this theory is extremely improbable at best and at worst is simply ad hoc. There are other theories posited as to how the women came to the belief that they saw the empty tomb and Jesus resurrected, but as mentioned before, these are reliant upon arguments from silence and thus have no evidence supporting the claims. None of the explanations contrary to the women seeing the empty tomb and resurrected Christ have the explanatory strength to rival the resurrection (R) as an explanation for the testimony of the women (W). Therefore, P(W|R)/P(W|~R) demonstrates that P(W|R) should (at a conservative estimate) be several times stronger than P(W|~R). Claims to the contrary, shoulder a great if not impossible burden of proof.

[1] Timothy McGrew and Lydia McGrew “The Argument from Miracles: A Cumulative Case for the Resurrection of Jesus of Nazareth” in The Blackwell Companion to Natural Theology, 620.

[2] Licona, Michael R. The Resurrection of Jesus: A New Historiographical Approach (Downers Grove, InterVarsity Press, 2010), 350.


[3] McGrew, 620.


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