Assessing the Resurrection Hypothesis: McCullagh, Craig, Cavin, and Colombetti

In this post, I want to consider the assessment of historical hypotheses such as the alleged resurrection of Jesus (R), using the writings of William Lane Craig as a foil. In doing so, I will rely heavily upon a recent article by philosophers Robert Greg Cavin and Carolos Colombetti, but I want to be clear that I have not reviewed this post with them, so any mistakes in this post are entirely my responsibility.

While Craig's position regarding the use of Bayes' Theorem has evolved over the years, to my knowledge one thing which has not changed is his reliance upon the work of historian C. Behan McCullagh.[1] Following McCullagh, Craig argues for R using an argument pattern called "inference to the best explanation" (IBE).[2] In this post, I will argue the following three points contra Craig. First, Bayes' Theorem is the foundation for logically correct arguments for any historical hypotheses. Second, neither McCullagh's IBE criteria nor Craig's restatement of them are sufficiently clear to enable a rigorous assessment of historical hypotheses, whereas the Bayesian approach avoids these problems. Third, Craig's defense of R fails to establish that the alleged event is more probable than not.

1. Is Bayes' Theorem Even Relevant to History?

In his 1995 debate with philosopher Robert Greg Cavin, Craig argued that Bayes' Theorem is not how historians justify historical hypotheses. What follows is a paraphrase of Craig, taken from notes I made while listening to the debate more than a decade ago.

C. Behan McCullagh points out that few historians have adopted a Bayesian approach. First, the information needed to estimate the various probabilities is not available. This is the problem, for example, with estimating the (prior) probability of R, i.e., the probability of R relative to our background information. Second, sometimes the results of using Bayes' Theorem are unacceptable, as McCullagh has documented. Virtually no historian has used Bayes' Theorem in justifying historical descriptions.[3]

I am sure that McCullagh's claim,[4] regarding the relative frequency of historical descriptions justified by historians using Bayes' Theorem, is correct. But the descriptive fact that few historians use Bayes' Theorem to justify historical hypotheses does not negate the normative fact that Bayes' Theorem underlies the justification for logically correct arguments for historical hypotheses. 

Consider the McCullagh-Craig alternative: Inference to the Best Explanation (IBE). In light of the fact that Craig vigorously defended IBE over and against Cavin's Bayesian approach, one would expect to find, on Craig's website if not in the debate itself, the logical form of IBE so that the two argument styles could be compared and contrasted. Indeed, one searches in vain the writings of both Craig and McCullagh for so much as the slightest acknowledgment that IBE even has a logical form! But since they (apparently) fail to do so, Cavin and Colombetti (C&C) have done so on their behalf. According to C&C, IBE arguments have the following logical form.

(1) Hypothesis H1 of the set H1 , …, Hn is the best explanation of the evidence E in being superior to its rivals H2 , …, Hn in satisfying the criteria for justifying historical explanations.

Therefore:

(2) H1 is probably true.[5]

The conclusion's use of the word "probably" gives away the entire game, set, and match. IBE is not a type of deductive argument; instead, it is an inductive argument which, at best, merely shows that the inferred explanation is probable.[6] The word "probably" in the conclusion refers to the inferred explanation's posterior or final probability. But as Bayes' Theorem correctly states, final probability is determined by prior probability, the so-called 'likelihood' (the probability of the evidence conditional upon the explanation), and nothing else. This mathematical fact creates a dilemma for partisans of the IBE approach (hereafter, "explanationists"): does a successful IBE show that the hypothesis to be inferred enjoys a greater balance of prior probability and explanatory power than rival hypotheses do collectively? If yes, IBE is not a rival approach to Bayesianism. The alleged obstacles to applying Bayes' Theorem to historical descriptions are not genuine obstacles. If no, then IBE is a rival approach to Bayesianism but a mathematically and logically incorrect one. 

What, then, of Craig's objection to using a Bayesian approach to assess historical descriptions? Craig apparently thinks that, by using IBE, he can somehow avoid the need to estimate the various probabilities. But this is misguided. For example, Craig's preferred IBE approach includes the criterion of "plausibility." Although he will surely deny it, I submit that it should be clear to any informed, unbiased observer that what Craig calls "plausibility" just is prior probability, albeit prior probability under another name masquerading as an alternative to prior probability. Both prior probability and plausibility come in degrees and both are measured relative to background information. As C&C point out, any problems in assessing prior probability will apply equally to Craig's plausibility.[7] 

Indeed, Craig himself implicitly admits that his earlier (1995) opposition to using Bayes' Theorem was misguided. In 2000, he wrote a response to Gary Habermas on apologetic methodology. As part of that response, Craig used Bayes' Theorem to assess the probability of the Resurrection. Furthermore, he specifically estimated the value of the prior probability of the Resurrection to be "not low," contrary to his earlier claim that we lack the necessary information.[8]

2. The Superiority of Bayesianism to McCullagh's IBE Framework

My plan in this section is as follows. First, I will quote McCullagh at length so that the reader can read McCullagh's explanation of his IBE criteria in his own words. Second, following the recent C&C article, I will argue that McCullagh's IBE criteria are not sufficiently clear to make possible a rigorous assessment of the Resurrection hypothesis or rival explanations. Third, I will argue that a Bayesian framework succeeds precisely where an IBE framework fails. 

2.1. McCullagh's IBE Criteria

Because the details matter, I want to quote the entirety of McCullagh's seven IBE criteria.

The theory is that one is rationally justified in believing a statement to be true if the following conditions obtain:

(1) The statement, together with other statements already held to be true, must imply yet other statements describing present, observable data. (We will henceforth call the first statement 'the hypothesis', and statements describing observable data, 'observation statements'.)

(2) The hypothesis must be of greater explanatory scope than any other incompatible hypothesis about the same subject; that is, it must imply a greater variety of observation statements.

(3) The hypothesis must be of greater explanatory power than any other incompatible hypothesis about the same subject; that is, it must make the observation statements it implies more probable than any other.

(4) The hypothesis must be more plausible than any other incompatible hypothesis about the same subject; that is, it must be implied to some degree by a greater variety of accepted truths than any other, and be implied more strongly than any other; and its probable negation must be implied by fewer beliefs, and implied less strongly than any other.

(5) The hypothesis must be less ad hoc than any other incompatible hypothesis about the same subject; that is, it must include fewer new suppositions about the past which are not already implied to some extent by existing beliefs.

(6) It must be disconfirmed by fewer accepted beliefs than any other incompatible hypothesis about the same subject; that is, when conjoined with accepted truths it must imply fewer observation statements and other statements which are believed to be false.

(7) It must exceed other incompatible hypotheses about the same subject by so much, in characteristics 2 to 6, that there is little chance of an incompatible hypothesis, after further investigation, soon exceeding it in these respects.[9]

As I read him, Craig 2008 appears to endorse McCullagh's criteria pretty much as is.[10] 

2.2. The Obscurity of McCullagh's IBE Criteria

In a recent article, C&C demonstrated there are multiple problems "regarding the meaning, justification, and ranking" of the proposed criteria. Since I find their argument convincing, I will merely summarize their main points and encourage interested readers to consult their article for details.

(1) Regarding the meaning of the IBE criteria, C&C note the following problems: (1.1) it is unclear what the word "imply" means in the various criteria; (1.2) it is unclear how to interpret explanatory scope and explanatory power and how they differ from one another; (1.3) it is unclear what "plausibility" means and how to assess it; and (1.4) the provided definition of "ad hoc" is idiosyncratic and unjustified.[11]

(2) C&C point out that, even among Christian scholars who appeal to McCullagh to defend the Resurrection hypothesis, there are differing opinions about the correct set of criteria. Whereas Craig has seven criteria, Licona has five. Not only do Craig and Licona use different sets of criteria, but "they each omit one or more widely accepted criteria--e.g., non-ad hoc-ness, simplicity, modesty, testability, and fruitfulness."[12]

(3) C&C observe that it is unclear how to rank, weight, or prioritize the different IBE criteria. For example, should we prefer a highly plausible hypothesis with middling explanatory scope over a moderately plausible hypothesis with greater explanatory scope? Again, C&C observe that Craig's approach is "markedly" different from that of Licona, but neither justify their approach.[13]

Because of these three sets of problems, it is difficult to rigorously assess the historicity of the Resurrection hypothesis and to compare it to rival hypotheses.

2.3. The Bayesian Framework Vindicated

Let us now consider the Bayesian approach in light of the difficulties just reviewed.

(1) Regarding meaning, all of the terms in Bayes' Theorem have rigorous definitions. Furthermore, as C&C argue, the Bayesian framework succeeds precisely where the IBE framework fails. 

• (1.1) A Bayesian framework does not rely upon the word "imply." 
• (1.2) In a Bayesian framework, explanatory scope and power are both represented by a single term, Pr(E | B & H), sometimes called the Bayesian "likelihood." This term is the epistemic probability of the evidence to be explained conditional upon the background information and the assumption that H is true. As C&C point out, the explanatory scope of H is "the range of facts contained in E," whereas the explanatory power of H is the "magnitude" of the term Pr(E  B & H). 
• (1.3) As mentioned earlier, in the Bayesian framework, "plausibility" just is the prior probability of H. It is represented by the term Pr(H | B), which is the epistemic probability of H conditional upon background information B alone. 
• (1.4) C&C point out that that the usual definition of "ad hoc" preferred by logicians is an explanatory hypothesis which satisfies two conditions: "it is introduced just for the special purpose of accommodating some particular observation that otherwise would constitute counterevidence (e.g., failed predictions) to the hypothesis of interest, and there is no independent evidence for it. But Craig’s formulation deviates from this standard definition."[14] Although they do not spell this out in a Bayesian framework, this is arguably easy to do. Because "ad hoc" ("for this special purpose") is not synonymous with "post hoc" ("after this"), we should not assume that a hypothesis devised after the evidence is collected (post hoc) is also arbitrary or overly complex (ad hoc).[15] Thus, genuinely ad hoc hypotheses may be excluded on the basis of prior probability and likelihood (where the evidence statement E includes all available and relevant evidence).

(2) Because the Bayesian approach bypasses IBE criteria in its entirety, Bayesianism does not have to justify a particular set of IBE criteria. 

(3) Likewise, the Bayesian does not have to justify a particular way to rank, prioritize, or weight IBE criteria.

Therefore, it seems to me that the Bayesian approach succeeds where the IBE approach fails.

3. The Failure of R as an Explanation

In this section, following C&C, I will show that Craig's defense of R fails to establish that R is more probable than not. Let us now consider Craig's defense of R using McCullagh's IBE criteria.

(1) Implication of other statements.

C&C agree that R satisfies this criterion, if "imply" is interpreted counterintuitively to mean "make probable."[16]

(2) Explanatory scope.

C&C agree with Craig that, if "imply" in McCullagh's first criterion means "make probable," then R (when combined with the fact of Jesus' burial) 'implies' an empty tomb. But, they argue, Craig does not show that R 'implies' the alleged postmortem appearances of Jesus. 

First, this criterion is comparative: it requires that Craig show that R is superior to rival explanations in terms of explanatory scope, but Craig's argument is non-comparative. At best, Craig merely shows that some naturalistic explanations for the appearances are defective; he does not show that R is superior. [17]

Second, C&C point out that the scope of a proposed hypothesis like R is not determined only by the content of R, but also by the content of the evidence to be explained (E). Thus it is trivial to show that R is actually inferior to some of its naturalistic rivals because some of them entail some of the specific historical facts included in E, whereas R does not. To cite just one of the examples mentioned by C&C, the hallucination hypothesis claims that the women, the disciples, and Paul experienced hallucinations which they mistakenly took to be of the risen Jesus. The hallucination hypothesis entails the postmortem appearances of Jesus, whereas R does not for the simple reason that R "states nothing about the post-Resurrection activities of the risen Jesus."[18]

Third, C&C argue that it is impossible for Craig to repair his argument by combining R with various auxiliary hypotheses about the risen Jesus, due to Craig's definition of R. Their argument on this point is quite technical and I will not attempt to summarize it here.

(3) Explanatory power.

As C&C observe, Craig fails to show that R is superior to its rivals regarding explanatory power. The reason why is essentially the same as C&C's first objection to explanatory scope: Craig needs a comparative argument for the superiority of R, but he only provides a non-comparative argument.[19]

(4) Plausibility

C&C argue that R is maximally implausible for two reasons.

1. The Standard Model (SM) of physics. Craig implicitly tries to avoid this issue by making a distinction between a natural and a supernatural revivification of Jesus. The natural revivification hypothesis is the view that Jesus rose naturally from the dead. In contrast, the supernatural revivification of Jesus, a/k/a the resurrection of Jesus (R), is the view that God raised Jesus from the dead. Craig agrees that the natural revivification of Jesus is "outrageously" implausible due to the laws of nature, but he argues that the content of the laws of nature are simply irrelevant to R.[20]

As C&C argue, however, Craig's distinction between a natural and supernatural revivification of Jesus fails to defend the plausibility of R. As they explain, even if God exists and God is omnipotent, the laws of nature tell us "what God does not do -- not what He does." And, as a matter of empirical fact, the laws of nature--specifically, the Standard Model (SM)--entail that God, if He exists, does not raise Jesus (or anyone else) from the dead. Because SM is an exceptionally well-confirmed law of nature, it follows that R has a "very high degree of implausibility."[21]

2. The alleged "religio-historical context" is not known to be true. Here C&C make three points. First, because the facts regarding Jesus' self-understanding (e.g., the "Son of Man" or "Son of God") are not known to be true, Craig cannot appeal to the "religio-historical context" of Jesus' life to show that R is not ad hoc.[22] Second, the facts regarding Jesus' alleged sinlessness are equally of no use in establishing Craig's religio-historical context: "since the disposition of humans to sin is so particularly strong and the meager New Testament evidence for the moral perfection of Jesus (as opposed to his general goodness) is hardly representative, being limited to certain childhood incidents and the last few years of his life (e.g., Jn. 8:46)."[23] Third, "The same goes for fulfillment of prophecies since it remains an open question among New Testament scholars whether these are historical or evolved for apologetic reasons in the early church."[24]

(5) Ad hoc-ness

C&C show that, even on Craig's definition of ad hoc, R is ad hoc. First, our background information includes SM which entails ~R; furthermore, Craig's appeal to the religio-historical context fails. Second, while Craig is correct that rival theories do require many new suppositions, "these are trivial in comparison to the supernaturalist suppositions" required by R. Craig likes to claim that R requires only one additional supposition, namely, that God exists. But this is false. Even if God exists, R requires additional suppositions: (a) that SM is false; (b) that God would resurrect, not merely resuscitate, a failed apocalyptic prophet; and (c) that Jesus was and is a contradictory being, namely, fully human and fully divine.[25] Third, R also requires suppositions that Jesus appeared in specific locations (the Emmaus road, in Galilee, etc.). Fourth, R also requires the supposition of Jesus' alleged Ascension. For all these reasons, then R is significantly more ad hoc than its rivals.[26]

(6) Disconfirmation

As C&C argue, SM disconfirms R.[27]

(7) Exceedance

Craig claims that, "There is certainly little chance of any of the rival hypotheses suggested to date ever exceeding the Resurrection Hypothesis in fulfilling the above conditions."[28] As C&C conclude, however, this claim lacks credibility. First, Craig simply claims that; he does not provide an argument. Second, in light of the points raised above regarding criteria (2) - (6), his claim is "mere apologetic bravado."[29]

4. Conclusion

In summary, we have seen that Craig's earlier rejection of Bayes' Theorem for the assessment of historical hypotheses is mistaken. Second, there are problems of clarity afflicting the IBE approach which do not apply to the Bayesian framework. Third, Craig has failed to show that R satisfies his own preferred IBE criteria. The upshot is that Craig's defense of R fails. Jesus is dead. 

Notes

[1] C. B. McCullagh, Justifying Historical Descriptions (Cambridge Univ. Press, 1984).

[2] E.g., William L. Craig, Assessing the New Testament Evidence for the Historicity of the Resurrection of Jesus (The Edwin Mellen Press, 1989); William L. Craig, Reasonable Faith: Christian Truth and Apologetics (Crossway Books, 2008).

[3] William Lane Craig, "Opening Statement" in Dead or Alive? The Craig-Cavin Debate, University of California at Irvine, 1995.

[4] McCullagh 1984, p. 57.

[5] Robert Greg Cavin and Carlos Colombetti, "Assessing the Resurrection Hypothesis: Problems with Craig's Inference to the Best Explanation" European Journal for the Philosophy of Religion 11:2 (2019): 205-28. https://doi.org/10.24204/ejpr.v11i2.2836.

[6] If someone wishes to object to this sentence and insist that IBE is abductive, not inductive, my response is to shrug my shoulders. In this context, all that matters to me is that IBE is not a type of deductive argument. At best, the conclusion of an IBE is made probable by the evidence to be explained.

[7] Cavin and Colombetti 2019.

[8] William Lane Craig, "A Classical Apologist's Response" In Steven B. Cowan (Ed.), Five Views on Apologetics (Zondervan, 2000).

[9] McCullagh 1984, p. 19.

[10] William Lane Craig, Reasonable Faith: Christian Truth and Apologetics (3rd ed., Crossway, 2008), 232-33.

[11] Cavin and Colombetti 2019.

[12] Cavin and Colombetti 2019.

[13] Cavin and Colombetti 2019.

[14] Cavin and Colombetti 2019.

[15] Fairfield, Tasha, and Andrew Charman. "A Dialogue with the Data: The Bayesian Foundations of Iterative Research in Qualitative Social Science." Perspectives on Politics 17, no. 1 (2019): 154-67 at 164. doi:10.1017/S1537592718002177.

[16] Cavin and Colombetti 2019.

[17] Cavin and Colombetti 2019.

[18] Cavin and Colombetti 2019.

[19] Cavin and Colombetti 2019.

[20] Craig 2008.

[21] Cavin and Colombetti 2019.

[22] Cavin and Colombetti 2019.

[23] Cavin and Colombetti 2019.

[24] Cavin and Colombetti 2019.

[25] Points (b) and (c) are mine; they are not found in C&C's article.

[26] Cavin and Colombetti 2019.

[27] Cavin and Colombetti 2019.

[28] Craig 2008.

[29] Cavin and Colombetti 2019.