Cavin and Colombetti on the Resurrection of Jesus Part 1: The Anti-Resurrection Prior Probability Argument

As I reported earlier, Greg Cavin has graciously allowed us to publish the slides for his debate with Michael Licona on the Resurrection of Jesus. While only Cavin debated Licona, both Cavin and Carlos Colombetti  (C&C) co-authored the slides used in the debate, so I’ve mentioned both C&C in the title.

What I want to do in this post is to summarize (and offer my own interpretation of) Cavin’s first main contention in his debate with Michael Licona on the Resurrection of Jesus:

CC1. The prior probability of a specifically supernatural Resurrection of Jesus by God is so astronomically low that the Resurrection Theory has virtually zero (0) plausibility.

1. Prior Probability, Explanatory Power, and Final Probability

In order to properly assess CC1, it’s crucial that we first clarify what “prior probability” means. In order to do that, let us begin by dividing the evidence relevant to the Resurrection into two categories. First, certain items of evidence function as “odd” facts that need to be explained.  Let us call these items the “evidence to be explained.” Second, other items of evidence are “background evidence,” which determine the prior probability of rival theories and partially determine how well those theories explain the evidence to be explained.

These two types of evidence have two probabilistic counterparts: (1) the prior probability of a hypothesis H and (2) the explanatory power of H. (1) is a measure of how likely H is to occur based on background information B alone, whether or not E is true. As for (2), this measures the ability of a hypothesis (combined with background evidence B) to predict (i.e., make probable) an item of evidence.

Bayes’s Theorem states that the final probability of a hypothesis is a function of both its prior probability and its explanatory power. So the final probability of a hypothesis is the probability that a hypothesis is true, conditional upon both our background evidence and the evidence to be explained.

A common mistake made by many people is to confuse prior and final probabilities. For example, suppose someone, call him Thomas, says that a hypothesis H has a prior probability of 1 in 100 billion. Does it follow that Thomas thinks H is false? No! All that follows is just that Thomas thinks the prior probability of H is 1 in 100 billion. In order to figure out whether Thomas thinks H is true, we need to know what Thomas thinks about H’s explanatory power. Thomas might think that H’s explanatory power is so high that it completely outweighs its prior probability, in which case Thomas will (if he is rational) think that H is probably true.

Let us now turn to C&C’s defense of CC1.

2. The Anti-Resurrection Prior Probability Argument

The statistical syllogism is an inductively correct argument that moves from general to particular: “what is generally, but not universally, true (or false) is also true (or false) for a particular case.”[1] It has the following form.

1. X% of Fs are Gs.
2. a is F.
3. Therefore, [it is X% probable] a is G.

Because the statistical syllogism explicitly refers to probability, the interpretation of a statistical syllogism is dependent upon the probability interpretation used in the argument. For example, if one adopts a frequency interpretation of the probability value X, then one will have a corresponding frequency interpretation of the statistical syllogism. According to the frequency interpretation of the statistical syllogism, F is called the reference class, the class of individuals or properties that a belongs to or is referred to. G is called the attribute class, the class that has the property attributed to a.[2]

In a statistical syllogism, regardless of how one interprets probability, X can refer to either a single value (i.e., 65%) or a range of values (i.e., 90-95%). We often use fuzzy probabilities for X to represent a range of values without providing actual numbers for the limits of the range.[3] Fuzzy probabilities are expressed with phrases like most of, usually, probably, often, frequently, almost all, vast majority, high percentage, and the like.

Also regardless of the probability interpretation used, inductively correct statistical syllogisms must obey two rules. First, X must be greater than 50%; the closer X is to 100%, the stronger the argument.[4] Second, the statistical syllogism, like all inductive arguments, must obey the Rule of Total Evidence, which is the requirement that the premises of an inductively correct argument must represent all of the available relevant evidence. “Relevant” here means something that can affect the probability (X) of the conclusion. In the context of the statistical syllogism, when selecting the reference class F, we must consider the class that is most relevant to the probability that a is a G. In practical terms, this translates into two requirements. First, the defining properties of F are relevant to a’s being G, and, second, F is the most narrowly specified of such classes.[5]

In support of CC1, C&C present the following statistical syllogism, which they label, accordingly, the “anti-resurrection prior probability statistical syllogism” (slide 108).

1. 99.999…999% of the dead are not supernaturally interfered with by God, and, thus, not raised by Him.
2. Jesus was dead.
3. Therefore, [it is 99.999…999% probable that] Jesus was not supernaturally interfered with by God, and, thus, not raised by Him.

Here we see the importance of the earlier distinction between prior probability and final probability. While the argument’s name refers to prior probability, the actual conclusion of the statistical syllogism does not. This might give one the incorrect impression that C&C are claiming that the final probability of Jesus’s being dead is 99.999…999%.

3. The Justification for the Probability Estimate in the Anti-Resurrection Prior Probability Argument

One incorrect way to interpret the statistical syllogism would be to think it refers refers to the percentage of the dead who are not supernaturally interfered with by God. In that case, one might get the impression that C&C’s basis for that prior probability value just is an appeal to observational-relative frequencies. Such an interpretation would be incorrect, however.

In the context of refuting Licona’s assumption that C&C’s argument presupposes atheistic naturalism, their anti-resurrection prior probability argument is based on negative natural theology, i.e., the Via Negativa, specifically on the tendency of God not to interfere with the decomposition of dead bodies – to not supernaturally raise the dead. Thus, according to C&C, the correct way to interpret the anti-resurrection prior probability argument is to interpret it using the epistemic interpretation of probability.

While observational-relative frequencies are often used for calculating prior probabilities, C&C make it clear that they believe observational-relative frequencies are “particularly ill-suited for the purposes of calculating the prior probability of the Resurrection” (274). This is because “for all or almost all of us the observational frequency of resurrections is strictly zero, yet inferential statistics does not permit us to calculate a strictly zero prior probability from (finite) observational frequencies of zero” (275-276).

So how, precisely, do C&C justify their astronomically low prior probability value for the Resurrection? Statistical Mechanics. Appealing to the “Postulate of Equal A Priori Probabilities,” C&C point out that all microstates having the same energy have the same prior probability. In the case of Jesus’ corpse, the equally epistemically probable microstates in which the corpse of Jesus is dead vastly outnumber those in which his body is alive (316). Because that is so, “the prior [epistemic] probability that the body will die and undergo complete decomposition”—in other words, the prior [epistemic] probability that the corpse will not resurrect—is “virtually 100%” (320-21).

It seems, then, that C&C want to make an inference from natural revelation, namely:

(NR) 99.999…999% of the dead decompose, viz., 99.999…999% of the potential microstates of a post-mortem body are microstates in which the body is dead.

to a generalization about supernatural resurrection:

(SR) 99.999…999% of the dead are not supernaturally interfered with by God, and, thus, not raised by Him.

This inference appears to rely upon the following principle (the “Via Negativa”):

(VN) Necessarily, if God causes it to be the case that P, then P.

Notice that VN entails that necessarily, if ~P, then God does not cause it to be the case that P.

In order to see an example of how C&C justify the inference from (NR) to (SR) using (VN), let us now turn to an objection. Their response to this objection illustrates how they believe the inference from (NR) to (SR) can be justified.

4. The Divine Interference Objection

One obvious objection to the anti-resurrection prior probability argument is that it ignores the possibility of divine interference: “the one hundred billion people who’ve died and stayed dead prove only that apart from God’s supernatural intervention the dead don’t rise” (61). Since God has the power to supernaturally raise the dead, the anti-resurrectionist must show that God would not supernaturally raise Jesus from the dead. C&C call this the “divine interference objection.”

In response, however, C&C argue that “it’s a blatant straw man” to saddle them “with the view that the antecedent probability of what God wills must be determined a priori” (95). The divine interference objection is fallacious, they argue, because it ignores “the evidence of God’s self-revelation in Nature—seen a posteriori in everyday experience and science” (96). That evidence shows that God “has an exceptionally strong tendency not to supernaturally intervene in natural affairs” and, indeed, “not to supernaturally raise the dead” (103-04). Thus, using the Via Negativa, we don’t need to speculate a priori about what God would do; rather, we can empirically discover what God does and, more important, does not do. “Since whatever God wills to happen must happen, it follows that the antecedent [epistemic] probability that God would will Jesus to rise from the dead is astronomically low” (105).  Accordingly, C&C conclude that the anti-resurrection prior probability argument stands.

Notes

[1] Merrilee H. Salmon, Introduction to Logic and Critical Thinking (third ed., Harcourt Brace: New York, 1995), 99.

[2] I owe these definitions to Salmon 1995, 100.

[3] Cf. L.A. Zadeh, Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers (River’s Edge, NJ: World Scientific, 1996).

[4] If Z were to equal 100%, then the generalization would be categorized as a universal generalization, not a statistical generalization. The argument would then become a deductive argument.

[5] William Gustafson, Reasoning from Evidence: Inductive Logic (Macmillan: New York, 1994), 50.

What is Faith? - Part 8
The Logic of the Resurrection - Part 3
The Logic of the Resurrection - Part 4
The Logic of the Resurrection - Part 1
About Jeffery Jay Lowder

Jeffery Jay Lowder is President Emeritus of Internet Infidels, Inc., which he co-founded in 1995. He is also co-editor of the book, The Empty Tomb: Jesus Beyond the Grave.


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