Doctrine of Creation (Part 18): Determining the Intrinsic Probability of the Resurrection

Determining the Intrinsic Probability of the Resurrection

We've been looking at Hume’s in principle argument against the identification of a miracle. We saw that it involves two claims: first of all, that by definition any miracle is utterly improbable, and secondly, that no amount of evidence could possibly demonstrate a miracle. Last week we examined the second of those claims and saw that it was demonstrably fallacious because Hume, at that time ignorant of the probability calculus, considered only the probability of the resurrection on the background information alone – the intrinsic probability of the resurrection – and he neglected the other crucial factor which is the explanatory power of the resurrection hypothesis – how well the resurrection explains the evidence as opposed to the denial of the resurrection.

Today we want to turn to Hume’s first claim that the evidence for a miracle is by definition utterly improbable. In order to show that no evidence could possibly establish the historicity of a miracle, Hume needs to show that the intrinsic probability of a miracle like the resurrection is unacceptably low. That takes us to the first claim of Hume’s argument, that miracles are by definition utterly improbable. Why did Hume think this? Hume claimed that the uniform experience of mankind supports the laws of nature rather than miracles, which violate those laws. At face value such an assertion seems to be clearly question-begging. To say that uniform experience is against miracles is implicitly to assume already that the alleged miracle has not occurred; that all miracle reports are false. Otherwise truly uniform experience would not be against miracles. So the whole argument is reasoning in a circle if we take uniform experience to rule out by definition the occurrence of miracles.

John Earman, whose book Hume’s Abject Failure I shared with you last week, interprets Hume to mean, not that uniform experience is against miracles, but rather that up to the case under investigation, uniform experience has been against miracles. That is to say, when we come to some alleged miracle claim we do so knowing that all miracle claims apart from that one have in the past been spurious. Earman takes Hume to construe the intrinsic probability of a miracle on the background information to be a matter of frequency. Miracles are events that are utterly infrequent up to the time of the miracle in question. But Earman points out that the frequency model of probability simply will not work in this context. For trying to construe the probabilities in Bayes’ Theorem as frequencies would lead us to disqualify many of the theoretical hypotheses in the advanced physical sciences. For example, Earman points out that scientists are investing thousands of man-hours and millions of dollars trying to observe an event of proton decay, that is to say, the decay of a proton into more fundamental subatomic particles, even though such an event has never been observed. On Hume’s frequency model of probability such research is an enormous waste of time and energy because the event will have a probability of zero. Based on frequency, it has no probability of occurring, so why are we spending millions of dollars and thousands of man-hours looking for something like this? Earman concludes that in the case of the intrinsic probability of a miracle (the probability of the miracle on the background information) the guidance for assigning the probability “cannot take the simple-minded form” of using the frequency of R-type events in past experience; that frequency may be flatly zero (as in an event of proton decay), but that doesn't mean that we should therefore set the probability of R on B [Pr(R|B)] to be equal to zero.[1] So frequencies won't work in the context of Bayes’ Theorem.

How we assess the intrinsic probability of Jesus’ resurrection on the background information is going to depend, I think, critically on how Jesus’ resurrection is characterized. The hypothesis “Jesus rose from the dead” is ambiguous. It actually comprises two radically different hypotheses. One is the hypothesis “Jesus rose naturally from the dead” (that this is a purely natural event); the other hypothesis would be that “Jesus rose supernaturally from the dead” (or in other words, “God raised Jesus from the dead”). The naturalistic hypothesis “Jesus rose naturally from the dead” is admitted on all hands to be outrageously improbable. Given what we know of cell necrosis, when someone dies, it is fantastically, even unimaginably, improbable that all of the cells in his body would spontaneously come back to life again. Conspiracy theories, apparent death theories, hallucination theories, twin brother theories – virtually any hypothesis, however unlikely, would be more probable than the hypothesis that all of the cells in Jesus’ corpse spontaneously came back to life again. Therefore, that improbability will significantly lower the probability of the hypothesis “Jesus rose from the dead” because that probability will be a function of its two component hypotheses, the one natural and the other supernatural. The improbability of the natural hypothesis will therefore drag down the probability of the hypothesis “Jesus rose from the dead,” which is not what we're interested in really. We're interested in the supernatural hypothesis – that “God raised Jesus from the dead.” The evidence for the laws of nature which renders the hypothesis improbable that Jesus rose naturally from the dead is simply irrelevant to the probability God raised Jesus from the dead. Since our interest is in this supernatural hypothesis, we can assess this hypothesis on its own without having to include the hypothesis that Jesus rose naturally from the dead.

So let's let R represent the hypothesis “God raised Jesus from the dead.” What is the intrinsic probability of that hypothesis on the background information [Pr(R|B)]?

Let's consider the supernatural hypothesis that God raised Jesus from the dead and ask: is that improbable relative to the background information?

When we ask that question, if we let G represent God's existence, and B as before be the background information, and R the hypothesis “God raised Jesus from the dead,” then the Theorem on Total Probability enables us to say that the probability of the resurrection on the background information alone is equal to the sum of two products:

Pr(R|B) = Pr(R|G&B) ☓ Pr(G|B) + Pr(R|not-G&B) ☓ Pr(not-G|B)

First, the probability of the resurrection given God and the background information times the probability of God's existence on the background information. Second, add the probability of the resurrection given no God and the background information times the probability of no God on the background information. So, in order to calculate the probability of the resurrection on the background information, we ask what is the probability of the resurrection given that God exists and our background information and what is the intrinsic probability of God's existence on the background information? And then you compute the probability of the resurrection given atheism and the background information and the probability that atheism is true given the background information.

How we assess the probability of God on the background information is going to depend on whether or not our background information B includes the facts that support the arguments of natural theology for God's existence such as the origin of the universe, the fine-tuning of the universe for intelligent life, the objectivity of moral values and duties in the world, and so on and so forth. If B does not include those facts, then the probability of God's existence on the background information will be a lot lower than if it does include those facts. In that case, the evidence E for the resurrection will also have to carry the full weight of proving God's existence and not just justifying belief in the resurrection.

As we've seen, the classical defenders of miracles did not treat miracles as evidence for God's existence; rather for them God's existence was taken to be implied by facts already included in B. So I suggest that we include in B all of the facts that support the premises in the arguments of natural theology like the origin of the universe, the fine-tuning of the universe, the objectivity of moral values and duties, and so forth. On this basis let's ask how probable is God's existence on this background information [Pr(G|B)]? Well, let's be conservative and say here that the probability of God's existence on the background information is only 0.5. You know that I think it's a lot higher than that on the basis of my defense of these arguments, but let's say on the basis of the background information alone it's a 50/50 chance that God exists. So we'll assign a probability of 50% to God's existence on the background information. The other probability that needs to be assessed is the probability of the resurrection given God's existence and the background information [Pr(R|G&B)]. Notice something here. What is the probability that God raised Jesus from the dead if God does not exist [Pr(R|not-G&B)]? It's 0, isn't it! If God does not exist, then the probability that God raised Jesus from the dead is 0, and since 0 times any number is 0, that cancels out the second half of the equation. That sum will just be adding 0. So the probability of the resurrection on the background information reduces to just these two figures – the intrinsic probability of God's existence on the background information [Pr(G|B)] and the probability that if God exists that he would raise Jesus from the dead [Pr(R|G&B)]. We can think of this probability as the degree of expectation that a perfectly rational agent would have, given that God exists and the background information, that God would raise Jesus from the dead. What is the expectation that God would raise Jesus from the dead if God exists and the background information is as it is?

Well, God has never before intervened to do such a thing in history as far as we know, and there are certainly other ways that he could vindicate Jesus, if he wanted to, even if he did want to. So how would a perfectly rational agent assess the risk of betting in this case that, given G and B, God would raise Jesus from the dead? What are you willing to gamble on that probability? This question has been called the problem of divine psychology – how do we know what God would do? Once again, I think that the religio-historical context is crucial in assessing this probability. In estimating the probability that given God's existence and the background information that God would raise Jesus from the dead, we mustn't abstract from the historical context of Jesus’ own life, ministry, and teaching, insofar as these are included in our background knowledge. If we include in B our knowledge of the life of the historical Jesus up until the time of his crucifixion and burial, then I don't think that we can say that God's raising Jesus from the dead is so improbable. Let's just say, for the sake of illustration, that the odds are 50/50 that God would raise Jesus from the dead. In that case, 50% times 50% is 25%, or the intrinsic probability of the resurrection on the background information is 1 out of 4. That certainly is easily overcome by the other factors in Bayes’ Theorem – the greater explanatory probability of the resurrection hypothesis. Therefore, I think this intrinsic improbability of the resurrection is easily overcome by the other factors that we talked about in Bayes’ Theorem.

I, in fact, think that it's impossible to assign numerical values to a probability like the resurrection on God and the background information [Pr(R|G&B)] with any sort of confidence. We don't have access to divine psychology. So I don't think we can really assign specific numerical values to these probabilities. I would say that these probabilities are, in the end, inscrutable; that is to say, you just put a question mark at that point in Bayes’ Theorem. These probabilities are not discernible by us. The difficulty in assigning numerical values is that we're dealing here with a free agent, namely, the Creator of the universe. How do we know what he would do with respect to Jesus? But I think what we can say is that there is no reason to think that the probability of R on God and the background information is terribly low. I don't see any reason to think that that probability is terribly low, as Hume claims, so that the probability of the resurrection on the background information alone would become overwhelmingly improbable. We certainly cannot take the probability of the resurrection on God and the background information to be terribly low simply because of the infrequency of resurrections. Think about it – it may be precisely because the resurrection is unique that it is highly probable that God would choose it as a spectacular way of vindicating his Son’s claims for which he was crucified. So it might actually be the very infrequency of resurrection-type events that makes it so highly probable that God would raise Jesus from the dead given God's existence and the background information.

By way of summary, in conclusion, I think it's evident that there really is no “in principle” argument here against the identification of a miracle. Rather what will be at stake, as the example of Jesus’ resurrection illustrates, is an “in fact” argument that handles an alleged miracle claim in its historical context, given the evidence for God's existence. So the skeptic has failed to show that any possible miracle claim has an intolerably low intrinsic probability. You couple that result with our earlier conclusion that even incredibly low intrinsic probabilities can be outweighed by other factors in Bayes’ Theorem, and I think it's evident why contemporary philosophers have come to see Hume’s in principle argument as an abject failure. [2]