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 does the resurrection explain 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, and therefore 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 Jesus’ 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)]?

START DISCUSSION

Student: But of course this position requires that you believe there is a God.

Dr. Craig: The hypothesis will depend upon the probability that there is a God. That's right. I'll say something more about that momentarily. But you're right – that hypothesis will depend on the probability that God exists.

Student: I think that if Hume is convinced God does not exist then obviously he's going to say only natural explanations can be used.

Dr. Craig: Fair enough. That’s right. Hume did his duty and attacked arguments for the existence of God and tried to show that they are at best inconclusive. That's fair. That's right. But I think that what you're simply underlining here is the importance of doing our natural theology and making sure we have in our quiver some good arguments for God's existence.

Student: I'm wondering if Hume’s argument can be said to be still question-begging in another respect even if you adopt this sort of frequency interpretation of Hume. I think you pointed out the other week that our movements of the will, those would be miraculous in the sense that we’re immaterial agents and are interacting with the world and that's not something that the nature itself can produce.

Dr. Craig: I'm not sure the charge here to be made against Hume would be begging the question, but it would be that his view would imply determinism, wouldn't it? It would imply that we don't really have freedom of the will, and so he would have to acknowledge that as being an implication of the argument – that uniform experience is against miracles. He would have to say uniform experience is against free acts of the will as well.

Student: So that would still be question-begging in that respect, right? You're just assuming toward determinism from the outset and given libertarian freedom . . .

Dr. Craig: It’s kind of like an earlier question – I think it would just show that that's an implication of his view, but I think that he would probably willingly embrace that view and say that uniform experience is against this. Then you can challenge him just as someone might challenge him on saying: Wait a minute! Uniform experience is not against miracles. Look at Craig Keener's two-volume book on contemporary miracles in the world today. Keener's book is chock-full of stories about contemporary miracles for which there is in some cases very good evidence. So one might simply say that Hume is wrong here. It's not that he's begging the question, but that he's incorrect in thinking that up to the case under consideration uniform experience has been against miracles.

END DISCUSSION

We want to consider the resurrection hypothesis to be not that Jesus rose from the dead but that God raised Jesus from the dead. The reason is because the hypothesis “Jesus rose from the dead” is ambiguous – it has two sub-components, one of which is unimaginably improbable and that would drag down the probability of the overall hypothesis. So why not just leave that aside as irrelevant? 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 plus 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, which is what someone earlier was asking about (how probable is it that God exists?) And then you compute what is the probability of the resurrection given atheism and the background information and what is 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 generous 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.

START DISCUSSION

Student: In assessing the resurrection on the background information, I'm just wondering does G in this case represent the Christian God that we're talking about?

Dr. Craig: That would be question-begging.

Student: That’s what I thought.

Dr. Craig: This is the God of natural theology.

Student: So when we consider the resurrection on G and B, we have to consider just a deistic form of God.

Dr. Craig: I hate to put it that way. I would say a generic form because the deistic form excludes miracles, right? So what we want to say is that we, on the basis of our arguments of natural theology which are included in B (or the facts that support them are included in B) that there exists a first, uncaused, beginningless, timeless, spaceless, immaterial, enormously powerful creator of the universe who is the locus of absolute goodness. Plus we include the life and teachings and ministry of the historical Jesus up until the time of his crucifixion and burial. Then the question will be: what's the probability that God would raise Jesus from the dead?

Student: Does this probability require that we assess other religions in the same stroke?

Dr. Craig: I think so. For example, if you had a really good reason to believe that Islam is true then you would say the probability that he would raise Jesus from the dead is negligible because Allah wouldn't do such a thing. But, as I'll say in a minute, I don't think we have any good reason to think that the God of natural theology is identical with Allah or a deistic god or anything of that sort.

Student: OK. So you just made the problem a bit easier by assuming a lower value to make the problem of defining this exact probability easier.

Dr. Craig: I guess I’m just assigning 50% to say it's an even shot. We don't know – it's 50/50. And if that's the case it turns out that the intrinsic probability of the resurrection is one out of four which is not at all difficult to overcome. It shows that the probability of R on B is not this astronomically inconceivably low probability that Hume thinks it is. What would be inconceivably improbable would be this naturalistic hypothesis that Jesus rose naturally from the dead. Yes, I agree that that's astronomically improbable. But I can't see any good reason to think that the hypothesis “God raised Jesus from the dead” is improbable relative to our background information.

Student: I understand when it comes to actually arguing for the resurrection of Jesus you don't use Bayes’ Theorem. You use the inference to the best explanation because I think you've stated, How can we really figure out the exact numbers of probability to plug into the equations? That being said though, I'm curious – what's your take on Richard Swinburne's case? He uses Bayes’ Theorem.

Dr. Craig: I find it hard to believe. He's talking about one of the great living Christian philosophers today, Richard Swinburne, who was Professor of Philosophy at Oxford University until his retirement several years ago. Swinburne actually assigns numerical values to these factors in Bayes’ Theorem, and I think he comes up with a probability of the resurrection of Jesus of about 97% as I recall. Well, when I see that I just sort of roll my eyes and think, come on! You can't assign those kinds of specific values. But what we can do, I think, is to say there's no good reason to think that this probability is terribly low, and that's what Hume would need to show. Remember the burden of proof is on him to show that the probability of R on B is astronomically low. I can't think of any good reason to think that it would be.

Student: Since so much of the equation depends upon the background information, is it fair to say then it's not just Christ's life and claims, it would be broader or greater than that.

Dr. Craig: I want it to include all of natural theology as well. The background information, B, is everything apart from E, the specific evidence for the resurrection which includes basically the discovery of the empty tomb, the postmortem appearances, the origin of the disciples’ belief in Jesus’ resurrection. We are going to exclude those from B but then everything else is in.

Student: Would you include Old Testament predictions of a Messiah?

Dr. Craig: Sure. Why not?

Student: Would you include the whole . . . I mean when you weave the Bible together, it seems to me he was the result of an expectation that God promised through Abraham and so forth. Am I being fair to want to include that in the background or is that too much?

Dr. Craig: Although I think many people would want to know what is the independent value of those evidences for Christ rather than sort of rolling them into this, but, as I say, B can include everything apart from the specific evidence that is adduced in support of the resurrection hypothesis.

Student: I had a question about Hume. It's been a long time since I've read him, but in Against Miracles, of course as you pointed out, he says that the uniform experience of nature counts against miracles. What does he say . . . I know he makes a famous argument against the design argument for the existence of God – creating the universe – but what does he say about the origin of the universe and would that be an event that he could not say can be explained by the uniform experience of nature?

Dr. Craig: Which is the argument you're asking about?

Student: Would Hume acknowledge that the uniform experience of nature cannot explain the origin of the universe and that therefore the origin of the universe would be an event that might require some supernatural explanation. I know he argues against the design theory . . .

Dr. Craig: You're talking about the cosmological argument. Now this is very interesting because, of course, writing in the 1700s Hume had no evidence of the origin of the universe. There was no evidence that the universe had a beginning because this was during this Newtonian age in which the universe was thought to have existed from eternity past. So the question of an origin didn't arise. But – and here is something that few scholars about Hume seem to know or appreciate – if you look at Hume’s footnotes in his Enquiry Concerning Human Understanding, he admits that the idea of an infinite regress of events in time is a metaphysical absurdity and he says no man whose understanding is enlightened rather than corrupted by the natural sciences could ever assent to the idea of an infinite regress of events into the past, which implies the beginning of the universe. Now you conjoin that with Hume’s belief in the causal principle – he didn't think you could prove the causal principle, but he wrote to John Stewart, I never affirmed so absurd a proposition that an event might arise without a cause. He said, I just said that we don't know this by intuition or demonstration but through another source. So Hume actually believed in and affirmed both premises of the kalam cosmological argument that the universe began to exist and that whatever begins to exist has a cause. So I think he is actually, implicitly, committed to the existence of a transcendent creator of the beginning of the universe.

Student: So I guess if Hume were forced to admit that the origin of the universe is a miraculous event, that counts against the uniform experience of nature, would that undermine his case against the miracle of the resurrection?

Dr. Craig: It certainly would. If we try to apply his argument against miracles to the origin of the universe, he would probably say the same thing – that no amount of evidence could possibly establish the origin of the universe or that there was this miraculous event that occurred. Then we're right back to what we've already talked about – that that is question-begging, or presupposes a model of probability that doesn't work and that it neglects all of the factors in the probability calculus. So he wouldn't have a good basis for denying this, and he admits the two premises. If anyone is interested in seeing those quotations from Hume, it's in the article that I wrote on J. L. Mackie's refutation of the kalam cosmological argument which is on the Reasonable Faith website.[2] Mackie was a British philosopher at Oxford University who was very much in the mold of David Hume, and so in rebutting Mackie I also looked at what Hume had to say and was quite surprised to see that Hume actually affirms both of these premises to be true.

END DISCUSSION

As someone earlier indicated, 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.

START DISCUSSION

Student: I'm having a hard time understanding how these theorems can come about by these so-called philosophers. When we go back to the Bible, if we trust the Bible as being the Word of God, he not only tells us this is going to happen – the resurrection – Jesus tells us it's going to happen. So how do these philosophers come up with a theory that maybe it did, maybe it didn't, because we have actually documented words that it did happen. And there were a lot of people. Not just one, but there were a lot of people.

Dr. Craig: That's E. That’s the specific evidence, E, that we have. Right? And we're not talking here about the probability of R on B and E. We're talking about just the probability of R on the background information. You take away any of the evidence for the resurrection specifically – you leave it out of account – and just ask: what's the probability of the resurrection on the background information alone? Where E comes into the picture is that second factor in Bayes’ Theorem – how probable is the evidence given the resurrection of Jesus compared to how probable is that evidence given that Jesus did not rise from the dead? Which one explains the evidence better? That was the crucial factor neglected by Hume. He ignored that factor, and that invalidates his argument all on its own. But I want to claim as well that the resurrection of Jesus properly understood as this hypothesis “God raised Jesus from the dead” has not been shown to be astronomically improbable. I don't see any good reason to think that that hypothesis is terribly improbable.

Student: Well, I would say the probability is 100% (the resurrection did occur) or 0 (the resurrection did not occur). The evidence that we have.

Dr. Craig: Not based on the evidence. You might say . . . I'm not sure how you would assess that, but what we're talking about here is what is the probability that God raised Jesus from the dead given the empty tomb, the postmortem appearances, the origin of the disciples’ belief in his resurrection, plus our background information of the world. And I don't think anybody would say that that's 100%. Swinburne says 97%, which is pretty close, but nobody would say that based on historical evidence you arrive at absolute certainty. This is not mathematics. This is history, and that's not the way history works.

END DISCUSSION

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[3] have come to see Hume’s in principle argument as an abject failure.[4]