Extraordinary Claims Demand Extraordinary Evidence: Did William Lane Craig Make a Mistake Here?

William Lane Craig is a Christian apologist and philosopher, famous for his debates with atheists. I do enjoy his debates: even if you don’t agree with Craig (or the atheist he is debating), there is value in the debate itself. For me, what’s most important is that the issues are constantly laid out in clearer ways, and debate is an engaging way to do this.

But here I wonder about Craig’s response to the common atheist aphorism, “extraordinary claims demand extraordinary evidence.” His response is that the proverb would prevent us from accepting that a particular ticket won the lottery, as the probability of any single ticket winning the lottery is very low. For him, one cannot just consider the inherent probability of a claim, but how improbable the observations we observe regarding the claim would be if the claim weren’t true. In the case of the lottery, it would be very improbable that a winner would be announced on the media if, in fact, that winner didn’t really win the lottery. So in this case, even if the probability of that person winning the lottery is very low, we can accept that she won.

The same goes for miracles like Jesus’ resurrection. Resurrections are improbable, but the odds of our relevant observations (the empty tomb, the resurrection appearances, the disciples’ radical belief changes) would be very improbable if the resurrection didn’t take place. Thus Craig argues that we can accept that Jesus rose just as we can accept that the lucky lottery ticket holder won.

I don’t disagree with Craig’s claim that explanatory power, discussed in the previous two paragraphs, is just as important as inherent probability. But that doesn’t disprove the aphorism. In fact, it’s completely compatible with it. The aphorism allows for the accumulation of evidence, that is, explanatory power, to override initial skepticism. It only requires that the evidence be extraordinary.

What the aphorism claims is that we can’t just look at evidence for a claim, expecting that if an amount of evidence  is enough for one claim, it should be enough for every other claim. It points out that less inherently probable claims require more evidence that mundane claims. Claiming that I drove to work requires less evidence than the claim that I flew to work, using my arms as wings.

So here I think is where the real dispute is between Craig and skeptics. Skeptics think the inherent improbability of God’s existence or the resurrection of Jesus is so low as to require a very radical amount of evidence to overcome it. Atheists I’ve talked to or listened to online mention a universally observable breakdown of the natural order, something like what’s in the Book of Revelation, to meet the evidential burden: nothing less than that would suffice. That is, the skeptics focus on what they take to be low prior probabilities, generally seeing any currently attainable amount of evidence as insufficient. Craig, however, focuses on the explanatory power. But I think that both need to be considered.

One other note, skeptics do think God is very improbable; just as improbable as Zeus, Big Foot, or the Flying Spaghetti Monster. True, the last three are inherently improbable, but does that make God inherently improbable? That would depend on how similar God is to those things. I don’t see a great similarity. God is completely immaterial, while the last three are either unusual physical objects or physical objects embedded with divine characteristics. I don’t think you can compare them. So I would submit that God’s prior probability is unknown,  and not low.


Why Historians Reject the Resurrection of Jesus: It’s a Miracle

David Hume, a pillar of skepticism
David Hume, a pillar of skepticism

For a little background, check out this debate between Christian philosopher and apologist William Lane Craig and the skeptical historian Bart Ehrman. Craig argues that Jesus rose from the dead, claiming that God raising Jesus from the dead is the best explanation for these facts:

1. Jesus’ burial
2. the discovery of the empty tomb
3. his postmortem appearances (at least in the minds of the disciples)
4. the origin of the disciples’ belief in his resurrection

What is interesting is that in the debates against Craig, the core of the response of Craig’s opponents isn’t about disputing these facts (Richard Carrier was an exception — he believes that no useful historical information can be taken from the New Testament). Their main argument is that God’s raising Jesus from the dead (call this the Resurrection Hypothesis, or RH) is not historical because it is a miracle claim.

One might think that this is just anti-religious prejudice. But they do offer a philosophical argument for the prejudice. It’s the 18th century philosopher David Hume’s argument against belief in miracles (Ehrman in the above debate denies this, but his argument is pretty much a simplified version of Hume’s argument).

What is Hume’s argument? Here’s a quote:

When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle. If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till then, can he pretend to command my belief or opinion. (Hume 1748/2000: 87–88)

There is much dispute between Hume scholars about what this argument amounts to (see this article in the Stanford Encyclopedia of Philosophy). But let’s consider this question using probability theory.

I have two versions of what follows, hard, and easy. Here’s hard (skip if you don’t want to go through the math):

Consider one formulation of Bayes’ Theorem:

P(RH|E) = P(RH) × P(E|RH)/P(E)

I’ll describe what this means. RH = God raised Jesus from the dead. E is the evidence now under consideration (background information understood to be always there and is not included in the formula). P(RH) is the probability of RH just in itself, without considering the evidence at hand (This is called the “prior probability”). P(RH|E) is the probability of RH given E (the probability of RH given the evidence). P(E|RH) is the probability of the evidence occurring if RH is true. This term is about the explanatory power of RH — RH accounts for E if RH gives one reason to expect E. That is, if RH gives us reason to expect E, then E’s occurring is evidence for RH. Finally, P(E) is the probability of E just given the background information. It is to normalize the equation. There is also the intuition that P(E|RH), even if high, wouldn’t mean much if we would expect E to happen anyway. Thus we divide P(E|RH) by P(E).

My own view is that Hume’s argument amounts to this: P(RH) is extremely low. That is, the probability of a miracle occurring, given our background information (including all of science), is low, for miracles are, by definition, a violation of the regularities of experience. Thus all of experience stands against them. If that’s true, then P(E|RH)/P(E) would have to be extraordinarily high to compensate if the Resurrection is to have any real probability of happening. In the real world no one could supply such evidence.

Here’s easy:

Two main things go into how probable some statement is given the evidence. The first is how inherently likely the statement is, without considering evidence. Let’s call this the prior probability. The second is how much does the evidence support the statement. With miracles, skeptics, like Hume, argue that their prior probability is sooooo low that no amount of evidence can make them reasonable to accept. The Resurrection of Jesus is no exception. We could grant that the evidence does give some support for the claim, but still reject the claim because it’s so inherently unlikely. It’s like trying to prove that someone saw an alien. The evidence that would be enough for an ordinary event wouldn’t be enough for something extraordinary like the appearance of an alien. As atheists and skeptics often say, “Extraordinary claims demand extraordinary evidence.”

Back to the main topic:

Though skeptics might admit that natural alternative explanations of the data surrounding Jesus’ resurrection have so far been disappointing, they would insist that even the worst of these is better than the Resurrection (Ehrman was explicit about this), presumably because of the Resurrection’s low prior probability.

Craig admits that, just by itself, the Resurrection is very improbable. Craig asserts, however, that he isn’t arguing merely that Jesus rose from the dead, but that God raised Jesus from the dead.1 This latter statement, at first, seems to have a higher prior probability: God would have the power to do something that has no precedent in experience. A skeptic, however, could reply that adding God into the hypothesis makes it more complex, lowering the prior probability. The more ad hoc additions we make to a theory, the worse it is in terms of prior probability.

Notwithstanding, Craig spends most of his time arguing for a high value for P(E|RH)/P(E) (arguing that the evidence is well explained by the hypothesis) — he argues that the evidence given above is far more probable on the Resurrection than on any natural hypothesis. But all this falls on deaf ears because of the low value of P(RH) (low prior probability).

What can be said? I think that P(RH) (the Resurrection’s prior probability) is low given naturalism. Adding God to the hypothesis seems ad hoc. But what if we had independent evidence for God’s existence? If God exists, then, given His goodness and the evil in the world, we might expect some sort of action on his part to address this evil. In particular, we could expect some sort of revelation. And for us to know the revelation was from God, we might expect some sort of miracle to validate the revelation. So we would be expecting something like RH (the Resurrection Hypotheis).2 This wouldn’t show that Jesus rose from the dead, but it would mitigate the low prior probability for RH: God wouldn’t just be some add on, but something independently supported. Then evidence for the Resurrection could be taken more seriously.

Thus I think that the case for Jesus’ resurrection by God needs to be made as part of a comprehensive case for Christianity. This would include a case for God’s existence as the best way to account for all the data of our experience (including our apprehension of a realm of value, our experience of ourselves as immaterial beings, the existence and fine-tuning of the universe, etc). This is, of course, what Craig does in God debates. However, I don’t think it appropriate to use Jesus’ resurrection as evidence for God (as Craig does) simply because Jesus’ resurrection would only be the best explanation for the facts he presents as evidence if we already knew that God exits. It would be a circular (or pretty close to circular) argument. I would instead try to argue for God’s existence, then, if successful, use evidence for the Resurrection to support the truth of Christianity.

  1. Craig also denies that Bayes’ theorem is applicable to historical analysis, as these probabilities cannot be determined. See his debate with Greg Cavin here: https://www.youtube.com/watch?v=Rmxi9o_xqkc.
  2. Similar ideas are worked out in Richard Swinburne’s Revelation.