Whenever we analyze the probability that some hypothesis is true, we have to know two things: how likely the hypothesis is apart from the evidence, how likely the evidence is if the hypothesis is true and how likely the evidence is if the hypothesis is false. From those things we can know how likely the hypothesis is in light of all our available information. I’ve written on this before.
Knowing how likely a hypothesis is apart from the evidence is certainly possible, and even necessary. For example, suppose that I take out a dice and roll it seven times. The numbers I roll are 1 – 2 – 6 – 5 – 3 – 6 – 1. Suppose that I come up with a hypothesis to explain this sequence: there are CIA agents using high – tech methods of influencing the dice’s roll, and the CIA agents wanted me to roll exactly that sequence of outcomes (1 – 2 – 6 – 5 – 3 – 6 – 1). This hypothesis would entail the evidence we have with 100% probability, whereas the hypothesis that the dice rolls resulted from various physical factors not controlled by anyone would only predict this sequence as 1 chance in 279,936 (the chance of each number is one out of six, and since there are seven numbers the total probability of this specific sequence winds up being one out of 279,936).
When it comes to predicting the evidence, the CIA hypothesis holds all the cards. However, the probability of this hypothesis apart from the evidence it predicts is sorely lacking. For example, our general knowledge about the world makes it absurdly improbable that CIA agents would want to do anything like this, and, moreover, we have no reason to suspect the CIA agents would want the sequence 1 – 2 – 6 – 5 – 3 – 6 – 1 instead of one of the 279,935 other possible outcomes. The prior probability of the CIA agent theory is so low that its evidence-predicting advantage just doesn’t save it, or even come close to saving it.
I say all that to say this: it has been a point of great contention in debates over Jesus’ resurrection what the prior probability is of God doing a miracle, or whether that even matters in the first place. For example, in the debate with Robert Greg Cavin, Mike Licona said that “If God exists and God wanted to raise Jesus from the dead, the probability would be 100%.” Right. And if the CIA exists and if they have high tech gear and can interfere with dice rolls and also want some exact sequence to come up, then it will. So what? Obviously, the real meat of the issue is whether God exists and whether God would want to raise Jesus from the dead. In order to have a case for the resurrection, you need not prove that the combination of these two things is highly probable. Nonetheless, you must be able to say something about the prior probability. Reason being that evidence-prediction isn’t enough all by itself, as the CIA agent example demonstrates. We must take into account both prior probability and evidential probability and compare it with known alternatives.
Don’t take my word for it though. Let’s look at what Christian experts on the subject have to say on the issue. Richard Swinburne, a philosopher who uses Bayes’ theorem, understands this and even attempts to argue the probability of both assumptions is high, see his book The Resurrection of of God Incarnate as well as in an article available online. See especially Swinburne’s comment in the linked article:
“So to determine whether Jesus rose from the dead, it is not enough to investigate whether what I have called the posterior historical evidence (what St. Paul and the Gospel writers wrote…) One must also investigate whether general background evidence supports the worldview that there is a God…And we must also investigate the prior historical evidence—that is, whether the nature and circumstances of the life of Jesus were such that if there is a God, he would be likely to raise this person from the dead.”
Timothy McGrew, another Christian philosopher who seems to have quite a bit of background knowledge in mathematics, makes a bayesian argument for Jesus’ resurrection and, for the sake of argument, he allows the prior probability of Jesus’ resurrection to be as low as one in ten to the fortieth power (see The Blackwell Companion to Natural Theology or the rough draft posted on Lydia McGrew’s website).
Swinburne deals with problem differently: he thinks he has demonstrated that God exists (I disagree, but that’s another story) and so estimates the prior probability of God’s existence at 50%, as a way of sort of “lowballing” the prior probability so that fewer people can take issue with it. Swinburne believes he can demonstrate that “if there was a God, he would be likely to raise Jesus” with at least 50% probability (see his arguments in his Philosophi Christi article) and so as he has it the prior probability of Jesus being raised is 25%. Swinburne’s argument for the latter isn’t too solid, and isn’t the kind of thing that would convince anyone who didn’t already believe Christianity. He argues something to the effect that ‘surely it would make sense for God to become incarnate and share in human suffering… Surely it would make sense that God would require atonement for sins… Surely it would make sense for God to raise himself from the dead to show that this atonement he made was accepted by himself…’ I’m not joking. This really is the gist of what Swinburne says. Read the linked article if you don’t believe it. My problem is that none of this seems objective at all. It’s just gut feelings of someone in the Christian religion, and the gut feelings he has. Other people have different gut feelings, and, moreover, I think that objective arguments can be made against the atonement-for-sin belief being completely wrong (see Ken Pulliam’s chapter in The End of Christianity).
VJ Torley, writing at Uncommon Descent, says the following:
“Sal Cordova points out that Cavin and Colombetti rely on a questionable assumption in their argument: they assume that if God made the laws of Nature, then those laws are immutable. Cordova offers a simple counter-example: ‘For example, I could write a computer program that spits out the number 3 every second, and then once a year it spits out 7.’ In a similar vein, the mathematician Charles Babbage… asked the reader to imagine a calculating engine that displays very predictable regularity for billions of iterations, such as a machine that counts integers. Then it suddenly jumps to another natural law, which again repeats itself with predictable regularity. If the designer of the engine had made it that way on purpose, argued Babbage, it would show even more intelligent design than a machine that merely continued counting integers forever. He concluded that miracles do not truly contravene the laws of Nature at a higher level…”
Let’s take the computer example: how would one be able to know that the computer program spit out a 7 once per year if it usually spit-out a 3? Well, if we knew the programmer and knew that he programmed it that way (or if we had some way of establishing independently of the evidence that he did). However, this analogy can’t be translated into the resurrection debate: we do not know apart from the evidence that God exists and that he programmed the laws of physics with an exception at Jesus’ death. It could be the case, but all that begs the question of how likely it is to be the case. Moreover, it would be entirely rational for someone watching the computer to predict a ‘3’ will show up next if that was all they had ever seen in the past (and, the observer would be completely correct in inferring “3” the vast majority of the time). Revising such a belief would only take place after incontrovertible evidence of a ‘7’ cropping up was obtained.
I would argue that the prior probability of the resurrection is incredibly low. The occurrence of miracles generally is not something reliably documented, whereas most people, I think, would readily admit that most occurrences in day to day life aren’t supernatural in nature. Moreover, we can be pretty sure that the overwhelming majority of miracle claims are false. And the exact nature of God seems difficult to determine a priori. After all, an agnostic on the matter would have no way of objectively saying which one of the many thousands of religious sects knows the true nature of God (or gods) assuming a God or gods exist in the first place. Any way we slice it, the prior probability of the resurrection is going to be extremely low, and therefore the evidence for it will have to be extremely good. Extraordinary claims require extraordinary evidence, and we don’t have it, as I have written on before.