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# #691 Problem of Dwindling Probabilities

July 19, 2020
Q

Hi Dr. Craig,

My name is Bram Rawlings and I am 16 years old. I have been studying the resurrection evidence over quarantine. Richard Swineburne, in his book "The Resurrection of God Incarnate", mentioned that Alvin Plantiga criticized the historical argument because of the problem of "dwindling probabilities". I also came across an article by Tim McGrew responding to Plantiga. It is quite scary when the giant of Christian philosophy says that the historical argument for Jesus's resurrection is weak. Do you have a take on his objection? Thank you!

Bram

United States

## Dr. craig’s response

A

It is scary, Bram! I was very surprised when I first heard Plantinga enunciate this objection to historical apologetics for the fact of Jesus’ resurrection.

What is the problem of dwindling probabilities? Plantinga explains that an explanatory hypothesis like “God raised Jesus from the dead” is not just a single hypothesis. Rather you are also supposing that God exists, that God would want to reveal Himself in the world, that Jesus of Nazareth lived and made certain radical claims about himself, as well as that God raised him from the dead to vindicate those radical claims. This is really a series of hypotheses.

So suppose we want to calculate the probability of these hypotheses given the evidence and background information. First of all, you need to calculate the probability that God exists. After that you would need to calculate not only the probability that God exists but also the probability that God would want to reveal himself in the world. Then on top of that you need to calculate the probability that Jesus lived and made certain radical claims about himself. Finally, you need to figure in addition to these hypotheses the probability that God raised Jesus from the dead. The probability that all of these hypotheses are true is the product of all of the probabilities multiplied together. Plantinga says even if each one of these hypotheses has a very high probability – say, 90% – nevertheless as you multiply these probabilities together, the probability that they are all true dwindles. For 0.9 x 0.9 x 0.9 x 0.9 = .66. The probability gets smaller and smaller until finally it may turn out that you actually get to less than 50%. Your probability may turn out to be very small. As a result, the hypothesis of Jesus’ resurrection may turn out to be not very probable at all. So Plantinga doesn’t think that we should base our belief in Jesus’ resurrection on historical evidence.

Now at face value, there has got to be something the matter with this objection. Even if you don’t know where the mistake lies, you know that something has got to be wrong with it. For this objection wouldn’t undercut merely belief in the resurrection of Jesus; it would make it impossible to believe almost anything in history that was based upon a series of events. Let me give an example from physical science. In the constellation Cygnus, there is an object that astronomers call Cygnus X-1. Based upon the scientific evidence most astronomers think that it is very probable that Cygnus X-1 is a black hole. Now think about that hypothesis in terms of Plantinga’s problem of dwindling probabilities. The hypothesis is based first of all upon the probability of the so-called Copernican Principle, the principle that we occupy no special place in the universe. The Principle implies that the laws of nature that we experience are the same laws of nature that obtain and hold in the constellation Cygnus. If Cygnus’ laws of nature were totally different than our laws of nature, we couldn’t draw any kind of conclusion about Cygnus X-1. Second, we have to consider the probability of the General Theory of Relativity, since it is on the basis of this gravitational theory that black holes are predicted. Third, there is the probability that the x-ray eclipse that we observe in Cygnus X-1 is due to a companion object that is rotating around X-1 – another stellar object in this binary system that helps us to identify X-1. Fourth, we have to hypothesize on the basis of the orbit of this companion object that X-1 has a mass of around three to four times the sun. Fifth, based upon the flickering x-rays that are emitted from X-1, we have to hypothesize that the size of X-1 is about nine miles in diameter. Finally, we have to consider the probability that there is no other object that could cause these phenomena – for example, a neutron star, which is a stellar object which is highly compacted but is not a black hole. Even if every one of these hypotheses had a 90% probability, the overall probability would soon dwindle in exactly the same way Plantinga imagines, so that no scientist could ever reasonably conclude that Cygnus X-1 is probably a black hole. And yet most astronomers do think that it is probably a black hole. There has got to be something wrong with Plantinga’s argument or it would undermine both scientific and historical reasoning.

Fortunately, as you mention, Timothy McGrew, who is a Christian philosopher at Western Michigan, has pointed out what the fallacy is. The fallacy is that Plantinga mistakenly holds the evidence constant while he refines the hypothesis. But that is incorrect. When someone says that the probability of the existence of God is 90% given the evidence, he is talking just about the evidence that is relevant to God’s existence. In the theistic arguments I defend based on evidence for the origin of the universe, or the fine-tuning of the universe for intelligent life, or objective moral values in the world, or the ontological argument, none of those arguments appeals to evidence about Jesus or the Gospels. They appeal to certain general facts of experience such as moral facts or facts about the origin of the universe, and so forth. When we figure the probability that God exists and that He would want to reveal Himself, then we augment that initial evidence with a little more evidence. Similarly, when we ask what the probability is that God exists and would want to reveal Himself and Jesus existed, then we add yet more evidence. As long as the evidence keeps increasing as new hypotheses are considered, it doesn’t matter that the hypothesis is being further and further refined. Plantinga’s mistake was thinking that the evidence is held constant as additional hypotheses are considered. That’s not right. As the evidence accumulates, the probability of the conjunction of the hypotheses can actually increase! Given the additional evidence, the probability that God has raised Jesus from the dead could actually be greater than the earlier probability that God exists because we have added in all the extra evidence pertinent to the further hypotheses. Therefore, Plantinga’s objection based upon dwindling probabilities turns out to be misconceived.

In all fairness, Plantinga agreed with McGrew’s analysis and insisted that he was objecting merely to the way Swinburne had originally formulated his argument, which Plantinga thought was subject to the problem of dwindling probabilities. Swinburne in reply said that his intention was to offer a probability argument along McGrew’s lines.

- William Lane Craig