A SURVEY OF THE DIFFERENT RESURRECTION HYPOTHESES PART VI: PLANTINGA’S PRINCIPLE OF DWINDLING PROBABILITIES

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Click here to read Part III of this series.

Click here to read Part IV of this series.

Click here to read Part V of this series.

A somewhat different objection that should be examined comes from Alvin Plantinga, one of the greatest Christian philosophers. Alvin Plantinga has not been very sympathetic to historical apologetics. He prefers that belief in Christian claims, like the resurrection of Jesus, be rooted in the testimony given by the Holy Ghost rather than in historical evidence. When you read scripture, the Holy Ghost bears witness that something is true so that you can justifiably believe in it. Plantinga is skeptical about the value of historical apologetics for events like the resurrection. Why is this? He says that the historical apologist faces the “principle of dwindling probabilities” (PDP). This means that in order to establish something like the resurrection of Jesus, you first have to establish another list of claims and show that those are probable.

Dr. Alvin Plantinga

For example, suppose you want to establish that God raised Jesus from the dead. First, you are going to need to establish that God exists, and that will have a certain probability. Let’s be generous and suppose that it is 90% certain that God exists. In addition to that, you will need to establish that Jesus of Nazareth ever existed;  lets suppose that probability is 90%. The joint probability of those will be .90 x .90 = .81; still pretty high but lower than 90%. Then you also have to establish that Jesus made certain radical claims about Himself – that He claimed to be the Son of God. Maybe you can show that with 90% probability. What happens? As you multiply all of these, the probability gets smaller and smaller. After just seven steps of 90% probability, you are already going to be less than 50%. Which makes it less probable than not, that Jesus rose from the dead. So Plantinga thinks that the problem of dwindling probabilities is an obstruction for certain people like,  Dr. Richard Swinburne, to establish the probability of the resurrection hypothesis – that God raised Jesus from the dead. However, intuitively the PDP just doesn’t seem to be right.

If we did this with everything, the probability of anything actually occurring, that depended upon a sequence of events, would be close to 0%;  something just seems wrong with this argument. Let’s take an example from science. In the constellation Cygnus, there is an object that astronomers call X1. Most astronomers think that it is very probable that Cygnus X1 is a black hole. This is based upon the scientific evidence. Think about this in light of Plantinga’s PDP.

Cygnus X1 being a black hole is first based upon the Copernican principle. The Copernican principle is the principle that we hold no special place in the universe. That is to say that the laws of nature we experience are the same laws of nature that exist in the constellation Cygnus;  if the laws of nature regarding Cygnus were different than the ones we experience here on earth, then we could not make any kind of scientific conclusions about the universe. Secondly, we have to presuppose the Law of General Relativity. It is on the basis of the Law of General Relativity that black holes are predicted. Thirdly, the x-ray eclipse that we observe in Cygnus X1 is do to a companion object that is rotating around this object X1; a kind of other stellar object in this binary system that helps us identify it. Fourthly, we have to, based on the orbit of this companion object, assume that X1 has a mass of around 3-4 times the sun. Fifthly, we calculate that the size of X1 is about 9 miles across based upon the flickering x-rays that are emitted from X1. Finally, we have to consider the probability that there is no other object that could cause these sort of phenomenon; for example a neutron star which is highly compacted but is not a black hole.

Even if everyone of these had a 91% probability, you could see that the probability of Cygnus X1 existing would dwindle in the same way as the resurrection hypothesis, so that no scientist could ever conclude that Cygnus X1 was a black hole. Yet, most scientists do think it is a black hole. According to Plantinga, even the likelihood of us existing at all would be small. Think of all the things that have to occur for a person to exist. Yet we know that we are here despite the dwindling improbability.

Is the PDP the Same as the Probability in a Coin Toss?

It seems that the tossing of a coin argues against the PDP. Every time the coin is flipped, there is s 50/50 chance that the coin will land on heads and 50/50 chance it will land on tails. What is the probability on the next flip? The same; 50/50 heads and 50/50 tails. This does not change, regardless of how many times the coin is flipped. If you did this 15 times in a row, it would not influence the probability of the next flip.  Thinking that a previous coin toss will influence the following coin toss(es) is describing what is called “the gambler’s fallacy.”

The gambler’s fallacy is found in asking, if you are informed that someone has already flipped a coin nine times and has been heads nine times in a row, what is the probability of it being heads ten times in a row? Surely you think it is going to be tails. There already has been an improbable run of nine in a row. What is the probability the next one is going to be heads? It will still be 50%. It is not effected by what has gone on before. However, that is not what we are dealing with here with Plantinga. Plantinga does not commit the gambler’s fallacy.

With Plantinga, what we are asking here is, what is the probability of flipping a fair coin two times in a row and getting heads both times? To get that joint event, heads two times in a row, that is going to be .5 x 5 = .25. So you have a 25% of flipping heads two times in a row. However, one would be correct in saying that just because heads was flipped once, does not reduce the probability of heads being flipped the next time (that is the gambler’s fallacy). What Plantinga is asking is what is the probability of a joint occurrence of a series of events? When we apply Plantinga’s theory to everyday life , history, or to science, it seems that there has to be something wrong with Plantinga’s probability theory, or it would undermine both science and history.

Plantinga’s fallacy is that he mistakenly holds the evidence constant while he refines the hypothesis. When someone says the probability of the existence of God is 90%, given the evidence, he is speaking of the evidence just about God’s existence. When we say there is a probability that God exists and that He would want to reveal Himself, then we augment that evidence with a little bit more evidence. When we add to that, that Jesus existed, we add yet more evidence. For Plantiga, as long as the evidence keeps increasing, it doesn’t matter that the hypothesis is getting further and further refined. Plantinga’s mistake was thinking that the evidence is held constant. That is not right. As the evidence adds up,each new probability can actually be greater than the prior.  The reason being, you have added in all this extra evidence that would make it more probable. Therefore, Plantinga’s objection based upon dwindling probabilities turns out to be fallacious. It becomes evident that there is no “Principle of Dwindling Probabilities” that show the historical argument for the resurrection to be weak.

As asked at the end of the last post,  do these arguments make the resurrection highly probable? No.  But they do render it very unlikely to be improbable.   I believe though, a better approach to use in defending the resurrection is what is called, inference to the best explanation.

With this approach, you arrange the different competing hypotheses and then asses them in terms of certain criteria like:  explanatory power (which one best explains the evidence),  less ad-hoc,  explanatory scope (which one explains the fullest range of the evidence), and plausibility.  In each of these cases the resurrection has strong explanatory power, explanatory scope, less ad-hoc, and it is plausible (given Jesus’ radicle claims).

Next week we will examine inference to the best explanation

Miguel Barker-Valdez

Miguel is a Guatemalan-American Mormon living in the Northwest with his family. He is one of the proprietors of the Rational Faiths blog.

All posts by Miguel Barker-Valdez