PROBABILITIES

by Richard Packham


Believers like to use mathematical probability to support their insistence that, for instance, biological evolution is highly improbable, or that the existence of the universe is highly improbable without assuming an outside creator, or that events which they claim fulfill biblical prophecies were highly improbable events, making the prophecies much more impressive.

Typical of this approach is Peter Stoner, in his book Science Speaks, Moody Press, 1963, where he shows us the statistical method at work to impress us with the power and accuracy of biblical prophecies. Here are examples, cited from Stoner in Josh McDowell's Evidence That Demands A Verdict.

"The estimates for the probable fulfillment of these items [relating to] the Moab-Ammon prophecies were given as (1) 1 in 5 for the take-over by men of the east; (2) 1 in 10 [for] palaces in Ammon; (3) 1 in 20 [for the] return of the Moabites and Ammonites. This gives an estimate in the whole prophecy of 1 in 10^3 [1000]." Stoner, p. 92.

"The probabilities for the fulfillment of these different items [for the Edom prophecies] were estimated as follows: 1 in 10 [for Edom's being conquered]; (2) 1 in 10 [on the subsequent desolation]; (3) 1 in 100 [on never being reinhabited]. This gives a probability for the whole prophecy of 1 in 10^4 [1 in 10,000]. ibid.

Thus, to obtain the probability for the occurrence of any combination of events, you can take the probability for the occurrence of each of the individual events in the normal course of things, expressed as a ratio or fraction, and multiply them together.

Fundamentalists seem to place great trust in this method, and expect us all to be quite impressed.

It occurred to me that we could apply the same method to obtain a mathematically expressed probability that the Bible is 100% inerrant. That probability should be just as impressive to the inerrantists as the probabilities that they have calculated to support their position.

We could begin by taking any one of the many reports of events in the Bible which appear to be contradictory.

For instance, what is the probability of biblical inerrancy in its report of the fate of Judas Iscariot? Matthew 27:5 says that he hanged himself. Acts 1:18 says he died in a fall and "all his bowels gushed out." If we had only the Matthew version, we could start by saying that we will grant Matthew the benefit of the doubt as to this purely factual statement, since it seems reasonable enough, and say the chances of biblical inerrancy in this one instance, with this one report, was close to 1 in 1, that is, 100%.

Considering Matthew's reliability on the whole, however, we would have good reason to suspect (note that I did not say that we can prove it) that Matthew tends sometimes to be unreliable, and furthermore Matthew does not claim to have been an eyewitness to this event. On that basis we could say that maybe the chances of Matthew's being correct in this one fact - still considering Matthew alone - are less than 100%. But to avoid any accusation of weighing the probabilities unfairly, let us give him close to a 100% chance of being correct. Not 100%, but close. We could only give him 100% if his account were absolutely proven beyond any reasonable doubt, with independent, unbiased corroboration. Let us be generous and say we would accept his account of Judas' death with a 90% chance of its being correct.

Now we turn to Acts, supposedly authored by Luke. Let us give Luke the same consideration given to Matthew. Standing alone, there would be no reason to doubt Luke, and for the same consideration we would give him also a 90% chance of being correct, reduced somewhat from 100% because he was not an eyewitness to the event.

Here comes the problem. Considering both of them, of course, the probabilities of both of them being correct in their account, since they are inconsistent and contradictory, is very small. The probability that just one of them is correct is still a possibility, although to the extent the two accounts are inconsistent and contradictory, and neither is more reasonable, more believable, or more authenticated than the other makes us wonder if either of them is giving us a correct account. In a court of law, if two otherwise equally credible witnesses give diametrically opposed or conflicting testimony, the testimony of both must be disregarded. To be most generous, we must say that the chances that one of them is mistaken is fairly large, because the alternative is that both of them are correct in every detail.

Suggestions have been made by apologists to show how both accounts could be correct. Judas hanged himself, but the rope broke and he fell to the ground and his bowels gushed out. Although this is not beyond the realm of possibility, what are the chances that this is actually what happened? If both of the narrators had told the story this way, we could say the chances are close to 100%. But each of them leaves out an important element, and if we accept this combined version of events, then we are casting doubt on the fundamental completeness (and therefore reliability) of the narrators. The probability of there being such an explanation we will arbitrarily put at 1 in 10, and that is probably very generous. This probability, remember, is the probability that, based on this single reported event, the Bible is inerrant.

Now we will look at another apparent contradiction in order to build up to a total inerrancy probability. Our discussion can be much briefer here, because it follows the same general lines as the previous discussion. When and where did Jesus ascend into heaven? We have five reports of this event. Luke 24:13-51 reports it as occurring at Bethany, after his dining with the disciples in Jerusalem, which was the same day as his appearance to the two disciples on the road to Emmaeus three days after the crucifixion. Mark's account (16:14-19) is similar, but much more vague as to time and place; if we only had Mark's report, we couldn't be sure when and where it occurred.

John's gospel does not mention the ascension. Neither does Matthew, but he says that the eleven went into Galilee, where Jesus appeared to them (28:16-17), which must have been at least several days after the resurrection. It could not have been after the ascension. Acts 1:3-12 puts the ascension from Mt. Olivet forty days after his first appearance after the resurrection.

Two of our five reports ignore the ascension completely. The two reporters who ignore it are supposed to be just as credible and authoritative as the reporters who do mention it, according to believers. Why do they not mention it? The Athanasian Creed insists that the ascension is an essential element of Christian belief, and yet Matthew and John seem unaware of it or feel it not worth mentioning. In light of this anomaly, what is the probability that the ascension actually occurred? We will be generous and arbitrarily say that the probability that something important occurred when only three out of five equally reliable and knowledgeable reporters describe it, certainly cannot be much better than three in five.

But what about those who do report it? Acts is completely different from Luke and Mark, both in the location (Mt. Olivet vs. Bethany) and in the time (forty days after the first appearance vs. the same day as the first appearance). Can both reports be correct? And Matthew's mentioning an appearance (supposedly before the ascension - if it occurred) obviously later than the ascension described in Luke makes Luke's story doubtful. We will arbitrarily assign a probability that both Luke and Acts are correct on both time and place as one in 100.

Based on the facts reported about the ascension alone, then, we can calculate that the probability that the Bible is inerrant in the reporting of this event as 3/5 (the mere occurence of the ascension) times 1/100 (the likelihood that the two conflicting times and places are both correct), or 3/500.

We have analyzed and assigned (admittedly arbitrarily) probabilities to only two Biblical events and the probability that the Bible is inerrant as calculated from each of these two events: 1/10 for Judas' fate and 3/500 for the ascension. In order for the Bible to be inerrant, both of these events must have occurred as reported, so that the probability that the Bible is inerrant can be calculated, based on only these two events, as 1/10 times 3/500, or 3/5000.

There are hundreds of such problematical reports in the Bible, but the probabilities of each could be calculated in the same way, as we have learned from Stoner and other inerrrantists. If you were to take a hundred of such probabilities and multiplied them together, each having an average probability of, let us estimate, 1/10, you would end up with a total probability, based on those hundred unlikely inerrant reports alone, of 1 x 10^100, which, as lovers of such probabilities like to point out, is "a one with a hundred zeroes after it!" Since there are a great many more contradictions in the Bible than 100, the total probability would be even less.

I would think that nobody would like to bet his life (or his eternal salvation) on a book which has such an infinitesimal probability of being completely correct.

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©  1998 Richard Packham    Permission granted to reproduce for non-commercial purposes, provided text is not changed and this copyright notice is included

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