Bradley Bowen has recently argued that it is highly improbable that God raised Jesus from the dead (See Why I Reject the Resurrection – Part 3: Improbability of the Resurrection). According to Bowen, the improbability of the resurrection is one of the reasons why he rejects the resurrection. Let H denote the hypothesis that God raised Jesus from the dead. Now, why does Bowen think H is improbable? Well, because when we multiply the probabilities of the following propositions, which are (allegedly) assumed or implied by H, we arrive at a small probability:
- (E1) God exists.
- (E2) God has performed miracles.
- (E3) Jesus was a Jewish man who existed in Palestine in the first century.
- (E4) Jesus was crucified in Jerusalem in about 30 CE.
- (E5) Jesus died on the cross on the same day he was crucified.
- (E6) Jesus was alive and walking around in Jerusalem about 48 hours after he was crucified.
- (E7) Jesus rose from the dead.
Bowen maintains that “we must in general multiply probabilities of individual events to obtain the probability of a complex event” (original emphasis). Consequently, even if E1 to E7 have high probabilities, when multiplied they amount to a small probability. For example, let each proposition above have the high probability of 0.8, then, according to Bowen, we should multiply them to arrive at the probability of H:
0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 = 0.2097
Accordingly, H is highly improbable (indeed, its probability is 0.2097!) even if E1 to E7 are each highly probable; or at least that is what Bowen argues.
What should we think of this? Well, Bowen’s argument is an example of what happens when a blogger who is untrained in probabilistic logic tries their hand at probability. When trying to determine the probability of some hypothesis H, one does not multiply the probabilities of the propositions implied by H. This is simply not how it is done. Indeed, if it were done this way, most hypotheses would be improbable. To illustrate this, consider the following example.
Suppose we find Jones lying dead in his house. Let H2 be the hypothesis that the butler murdered Jones. Now, H2 implies the following propositions:
- (B1) The butler exists.
- (B2) The butler is a murderer.
- (B3) The butler has the ability to overpower Jones and kill him.
- (B4) The butler had/has a reason for wanting Jones dead.
- (B5) Jones was murdered, as opposed to having a deadly accident.
Let’s assign a high probability to these propositions respectively as follows: 0.9, 0.6, 0.7, 0.8, 0.7. If we follow Bowen’s line of reasoning, we should calculate the probability of H2 like this:
0.9 x 0.6 x 0.7 x 0.8 x 0.7 = 0.21168
Consequently, the probability of H2 is ~0.2, which is very improbable. At this point you can see that something has gone horribly wrong. This is not how we determine probabilities. Since B1 to B5 are implied or form part of H2, we should not be concerned with them. Instead of focusing on what H2 entails we should focus on any evidence that affects the probability of H2. Such evidence could look something like this:
- (C1) The butler had a fight with Jones the day before Jones died.
- (C2) The butler was the only other person in the house when Jones died.
- (C3) The butler’s fingerprints are all over the brick that Jones’ head collided with.
We may now use Bayes’ Theorem to calculate the probability of H2. (By the way, Bowen does not seem to be aware of Bayes’ Theorem; it appears that he has come up with his own idea of how probabilities should be calculated.) Using the odds form of Bayes’ Theorem, our calculation would look something like this:
P(H2 | C1 & C2 & C3) / P(~H2 | C1 & C2 & C3) = [P(H2) / P(~H2)] x [P(C1 | H2) / P(C1 | ~H2)] x [P(C2 | H2) / P(C2 | ~H2)] x [P(C3 | H2) / P(C3 | ~H2)]
Interestingly, even if the probability of each C1 to C3 is low, together they raise the probability of H2. For example, let’s fill the equation with average probabilities:
(0.6 / 0.4) x (0.7 / 0.5) x (0.8 / 0.5) x (0.9 / 0.3) = 0.3024 / 0.03 = 30.24 / 3 = 10.8:1
In this case, the odds in favour of H2 is about 10:1 (ten to one), which converts to a probability of 0.9 (or 90%) for H2.
What this shows is that, contra Bowen, the various pieces of evidence in favour of the resurrection do not need to be very probable in order for them to cumulatively render the resurrection very probable.