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God and Rev. Bayes

Reality Check

Victor Stenger

Volume 17.2, June 2007

Bayes’ theorem (Thomas Bayes, d. 1761) provides a means for directly calculating the probability of a statement being true based on the available evidence. In a 2003 book, The Probability of God (New York: Three Rivers Press), Stephen Unwin attempted to calculate the probability that God exists.

Unwin’s result: 67 percent. Physicist Larry Ford (private communication) has examined Unwin’s calculation and made his own estimate using the same formula. Ford’s result: 10-17.

Here’s how the Bayesian method works. Let P(G) be the prior probability that a proposition G is true. Now, suppose we have some new evidence E. Let P(G|E) be the probability that G is true in light of the evidence E. Let P(E|G) be the probability that E is true if G is true and P(E|G*) be the probability that E is true if G is false. Then is it easy to prove that

Equation 1

This is Bayes’ Theorem. Let G be the proposition that God exists. Unwin rewrites (1) as

Equation 2

where

Equation 3

he calls the “divine indicator,” which represents how much more likely the evidence E would be if God exists compared with him not existing.

Unwin then puts in some numbers. He takes the prior probability of God existing, that is, the probability before any evidence is submitted, to be Pbefore=0.5. Then he introduces a series of six observations and estimates the divine indicator D for each. At each step he calculates a Pafter and equates that to Pbefore for the following step.

  1. The evidence for goodness, such as altruism: D=10 fi Pafter = 0.91.
  2. The evidence for moral evil, done by humans: D=0.5 fi Pafter =0.83.
  3. The evidence for natural evil (natural disasters): D=0.1 fi Pafter =0.33.
  4. The evidence for “intra-natural” miracles (successful prayers, etc.): D=2 fi Pafter =0.5.
  5. The evidence for “extra-natural” miracles (direct intervention by God in nature): D=1 fi Pafter = 0.5.
  6. The evidence for religious experience (feeling of awe, etc.): D=2 fi Pafter = 0.67.

Unwin then adds a boost based on faith raising the final probability of God to 0.95.

Now let’s look at Ford’s alternate estimate of these numbers. First he notes: “propositions that postulate existence have a far less than 50 percent chance of being correct.” That is in absence of any evidence or other reason for us to believe some entity exists, it is highly unlikely that it does. So the prior probability of God should be more like one in a million or less. So let’s take Pbefore =10-6.

With respect to the divine indicator, D, we must evaluate it for each kind of evidence. Taking miracles for example, P(E|G) is the probability of the observed evidence of miracles given God exists. We see no evidence of miracles, and since God should be producing them if he existed, this probability is small. On the other hand, the absence of evidence for miracles is just what we expect if there is no God, so P(E|G*) is near one. Consequently, the divine indicator based on the absence of evidence for miracles is D < 1.

Unwin exhibits the typical theistic fallacy that goodness can only come from God and assigns a high divine indicator D=10 for this. Ford points out that we should see a lot more goodness in the world than we do if God exists. So he assumes D=0.1.

Ford notes that the existence of both moral and natural evil in the world is evidence against God’s existence. Unwin seems to agree by assigning D-values less than one, but not sufficiently low to describe the true situation in which millions die or suffer needlessly each year from the evils of both humanity and nature. Ford’s values of D=0.01 and D=0.001 for moral and natural evil respectively, are far more reasonable.

Unwin thinks that miracles such as prayers being answered have been observed and so assigns a diving indicator D=2 to what he calls intra-natural miracles. However, the scientific fact is that the best, controlled experiments on intercessory prayer show no positive effects. These scientific results make Ford’s estimate of D=0.01 in better agreement with the data.

Unwin assigns D=1 for extra-natural miracles where God intervenes directly in nature. Since there is not a scintilla of evidence that God does this, including the fact that no miracle was required to bring the universe into existence, Ford’s estimate of D=0.1 for this property actually strikes me as far too generous.

Finally, there is no evidence that so-called religious experiences have any divine content. If they did, we would expect the people having them to return with information about reality that they could not have known before the experience. These “prophecies” could be tested scientifically to see of they came true. None ever have. So, instead of Unwin’s D=2, Ford’s D=0.01 is also more reasonable.

In any case, here is the summary of Ford’s calculation: Pbefore = 10-6.

  1. The evidence for goodness, such as altruism: D=0.1 fi Pafter =10-7.
  2. The evidence for moral evil, done by humans: D = 0.01 fi Pafter =10-9.
  3. The evidence for natural evil (natural disasters): D = 0.001 fi Pafter =10-12.
  4. The evidence for “intra-natural” miracles (successful prayers, etc.): D=0.01 fi Pafter =10-14.
  5. The evidence for “extra-natural” miracles (direct intervention by God in nature): D=0.1 fi Pafter =10-15.
  6. The evidence for religious experience (feeling of awe, etc.): D =0.01 fi Pafter =10-17.

Of course, many of you are likely to say this is a silly exercise, that the numbers used are a matter of taste and obvious prejudice. However, I think it is useful to go through it anyway. The mathematically challenged are often awed by any sort of quantitative calculation, which they are unable to evaluate, and are likely to view Unwin’s work as providing scientific support for their beliefs. It does no such thing. Unwin loses. If anything, his method demonstrates the high unlikelihood of God’s existence.

Victor Stenger

Victor J. Stenger is emeritus professor of physics and astronomy at the University of Hawaii and Visiting Fellow in Philosophy at the University of Colorado. His latest book is The Fallacy of Fine-Tuning: How the Universe is Not Designed for Humanity. His previous books include Not By Design, Physics and Psychics, The Unconscious Quantum, and Timeless Reality: Symmetry, Simplicity, and Multiple Universes.