Computing the Probability of God

Computing the Probability of God October 19, 2017

probability of god

Have you heard of the Drake equation? It’s a simple product of seven values, and it attempts to compute the number of civilizations in our galaxy with whom radio communication might be possible.

Now that we have found clear evidence of planets around other stars, the equation is slightly more practical than when it was first proposed over a half-century ago, but it still demands reliable figures for factors we can now only guess at: the fraction of planets in the average solar system that could potentially support life, the fraction of those that produce life, that continue on to develop intelligent life, whose intelligent life develops technology, and so on.

How likely is God?

We have a similar problem when we evaluate the claims of Christianity.

Physicist Stephen Unwin wrote The Probability of God (2004) and, yes, he proposes to compute the likelihood that God exists. He uses Bayes’ theorem (I wrote an introduction to Bayes’ theorem here). You can take his equation below as a given, or you can see how it is derived from a more conventional form of Bayes’ theorem in the appendix. You’ll soon see that the interesting part isn’t the math but the assumptions that Unwin makes.

Probability of God

We start with a beginning probability of God’s existence, Pbefore. Use a scaling factor D—Unwin’s “divine indicator,” which is a measure of the likelihood of God given certain evidence—we compute Pafter. Unwin uses values of D from 10 (given a particular bit of evidence, God is much more likely to exist than not) to 0.1 (given this evidence, God is much less likely to exist).

Once he has a new probability Pafter, he uses that value as his new Pbefore and repeats the computation with another value of D, reflecting the likelihood of God given another piece of evidence. The computation is quite simple. The unreliable part, as with the Drake equation, is determining the probabilities.

Unwinding Unwin

We need an initial probability—the likelihood of God given no evidence. Unwin uses Pbefore = 0.5 and calls this “maximum ignorance.”

His first bit of evidence is evidence for human goodness. For this, he uses D = 10 (God is much likelier given that human goodness exists). Plug in the numbers, and the equation gives Pafter = 0.91. The equation simply provides a way to merge these different factors into a single probability for God. Here are his six factors with their associated D values:

  • Human goodness, such as altruism (D = 10)
  • Existence of moral evil—that is, evil done by humans (D = 0.5)
  • Existence of natural evil such as natural disasters (D = 0.1)
  • Minor miracles such as answered prayers (D = 2)
  • Major miracles that break the rules—a dead person brought back to life, for example (D = 1)
  • Evidence of religious experience such as feelings of awe (D = 2)

And after all that, the probability of God is 0.67. God is likelier to exist than not.

It’s math! How you gonna disagree with that?

(Let me note that I haven’t read Unwin’s book but instead have relied on helpful critiques by Vic Stenger and The Friendly Atheist.)

I take exception to Unwin’s assumptions. First, let’s revisit our starting probability about God. Does Zeus exist? Thor? Osiris? Shiva? Quetzalcoatl? If the answer is “Are you serious? Of course not!” then why do we start with a 0.5 probability for Yahweh, especially when he looks like just another Canaanite god?

If Unwin wants to dismiss this information at the starting gate, I can accept that. But then let’s add it in as a new factor:

  • Humans have a passion for inventing supernatural gods. Believers make contradictory claims, so most of these claims must be false. Yahweh looks like just one invented god. (D = .001)

Next, let’s reevaluate Unwin’s six factors.

  • Goodness: Altruism exists in humans. This isn’t surprising since we’re social animals. Evolution has selected us with an innate sense of the Golden Rule. The Christian view also explains good traits in humans, so this gives no preference either way. (D = 1)
  • Moral evil: Humans do terrible things sometimes, and the natural explanation has no trouble with this. But Man made in God’s image with an innate sense of God’s existence? The popular free will defense fails. No, this Christian claim maps poorly to the unpleasant reality. (D = 0.01)
  • Natural evil: Indiscriminate killers like natural disasters, disease, and other calamities—things that an omnipotent God could eliminate—are hard for Christianity to explain. Birth defects and other gratuitous evil compound the problem. (D = 0.0001)
  • Miracles: The Bible says, “Ask and ye shall receive,” but prayers aren’t answered the way the Bible promises, not even the selfless ones. Coincidences abound, but we have little besides wishful thinking to imagine that they are the work of God. (D = 0.001)
  • Rule-breaking miracles: Jesus promised, “Whoever believes in me will do the works I have been doing, and they will do even greater things than these,” but science knows of zero amputated limbs that have grown back or dead people supernaturally returned to life. Surely there have been millions of earnest prayers for these, but they have been unanswered. (D = 0.0001)
  • Religious experience: We feel awe in response to both natural realities and supernatural claims. (D = 1)

The probability is now down to 10–16, but we’re just getting started. There are lots more uncomfortable facts about Christianity.

Piling on: more factors to consider

The probability of God is now basically zero (10–38 if you’re keeping score at home).

The apologist might demand equal time for the Transcendental Argument, the Design Argument, the Moral Argument, and so on. I don’t think they get out of the gate (click on the links for more).

The underlying problem with Unwin’s argument is that different people will weigh the factors differently. Clues for God’s existence aren’t unambiguous. I’m sure you thought that at least some of my numbers above were off, and you may have thought of other facts that have been overlooked. Nevertheless, the attempt to make the God question quantitative, interesting though it may be, seems hopeless.

The subtitle of Unwin’s book is A Simple Calculation That Proves the Ultimate Truth. Yes, it’s a simple calculation, but no, it doesn’t prove God. In fact, the evidence points in the opposite direction.

All Westboro [Baptist Church] was 
was evangelical Christianity minus polite behavior.
— Frank Shaeffer interview on Point of Inquiry

(This is an update of a post that originally appeared 04/09/14.)

Photo credit: Andy Melton, flickr, CC



Bayes’ theorem is easy to understand visually by using a probability tree. See my introductory post for a discussion of that. It’s less easy to understand (for me, anyway) through equations.

Here’s the derivation of the equation used by Unwin, starting with Bayes’ theorem. We’re computing P(G | E), the probability (P) of God existing (G) given (|) the evidence (E). Bayes’ theorem says:

Probability of God

where P(~G) is the probability of God not existing. Define D as follows:

Probability of God

D is Unwin’s “divine indicator,” the scaling factor that represents how likely the evidence E would be if God existed rather than God not existing. Now multiply top and bottom of Bayes’ equation by 1/P(E | ~G):

Probability of God

Since P(~G) = 1 – P(G),

Probability of God

Or, using the terminology of Unwin:

Probability of God

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