The Essential Equation of Theology

Most theological questions cannot be answered by direct observation. Some might be unknowable. Many require understanding an ancient language and culture that nobody fully understands. Nearly all involve uncertainty. They are matters of belief rather than knowledge. In other words, most theological questions require probabilistic answers. Unfortunately, the human brain is not very good at processing probability and uncertainty.

Fortunately, there is a practical solution: Bayes' theorem. It is a mathematically valid method to calculate probability when there is uncertainty in the data. The formula (color-coded to help you keep track of the terms) is:

 Where:

• P(H|E) is the probability that hypothesis H is true, given evidence E 
• P(E|H) is the probability that E would be observed if H is true
• P(H) is the prior probability that H is true, without considering E
• P(E|¬H) is the probability that E would be observed if H is not true

Bayes' theorem has important implications for theology. It suggests we should adjust our beliefs whenever we learn new evidence. It also implies that the way many of us interpret the data is wrong. Instead of asking "What (if anything) does the evidence prove?", which does not account for uncertainty and can lead to erroneous conclusions, Bayes' theorem implies that we should instead ask 3 questions:

1. P(H): What is the probability that our belief is true without considering the new evidence?
2. P(E|H): What is the probability that the new evidence would be what it is if our belief is true?
3. P(E|¬H): What is the probability that the new evidence would be what it is if our belief is not true?

The probability that the belief is true is adjusted whenever new evidence is considered. It increases if the answer to #2 is larger than the answer to #3 and decreases if #3 is larger than #2. If #2 and #3 are the same, the data (not really "evidence" in that case) does not move the original probability (#1).

Let's apply Bayes' theorem to a basic theological belief: "God exists". For this example, I'll define "God" only as a personal being who created the universe.


The first evidence to consider is that all relevant observations indicate that our universe had a beginning (which is the scientific consensus). To answer the 3 Bayesian questions:

1. P(H): A prior probability of 0% or 100% would be circular and would neglect uncertainty. 50% seems too high when no specific evidence has been considered yet, so I'll use 10%. It's somewhat arbitrary, but if enough evidence is considered, what we use for P(H) shouldn't matter.
2. P(E|H): If God is the creator of the universe, the probability is very high that the observations would indicate the universe had a beginning. I don't trust my mind enough to use probabilities above 95%, so I'll call it 95%.
3. P(E|¬H): If there is no God, this is a more difficult question with a high level of uncertainty. I can't go too high because it would seem to defy the First Law of Thermodynamics. However, I've heard some interesting theories that don't seem entirely implausible. I'll go with 25%.

Plugging into the equation, P(H|E) = 0.95*0.10/(0.95*0.10 + 0.25*(1-0.10)) = 0.297, the probability that God exists becomes approximately 29.7%.

Now let's consider negative evidence: the current lack of any direct observations of a God. The prior probability is now the previous result: 29.7%. If there is a God, a lack of any direct observations of him may or may not be probable, depending on what kind of God it is. I'll say 50%. If God does not exist, a lack of direct observation is almost certain. I'll again use my 95% rule. The result, P(H|E) = 0.50*0.297/(0.50*0.297 + 0.95*(1-0.297)) = 0.182, is an updated probability of 18.2%.

Finally, let's consider neutral evidence: religious writings contain apparent errors and contradictions. If God exists, it's still highly probable that religious writings would contain apparent errors and contradictions, whether real or perceived. P(E|H) = 90%. The same would be true if there is no God. P(E|¬H) = 90%. The result, P(H|E) = 0.90*0.182/(0.90*0.182 + 0.90*(1-0.182)) = 0.182, 18.2%, no change.

This process should be repeated until all data is considered.

There is much more (and in my opinion, much better) evidence to consider, but my point here is the thought process, not the numbers. We can disagree about what the numbers should be, but if that's what we're debating, we've come a long way. It would mean we're asking the right questions and analyzing the data in a way that properly accounts for uncertainty.