I was quite pleasantly surprised when I became a Christian to find that there is a great deal of rational and logical analysis in Christian theology. Reading or listening to people like NT Wright or John Walton is not at all different in this regard from listening to a good physicist describe evidence for a theory. How far can we go in the application of logical tools to issues in theology? Let’s find out.

We can consider some theological ideas in terms of probability. Probability notation describes the likelihood of something happening. For almost all applications of probability theory, that likelihood is unknown and is somewhere 0 and 1.

Sometimes the use of probability is extended to truth statements, which are binary – they are either true or false. This allows us to include all statements under the general umbrella of probability. In this way, we can define three categories of probability P. P = 1 is a statement of certainty of truth, while P = 0 is a statement of certainty of falsehood or impossibility. For P = anything else (0<P<1), we have a statement of uncertainty.

As examples, the probability that the USA is a nation, P(the United States exists as a nation) = 1. That is a statement of certain truth.  P(the moon is made of jello) = 0. That is a statement known to be factually false. But for many interesting questions, like what is the probability that the stock market will rise in value tomorrow?  P(the stock market will rise tomorrow) >0, <1. For some things, we can calculate the probability – for example, we know the probability that a flipped coin will land on heads  is P(heads) = 0.5. This still doesn’t tell us how a particular coin toss will turn out, but it does tell us the likelihood of getting a head.

How does belief connect with probability? We have free will to believe in anything. We can believe in God, in Allah, in Christ, in aliens, in conspiracy theories, in a flat earth, or that we are Napoleon. However, there are limits to belief. It is not possible to believe that something is true if the P = 0, nor is it possible to believe that something is false if the P = 1. Such beliefs might claim to be held by some people, but this is the definition of insanity. For example a belief that you are in fact a dead historical figure like Napoleon violates the impossibility of believing that something with P = 0 (which is the P that you are in fact Napoleon) can be true.

As a corollary, it also makes no sense to say that we believe in things that are factually true. It doesn’t make sense to say “I believe in the existence of France”, unless of course, we were in a period where the existence of France as a nation were not a certainty.  We do not have the freedom to believe that the IRS exists, because we know that “the IRS exists” is a demonstrably true statement.

However, the exercise of free will does apply  to when it comes to belief in a statement for which P is greater than 0 and less than 1.  For example, we have free will to believe that God exists (or not) because P(God exists) > 0, but < 1. I know of no proof that God exists or does not exist. Atheists are fond of saying that there is no evidence for God’s existence, which may or may not be true, but it doesn’t matter, because evidence does not prove a proposition, and lack of evidence does not disprove it.

Since the probability of the existence of God is neither 1 nor 0, belief in God is subject to free will. Turned around, if we assume that belief in God is always subject to free will, then P for God’s existence can never be 1 or 0, meaning that God’s existence can never be proven to be true or false. What this is saying is that if free will exists, the existence of God can never be proven beyond doubt. If it were, then only insane people could not believe (or believe) in God, and therefore there could be no free will to believe. If our theology requires free will, which it does, then the existence of God cannot ever be proven.

We can use evidence for God’s existence (some of it scientific, some not) to allow us to assume that that P is large. This evidence can allow us to feel comfortable with the assumption that God exists. The more evidence for or pointers to God’s existence, the more likely it is that God exists. But there will always be room for doubt – there MUST be room for doubt. While there are pointers that increase the P of God (such as the fine tuning of the physical constants), it is to be expected (and welcomed) that atheists can find ways to demonstrate that such evidence is not conclusive and that alternative theories, such as the multiverse, are at least possible.

These alternatives allow an element of doubt and therefore allow free will to remain a reality. The same arguments apply to any attempt to scientifically prove the existence of the Creator. So that when some creationists say that life’s diversity is proof of God, because there is no other way to account for it, they are trying to prove the wrong thing. If they were successful, they would have destroyed the possibility of doubt, and with it, free will. God’s gifts to us of faith and freedom are precious. So is His gift of reason and logic. Let us not hesitate to accept them all with gratitude and humility.