In many arguments where evidence is either inconclusive or hard to come by, the question is raised as to which side has the burden of proof. In other words, if I claim that something is the case, do I have to support my claim, or do my opponents have to support the opposite, or is it neither, or is it both? Should one have to show evidence that God exists, or evidence that he doesn’t, or is the burden of proof lying equally on theists and atheists?

Assuming that I hold that X is true and that you hold that X is false, I would argue that:

• If both you and I agree on a system to assign probabilities to statements given evidence, then whoever holds that the least probable statement is true has to find evidence in order to boost that probability. The other doesn’t have to do a thing.
• If we cannot agree on such a system, then we need to find one that we agree on.
• But all systems that work behave in a roughly similar way, which I will describe further down.

Positive and negative statements

In my terminology, a positive statement is a claim that a particular state of affairs obtains. For instance, “there is a pen in front of me” is a positive statement. By contrast, a negative statement is a claim that a particular state of affairs does not obtain. For instance, “there is not a pen in front of me” is a negative statement, and in fact from any positive statement you can construct a negative statement, and vice versa.

Now, what I propose is this: in general, positive statements are false. Conversely, in general, negative statements are true. The argument behind this is as follows: first, the number of things that could possibly obtain is much, much larger than the set of things that do obtain. Consider that regardless of the size of the universe, the number of possible states it could take is exponential in it (and regardless of how infinite the universe is, the number of possible things it could contain, by diagonalization, can be shown to be even more infinite). It follows that only a measly percentage of all possible positive sentences can possibly obtain. Second, in absence of evidence, it does not make any sense to favor a proposition over another: if you were sequestrated in a dark room all your life, horses and unicorns are just as probable. It’s acceptable to organize probability systemically, for instance, with larger probabilities assigned to simple things, but nonetheless there is no way an arbitrary, particular idea about what the universe contains could be expected to be true without evidence. Since a negative statement is the negation of a positive statement, it follows that only a measly amount of them are false.

Example: theism vs. atheism

Let’s take a simple example: assuming that there is no evidence that he exists, how probable is it reasonable to think that God is? Well, if we define God as a “unique, sentient, omniscient, omnipotent, omnibenevolent being who created the universe”, then we’re already down to a probability of (100% / 32) = 3.125%. Indeed, there are 32 possible incompatible combinations of these attributes (assuming we keep “unique”). Maybe a “sentient, non-omniscient, omnipotent, non-omnibenevolent being who created the universe” exists. According to our definition, that is no God. Maybe it didn’t create the universe. Only one out of 32 possible combinations can be called a God, and there is no reason to consider it more probable than any other. Now, how many possibilities does atheism cover? Technically, it only denies that God exists, so it covers 31 of them. Any evidence put aside, blind atheism is thus correct with probability 97%.

Now, maybe you would say that atheism rejects all 32 of these possibilities, but that was a very rudimentary example and you’re missing the larger point. The point is that the concept of “God” or “supreme being” has some precise meaning that must be disambiguated against other, competing possibilities. You have to expend information to describe such a thing (say, in a dictionary), and that information could have been used to describe something else. But how many things can be described as succinctly as a supreme being? Many, many things, none of which are supreme beings. And the point is that unless you indulge in special pleading to boost a supreme being’s “probability”, that probability ought to be inversely proportional to that number. If I can describe ten unfalsifiable non-theistic possibilities, theism is already down to 10%.

In roughly the same time you take you describe “our universe, created by God”, I can describe “our universe, simulated on a computer in another universe”, or “our universe, run by a Turing machine on a Game of Life grid”, or “our universe, created by colliding space balls”, replacing the concept of God by whatever whimsical concept I can think of. An atheist only states that he or she rejects that our universe was created by God, and even though they might reject all the other things I mentioned, they also might not, because that’s beyond the scope of “atheism”. There is a staggering amount of possibilities that don’t involve a God at all and against which theism has to compete, and that’s a clear probability sink. That is why the existence of God is extremely unlikely, until evidence is shown that boosts its likelihood with respect to other things.

False dichotomies

The perception according to which theism is probable, or is assigned the very naive probability of 50% stems from a false dichotomy: basically, that God existing is one distinct possibility, and that God not existing is another distinct possibility. However, since it is a negation, atheism is much less informative than theism. Theism is a completely arbitrary statement about the state of affairs, which is widespread because it is reassuring and purports the existence of some higher being to relate with. That other arbitrary statements on the state of affairs are not made does not erase them from existence. The belief that the universe is all there is and the belief that our universe is a simulation in an external (real) universe are two non-theistic beliefs, both covered by atheism. So why would theism get 50% rather than 33%? What about all the ideas nobody thought about and probably never will? In order to assign a meaningful probability, you need a systematic account of possibilities, which naturally involves information theory: that way you can reason about what can be expressed, rather than about what is or isn’t expressed, which is always a very small subset.

Evidence and faith simply cannot be valued the same: evidence is the only way to have a good idea of what exists and what doesn’t with higher confidence than wild guesses, because evidence is what allows theories to rise from the probability hell they all live in. Faith, on the other hand, is mostly an emotional crutch: it allows you to believe in something pleasant or convenient without the trouble of gathering evidence for it. All statements should stand to the same standards of scrutiny, depending on how much information they give about the world – since most positive statements provide many bits of information (like trying to predict the lottery numbers) they are all very unlikely a priori. Negative statements, on the other hand, contain much less than a single bit (like saying your lottery numbers won’t come up – yeah, sure, that’s a pretty safe bet), and should be considered very likely a priori. Many people make the mistake of thinking there are only two numbers in the draw, because they can only count up to two.