In this essay, I’m going to take on a common claim that a form of narrow naturalism can rightly be called faith. The form of naturalism I have in mind is one that says for any given unexplained event, it is overwhelmingly likely that the real explanation will be a naturalistic one. So, for example, such a person would claim that something natural probably caused our universe via the Big Bang or other means. Or they would claim that something natural probably brought about the origin of life on this planet. These are events currently not explained by science, but the narrow naturalist is confident that science can one day explain them, if the opportunity actually presents itself.
I don’t want to get too mired in a discussion of what we may rightly call faith, so I’ll just consider whether that confidence in science’s explanatory capability is justified and to what extent it is justified. If the belief is very justified, say at a probability of 0.75 or higher, then I don’t think we can rightly call it faith under any definition except those that are too all encompassing to be useful.
What will be our method of determining this probability? You probably guessed it, if you’re a regular reader—Bayes’ Theorem! If you just read that and thought, “WTF is Bayes’ Theorem?” then you may want to start here, here, and here to see my attempts at instruction.
As a reminder, here is Bayes’ Theorem, and the sections below will attempt to replace these abstractions with real numbers so we can run the formula:
p(h|e.b) = p(h|b) x p(e|h.b) / [ p(h|b) x p(e|h.b) ] + [ p(~h|b) x p(e|~h.b) ]
Prior Probabilities: p(h│b) and p(~h│b)
To determine our prior probability, we’ll use Laplace’s Law of Succession. This offers a great advantage in determining our prior probability compared to situations that require more subjectivity. Laplace’s Law is p = (r + 1) / (n + 2) where r is the number of times in past trials that an outcome has occurred and n is the total number of trials. I’ll give a quick explanation: If you were rolling a die that you knew was biased, but weren’t sure toward which number, you could test it by rolling it several times. Let’s say that the 6-side is rolled 47 times out of 100 rolls. The expected prior probability of rolling a six is 1/6, but on this particular die we see it’s 48/102 or simplified is 8/17. When you have past data, Laplace’s Law is a good way to provide an objective prior probability.
Now, in the case of naturalistic explanations, we have an extensive track record. In fact, everything that has ever been conclusively explained has been done so by a naturalistic process. This includes the birth of every person, the formation of rivers and mountains, diseases, genetics, the outcomes of wars, and on and on. All of these things used to be attributed to the acts of gods or other divine creatures, but are now understood as natural phenomena. This means that using Laplace’s Law, r and n are the same. This can quickly get out of hand because so many things have happened like these in the history of Earth. I’m going to limit my occurrences to 100 billion. That’s the number of people estimated to have ever lived. So, even if we were only counting the number of sneezes that have ever occurred, we would be justified in using this large of a number. If we run Laplace’s Law, we get a result of p(h│b) = 0.99999999999. This is the probability that our hypothesis of narrow naturalism is true given our background knowledge of history and science.
The other number we want here is simply derived from the previous number: p(~h│b) = 1 – p(h│b) = 0.00000000001. Now we have two of the four terms necessary to calculate an answer.
Consideration of Evidence: p(e│h.b) and p(e│~h.b)
We’ve just seen that prior to considering any particular example, like the Big Bang, naturalism has a significant statistical advantage in its potential to explain based on a strong track record. What this tells us is that even if we are very generous to the opponent (like a supernaturalist) in the consideration of evidence, h (narrow naturalism) should still come out as much more probable. So, let’s try and be generous so that no one can accuse me of bias. I’m going to offer three sets of possible numbers that stack the deck in favor of supernaturalism by making the likelihood of evidence given ~h way more probable than the likelihood of evidence given h.
p(e│h.b) = 0.01
p(e│~h.b) = 0.99
p(e│h.b) = 0.001
p(e│~h.b) = 0.999
p(e│h.b) = 0.0001
p(e│~h.b) = 0.9999
Now, we are able to solve for p (h│e.b), which stands for the probability our hypothesis of narrow naturalism is true given available evidence and background knowledge. I’m going to show the outcome for all three scenarios:
p (h│e.b) = 99.999999901%
p (h│e.b) = 99.9999990009999%
p (h│e.b) = 99.9999900010002%
Even in the best case scenario, the result of the confidence we should place in narrow naturalism being true given history is practically 100%. And that is with the likelihood of available evidence being 9,999 times more probable under supernaturalism!
Unless someone can start coming up with confirmed supernatural causes in the past (and it had better be a whole lot of them if they plan to make a dent in the probabilities), then narrow naturalism is incredibly well justified. To call this level of confidence faith is misleading at best, dishonest at worst.