What does the internet's greatest search engine, email technology's hottest spam filters, the location of a missing nuclear submarine (the USS Scorpion), the location of a missing H bomb, and a Presbyterian minister who lived in London in the mid 18th century all have in common?

A little mathematical theorem that took the name of its discoverer : Reverend Thomas Bayes. The theorem, known as Bayes Theorem, is making inroads in science, technology, philosophy ... and yes, apologetics.

Bayes Theorem allows one to calculate something known as a posterior probability. A posterior probability is a revised probability conditional on evidence and the likelihood of that evidence being observed in two competing hypotheses. In other words, it allows us to revise our belief (expressed as a probability) in light of evidence. That is why it has such a wide application. Apologetics certainly deals with evidence, likelihoods and degrees of belief.

For starters, Dr. Alvin Plantinga uses a Bayesian argument in his famous Evolutionary Argument Against Naturalism. Plantinga examines the probability of human cognitive faculties being reliable, given the theory that human cognitive faculties have been produced by evolution. I'll give you a hint: the probability of our cognitive faculties being reliable if evolution is true ... is low.

Dr. JP Moreland uses Bayes Theorem in his argument for design offered in The Creation Hypothesis. Moreland uses Bayes to calculate a positive posterior probability that a theistic designer likely exists. This blogger does a nice write up on Moreland's use of Bayes.

Then we have Dr. Robin Collins in his fine essay, God, Design, and Fine-Tuning. He applies Bayesian thinking in comparing two competing hypotheses: the atheist single-universe hypothesis versus the theistic universe hypothesis. Collins says,

"The prime principle of confirmation is a general principle of reasoning which tells us when some observation counts as evidence in favor of one hypothesis over another. Simply put, the principle says that whenever we are considering two competing hypotheses, an observation counts as evidence in favor of the hypothesis under which the observation has the highest probability (or is the least improbable). (Or, put slightly differently, the principle says that whenever we are considering two competing hypotheses, H1 and H2, an observation, O, counts as evidence in favor of H1 over H2 if O is more probable under H1 than it is under H2.) Moreover, the degree to which the evidence counts in favor of one hypothesis over another is proportional to the degree to which the observation is more probable under the one hypothesis than the other."What Dr. Collins is talking about are conditional probabilities given evidence : once again, Bayes is used to show how evidence favors one hypothesis versus another, and to what degree it supports one hypothesis over another. Good stuff.

Finally, we have the famous "Bart's Blunder" comment in the Craig-Ehrman debate. Craig shows that Ehrman makes probabilistic claims based on conditional probabilities, but makes an egregious error by failing to use Bayes Thereom to do it. Ehrman walks into a buzz saw. Perhaps if he had seen this blog post he could have avoided an embarrassing moment in his recent debate.

Bayes Theorem has done more than make Google's founders billionaires. It offers a compelling tool to use in your next apologetic encounter.

I have done a series on Bayes Theorem if you wish to learn more.