Daily Archives: March 9, 2012

Bayes’ Theorem and the Existence of God, Part 1

So in my previous post on why I’m not a Christian, I left the question of god’s existence out of the critique. This post can probably be seen as an appendix that addresses the question of god’s, specifically the Christian god’s, existence.

Many religious believers think that the probability of their god’s existence is high. I thought I would attempt to see what would happen after I compiled all of the usual suspects classified as “evidence for god” and see what that does to an assumed high prior probability of god’s existence. Throughout this post, I’ll assume that the “god” here is the typical Abrahamic god of your average Christian. So I won’t be questioning the “god” of Taoism, or Buddhist Devas, the Hindu god(s), or various Native American gods, Cargo Cults, etc. but only the common conception (i.e. not the god of the sophisticated theologians, which is basically the god of the philosophers) of the Christian god.

Religious Experiences

Like I said, I’m going to assume that the prior probability of god is high. Let’s assume 97.7%, or .977 (the percentage of the world population that believes in god). How does the evidence from religious experiences, or the more general “experiences a person can’t explain”, weigh on the prior probability of god’s existence? Or, what is the success rate and false positive rate for religious experiences correlating with the Christian god?

A quick glance at Wikipedia gives our stats for world religions:

Christianity: Approx. 2.1 billion or .33
Islam: Approx. 1.5 billion or .22
Buddhism: Approx. 500 million or .7
Hinduism: Approx. 1.0 billion or .152

This makes up about 5.1 billion, or 77% of the world’s population. The reason I picked the lower bounds was because self-identified atheists make up about 2.3% or .023 of the entire population. If I had picked the higher bounds this would have left only about .1% for not only professed atheists, but every other religion besides the big four listed there. Jewish people do not make up less than .1% of the population!

One problem I have is that not every single theist has had a religious experience. If every single theist did have a religious experience, then I could simply use the probability of being a theist, .977, with the probability of having a religious experience. This would make P(E) equal to P(H) and thus the success rate would be equal to the posterior probability.

What is the success rate then? The success rate, or the rate that religious experiences lead a person to Christianity (i.e. the Christian god) is low since only 33% of the population are Christians. And that would drag the prior probability of the Christian god from .977 to .33; religious experiences would actually be very bad evidence for the existence of the Christian god.

But not every single theist has had a religious experience, so this wouldn’t be a good way to go about doing a Bayesian update.

Another problem is if I assume that the rate of religious experiences of Christians is equal to the religious experiences of every other religion, this would make the success rate and the false positive rate equal, which makes the Likelihood Ratio 1. This would mean that religious experiences have no weight on the existence of the Christian god. Religious experiences would be an independent variable. It would be like saying that scientists demoting Pluto from a planet is responsible for me waking up late this morning.

To look at this another way, if I assume that religious experiences in general are extraordinary, then this shows what happens when we favor either group for success/false positive rate. Extraordinary religious experiences would be a low P(E). P(E) is just the denominator of Bayes’ which is P(E | H)*P(H) + P(E | ~H)*P(~H).

I already assumed a high prior probability for the Christian god so we have only two variables to play with. So if, for example, P(E) was .01 and Christians claim that their success rate is high like .99, then this in turn assumes that other religious believers never have religious experiences. It would make P(E | ~H) a literally impossibly low number in order to get the entire equation equal to .01.

Even if the false positive rate, P(E | ~H), or the rate of other religious believers besides Christians having religious experiences was zero, the success rate couldn’t be more than around .0101. Which is a negligible boost in prior probability.

So without having actual values for the number of Christians who have religious experiences and the numbers of the adherents of other religions having religious experiences, I can only either conclude that religious experiences are not evidence for the Christian god (statistical independence) or extremely horrible evidence for the Christian god that moves the prior from .977 to .33. I would lean towards the independence conclusion, because even atheists have religious experiences or experiences they can’t explain.

Tradition / Cultural Language

So we still have our prior probability of .977. For my definition of “tradition”, this is the fact that most people are theists because their parents, close family, immediate community, and most people who speak their native language are theists. So what flavor of theism a person is pretty much depends on their surrounding environment. Not every theist has had a religious experience, but just about all theists have family.

Our evidence in this case is “tradition”, which I defined in the second sentence above. Like I said, I don’t know what the numbers are for religious experiences, but for most people they’re Christian, Muslim, Hindi, etc. because that’s their cultural language. What is the probability that “cultural language” leads someone to the Christian god? Everyone is affected by cultural language so this would apply across the board.

The question then becomes: What is the success rate of deferring to cultural language for leading to the Christian god? Assuming that religious experiences account for .1 of the population of theists (since religious experiences are extraordinary), cultural language would account for the remaining .9 of theists.

This might be a false dichotomy though. If I’ve claimed that religious experiences account for .1 of conversions, and .9 is cultural language, are those the only two reasons that people become theists? I should probably add a buffer for other reasons I haven’t thought of (like actually being convinced by sophisticated Christian arguments, which in my estimation is more rare than religious experiences). So maybe I should adjust my .9 to something like .85 and have the remaining .05 go towards “everything else” or P(~E).

Then, in the case of cultural language, the Total Probability is .85 (i.e. approximately 85% of theists are so due to cultural language). This means that, in the case of cultural language, P(E | H) * P(H) + P(E | ~H) * P(~H) = .85. P(H) is still .977 and P(~H) is still .023. So we are back in the same position as before. What is P(E | H), or the rate that cultural language leads people to the Christian god? Out of the total population of Christians, how many are Christians due to cultural language? What is P(E | ~H), or the rate that cultural language leads people to some other god or atheism? Out of the total population of non-Christian theists, how many are non-Christian theists due to cultural language?

This seems to run into the same dilemma as before. If I try to assert a high P(E | H), or that the number of Christians that are Christian due to cultural language is higher than other religions, then it sucks up probability from P(E | ~H), which in turn makes P(~E | ~H) – the rate of “other” reasons leading to the other theisms – a high number. Similarly for the other way around; that a low number of Christians are only Christians due to cultural language (and thus a higher number for its compliment P(~E | H), which is the rate of “other” reasons besides religious experiences and cultural language). So it seems I’m stuck with independence again. P(E | H) in this case is equal to P(E | ~H).

It should also be noted that this situation happens with either low or high prior probability of the Christian god’s existence.

Essentially, both of the two above points are a major premise for John Loftus’ “Outsider Test For Faith”. Religious experiences and cultural language aren’t good indicators that you have actually landed on the correct faith. As a matter of fact, it seems as though religious experiences and cultural language have no necessary correlation with the correct religion. You would need some other evidence to support religion. And on the flip side of that, to the chagrin of some atheists, religious experiences and cultural language aren’t good evidence against the Christian god for the same reason. Evidence against would have to be any evidence that decreases the prior probability.

Think about it this way. Say some Christian “Sarah” has an experience she can’t explain, and then concludes “Jesus!”. Over in India, “Silvi” has an experience she can’t explain, and then concludes “Vishnu!”. Then over in Pakistan “Tamica” has an experience she can’t explain and then concludes “Allah!”. Does an experience you can’t explain, then, have a necessary relationship with landing on the correct religion, whatever that religion is? Nope. An experience you can’t explain seems to be more of a statement about the person who can’t explain it, and has no bearing on the truth of whatever religion they arrived at. Obviously, since an experience “you” can’t explain is logically a statement about you. So it makes sense that cultural language and religious experiences aren’t evidence for (or against) the existence of the Christian god.


Because I don’t want this to be a super long post as I continue adding all of the evidence for the Christian god’s existence (besides the original Christian claims I critiqued in my “Why I’m Not A Christian” post), I think I’ll stop here. I’ll make this part 1 of a couple of posts. Be on the lookout for part 2!

But so far not so good. The majority of the reasons why people are Christians seems to have no actual bearing on the existence of the Christian god. Next I’ll have to look at the last .05 of the actual things that convince Christians of the truth of Christianity and see if those arguments increase, decrease, or have no affect (i.e. are independent) on the prior probability. Arguments like morality, the anthropic principle, and maybe even some sophisticated theology.

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Posted by on March 9, 2012 in Bayes

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