Thursday, August 13, 2009

The Probability of God

I had a revelation this morning while I was swimming.

I had been thinking of something I read regarding a common atheist response to the anthropic principle (see my post from June 1). There is so much design apparent in the universe, it would be a monumental coincidence for all of this to happen by chance. But the atheists say that that does not prove God exists, because no matter how improbable our universe is, the statistical probability of God existing is even more remote. (Apparently, this is one of Richard Dawkins' arguments in The God Delusion; I haven't read it, but I was reading a book that critiqued it.)

The more I thought about it, the more absurd that argument seemed. First, my response was, "Who sez?" Or perhaps more eloquently, "How can you demonstrate that?" It seems to me that there is a fallacy of burden of proof here. After a statement like Dawkins', proponents of the Christian faith may be left sputtering, trying to figure out how to show that the probability of God existing is not as remote as Dawkins says it is. However, that is overlooking two things. First, perhaps Dawkins should be proving that it is remote, rather than the other way around. Looking at it that way, Dawkins' counterargument here to the anthropic principle seems to rest on an unprovable assumption. But even more intriguing is that this is a red herring fallacy as well. Simply saying that God, as an explanation for the improbability of this universe, is Himself improbable does not explain how we got here. It's just a negative argument against one explanation of how we got here. What we're left with in Dawkins' treatment of the situation is that we are here because we are here. Which doesn't answer any of the big questions at all.

So that's two logical fallacies Dawkins seems to be committing here. (And please forgive me if I'm not representing his case very well. I really should do my homework before critiquing someone else's position.) First is shifting the burden of proof, and second is the red herring fallacy.

But it gets worse.

The second thing I realized this morning is that the statement "no matter how improbable this universe is by chance, the probability of God is even less" is tantamount to saying "the probability of God existing is zero." Think about it. The only non-negative number that is guaranteed to be smaller than all positive numbers is zero. This is quite a strong statement. It goes far beyond saying God doesn't exist. It says that God cannot exist. In other words, Dawkins is using an assumption that God cannot exist to try to prove that God does not exist. It is a completely circular argument.

Here's another way to think about it, for the more math-oriented folks. In probability and statistics, the proof we're trying to make is something called a conditional probability. We see an improbable universe around us. What is the probability that God exists given we live in an improbable universe (ie, what's P(G|U))? Using Bayesian inference, we can easily come up with:

P(G|U) = P(G)/(epsilon + P(G)).

Here P(G) is the prior probability that God exists, and "epsilon" is the small chance that this universe came together by coincidence (all scientists would agree that epsilon is very small...something like 10^-50 or less). When doing Bayesian inference, you often have to bring in some a priori assumptions to assign prior probabilities (hence the name), so we have to guess at what P(G) is. But you never outright assume that P(G) is identically zero (or one). That would be the same as saying "no matter what our studies tell me, I will choose to believe X." (That's called blind faith.) Usually, when you don't know, you simply set your prior probabilities equal to 1/2. It's easy to see that P(G|U) (the probability that God exists given the universe we live in) would be extremely close to one for any reasonable choice of P(G). The only choice that makes P(G|U) small is P(G) = 0. Which is apparently what Dawkins wants to say.

Perhaps I'll write more on this later, but for now, I'd appreciate any comments.


  1. I am reminded of some modern forms of biblical criticism (i.e. the search for the historical Jesus or Jesus Seminar if you want to look them up). SOME biblical scholars (John Dominic Crossan, for example) start with the assumption that the New Testament is unreliable and that the sayings of Jesus are inauthentic. They have effectively shifted the burden of proof to the Christian community (thanks, Bultmann!). They use various criteria to get down to the "real" sayings of Jesus. The problem is that they prove some sayings are RELIABLE. If we can account for those sayings as being reliable, that seems to testify to ME that the rest of the New Testament stands a fair chance of being reliable as well:-) For example, one of the criteria is that a saying is "inauthentic" if it matches with the beliefs of the early church's community. That seems illogical and silly with me unless you ASSUME that the early church had NO connection with Jesus. If they had no connection with him, then it seems crazy that they claimed to be his followers and risked death for it. Ummm... or is it just me? They move Jesus out of his context in history and start with an assumption that influences their scholarship.

    My NT professor told me to just play their game and beat them at it. Hahaha. Should faith or disbelief should be the basis for our interpretation? What should mark the Christian community? Hmmm... Certainly, their method is wonderful for apologetics purposes, but as a community we have accepted Scripture as our authoritative text. It's not enough for me to simply throw out parts. I have to make sense of texts within the entire canon (collection) of Scripture. Critical methods help me learn about the background of texts and get at the author's original meaning. I'm not sure I want to set aside certain texts though. Certainly, their methods prove some sayings are "authentic," but I've seen nothing in the methods that can actually rule out the other sayings as "inauthentic." If anything, if some sayings can be proved authentic beyond a shadow of their doubt, then this should lend testimony to the fact that the ones they ruled out (as too similar to the early church or whatever) may also very well be authentic. They demand the burden of proof be put on conservative scholars though. Why should it? As I said, I appreciate their methods for apologetics reasons, but in the end, find it flawed. Skepticism or belief in biblical texts requires a faith commitment. The question simply is: What kind of faith commitment?

    As for the math, hmmm.... yeah... not my thing:-P

  2. That's a good analogy you drew there, Laura. I have heard this criticism of the Jesus Seminar from other scholars, but never actually read any of their work myself.

    I was /not/ aware that they actually proved some of his sayings as authentic. That's really interesting. Once you do that, in the face of the most stringent tests, I'll bet you find that there is less reason to believe that the other sayings are inauthentic. I guess you're right that it all comes down to two things: (1) burden of proof, and (2) challenging our unassailable assumptions.

    In the case of Dawkins, his unassailable assumption was that God cannot exist (whether he realized that or not). Apparently, the preconceived assumption on the part of the Jesus Seminar was the unreliability of the NT, or that Jesus was /not/ God incarnate. In both cases, we have wildly popular, yet fatally flawed, scholarship (if you can even call what Dawkins writes "scholarship").