## Tuesday, July 8, 2014

### More on Richard Dawkins' Circular Reasoning.

In line with our most recent post here at The Cumulative Case, which exposes Richard Dawkins' circular reasoning, there is a nice post from the Two Books Approach that discusses the same idea.  Below is the relevant excerpt from that post (But math-o-phobes beware: there is a dose of Bayesian inference!).  Enjoy!

[T]he 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.