Continuing my response to Carrier (here’s Part 1 and Part 2).

### Part Four: The Real Heart of the Matter

Note that this is actually not “my” conclusion. It is the conclusion of three mathematicians (including one astrophysicist) in two different studies converging on the same result independently of each other.

Wow! Two “studies”! (In academia, we call them “papers”. Though, neither were published in a peer-reviewed journal, so perhaps “articles”.) Three mathematicians! Except that Elliott Sober is a philosopher (and a fine one), not a mathematician – he has never published a paper in a mathematics journal. More grasping at straws.

Barnes wants to get a different result by insisting the prior probability of observers is low—which means, because prior probabilities are always relative probabilities, that that probability is low without God, i.e. that it is on prior considerations far more likely that observers would exist if God exists than if He doesn’t.

Those sentences fail Bayesian Probability 101. Prior probabilities are probabilities * of hypotheses*. Always. In every probability textbook there has ever been

^{1}. Probabilities

*given a hypothesis – such as the probability that this universe contains observers given naturalism – are called likelihoods. So, there is the prior probability of naturalism, and there is the likelihood of observers given naturalism, but*

**of data***there is no such thing as the “prior probability of observers”.*

This is not a harmless slip in terminology. Carrier treats a likelihood as if it were a prior. He has confused the ** concepts**, not just the names. Carrier states that “the only way the prior probability of observers can be low, is if the prior probability of observers is high on some alternative hypothesis.”

^{2}This is true of prior probabilities, but it is not true of likelihoods. In the vernacular, likelihoods are not normalised with respect to hypotheses. They are normalised with respect to evidence: p(e|h.b) + p(~e|h.b) = 1.

It follows that this entire section on the “prior probability of observers” and the need to consider “some alternative hypothesis” is garbage. There is simply no argument to respond to, only a hopeless mess of Carrier’s confusions. It’s an extended discussion about prior probabilities from a guy who doesn’t know what a prior probability is. Given that he has previously confused priors and posteriors, he’s zero from three on the fundamentals of Bayes theorem. You cannot keep getting the basics of probability theory wrong and expect to be taken seriously. Continue Reading »