In a recent episode of his podcast, author Sam Harris reiterated an observation about probability theory. The broader context was to criticize the popular notion that all religions are the same. They aren’t — some specific propositions associated with religions are more plausible than others, and their consequences if believed and acted upon also vary. The probabilistic point was that the second coming of Jesus envisioned by Mormons is ‘objectively less plausible’ than a generic Christian version. Commentator Cenk Uygur then responded, saying that this is nonsense because the probability of both is zero if atheism is true (he also replaced the generic Christian version with a specific Christian version so he was talking about different propositions from Harris). The purpose of this post won’t surprise my readers: I’m going to pick nits about what probability theory actually says.
If we consider the proposition, associated with more traditional versions of Christianity, that Jesus will return to Earth to judge the living and the dead, and label this proposition A, then given information I this has probability P(A | I) (the probability of A given I).
Now consider the proposition, associated with Mormonism, that Jesus will return to Earth to judge the living and the dead and this will occur in the US state of Missouri. The first part of this proposition is A, but a second proposition B (about it happening in Missouri) has been attached via the and operator. Given information I, the probability is P(A, B | I).