## The probability of a Mormon second coming

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 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 $P(A, B | I)$.

Probability theory says that $P(A, B | I) \leq P(A | I)$ for any propositions A, B, and I. Applying it to our case, the probability of the Mormon proposition must be less than or equal to the probability of the Christian one. I put “or equal to” in bold because it’s the nit I want to pick in Harris’s original statement. Probability theory itself says $\leq$. I think any reasonable person would assign probabilities such that the strict inequality $<$ applies, but that’s not a property of every possible probability assignment.

That adding extra stipulations with and can only decrease the plausibility (or keep it the same) isn’t just a consequence of probability theory, it’s a core part of the arguments for why probability applies to rational degrees of plausibility in the first place.

What happens if we do as Uygur did, and consider another proposition C, which is like B but specifies the location as Jerusalem instead of Missouri? Then probability theory in itself doesn’t constrain the values of $P(A, B | I)$ and $P(A, C | I)$. However, I’d assign a greater, but still small, probability to the latter.

Now what happens if we do another thing Uygur did, which is assert that anyone associated with the worth atheist (even though they do not like the term and would prefer it went away) should assign precisely zero probability to all of these propositions? Nothing much changes about the above discussion. Define $I_2$ as the proposition God doesn’t exist and Jesus was a regular person and will never return. Then, as probability theory requires $P(A, B | I_2) \leq P(A | I_2)$. It just so happens that both are zero (again, given $I_2$), and it’s the equality part of $\leq$ that applies.