## Introduction I want this neon sign!

I've poked at prophecy in the past. I assert that it's better explained as post-hoc favorable interpretation than as legitimate future-telling. A Christian asked me to expand on how we can apply Bayes' Theorem to prophecy.  On the surface, this seems like a trivial task, but it turns out to become pretty murky since the likelihoods of the various events are very hard to quantify. Nevertheless, I think it's instructive to consider.

## Background

Bayes' Theorem is a theorem in probability and statistics which computes the likelihood of related events given some assumptions.  In its simplest form, it states:

$P(A|B) = \frac{P(B|A) P(A)}{ P(B) }$

Where P(x) is the probability of x being true, and P(x|y) is the probability of x being true, assuming that y is true.  x and y being events or observations.

## Method

For starters, let's consider what I think is the meat of prophecies: That they support the claim of divine and infallible nature of a holy book. Let us ask Bayes, "What is the probability that a holy book is divine ($div$) given that a prophecy it contains is true ($pro$)." That is to say:

$P(div|pro) = \frac{P(pro|div) P(div)}{ P(pro) }$

I'm not sure if we'll be able to get very far, but let's dive in, shall we?

### Divinity Yields Accurate Prophecy?

$P(pro|div)$
What is the chance that a prophecy will be true in a divine book?  That depends on who you ask and what you assume for the nature of the divinity which inspired the book.  That being said, be careful what you apply to this probability.  Too low and the $P(div|pro)$ approaches zero.  Too high and a failed prophecy will prove the Bible isn't divine.

### Likelihood of Divinity

$P(div)$
What is the chance that a particular holy book is divine without any other assumptions?  Again, this depends dramatically on the incoming assumptions about the holy book in question.
• Many presuppositionalists enter the discussion with $P(div) = 1$.
• If you assume that one book is divine among all titles ever written, your value for $P(div)$ is very close to 0.
• If you assume that of the four holy books (Torah, Bible, Quran, and Book of Mormon), one and only one is divine, you get $P(div) = 0.25$
To be honest, I'm not satisfied with any of these answers.  All of them are pretty arbitrary given that we have no way of knowing if or how often books are divine.

### Likelihood of Prophecy being True

$P(pro)$
What is the likelihood of the prophecy coming true without any assumptions about the divinity of the book in question? In evaluating this likelihood, it's important to consider:
1. If people believing the book is divine will make the prophecy more or less likely to come true
2. The likelihood that the event would happen anyways
In other words, to determine if the prophecy is true, we must consider it in the context of the events we know to be true

$P(pro|evt) = \frac{P(evt|pro) P(pro)}{ P(evt) }$

$P(evt)$ in the denominator means that if the event would be likely to happen anyways ("There will be wars and famine and disease!!!") then the prophecy isn't likely to be true.

$P(pro)$ in the numerator means you have to guess at the likelihood of the specific prophecy being true. I'm not sure how to estimate this value. Perhaps this could be done by comparing it to other prophecies in the book?

$P(evt|pro)$ is the probability of the specific events, given that the prophecy is true. Again, this is very subjective, but it means you must clearly define what your "event" is and assess its likelihood given the prophecy being true.  If there are other ways of fulfilling the prophecy, they reduce this likelihood.

## Discussion

I'm not going to drag you all the way through a specific example.  My intention in this post is to communicate the various terms that need to be considered when assessing the likelihood of a book's divinity given that a prophecy is true. Hope this helps.

## Extra Credit

Suppose we believed that $P(div) = 1$ and $P(pro|div) = 1$. Show that $P(pro)$ must be equal to unity and that therefore ANY prophecy which can be shown to be false proves the assumptions are wrong -- either the Bible is not divine or the divine agent produces false prophecies.