The "dead men stay dead" argument

Another piece from this article by Than Christopoulos which caught my eye.

Among the many arguments skeptics use to support an exceedingly low prior probability of the resurrection, one of the most common is what we might call naive enumerative induction. It sounds technical, but it’s really just the old slogan: “Dead men stay dead”—with a statistical twist.

The objection goes like this:

“Look, this is all nice and thoughtful, but at the end of the day, the probability that someone rose from the dead is still astronomically low. Out of all the people who’ve died, how many have come back? None. That makes the statistical frequency—and thus the prior probability—effectively zero. No amount of testimony could possibly overcome that.”

Put simply, this is the “dead men stay dead” argument with a statistical spin! The statistical frequency of observed resurrections is 0. So the prior probability of the resurrection is either 0 or at least astronomically low!

At first glance this may seem like a rather intuitively true argument, but let’s unpack the logic and see how it actually leads to counter-intuitive results.

First let’s translate this into probability language.

Given a sample size of 1,000 (or any number you want) people and none have risen from the dead, the prior probability that Jesus rose from the dead is low.

Let..

• k= background knowledge (sample size)

• R = resurrection

P( R | k) = ~0

this logic only works if we use a frequentist interpretation of probability. Frequentism says:

“The probability of A in a class B is the relative frequency of A occurring in B.”

In other words

• Jesus is a human, therefore He is part of the reference class called Humans
• No occurrences of humans raising from the dead in the reference class have been observed
• Therefore, the probability that Jesus rose from the dead is very low

This is not just a frequentist perspective! Part of the problem seems to be for Than that he wants to jump right into a prior probability value, rather than actually try to estimate it. How does one estimate a prior probability? Historically, there have been three methods of obtaining prior probabilities.

1. principle of maximum entropy. This is the generalization of Laplace's Principle of Indifference, where without any other information, all possibilities are given equal prior probabilities.
2. transformation groups. This is an idea proposed by E. T. Jaynes, where he uses symmetry to assign prior probabilities.
3. one person's posterior is another person's prior. This is where you start with methods 1 or 2, augment with some information to obtain a posterior probability, and then use that as the prior for your next calculation.

The "dead men stay dead" argument would run something like this, as an estimate of the prior from Than's argument above.

• There is some prior probability for someone rising from the dead, which we will denote as $\theta$. Think of this as a potentially biased coin.
• We'll say that the prior probability is uniform across all values of $\theta$, from the Principle of Indifference.
• We observe 1000 people who have died -- and none of them have risen. This is like flipping a coin 1000 times, and it comes up tails every time.
• What is the probability that the next person rises from the dead, or flips heads on the coin?

The math is straightforward, applying Bayes theorem to update our probability $\theta$, and leads to Laplace's Rule of Succession for the best estimate of this probability: $$\bar{\theta }=\frac{h+1}{N+2}$$ where $h$ is the number of heads flipped in $N$ flips of a coin. For Than's numbers, the best estimate of the probability of rising from the dead is thus, $$\bar{\theta }=\frac{1}{1000+2}$$

this fully Bayesian solution is very close to what Than accuses as "only working if we use a frequentist interpretation of probability".

Of course, we've seen many more than 1000 people dying and "staying dead", so that number should be closer to 100 billion.

Also, it should be clear that "staying dead" is not entirely analogous to flipping a coin -- we know quite a bit more about human biology and the physics of entropy to inform our model. A body "not staying dead" would go against some of the best knowledge we have, and literally trillions of experimental results which back it up. It's hard to estimate a prior so small, and our intuitions will certainly fail quantitatively, but regardless we know it must be much smaller than 1 over 100 billion.

I'd say if the apologist ever had evidence that could legitimately raise things above 1 over 100 billion I'd start looking at it in more detail -- not that I'd be convinced, but it would rise to the level of getting a second look.

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