### On the Prior Probability of the Resurrection

Recently a friend on Facebook argued that Christians have no business declaring the Resurrection of
Jesus to be the most probable (

*a posteriori*) explanation for the relevant facts, since they are unable to first pin down the prior probability of the Resurrection independent of those facts. I think that's a reasonable enough objection and deserves a reply. After all, posterior probability by definition is a function of both likelihood on the evidence and prior probability.[1] Clearly, then, one cannot determine posterior probability without some idea of the prior.
My friend went on to say that the prior
probability of a hypothesis is typically established as a ratio of previous instances
of the event and total opportunities for the event to have occurred: "Normally
we determine the probability of X by how many occasions of X we have seen out
of how many opportunities for X there have been. Is the resurrection of Jesus
some kind of exception?" This amounts to an appeal to frequentism for
finding the prior. Right here is where I begin to take issue with the typical
skeptical-Bayesian approach to miracle questions like the Resurrection. What appears
missing from so many of these calculations is any consideration of relevant
background knowledge. I do agree with Swinburne when he says that "any
division of evidence between

*e*[observational evidence] and*k*[background knowledge] is a somewhat arbitrary one."[2] That said, numerous facts indirectly relevant to the question of the Resurrection are too often overlooked, perhaps lost between very specific, directly relevant evidence (like the empty tomb or post-resurrection appearances of Jesus to the disciples) and very general knowledge about the world.
First, there are the evidence and arguments from
natural theology that suggest the existence of God. Evidence in the way of
fine-tuning in the physical universe, specifiable complexity of biological
systems, and the universal moral intuition of human beings, among other things,
suggests that the probability that God exists is quite high. Moreover the prophetic
history of Israel, in which the Jewish people were scattered throughout the
world and then re-gathered to her ancestral home in the "last days,"
suggests the existence of the God invoked by Jesus in particular. Though it is
certainly right to bear in mind the number of previous recorded and confirmed
resurrections in history (arguably zero), the evidence for the God of Israel is
important information to bring to the question of prior probability.

Next, consider the particular personality
and historical circumstances of the central figure involved. The question
before us is not, "What is the probability that some random guy rose from
the dead?" but "What is the probability that Jesus of Nazareth rose
from the dead?" I do not dispute that the probability of a random guy rising
from the dead is negligible. But from all indications Jesus of Nazareth was not
some random guy. Jesus claimed for himself, both explicitly and implicitly, to
be the Son of God and the King of the Jews, the Messiah; and elements of his
life indeed fulfilled various messianic prophecies from the Old Testament.
Jesus was widely reported by followers and detractors alike to have performed
healing miracles and miracles of provision. (The Pharisees attributed these to
the work of Beelzebub, but did not deny their occurrence; and the later rabbis
of the Tannaitic period likewise attributed the miracles of Jesus to "sorcery.") In addition,
Jesus frequently foretold his own crucifixion and resurrection – most often to disciples
who refused to believe it. These considerations together would seem to make the
Resurrection of Jesus much more antecedently probable than the resurrection of
some random guy.

Finally, I would suggest there is precedent
for a miracle, even a "raising of the dead" of sorts, in the origin
of life. The fact is that at one point in our prehistory a dead collection of
elements became a living organism – whether by God breathing life into the
"dust of the earth" as recorded in Genesis, or by some sort of chemical
evolution. And of course no origin of life event has ever been witnessed by anyone
(not even in principle). The prior probability of the origin of life just
before life actually originated therefore must have been at or very near zero. Yet
here we are reflecting on the fact that life originated. Thus our continually
being alive constitutes evidence strong enough to overcome the seemingly
overwhelming prior probability against life originating. In a very real sense
the origin of life is evidence of a miracle.

Taken together, these background factors
arguably make the prior probability of the Resurrection much higher than any
prior probability that would be reached by a frequentist interpretation of
probability alone. When that higher prior probability is conjoined with a
similarly high likelihood ratio (a measure of explanatory power)[3], the posterior probability
that Jesus Christ actually rose from the dead increases accordingly. I would
argue, in fact, that while intuitively implausible, the Resurrection is evidentially
probable. This is just the sort of thing we should expect of a God who intends
to reveal himself through the "sign" of a miracle in history.

[1] This is essentially an
informal statement of Bayes' Theorem,

P(E│H & K) x
P(H│K)

P(H│E &
K) = -----------------------------

P(E│K)

where
P(H│E & K) is the posterior probability of hypothesis H, given new evidence
E and background knowledge K; P(E│H & K) is the probability
of the evidence given the truth of the hypothesis and background knowledge; P(E│K) is the probability
of the evidence given background knowledge alone; and P(H│K) is the prior
probability of the hypothesis, again conditional on background knowledge.

[2] Richard Swinburne,

*The Existence of God*(New York: Oxford, 2004), p. 67.
[3] See "Understated Evidence and the Resurrection of Jesus" for reasons to think that the
explanatory power of the Resurrection hypothesis is very high relative to
competing hypotheses.

## Comments

Recently a friend on Facebook argued that Christians have no business declaring the Resurrection of Jesus to be the most probable (a posteriori) explanation for the relevant facts, since they are unable to first pin down the prior probability of the Resurrection independent of those facts. I think that's a reasonable enough objection and deserves a reply. After all, posterior probability by definition is a function of both likelihood on the evidence and prior probability.[1] Clearly, then, one cannot determine posterior probability without some idea of the prior.So what is a reasonable estimate of the prior probability?

DM:

I would argue, in fact, that while intuitively implausible, the Resurrection is evidentially probable.Okay, so argue it. Estimate the probabilities and do the maths.

Pix

Hey there my friend. no I wont do math, you have the advantage on that one. But most of what I see atheists putting into the calculation, the folks @ SOP, the finest intellectual blog new atheism has, who have hashed this out more than most atheist bloggers, when they calculate priors it's all question begging,

In would set at 50-50 because both sides are biased and I don't see anyway to overcome it because it';s based upon metaphysics which can;'t be proved one way or the other.

I take it you have no objections to the various points I made about background knowledge.

Maybe next week I can go beyond discussion of relative and subjective probabilities (though these are perfectly valid) and set a range for what I think the prior should be, then calculate a corresponding range for posterior probabilities.

But you have to say "please." :-)

I agree Joe. Thanks for that.

1).

The question before us is not, "What is the probability that some random guy rose from the dead?" but "What is the probability that Jesus of Nazareth rose from the dead?"- This is a misdirection. We might ask, what is the probability that

anyonearose from the dead? This actually works in your favor, because it is more probably that someone (out of all humanity) has done this, than that any one particular person has done it. On the other hand, without specific knowledge of even a single specific instance of it, the prior probability remains quite low.2).

there is precedent for a miracle, even a "raising of the dead" of sorts, in the origin of life.- Again, a misdirection. We all can agree that life arose (by whatever means). But that's not at all the same thing as a dead, rotting corpse coming back to life.

It's not meaningful,. mathematicians don't like Bayes. they don't think Bayes is science they think it;s a parler trick.

It's not meaningful,. mathematicians don't like Bayes. they don't think Bayes is science they think it;s a parler trick.Joe, you don't know what you're talking about. Bayes' theorem is a mathematically correct statement of probability. And it is universally accepted by both mathematicians and scientists. Read, for example, Sean Carroll. Or this brief article by Victor Stenger.

this is documented by

Sharon Berstch McGrayne, The Theory that would not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy. New Haven: Yale University Press, 2011, 3.

besides it doesn't matter how good the theorem if probability can't be used on God.

part 1part 2So, you're saying that if there has never been a confirmed observation of a particular thing, the possibility of it happening is zero? Wow. Guess the Twin Towers didn't fall on 9/11 because no one had ever observed anything like that before. Thanks for the insight.

Bayes theorem has to be used appropriately. If you don't have a basis for calculating a prior probability, then it is just a parlor trick. This is typically the case with theists trying to show that supernatural phenomena are probable. The fact of the matter is that the ACTUAL prior probability for any such event is zero, because there has never been any confirmed observation of of these things. If you use the correct values for your calculation, you the the correct result.

yes but it works both ways, you also can't use it to show SN stuff is improbable.Guess the Twin Towers didn't fall on 9/11 because no one had ever observed anything like that before. Thanks for the insight.No. Remember the definition of prior probability. We do see terrorist attacks, so we can say that there is some probability of terrorist attacks. But every unique event is something that has no historical track record, so there is no basis to calculate a prior probability for that specific event.

you have not even begun to address the two reasons I gave as to why you can't curate probability of god,or of the things God does. It's equally ridiculous to assert probability for unknown past events.

all historical events are unique, if go trying to portion based upon similar circumstances your are just basing the outcome.The twin towers made been boned before but suppose they had not been, You way but we there some attacks somehwere but that's not really the same;

And what's the likelihood all the other accounts of resurrections are true based on your reasoning in the article? Are you saying that the probabilities go from slight to very probable simply because Jesus suggested he would rise?

And what is the likelihood that the writers of the gospels invented what Jesus said about rising? Isn't the likelihood that someone would lie about a resurrection greater than an actual resurrection?

And can we see some actual probabilities reflecting what you wrote in the article? I tend to think it is a bit senseless to talk about the probabiliity of the resurrection without an actual probability and it's equation presented.

When we talk about prior probabilities, we are referring to a genre of events. We can talk about the prior probability of a dead person rising by considering all instances of dead people and noting what proportion of then actually rise. We can talk about the prior probability of amputees regrowing their limbs by considering all instances of amputees and noting what proportion of them actually have regrown their limbs. It is meaningless to talk about the prior probability of a unique event, because there is no basis to say that it happens some specific proportion of the time.

I agree that you can't talk about the prior probability of God. But you can talk about the prior probability of certain types of events such as miracles of the sort that I described above. There is a track record for resurrections (we don't ever see it), and there is a track record for regrown limbs (we don't ever see it). So for things like that, we can say the the prior probability is zero. You might argue that these things have occurred rarely. OK, then we can assign a prior probability of "practically zero".

Meanwhile this is for anyone insisting that only a precise numerical calculation can meaningfully estimate "the" probability (prior or other) for a given event:

Imagine for a moment your friend is planning to meet you for dinner this evening. The two of you set a tentative reservation time of 8:00. Your friend says, "I need to finish up some paperwork and then swing by the grocery store after work, and there's road construction on my usual route to the restaurant, but I can probably still get there before 8:00." He "probably" has in mind, not only paperwork, the grocery store, and road construction, but any number of other related factors: how much gas is in his tank, how long the lines are at the store, how fast he's willing to drive past the speed limit (and how relatively likely it would be for him to get stopped for it), and, yes, how successful he's been when facing similar, but certainly not identical, scenarios in the past. Etc. Now you could, I suppose, turn around and say to your friend, "Probably? Unless you present an equation demonstrating an actual probability, your reference to probability is meaningless." But your friend would "probably" think you're kidding. He is simply saying that all relevant factors considered (and a rational approach would account for relevant factors), he has reason to believe it more likely than not that he'll be able to make it on time.

Our skeptic contributors here seem to be appealing to theoretical and empirical probabilities to define "probability," but there are also epistemic or inductive probabilities, subjective probabilities, and of course probabilities specifically obtained through Bayesian methods (and even then useful Bayesian analyses are often assumed relative to other variables in the theorem, not by a straight calculation: I.e., one may know as a direct result of the theorem that if probability of the total evidence has decreased by some amount, or estimate of prior probability or predictive power has increased by some amount, posterior probability of the hypothesis should be increased in the proportion determined when those amounts are "plugged into" the theorem. So if we were to introduce a new well-verified form of evidence – say the finding of a sealed official record of the Roman guards' testimony to authorities under oath that Jesus emerged from the tomb unaided – a fact which would be expected given that the Resurrection occurred, but would not be expected otherwise, the probability that the Resurrection actually happened should be revised upward. By how much exactly? I couldn't say, but that's not the point.

As I mentioned to Phil earlier, if it is possible to use Bayesian methods to obtain a posterior probability, it is also possible to use a posterior probability obtained earlier by Bayesian methods to set a prior probability for a different scenario. I.e., Bayes' rule does not require a frequentist approach to determine the prior. Also, one may infer to a best explanation (and rightly consider it the "more probable" explanation), without supplying any calculations at all.

you could shoot down enough naturalistic causes as improbable until the other guy gives in and says maybe it is probably miracle. still not proof.

what you can't do is assign probablity to God'ss actiomns, miracles are God's actions.

In addition, abduction is intrinsically a lower resolution than induction. It is a tool of science to determine priorities of focus, but is not appropriate for a general epistemology since it blurs out the relevant probabilities. The more quantified your probabilities are, the stronger your position. Rational belief is a degree of belief that maps to the degree of the relevant evidence. Abduction does not allow for this.

God arguments are not epistemology, epistemology is not about determining the existence or being of a particular concepts or objects. Bayes is not epistemology, other from of probability are not epistemology.

Abduction may be "intrinsically a lower resolution" is high enough to warrant belief in God.

I didn't understand your reasoning. Can you apply the reasoning in your article to the probability an amputee will grow back their missing limb after prayer? Your article seemed to imply that the existence of a God who can resurrect makes a resurrection quite probable. Do Christians believe God can heal amputees?

suppose an amputee grew back a severed limb. what would cause that? It can't be nature because nature doesn't do that. We have no examples of that that can be called nature.So if that happened it would have to be a miraculous event. What causes miracles? God. if miracles happen it is God who causes them,Thus a miracle is an event caused by God.

Is God determined by the laws of natgure? If he was his actions would be natural they would be found in nature.Since they are not (we just established this in terms of amputees) then they are not natural so they they are not determined; that God chooses freely.

what does this mean? It means that God decides what miracles he does it is not subject to laws or nature nothing we can do can make it happen. for that reason we cannot set a probability to it. Because we don;t know enough about God's decision making process.

we can say probability of nature causing an amputee to grow back a limb is 0, rather, there is no probability, but does not prove there's no God it does not even cast doubt on God because is not subject to nature. you following this?

you must be talking to Don. I dom't attempt to prove probability of past events,And what is the likelihood that the writers of the gospels invented what Jesus said about rising? Isn't the likelihood that someone would lie about a resurrection greater than an actual resurrection?

that's based upon assumptions you have not established and question begging. assumptions,your foundation assumption is tacit miracles never happen so must not have happened in this case and you want to use that as proof that our arguments are false and it didn't happen. You think that beats evidence that it did, you are just using your position as a proof of your position,call me a Texas hick but at UT that is called circular reasoning. it's circular reasoning of a variety known as begging the question.that's based upon assumptions you have not established and question begging. assumptions,your foundation assumption is tacit miracles never happen so must not have happened in this case and you want to use that as proof that our arguments are false and it didn't happen. You think that beats evidence that it did, you are just using your position as a proof of your position,call me a Texas hick but at UT that is called circular reasoning. it's circular reasoning of a variety known as begging the question.Maybe skeptics simply make the assumption that miracles never happen. Or maybe they look objectively at the evidence and observe that miracles never happen. Because when all is said and done, you still can't show me one single confirmed case of a miracle. Not once. Not ever. The best you can do is show me claims that other believers have made. But a skeptic (not under the influence of "faith") never has the opportunity so see it for himself. Not once. Not ever.

65 officially validated at LourdesBy the church. Sorry, I don't buy it. Show me a miracle that has been observed by someone who isn't under the influence.

I have decided I will use Monday's post to answer this.

Description: Any form of argument where the conclusion is assumed in one of the premises. Many people use the phrase “begging the question” incorrectly when they use it to mean, “prompts one to ask the question”. That is NOT the correct usage. Begging the question is a form of circular reasoning.

that is possible for me to see for myself, then I have no reason to believe what you claim.Any problem with this type of reasoning?

Imagine a Muslim who believes Muhammad literally split the moon tells you that the probability the moon actually split is greater than any other possible explanation such as a misperceptions of the witnesses, or the fabrication of the account.

Their argument is as follows. Since we know there is a God who has an interest in performing signs and wonders, we should not be surprised the moon was split. And therefore the probabliity the moon actually split is greater than the probability of misperception, fabrication, or any other natural cause.

Is this argument not parallel to the argument you are presenting for the probability of the resurrection?