Let’s represent the Christian doctrine of the resurrection of Jesus as follows:

(C) The Christian doctrine of the resurrection of Jesus is true.

Sometimes the Christian doctrine of the resurrection of Jesus is summed up this way:

(R) God raised Jesus from the dead.

The Christian doctrine of the resurrection asserts that the resurrection of Jesus was a miracle, and that God caused it to happen:

12 Now if Christ is proclaimed as raised from the dead, how can some of you say there is no resurrection of the dead?

13 If there is no resurrection of the dead, then Christ has not been raised;

14 and if Christ has not been raised, then our proclamation has been in vain and your faith has been in vain.

15 We are even found to be misrepresenting God, because we testified of God that he raised Christ—whom he did not raise if it is true that the dead are not raised.

(1 Corinthians 15:12-15, NRSV, emphasis added)

The belief that God raised Jesus from the dead is even declared to be a requirement for salvation:

9 because if you confess with your lips that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved.

10 For one believes with the heart and so is justified, and one confesses with the mouth and so is saved.

11 The scripture says, “No one who believes in him will be put to shame.”

12 For there is no distinction between Jew and Greek; the same Lord is Lord of all and is generous to all who call on him.

13 For, “Everyone who calls on the name of the Lord shall be saved.”

(Romans 10:9-13, NRSV, emphasis added)

Clearly, (R) must be true in order for (C) to be true. (R) is a necessary condition for (C):

C -> R

However, (R) is NOT equivalent to (C). Taken literally, (R) only captures a part of the Christian doctrine of the resurrection of Jesus. For example, if Jesus had died on a cross in Jerusalem in 30 CE, and remained dead for 1,983 years, and then God brought Jesus back to life yesterday, on November 4th, 2013, then (R) would be true, but the Christian doctrine of the resurrection of Jesus would be false, because the Christian doctrine implies that Jesus came back to life early on a Sunday morning less than 48 hours after Jesus was crucified. Or to be a little less precise, the Christian doctrine of the resurrection implies that Jesus was dead for less than one week, and then came back to life.

Similarly, if Jesus had been stoned to death by Jews in Nazareth in 30 CE, and then brought back to life by God a few days later, (R) would be true but the Christian doctrine of the resurrection would be false, because the Christian doctrine implies that Jesus died on a cross in Jerusalem, not by being stoned to death in Nazareth.

Alternatively, suppose that Jesus was stabbed to death in Rome in 30 CE, and then God brought him back to life a couple of days later. Again, (R) would be true, but (C) would be false.

Suppose that Jesus was crucified in Jerusalem by the Romans in 70 CE and he died and God brought him back to life a couple of days later. In this case (R) would be true, but (C) would be false. Note that Pilate would not have been running the show in Jerusalem in 70 CE, and Paul would have already written his letters (about the death and alleged resurrection of Jesus!) and been executed before 70 CE.

So, we see that although the truth of (R) is a necessary condition for the truth of the Christian doctrine of the resurrection of Jesus, it is not a sufficient condition. (R) encompasses other possibilities in which (C) would be false. Therefore, the probability of (R) is greater than the probability of the Christian doctrine of the resurrection:

P(R) > P(C)

The claim that ‘God raised Jesus from the dead’ assumes or presupposes a couple of basic Christian beliefs:

(G) God exists.

(J) Jesus existed (as a flesh-and-blood human being).

Each of these basic Christian beliefs is a necessary condition for the truth of (R):

R -> G

R -> J

If (R) is true, then both (G) and (J) must also be true:

R -> (G & J)

Let’s summarize the two basic Christian assumptions as a single claim:

(B) God exists AND Jesus existed (as a flesh-and-blood human being).

This conjuctive claim is a necessary condition for the truth of (R):

R -> B

Either (B) is true or it is not (assuming that ‘God exists’ makes a coherent claim). If (B) is not true, then (R) is also not true:

~B -> ~R

We can divide the probability of (R) into two possible cases:

P(R) = [P(R|B) x P(B)] + [P(R|~B) x P(~B)]

In English:

The probability of (R) is equal to the sum of the following two probabilities:

1. The product of the probability of (R) given that (B) is the case and the probability that (B) is the case.

2. The product of the probability of (R) given that (B) is NOT the case and the probability that (B) is not the case.

We already know the probability of (R) given that (B) is NOT the case is ZERO, because (B) is a necessary condition for the truth of (R). So, if (B) is NOT the case, then it follows that (R) is false. This means that we can simply ignore the second case, since (R) has no chance of being true unless (B) is the case:

P(R) = P(R|B) x P(B)

In my opinion the probability of (R) given that (B) is very low, and the probability that (B) is the case is also very low. Based on these assumptions, the probabiity of (R) is very very low, and given that (R) is a necessary condition for (C) and that there are various possibilities in which (R) could be true while (C) is false, the probability of (C) would be something less than the very very low probability of (R).

I’m not going to try to prove that my estimate of the probability of (R) is true, at least not in this post. Richard Swinburne wrote a fairly long and very dense book developing a philosophical argument for the claim that the probabiltiy of the existence of God is (at least) a bit higher than .5, and so I won’t attempt to build a case for a lower probability in just one short blog post. But I do want to illustrate the implications of the above simple probability equation.

In my view, the question of the existence of God is not one about which one can arrive at a conclusion with certainty. So, if knowledge requires certainty, then I would be correctly categorized an ‘agnostic’. However, I don’t believe that knowledge requires certainty, especially when the question at issue is ‘Does God exist?’ or ‘Did Jesus really exist?’ So, I don’t think of myself as an agnostic on either question. I prefer to think of both of these questions in terms of evidence and probability. It is possible that by examining the available relevant evidence one could arrive at a justified true belief about the existence of God, or about the existence of Jesus. But the justification would not be one that makes the belief certain.

Probability is generally measured on a scale from 0 to 1. If the probability of (G) was 0, that means that it is certain that God does NOT exist. If the probability of (G) was 1, that means that it is certain that God does exist. Given my misgivings about certainty on these questions, I like to focus in on nine other possible positions:

P(G) = .9

P(G) = .8

P(G) = .7

P(G) = .6

P(G) = .5

P(G) = .4

P(G) = .3

P(G) = .2

P(G) = .1

If the probability of (G) is estimated as .9, this means that (G) is very probable.

If the probability of (G) is estimaged as .1, this means that (G) is very improbable.

There are various other positions between these extremes. If the probability of (G) is estimated as .5, this means that (G) being true is about as probable as (G) being false.

Currently, I favor the view that Jesus existed as a flesh-and-blood human being, but there are grounds for doubt about this, so I would estimate the probability of (J) to be about .8. I’m much more skeptical about the existence of God, so I would estimate a probability of no more than .1 for (G). Since (B) is simply the conjunction of (G) and (J), the probabity of (B) equals the probability of the conjunction of (G) and (J):

P(B) = P(G & J)

The probability of a conjunction is calculated this way:

P(G & J) = P(G|J) x P(J)

What is the probability that God exists given that Jesus existed (as a flesh-and-blood human being)? I believe that this probability is equal to, or is very close to being equal to, the probability that God exists, period. In other words, the existence (or non-existence) of a flesh-and-blood Jesus is irrelevant to the question of whether God exists. If it could be proven that Jesus performed miracles, or that Jesus was omnipotent or omniscient, then those facts might well be relevant to the issue of the existence of God, but we are not talking about such claims here. What is in view here is the bare-bones claim that Jesus existed as a flesh-and-blood human being, and this claim tells us nothing about whether Jesus performed miracles or demonstrated amazing powers. The mere existence of an historical Jesus does not help decide the question ‘Does God exist?’ Thus, we can simplify the above equation:

P(G & J) = P(G) x P(J)

This equation is not entailed by the more complex equation, but based on our understanding of the relationship between (G) and (J), we are able to substitute ‘P(G)’ for ‘P(G|J)’.

I would estimate the probability of (G) to be very low, and would represent this as follows:

P(G) = .1

I would estimate the probability of (J) to be high, but not very high, so I would represent this as follows:

P(J) = .8

P(G & J) = P(G) x P(J) = .1 x .8 = .08

Since P(B) = P(G & J), we can infer that:

P(B) = .08

In order to calculate the probability of (R), I need to come up with an estimated probability for it being the case that God raised Jesus from the dead given that God exists AND Jesus existed (as a flesh-and-blood human being). I believe that I can assign this scenario a very low probability on the following grounds:

1. God (if God exists) would not raise a false prophet from the dead.

2. Jesus (if Jesus existed) was a false prophet.

Therefore:

3. God (if God exists) would not raise Jesus (if Jesus existed) from the dead.

Based on this argument, and my great confidence in the correctness of the premises, I would estimate the probability that God raised Jesus from the dead given that God exists and that Jesus existed to be very low:

P(R|B) = .1

So, given my judgments, my estimated probabilities, the overall equation goes like this:

P(R) = P(R|B) x P(B) = .1 x .08 = .008

So, the probability that God raised Jesus from the dead would be about .01 (rounding the calculated answer), or one chance in 100, and the probability that the Christian doctrine of the resurrection was true would be something less than that, because P(R) > P(C):

P(C) < .01

OK. Enough about me and my opinions. Let’s consider some other possible viewpoints, and see how the probability equation works in other cases.

Some people might be more skeptical than me concerning the existence of Jesus. Suppose some skeptical person agrees with me that the existence of God is very improbable, but is convinced that it is also very improbable that Jesus existed as a flesh-and-blood human being. The following would be reasonable probability estimates for such a person:

P(G) = .1

P(J) = .1

Given these estimates we could calculate the probability of (B):

P(B) = P(G & J) = P(G) x P(J) = .1 x .1 = .01

Suppose this skeptic agreed with me that Jesus (if Jesus existed) was a false prophet, and that God (if God existed) would never raise a false prophet from the dead. In that case this skeptical person might well agree that it was very improbable that God raised Jesus from the dead given that God exists and the Jesus existed:

P(R|B) = .1

Now we can plug this skeptic’s estimated probabilities into the equation:

P(R) = P(R|B) x P(B) = .1 x .01 = .001

Given that the probability of the truth of the Christian doctrine of the resurrection is lower than the probability of it being the case that God raised Jesus from the dead, this skeptic should conclude that the probability of the Christian doctrine of the resurrection being true is less than one chance in a thousand:

P(C) < .001

Now let’s consider a person who was not as skeptical as I am, and how the probability equation would work for such a person.

Let’s suppose that this person read Swinburne’s case for God in the book The Existence of God and agreed with the conclusion that the probability of the existence of God was greater than .5. Suppose this person agreed with my view that Jesus probably existed but that his existence was less than very probable. In that case, the probability estimates for this person might well be as follows:

P(G) = .6

P(J) = .8

In this case the probability of (B) could be calculated this way:

P(B) = P(G) x P(J) = .6 x .8 = .48

Suppose this person was unconvinced by my argument concerning Jesus being a false prophet, and was inclined to say that given the existence of God and of an historical Jesus, it would be somewhat probable that God raised Jesus from the dead, but not very probable. In that case this person might well agree with this probability estimate:

P(R|B) = .7

Now we can use the equation to calculate a conclusion:

P(R) = P(R|B) x P(B) = .7 x .48 = .336

If we round the conclusion off, the probability of (R) would be .3 or three chances in ten. Given that the truth of the Christian doctrine of the resurrection of Jesus is less probable than (R), this person, would properly draw this conclusion:

P(C) < .3

So, even this person who was much less skeptical than I am, ought not to accept the Christian doctrine of the resurrection.

Let’s consider a person who was even more inclined towards Christian faith, and see how the probability equation works for this person. Suppose this person believes that it is very probable that God exists, and believes that it is probable that Jesus existed, but not very probable. In that case this person might well accept the following probability estimates:

P(G) = .9

P(J) = .8

We can now calculate the probability of (B):

P(B) = P(G) x P(J) = .9 x .8 = .72

Suppose this person rejected my argument about Jesus being a false prophet, and agreed with the above view that it was somewhat probable that God raised Jesus from the dead given that God exists and that Jesus existed. This person might well agree with the following probability estimate:

P(R|B) = .7

Now we have the input required to calculate a conclusion:

P(R) = P(R|B) x P(B) = .7 x .72 = .504

So, this person should conclude that the probability of (R) is about .5, and since the probability of the truth of the Christian doctrine of the resurrection is less than the probability of (R), this person, who is much more inclined towards Christian faith than I am, ought to draw the conclusion that the probability of the truth of the Christian doctrine of the resurrection is less than five chances in ten:

P(C) < .5

Clearly, in order to rationally arrive at a positive conclusion about the Christian doctrine of the resurrection of Jesus, one must believe that each of the three key items are very probable:

P(G) = .9

P(J) = .9

P(B) = P(G) x P(J) = .9 x .9 = .81

P(R|B) = .9

Here is how the calculation would work for such a person with such a strong inclination towards the Christian faith:

P(R) = P(R|B) x P(B) = .9 x .81 = .729

If we round off the calculated probability, we see that even starting with the assumption that each key item was very probable (i.e. probability of .9), the conclusion would be that there were about seven chances in ten that God raised Jesus from the dead, and the Christian doctrine of the resurrection of Jesus would be a bit less probable than that:

P(C) < .7

Based on these examples and calculations, it seems to me that nobody has a right to be dogmatic about the truth of the Christian doctrine of the resurrection of Jesus, nor even about the weaker claim that ‘God raised Jesus from the dead’. The best case scenario for Christianity is that a reasonable person could justifiably believe that it was somewhat probable that the Christian doctrine of the resurrection of Jesus was true. Such a conclusion would be based on assumptions that each of three key probability estimates concerning controversial claims were in the ‘very probable’ range.