Why a Methodological Naturalism Approach to the Resurrection is (Usually) Circular
McLatchie vs Paulogia Resurrection Debate: Why Priors Matter
Jonathan McLatchie (a Christian apologist) and Paulogia (an ex-Christian YouTuber) debated the resurrection in February 2023. This post is not a review of their debate. Instead, I want to reflect on the role of priors in discussions between Christians and atheists on the resurrection.
Both McLatchie and Paulogia claimed to follow the evidence. Yet they came to very different conclusions. Philosopher Philip Goff’s assessment of the Licona/Ehrman debate could as well apply here:
Rather than disputing the history, a lot of time was taken up arguing about whether it is possible for a historian, as a ‘historian’, to argue for a miracle. This seems to me a very silly thing to argue about. We could define the word ‘historian’ however we wish. Surely the interesting question is what we have reason to believe. (Philip Goff, Can you prove a miracle?)
How do we get beyond these lost in translation moments of mutual incomprehension? Goff’s solution is to use a Bayesian framework:
…what this debate should have been about is:
(A) What is the prior probability?
(B) How strong is the evidence?
(C) What probability do we end up with as a function of (A) and (B)?
Before we tackle these three points, I will illustrate what I mean by priors.
What is a prior probability?
A prior probability sets out our starting point before looking at the evidence:
posterior probability= prior probability x evidence for the hypothesis
A key distinction is that a prior can aim to be non-informative or informative. Most people want to be evidence-based. Priors are often subjective and hard to justify. So limiting the prior’s contribution to conclusions is a key aim.
The impact of strongly informative priors
Debates on miracles can get heated. So it may help to look at priors in a different context.
I used to live in Kyrgyzstan. There are two official languages: Kyrgyz (a Turkic language) and Russian. One afternoon, I heard a knock at the door. I spoke to the woman in Kyrgyz, and she asked if my flat was for sale. Just before she left, she asked me, “Why do you Turks never learn Russian?”
Anywhere else this would have been surprising, as I don’t look Turkish. But it was common to have mildly informative priors that foreign Kyrgyz speakers were from Turkey — as most other foreigners learnt Russian.
I got used to clarifying I was from England. Most people happily switched to practising their English. My visitor reacted differently: “No, you’re not. You’re a liar! You don’t even speak English properly” (Another informative prior — native English speakers were American!).
Ironically, speaking with a native English accent became evidence I couldn’t be English! I was making a self-evident statement. Yet there was no data that would convince her. I shrugged my shoulders and took it as a compliment to be thought Turkish.
Prior probabilities for the resurrection
There was a discussion of prior probabilities in the McLatchie/Paulogia debate. McLatchie argued the evidence was sufficient to overcome a reasonable prior. In contrast, Paulogia argued for an informative prior against the resurrection. The evidence, in his view, was insufficient.
I followed up with Paulogia on Twitter. He was helpfully transparent. I asked him how likely he thought the prior should be for a God unlimited by the regularities (or laws) of nature.
What other factors influence the prior?
I have developed a Bayesian model on evidence for the resurrection (summarised here). One of the inputs is the prior probability of theism — a God unlimited by the laws of nature. There are two other factors to consider in the prior:
- If God exists, how likely would he send a rescuer (Messiah): p(M|T)? I think it’s reasonable to expect it is at least as likely as not (that is, a probability of 0.5 or 1/2).
But I will propose a moderately informative prior against my position — it is more likely God would not send a Messiah:
p(M|T)=0.25. If God exists (T), there is a 0.25 (1/4) probability he will send a Messiah (M) and a 0.75 probability he will not send a Messiah (~M).
2. The second factor is the probability that God would resurrect this Messiah as confirmation of their ministry. Again, the model’s prior is moderately informative against my position. It is more likely God would not resurrect the Messiah:
p(R|M)=0.25. If there is a Messiah (M), the probability God raises (R) him from the dead is 0.25 (1/4) and 0.75 against (~R).
What about the evidence?
There are two aspects of evidence about Jesus included in the model:
- Probability that Jesus is the Messiah: Richard Swinburne would call this prior historical evidence.
- Data from the Hebrew Bible predicted before the time of Jesus what the Messiah would be like.
- Jesus claimed to be the Messiah.
- If Jesus met these criteria, this would increase the probability that God would raise him from the dead. A suitable confirmation of his divine mission.
I discuss these data in more detail here.
2. Probability that if Jesus was resurrected, we would observe the evidence we have about him (i.e. Jesus’ burial, empty tomb, his disciplines claimed he appeared to them after death, Paul’s belief in Jesus’ resurrection). Discussed further here. I plan to cover the evidence in more detail in future.
Evidence for a naturalistic explanation
We must also consider the other side of the coin. The probability of the evidence, given Jesus was not resurrected: p(E|~R).
A naturalistic explanation must also account for:
- Evidence of an empty tomb —The main difficulty is that there is limited, to no evidence, in support of a naturalistic explanation. Therefore all such explanations are speculative. A naturalistic explanation isn’t impossible but unlikely. This will be reflected as p(E1|~R)=0.1
- That Jesus’ disciples claimed to see Jesus after his death — there are potential naturalistic explanations, for example, the disciples were hallucinating or lying. These explanations are unlikely to be probable, as historical evidence is lacking. In addition, they are unsupported by current psychological evidence on hallucinations. This uncertainty will be reflected as p(E2|~R)=0.1
- Paul’s belief in Jesus’ resurrection — there is no, or at best very limited, counter-evidence to account for Paul’s belief. A recent YouTube video proposed that somehow Paul was identifying with the enemy — like a prison guard with a prisoner. Not impossible, yet not very probable. Again reflected as p(E3|~R)=0.1
A naturalistic explanation must account for at least these three data points. Each on its own is unlikely, but multiplied together, is even more improbable:
p(E|~R)=p(E1|~R) x p(E2|~R)x p(E3|~R)=0.001
Testing circularity of Paulogia’s conclusions
We shouldn’t get too precious with these probabilities. Historical judgments are always made under uncertainty. However, they can be helpful for testing assumptions. For example, we can assess the circularity of Paulogia’s argument by varying the strength of evidence for p(E|R) and p(E|M).
Could Paulogia conclude Jesus was raised from the dead if there was strong evidence? We can investigate this by combining his prior with strong evidence for the resurrection. If this leads to a posterior probability (final conclusion) > 0.5 then his conclusion is amenable to evidence.
Let’s start with the lowest bar to clear — evidence of absolute certainty:
p(E|R)=1, the probability of the evidence for Jesus, given he was raised from the dead, is 1.
p(E|M)=1, the probability of the evidence for Jesus, given he was the Messiah, is 1.
I’m not claiming the evidence is that strong. We’re testing whether Paulogia’s prior for God’s existence can be overcome with strong evidence.
Impact of Paulogia’s prior
I interpret Paulogia’s statement about his prior for T (the probability a God exists, unlimited by the laws of nature) to mean:
p(T)= 1 in a million to 1 in a trillion
Table 1 examines the middle value in this range (1 in a billion) and extremes at either end. For all three priors, absolutely certain evidence cannot raise the posterior probability greater than 0.5.
Priors between 1 in a billion and 1 in a trillion lead to near identical posterior probabilities. In other words, conclusions are unchanged by evidence of any strength. Absolutely certain evidence for Jesus’ resurrection leads to absolute certainty he was not resurrected.
Even at the lowest end of Paulogia’s prior range (p(T)=1 in a million), absolutely certain evidence raises the posterior probability — but only to 0.06. In other words, we would still be 94% certain Jesus wasn’t resurrected.
Further exploration of priors: theism and naturalism equally likely
I have argued elsewhere, using another Bayesian model, that the evidence for God’s existence is at least no worse than the evidence against God’s existence. In fact, the model shows God’s existence is much more likely than his non-existence.
Therefore, a prior that gives equal weight to naturalism and theism is a generous estimate of naturalism’s likelihood. We tested three types of strength of evidence:
p(E|R) the probability of the evidence for Jesus’, given he was raised from the dead and
p(E|M) the probability of the evidence for Jesus, given he was the Messiah.
- low: p(E|R)=0.1, p(E|M)=0.1
2. low-to-moderate: p(E|R)=0.4, p(E|M)=0.4
3. moderate: p(E|R)=0.6, p(E|M)=0.6
Table 1 shows for all three strengths of evidence, the prior for resurrection (0.03)* is updated to a high posterior probability (p(R)=0.97 to 0.995).
How unlikely does theism need to be to deny Jesus’ resurrection?
Most atheists argue naturalism is more likely than theism. Yet, even with a prior as low as 0.005 for God’s existence, Jesus’ resurrection remains highly probable. Denial of Jesus’ resurrection is only possible for relatively extreme priors (p(T)≤ 0.001).
In conclusion, Paulogia’s prior for God’s existence determines his denial of Jesus’ resurrection. For most priors, Jesus’ resurrection is probable even if there is low or moderate evidence.
Therefore, those who deny Jesus’ resurrection must show the probability of God’s existence is very low (p<0.005). Alternatively, those who affirm Jesus’ resurrection, must only defend that the probability of God’s existence is not prohibitively low (p≥ 0.005).
*prior for p(R)=p(T)x p(M|T) x p(R|M)=0.03, where p(T)=0.5, p(M|T)=0.25, p(R|M)=0.25
