Does Evidence for Jesus’ Resurrection Meet Hume’s Criteria for Miracles?
An adaption of Richard Swinburne’s argument for the resurrection of Jesus
Part I of the series began with Hume’s criteria for establishing a miracle.
That no testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous, than the fact which it endeavours to establish. (David Hume, Of Miracles, Part I)
This article aims to sketch out how these criteria apply to Jesus’ resurrection. Future articles will justify these estimates in more detail.
Bayesian approach to Hume
JH Sobel, an atheist philosopher, summarised Hume’s criteria mathematically:
p(A) > p(α |~A), where A=miracle, α=evidence for a miracle, ~A=no miracle
In words, the probability of a miracle must be greater than the probability of there being evidence to support a miracle that did not happen.
I will summarise (with some modifications) Richard Swinburne’s Resurrection of God Incarnate and then use a Bayesian network (using Genie software) to evaluate this evidence. This is a common technique used in computational biology, ecology, medicine, and engineering — combining graph theory with Bayesian probability theory.
Prior probabilities
Bayesian approaches require prior probabilities (starting point before we assess the evidence). After assessing the evidence, we update our judgment (posterior probability).
Is the prior probability of resurrection the number of people ever resurrected divided by the total number who have lived? However, this assumes naturalism, and that the laws of nature are the only background knowledge. If so, the probability of resurrection is close to zero (P(A)~0).
However, the possibility that God exists is further background information to consider. Since the laws of nature depend on God, he is not bound by them and free to depart from these regularities on isolated occasions (P(A)>0).
Defining theism
Richard Swinburne defined theism as the belief in a God who is the source of being, omnipotent, omniscient, perfectly good and ontologically necessary (see table 1).
Theism compared with polytheism
Swinburne argues theism is simpler and has greater explanatory power than polytheism (“a committee of gods with limited power”):
- To propose one cause (God) is simpler than proposing many causes (gods).
- Polytheism requires further explanation than theism for how and why the gods cooperate to produce the laws of nature. Since we expect this data on theism, but not if polytheism is true.
Therefore, this argument will focus on the most promising explanations of reality — theism and naturalism.
1. Probability of Theism
The argument makes an agnostic assumption. Similar to atheist philosopher Paul Draper’s argument for naturalism, which also includes a prior of p(T)=0.5.
p(T)=0.5 — the probability of theism (God’s existence) is 0.5 (50%) and the probability of naturalism (God’s non-existence) is 0.5 (50%)
This is a conservative assumption for theists. For example, Swinburne’s Existence of God shows that theism has greater explanatory power than naturalism in accounting for the existence of the universe, the laws of nature, and consciousness.
2. Prior Probability of a Messiah
The concept of the Messiah — a rescuer sent by God — is common in many theistic religions. The Hebrew Bible is the basis for understanding the Messiah (‘anointed one’) in Judaism, Christianity, and Islam.
Differences in how these religions understand the Messiah are of limited importance. The argument only assumes how likely God would send a representative to teach, intervene in a suffering world, and provide an example.
Given that this is a common theme across many religions, if theism is true, it is not unlikely that God will send a Messiah. However, to be conservative, we will assume p(M|T)=0.25, the probability of a Messiah if God exists is 0.25 (25%).
Therefore, the prior probability of a Messiah p(M|K) is 12.5%:
- p(M|T)=0.25 probability of Messiah if there is a God, multiplied by
- p(T)=0.5 probability of a God
3. Prior probability of a resurrection
If God sends a Messiah, it is likely a vivid miracle would testify God sent them. Few miracles can match a resurrection. Humans can overcome many challenges — death is not one of them. In addition, the messianic kingdom brings the defeat of death:
On this mountain he will destroy the shroud that enfolds all peoples,
the sheet that covers all nations; he will swallow up death forever. (Isaiah 25:7-8, NIV)
So the Messiah’s resurrection would be an apt confirmation of their mission. Therefore, we propose p(R|M&K)=0.25 (25%) probability of resurrection given there is a Messiah.
The prior probability of a resurrection given our background knowledge p(R|K) is 0.03 (3%):
- p(R|M&K) — probability of a resurrection if there is a Messiah multiplied (0.25) by
- p(M|T) — probability of a Messiah if there is a God (0.25) multiplied by
- p(T) — probability of God’s existence (0.5)
4. Probability of Jesus being the Messiah
There are numerous passages in the Hebrew Bible about the Messiah agreed by many Jews and Christians. Below summarises some criteria a Messiah must fulfil:
- Son of David — Jesus was from the line of David.
- Daniel 7 the divine son of man — Jesus claimed to be the one like a son of Man in Daniel 7 (Mark 14:61–62) and his followers reported miracles to support his claim.
- Isaiah 53 Suffering servant — early Jewish tradition often considered this passage (about a dying and rejected servant) to be about the Messiah. The gospels speak of Jesus’ suffering and rejection.
- But the Messianic kingdom of Isaiah 65–66 has not yet arrived. For Jews, this confirms Jesus could not be the Messiah. For Christians, and many Muslims, this will happen when Jesus returns.
Jesus may be the Messiah — as he already met many of the expectations. No one else in history has come close to matching these criteria.
Daniel 9 and Haggai 2 suggest the Messiah would appear within a fixed period — before the destruction of the second temple (70 CE). So a future Messiah is unlikely.
I will give a very conservative assumption: 0.1 probability that there would be the type of evidence summarised above if Jesus was the Messiah: p(E|M&K)=0.1 (10%)
The probability of Jesus being the Messiah and there is evidence described above p(E&M|K)=0.0125 (1.25%):
- p(E|M&K)=0.1 (10%) — the probability of the evidence above, given there is a Messiah, is 0.1 (10%) multiplied by
- p(M|K)=0.125 — the probability of a Messiah is 0.125 (12.5%), see section 2.
5. Probability of evidence for the resurrection
A summary of key evidence for Jesus’ resurrection:
- Jesus was crucified and buried, but three days later, his tomb was empty (e.g. Mark 16:4–6).
- After Jesus’ death, “the twelve” his closest disciples, his brother James, Paul, and 500 other people saw him (1 Corinthians 15: 3–8). This passage cites a creed dated between 1 and 15 years after Jesus’ death. Confirmed later in the gospels. Many of his disciples, including Peter, Paul, and James, were killed for their testimony.
- Paul was a persecutor of Christians until he saw the resurrected Jesus (1 Corinthians 15:9; Acts 9:1–19)
- No one else in history has come close to matching the evidence for the resurrection
Although there was physical evidence (the empty tomb) and many early witnesses to Jesus’ post-mortem appearances, we will make the conservative assumption:
p(E|R&K)=0.1 — the probability of this evidence given Jesus’ resurrection is 0.1 (10%).
The probability of the evidence above and Jesus’ resurrection p(E&R|K)=0.003 (0.3%):
- p(E|R&K)=0.1 (10%) — the probability of the evidence above, given Jesus was resurrected, is 0.1 (10%) multiplied by
- p(R|K)=0.03 — the prior probability of a resurrected Messiah is 0.03 (3%), see section 3.
6. Naturalistic explanations for the resurrection
Our estimates must also account for the strength of naturalistic explanations of the evidence for Jesus’ resurrection.
6a. the empty tomb
The main naturalistic explanation is that Jesus was not buried. However, this assumption contradicts the earliest accounts. They state Jesus was buried and no contemporary evidence challenges this data. In addition, an article in New Testament Studies shows it was common for crucifixion victims to be allowed burial.
It is possible that Jesus wasn’t buried. But given the lack of evidence — not probable. Therefore, we assume p(E1|~R)=0.1 the probability of evidence for the empty tomb given Jesus wasn’t resurrected is 0.1 (10%).
6b. post-mortem appearances
Another naturalistic explanation is that eyewitnesses (the twelve, James, and the additional 500 witnesses) experienced bereavement hallucinations.
There is evidence, from an article in Schizophrenia Bulletin, showing those who experience bereavement hallucinations rarely consider the dead person was resurrected. First century accounts also spoke about visions of dead people — but none considered these to be resurrections. So this explanation is implausible.
Others consider it more likely that the disciples lied. But we then have to account for why they died for a known lie. People die all the time for causes they believe in. But there are few examples where people explicitly die for a lie:
p(E2|~R)=0.1 the probability of this evidence for Jesus’ post-mortem appearances if no resurrection is 0.1 (10%)
6c. Paul’s conversion
Paul was a well-known persecutor of Christians. However, after seeing Jesus, he converted.
No one claims Paul experienced a bereavement hallucination about Jesus. There’s also little reason to conclude he was lying — he was killed for his testimony about Jesus. To be conservative, we will assume: p(E3|~R)=0.1
7a. Probability of a naturalistic explanation
These three pieces of evidence require separate naturalistic explanations. As no single explanation accounts for all evidence. We have to multiply the probabilities:
p(E|~R)= 0.001 [1/1000 or 0.1%] — the probability of the evidence for Jesus’ resurrection given that he wasn’t resurrected is 0.001:
- we multiply the probability of evidence for the empty tomb by
- the probability of people claiming to see Jesus after his death, and we multiply
- the probability of Paul converting to Christianity, given Jesus was not resurrected
7b. Hume’s criteria for a miracle
Hume required an accepted miracle to meet the following criteria:
p(A) > p(α|~A) — “the testimony be of such a kind that its falsehood would be more miraculous, than the fact which it endeavours to establish.”
The evidence for the resurrection meets these stringent criteria:
- p(A)=P(R|K)=0.03, see section 3 (the prior probability of resurrection given background knowledge)
- p(α|~A)=p(E|~R)=0.001, see section 7a (probability of evidence for the resurrection presented above given Jesus was not resurrected)
- therefore p(A) > p(α|~A) since p=0.03 > p=0.001
8. The probability of Jesus’ resurrection
Entering the probabilities discussed above in the Bayesian network leads to interesting conclusions:
- the prior probability of resurrection (0.03 or 3%) when updated with the evidence across the network leads to a posterior probability of 0.97 (97%)
- the prior probability of theism (0.5 or 50%) is updated to a posterior probability of 0.999 (99.9%)
- the prior probability for a Messiah (0.125 or 12.5%) is updated to a posterior probability of 0.999 (99.9%)
The posterior probability for the resurrection is high (97%) — enough to meet Hume’s criteria for an established miracle and to proceed from an agnostic lack of belief to a near certain conclusion of God’s existence.