The majority of biblical scholars, and those with an interest in the origins of Christianity, see the crucifixion of Jesus of Nazareth as a historical reality. While it is important to recognize a vociferous and often well-informed ‘Jesus mythicism’ movement whose members hold that none of the events in Jesus’ life actually happened, the Crucifixion passes a number of tests used by historians. First, references to it appear in independent sources, and while one must be very cautious indeed when considering the hugely hagiographic Gospels, renowned chroniclers such as Tacitus and Josephus refer to it. The Crucifixion is also historically consistent with practices within the Roman Empire; those who were deemed to be a threat to Roman order were summarily nailed to a cross and left to die. Most convincingly, Jesus’ execution passes the so-called ‘criterion of embarrassment.’ This suggests that statements are more likely to be true if they are embarrassing to those making them and are unlike what they would be expected to invent. For the early Christians to have invented the detail of the Crucifixion seems implausible. Jesus was meant to have led Israel into a new golden age, not to be ignominiously killed by its enemy, the Romans. The Crucifixion also requires no supernatural beliefs and so does not demand that we suspend our belief that the laws of biology apply at all times.
The Resurrection is a different matter. Ultimately, organisms cannot come back to life if all biological functions have ceased for a few days. For this reason, the necessary position for humanists to take is that the events following the Crucifixion did not happen as the Bible portrays: that a human verified to be dead by a Roman centurion (Mark 15:44), wrapped in cloth, and placed in a tomb with a rock rolled in front of its entrance (Mark 15:46) was able, two days later, to revive, roll the stone away, and leave (Mark 16:4-6). It helps us, however, to have a hypothesis for the events following the Crucifixion, particularly as many of the early followers of Jesus seem to have genuinely believed and testified to the fact that he had risen from the dead.
In fact, they did not kill him, nor did they crucify him, but it appeared to them as if they did. (Qur’an 4:157)
Interestingly, one of the first attempts at supplying a naturalistic explanation for the Resurrection comes from the early days of Islam. Muslims to this day have believed that Jesus was a mere prophet, unblessed with divine powers. The most common interpretation of the above verse from the Qur’an is that someone resembling Jesus was crucified, thus providing us with an explanation as to why he was seen following the Crucifixion; it was not him on the cross, but either a willing volunteer, a stooge, or a victim of Roman mistaken identity. Another hypothesis based around the idea that Jesus did not die on the cross—the ‘swoon hypothesis’—had its first famous exponent in the form of maverick German biblical scholar Karl Friedrich Bahrdt. In the 1700s he proposed that it was actually Jesus who was crucified, but that a combination of drugs and resuscitation by Joseph of Arimathea (a follower to whom the body was subsequently entrusted) enabled him to cheat death.
There is evidently a state of being when someone can appear to be dead, when the heartbeat is undetectable, though he/she is still technically alive. In the modern era, methods of determining death are of course more exact, but even as late as 1895, the physician J. C. Ouseley claimed that as many as 2,700 people were buried prematurely each year in England and Wales for this reason alone. Many give the fact that the Gospels say that Jesus was only on the cross for six hours as evidence for this hypothesis—it would generally take people a couple of days before they finally expired. However, there are alternative explanations as to why Jesus was reported to have been on the cross for a short space of time. One is that the flogging that he had received prior to being crucified hastened his death (John 19:1, Mark 15:15, & Matthew 27:26). It could also be suggested that he was merely reported to have been on the cross for a short time to make events compliant with Jewish law. Not only would leaving him overnight have meant that anointing would have to take place on the Sabbath—which would have involved work in contravention of the Ten Commandments (Exodus 20:8)—but there was also a law in the Torah that a body should not be “left on a tree overnight” (Deuteronomy 21:22).
However, the swoon hypothesis fails, as it takes as given the historically inconsistent assertion that Pontius Pilate, the Roman governor who presided over the province of Judaea from 27 to 37 CE (and over the Crucifixion), would allow a body to be taken down from a cross and given a burial. First, one of the purposes of crucifixion was to act as a deterrent to anybody who even harbored thoughts that they might challenge the power of Rome. To this end, crucified corpses would be left on crosses for days for all to see, with birds of prey feasting on the remains. Victims were then typically ‘buried’ in a crude common grave. Second, for Pilate to allow someone to be taken down prematurely is at odds with what we can learn about his character from the sources available to us. The Gospels paint the picture of Pilate as an amenable and weak figure. However, their writers wanted to make Jesus’ Jewish opponents guilty for the sentencing of Jesus, so it was necessary to depict Pilate as being so easily swayed by them.
Two other sources may give us a more accurate description of Pilate. Philo of Alexandria, a Jew who chronicled 1st-century Jewish life in the Levant, describes Pilate as “a man of inflexible, stubborn and cruel disposition” and recalls an incident that may have occurred in the very same year as the Crucifixion itself. Pilate had commissioned some golden shields to be made honoring the then-emperor Tiberius, which he displayed at his palace in Jerusalem. Local Jews protested at the tribute to a figure regarded as a deity, or at least a ‘son of god,’ by Romans, and requested their removal. Pilate flatly refused. He refused again when members of King Herod’s family intervened, only eventually agreeing to move them out of Jerusalem when the Emperor himself intervened after being petitioned by the Herodians. The Jewish historian Josephus tells of Pilate using treasure looted from the Jewish temple in Jerusalem to pay for an aqueduct. Pilate had those taking part in the subsequent protest beaten with clubs, with many dying from the brutality of the punishment or through being trampled by horses. Both events suggest that Pilate was a much more intransigent figure, unsympathetic or even ignorant of Jewish sensitivities. The suggestion that he would show compassion towards a Jewish sect’s wishes towards a leader that he had put to death for sedition seems implausible.
That said, the Resurrection was not completely an invention of the Gospel writers, writing as they did at least thirty years after the events that they claim to recount. The Resurrection was not a late addition to the legends about Jesus. Instead, it was a tradition that can be traced back to the very roots of Christianity. Our very first Christians scriptures were written in the 50s CE by Paul, who, although he had never met Jesus in his lifetime, became a key player in the early development of Christianity. Paul mentioned the Resurrection of Jesus throughout his writings, and it is clear that in his letters to churches based around the Mediterranean that it was a firmly established belief. However, there are a number of other aspects of later Christian beliefs that he did not seem to know about, such as the Virgin Birth and the Ascension (Jesus’ bodily return to Heaven after the Resurrection). Paul also made no mention of any of Jesus’ miracles, and the only quote in any of his writings is where Jesus asked his followers to partake in the breaking of bread and drinking of wine in remembrance of him (1 Corinthians 11:24-25).
Similarly, there was no mention of what many of us recognize as the key elements of the Christian account of the resurrection of Jesus in Paul’s writings. There was no mention of the taking down of the body from the cross, the tomb, the stone, the visit two days later by followers, the stone being rolled away, or the earthquakes and the presence of angelic beings (Matthew 28:2). There was no talk of the discourse and meetings that Jesus is said to have subsequently had with his disciples (Matthew 28, Luke 24, John 20 & John 21), or any reference to the Ascension.
[H]e appeared to Cephas [St. Peter], then to the twelve [disciples]. Then he appeared to more than five hundred brothers and sisters at one time, most of whom are still alive, though some have died. Then he appeared to James, then to all the apostles. Last of all, as to one untimely born, he appeared also to me. (1 Corinthians 15:5-8)
Paul does not mention these traditions because ultimately they did not yet exist. The renowned New Testament professor and theologian Rudolf Bultmann remarked: “the accounts of an empty tomb are legends, of which Paul as yet knew nothing.” Another important point to consider is that Paul’s quote above does not reveal any distinction between the Resurrection experiences of the disciples—men who spent their time with Jesus during his earthly life—and those of his own; his encounter with the risen Jesus is not distinct from that of the disciples. And to Paul, the body that Jesus was resurrected in was “not natural,” but “spiritual” (see 1 Corinthians 15:44), and one with which he did not record any interactions, by either himself or anybody else. One can almost envisage the viewings of Jesus as akin to a ghostly apparition; this was perhaps the only way that he could be seen by followers who were cognizant of the fact that Jesus could not be resurrected in his earthly body—it would have simply been too badly damaged after days (not hours) on the cross.
In the Gospels, written at least thirty years after the event, Jesus becomes essentially a reanimated human body after the Resurrection, able to talk with disciples and eat fish—so possessive of a material digestive system and vocal tract—and with a body whose crucifixion wounds could be touched by Thomas (John 20:27). The writers of the later book of Acts, said to have been written by the same author who wrote Luke’s gospel, had to deal with the fact that Paul could not have experienced this type of risen Jesus; Paul was not part of the inner circle of the Jesus movement until some years after the Crucifixion, and was certainly not around within the forty-day window that the Book of Acts says was afforded to other followers before the Ascension (Acts 1:3). Paul is therefore depicted as seeing Jesus as a light in the sky while he is traveling on the road to Damascus some years later (Acts 9:3-9).
One of the methods used by historians to determine historical truth is to show a preference to those sources that originate closest to the time of the events that they report. As Torsten Thurén states in his highly regarded 1997 book Source Criticism, “the closer a source is to the event that it purports to describe, the more one can trust it to give an accurate historical description of what actually happened.” Therefore, if we are to find any kernel of truth in the Resurrection narratives in the Bible, it must be in Paul’s initial nebulous, vision-type experiences that he suggests are experienced both by Jesus’ closest contemporary followers and by himself, a later convert. The later Gospel accounts (that disagree with each other in a number of ways) can be dismissed as fanciful invention.
In his book How Jesus Became God, Bart Ehrman gives three criteria that make such visions of the deceased much more common. All of them are met in the case of the death of Jesus of Nazareth. They happen when “the deceased was especially beloved; when his or her death was sudden, unexpected, or violent; and when the visionary feels guilt.” With regards to the latter, the criterion of embarrassment might suggest that there might be some truth in the Bible accounts of disciples deserting Jesus in the hours approaching the Crucifixion (see Mark 14:50 & Matthew 26:56)—an act about which Jesus’ followers may have experienced considerable guilt, thus exacerbating their visionary experiences further. Such postdeath encounters with the dead are very, very real to those undergoing them. They explain why Jesus’ early followers insisted so fervently on the resurrection of Jesus as an event grounded in reality, helping to make it such a widely held belief almost two thousand years later.
 More details about the swoon hypothesis can be found on Wikipedia.