Resurrection is the act of rising from the dead. The Bible claims that Jesus was resurrected three days after his crucifixion. Many Christian apologists claim that the resurrection of Jesus is an established historical fact, and that this proves the truth of Christianity.
The Problem of Miracles
Main Article: Miracles in History
One problem with this line of apologetic argument is that it is difficult to establish historically that a miracle has occurred. The reasons for this include practical difficulties such as the many cases of definitely bogus miracle claims as well as the epistemic problem raised by Hume. However, the most basic reason may be that most Christians would demand a very high level of proof before accepting a miracle of another religion. Therefore, we should apply a similar standard to Christian miracles such as the resurrection.
There is very little historical documentation for the resurrection outside the Bible itself. Apologists must therefore claim that the books of the Bible can be established as reliable historical documents.
Main article: The Gospels
Today, even many fairly conservative scholars admit that the gospels are not eyewitness accounts but rather anonymous compositions written decades after the alleged events they record. As hearsay, they are almost entirely worthless as proof of an actual miracle.
Mark has no actual resurrection story. The resurrection story in Mark 16:9-20 , the so-called Longer ending, is found in the King James bible, but not in the oldest manuscripts. The first recorded mentioning of it is by Irenaeus (2nd century AD - c. 202). Most theologians conclude that it's a later construct to bring Mark into line with the other Gospels.
In 1 Corinthians 15 , Paul briefly lists some post mortem appearances of Jesus, including appearances to himself and the disciples. As evidence for the resurrection, it has an advantage over the gospel reports in that most scholars agree that Paul really wrote the relevant passage from 1 Corinthians. (A few scholars, most notably Robert M. Price, disagree with this conclusion, however.)
Nevertheless, there are problems with Paul's report. It lacks all the details of the gospel reports which apologists use to show an actual miracle is the only viable explanation for the evidence. Conspicuously absent is any reference to the discovery of Jesus' tomb, a fact that has led some scholars to question the historicity of the tomb story.
Paul says nothing about how he received his information, leaving a real possibility that some of it has been mis-reported.
In his debate with Michael Horner, Farrell Till pointed out that most evangelicals do not believe that an angel authenticated the Book of Mormon, in spite of the purported eyewitness statement that comes with every copy of the book. Paul's testimony in 1 Corinthians is certainly no stronger than that testimony.
In public debates, Antony Flew has pointed out that organizations such as the Society for Psychical Research (of which Flew is a former member) would not accept Paul's report as evidence of ghosts or telepathic projection. The problem is that experience with such reports shows that human memory is much less reliable than most people realize, and even a year after an event is long enough to introduce significant distortions in recollection. Paul's letter to the Corinthians was written not a year after the fact, but two to three decades after.
The evidence for the resurrection is open to a number of naturalistic explanations
"Swoon theory" refers to the hypothesis that Jesus didn't really die on the cross, but rather was taken down alive and recovered in the tomb. It was made famous in the 19th century by Heinrich Paulus, as well as by fictional works that postulated an Essene conspiracy that assisted in the ruse. Today it has few advocates, though Richard Carrier recently published a partial defense of it.  Carrier argued that it was actually the least likely naturalistic explanation, but it still had a chance of occurring of 1 in 6,800. This is sufficient to rule out a miracle, because if every 1 in 6,800 event were declared miraculous, we would have to believe that royal flushes are miraculous.
A related but arguably distict theory is the "Autoresuscitation Theory", invoking an unusual phenomenon of spontaneous, natural return from a state of clinical death accepted as a naturalistic occurrence in the medical literature, including a set of 32 cases compiled here: 
Assimilation of hearsay
Psychological research by Loftus and Palmer in 1974 demonstrates that testimony assimilates external information and cues without the person even realizing it. Psychological research carried out by Festinger and Carlsmith in 1959 shows that people can change their understanding when there is otherwise insufficient evidence to justify a conclusion that the subjects wish to come to. Both of these can lead to exaggerated or inaccurate narratives being given.
The effect studied by Festinger and Carlsmith also poses a fatal problem for David Strauss's argument that the swoon theory fails to account for the amazement of the disciples.
Wars and fights don't generally end suddenly for poitical reasons, as it would amount to an admission that it wasn't right in the first place. Paul wanted something to say along with his ceasing to persecute Christians, giving him motivation to invent or modify a story as to what happened. Paul's visions (even if they existed) are obvious embellishments, as he would have no way of knowing it was Jesus, as he didn't even know what Jesus 's face looked like. We can see him saying many things that he clearly did not do any fact-checking on, and this must include the purported appearance of Jesus to a group of 500 people claimed by Paul. (Source: New Testament historian Bart Ehrman) This was combined with the above effects to result in exaggerated claims made later by others.
1908 psychological research by Yerkes and Dodson shows that high anxiety can impair judgement in non-trivial situations. Claims apologists make that a centurion pronouncing death or later recollection by early church members would be accurate under death threats can be turned on their head: Anxiety impairs, not enhances judgment, in such cases.
Twin and moved body
Jesus had an identical twin and the body was moved by someone (several possibilities here)
Twin and wrong tomb
Jesus had an identical twin and Mary Magdalene made a mistake while locating the tomb. Others may have been induced to make a mistake by the effect documented in the psychological research "Asch Conformity Experiments" (1950's) although the Gospels are inconsistent on who exactly was and wasn't there.
Minor details may have been corrupted. Even those who subscribe to the "minimal facts" approach must admit that some of the minor details are unreliable and inconsistent among the Gospels. This poses problems for those apologists trying to debunk some of the naturalistic explanations, as they often need to assume the truth of a minor detail. Example: claiming that the inability of Jesus to push away the stone according to "swoon theory" depends on an unreliable detail - namely, the weight of the stone.
Keith Parsons has recently argued that recent experience with people who believe themselves to have been abducted by aliens makes the hallucination hypothesis more plausible, and that many standard apologetic objections to the hypothesis would also require us to believe in alien abduction.
Biblical scholar Dale Allison has made a similar argument based on reports of apparitions of the dead. In particular, he notes "examples of collective hallucinations in which people claimed to see the same thing but, when closely interviewed, disagreed on the details, proving they were not, after all, seeing the same thing."
Primary and Composite naturalistic explanations
The swoon and hallucination theories are "primary", only invoking one part. By contrast, the "twin plus moved body" and "political correctness plus hearsay assimilation" are composite, requiring a "synthesis" of more than one part. Apologists essentially never mention these, or even the possibility of composite theories, because it would show that their case can have holes poked in it.
The standard objection to the fraud theory is that the disciples would not have died for a lie. However, documentation of their martyrdoms is weak. The earliest comes at the end of the 2nd century and is only for Peter and Paul. Also, it has been suggested that the disciples may have lied for what they believed was a higher cause.
The resurrection and Jesus mythicism
To some extent, the debate over the resurrection would be moot if it were demonstrated that Jesus never existed. However, some mythicists, notably Richard Carrier, accept that early Christians reported visions of Jesus, and these are explained as hallucinations.
Even assuming that a person named Jesus existed, there is no reason to believe that the Bible provides an accurate account of events in his life. The resurrection and the accompanying details may have been invented at a later date.
Generalized Littlewood's Law
If we generalize Littlewood's Law of Miracles to an approximately 1,000-month-long human lifespan, and to a total population of humans who have ever existed of 100,000,000,000 then to reject the null (no supernatural intervention in the natural world) hypothesis with 95% confidence we need, to avoid the so-called multiple testing fallacy , the probablity of all naturalistic explanations to be below 5 * 10-22 or 1 in 2,000,000,000,000,000,000,000. The apologist has no case unless every single potential naturalistic explanation is truly astronomically improbable, not just seemingly unlikely.
- Allison, Dale. Resurrecting Jesus T. & T. Clark Publishers, 2005
- Habermas, Gary R. and Antony Flew. Did Jesus Rise from the Dead?: The Resurrection Debate Harpercollins, 1987
- Habermas, Gary and Michael Licona. The Case for the Resurrection of Jesus Kregel Publications 2004
- Price, Robert M. and Jeffery Jay Lowder (editors). The Empty Tomb Prometheus Books, 2005
- Telford, W.R. The Theology Of The Gospel Of Mark Cambridge University Press, 1999