With eyewitnesses, of course, there are important questions to be asked. Is it possible the eyewitness is mistaken, and is it possible the eyewitness is lying? These are obviously crucial concerns, as not all eyewitness testimony is credible. People can be mistaken, and people can be intentionally deceptive in their testimony.
When it comes to the Resurrection, we are confronted with claims of having eyewitness testimony of several events. First, there is the death of Jesus by crucifixion. Second, there is his burial in a tomb. Third, there is the finding of the same tomb empty on the third day. Fourth, there are reports of several different appearances of Jesus to his followers after his resurrection. There are no eyewitness reports in the New Testament of anyone actually observing the Resurrection itself. The question, however, is if we actually have credible eyewitness testimony of these events, and if so, is there some explanation of them other than that offered by the New Testament writers: that God raised Jesus from the dead.
One skeptic on another website argued that Luke never claimed to have met anyone who was an eyewitness to Jesus. Note that this wasn't simply a claim that Luke hadn't met an eyewitness to the risen Christ, but that Luke never claimed to have met anyone who saw Jesus when he was alive. I pointed out that Luke writes in Acts 21:18-19 about a meeting between Paul and his traveling companions (including Luke) and James, along with all the elders in Jerusalem. Keep in mind that this was not James the son of Zebedee, one of the original twelve apostles. That James was executed by Herod in Acts 12:2. This was James the brother of Jesus mentioned in Matthew 13:55 who became one of the leaders of the early church in Jerusalem. This is also the James whom Paul records in 1 Cor. 15:7 as one of the witnesses to whom Jesus appeared after his resurrection. So not only was James an eyewitness of Jesus's life (having been his brother), but was also a witness of the resurrection. But, this skeptic argued, Luke didn't specifically say that James was an eyewitness of Jesus. But this point is moot. Paul specifically identified James as the brother of Jesus (Gal. 1:19) and as an eyewitness to the Resurrection. Luke was present when Paul conferred with James and the elders in Jerusalem. It's impossible to believe that Luke wasn't aware of James's background just because he didn't write about it. What this does, however, is point to the importance of eyewitness testimony. The skeptic wants to exclude any possibility of the Gospels being actual eyewitness accounts.
For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures, and that He was buried, and that He was raised on the third day according to the Scriptures, and that He appeared to Cephas, then to the twelve. After that He appeared to more than five hundred brethren at one time, most of whom remain until now, but some have fallen asleep; then He appeared to James, then to all the apostles; and last of all, as to one untimely born, He appeared to me also.
1 Cor. 15:3-8
Scholarly consensus, even among critics of the New Testament, is that 1 Cor. 15:3-8 is an early church creed. 1 Corinthians was written around AD 55-57. Paul says that he had previously passed this creed on to the Corinthians, which would have been at the latest during his previous visit to Corinth, which was around AD 51. This is already within 20 years of the crucifixion. But he also says that he had passed on "what he had received", which means he received this tradition even earlier. It's probable that he received it during meetings with the apostles in Jerusalem or Damascus around AD 32-38, within a few months to a few short years after the crucifixion. There is no question then that we have actual claims of eyewitness testimony to the post-resurrection appearances. These were not legends that developed over a long period of time.
Were the eyewitnesses mistaken? We're not talking about an "Elvis" sighting at a distance for a brief moment. The independent testimony of the Gospels (which corroborate most of the specific details of Paul's testimony) record several encounters with the risen Christ which included extended conversations. It's impossible to conceive that the witnesses were mistaken. If Jesus did not actually appear to them, they were in a position to know it.
Were the eyewitnesses lying? It has been often observed that the conviction of the disciples in the truth of their message was that they died for their belief. While it's true that tradition records that all of the apostles except for John were martyred, the independent evidence is not always that strong in every case. But, as philosophers Tim and Lydia McGrew point out in a chapter in the upcoming Blackwell's Companion to Natural Theology, there are several cases where we do have strong evidence for the martyrdom of those who claimed to be eyewitnesses. The earliest of these is in the book of Acts itself, James the son of Zebedee (see above). The rest of the apostles knew, then, that death was a highly probable outcome of continuing to proclaim the Resurrection. And yet they persisted in that proclamation in spite of that fact. Thus, not only did the disciples have no good reason to lie about their testimony, they had very good reason not to lie, namely to save their own skins.
Legal scholar Simon Greenleaf, whom many regard as one of the greatest experts on eyewitness testimony who ever lived, applied the rules used in courts of law to the testimony of the evangelists. He wrote, "The result, it is confidently believed, will be an undoubting conviction of their integrity, ability, and truth."