... aspects of the history of the Second World War are debated vigorously, sometimes fiercely, even though the events are massively documented and occurred within the living memory of millions of people. Often the only honest thing to say is that the evidence is compatible with various hypotheses. A fortiori we should be very circumspect in our conjectures about what happened nearly 2000 years ago in obscure circumstances.
Parsons mentions the hallucination hypothesis for the resurrection appearances (though he doesn't claim it is the only, or even the best, explanation). I have often felt that there is an even simpler explanation, that comes right out of the Bible:
13 Now that same day two of them were going to a village called Emmaus, about seven miles[a] from Jerusalem. 14 They were talking with each other about everything that had happened. 15 As they talked and discussed these things with each other, Jesus himself came up and walked along with them; 16 but they were kept from recognizing him.
17 He asked them, “What are you discussing together as you walk along?”
They stood still, their faces downcast. 18 One of them, named Cleopas, asked him, “Are you the only one visiting Jerusalem who does not know the things that have happened there in these days?”
19 “What things?” he asked.
“About Jesus of Nazareth,” they replied.....
25 He said to them, “How foolish you are, and how slow to believe all that the prophets have spoken! 26 Did not the Messiah have to suffer these things and then enter his glory?” 27 And beginning with Moses and all the Prophets, he explained to them what was said in all the Scriptures concerning himself.
28 As they approached the village to which they were going, Jesus continued on as if he were going farther. 29 But they urged him strongly, “Stay with us, for it is nearly evening; the day is almost over.” So he went in to stay with them.
30 When he was at the table with them, he took bread, gave thanks, broke it and began to give it to them. 31 Then their eyes were opened and they recognized him, and he disappeared from their sight. 32 They asked each other, “Were not our hearts burning within us while he talked with us on the road and opened the Scriptures to us?”
Now, if you discount the idea that this was actually Jesus and the magical disappearance, this all seems very reasonable. Two followers were walking along and discussing Jesus's death (not implausible). They met a traveling rabbi who didn't look like Jesus (not implausible). They told him they were discussing the Messiah, and the rabbi began explaining the messianic interpretation of various scripture passages (not implausible). Later on, they reflected on this conversation and decided it was Jesus himself who had met them. This last step might strike some as implausible, but I think if there were already stories of Jesus's appearance circulating, it would actually be quite psychologically reasonable.
In this scenario we see how, without any dreams, hallucinations, or weird psychological experiences, Jesus's followers could come to believe that Jesus had "appeared" to them. This explanation might not work for all of the appearance stories, because it relies on the disciples having a predisposition to interpret experiences in terms of appearances of Jesus. Perhaps the first "appearance" was a dream or something. But it might help explain how, once the resurrection meme was in place, it spread so widely. We don't need to posit mass hallucinations, just people re-interpreting their very ordinary experiences in extraordinary terms.