The Historical Evidence for the Resurrection of Christ
Christ's followers claimed that after Christ's death he had eaten and drunk with them for many days. Some of them were killed for refusing to withdraw this claim. Some of the witnesses (the first witness, according to one of the accounts) were women, a fact that would not have been invented because women were regarded as inferior witnesses. The fact that the several written accounts of these events give slightly different versions (of the sequence of events, who said what, and so on) is, incidentally, perfectly compatible with what is known to happen when there are several witnesses of the same events, in fact it is probably, paradoxically, evidence against the idea that it was all rumours based on fiction. And 20 years later (1st Corinthians 15) Paul of Tarsus pointed out that most of the 500 witnesses were still alive. The most plausible explanation of all this, perhaps the only plausible explanation, is that Christ rose to new life. This is not Loch Ness Monster land! As Paul of Tarsus (who met many of the witnesses) put it, "This was not done in a corner" (Acts 26:26).
Much has been written about the detailed evidence for the resurrection, but I will not repeat it here, because the real problem lies elsewhere. Instead I will state some general principles of evidence and show how they apply.
For any set of facts there are many possible explanations. When choosing between them, two questions are relevant. The well-known Occam's razor says, Which is simpler? The other says, Which is more plausible?
Simplicity is fairly objective. This means that there is usually little room for dispute about it.
But plausibility is more subjective. This means that people's previous beliefs affect their assessment. There is no neutral ground. If you and I have different beliefs, we will reach different conclusions about specific events. We will not agree about the events until we agree about the beliefs.
When simplicity and plausibility clash, there are no rules. You just have to judge for yourself.
Now the simplest explanation by far of the facts in question here is that the resurrection occurred. Any alternative involves what would usually be called a conspiracy theory. ("They stole the body.") In that sense, the evidence for the resurrection is overwhelming, even if one starts by regarding it as relatively implausible.
On the other hand, you may start with the prejudice that the resurrection is so implausible that we can regard it as impossible for all practical purposes. If this is your approach, there is no point in your examining the evidence. You have already made up your mind, and no facts will convince you, however implausible all the other theories are. This is fine so long as you admit that you disbelieve as a matter of principle, and do not pretend it is because there is "not enough evidence".
In theory there is the option of supposing that Christ returned from death "in some sense"; but that this is of no great significance. This option raises more questions than it answers, and the only people I know of who have adopted it are the kind of people who have no coherent view of life at all but uncritically believe every strange story they are told.
"The accounts of Christ's resurrection (and other remarkable deeds) were first written down far later, and so are not serious historical sources."
"... several decades later ..."
BBC Today presenter, 29-Mar-2011, instinctively exaggerating the period from Christ's death to Paul's writings
This is wishful thinking. In fact Christ's resurrection was recorded during the lifetime of the eyewitnesses. No scholars disagree about this, even the ones who refuse to believe that the event occurred.
Never before or since have so many remarkable and well-documented cures occurred.
"We only have the word of a handful of Christ's cronies, who might have lied."
In fact it is recorded that Christ appeared to over 500 witnesses. This statement is in a document (1st Corinthians 15) that undisputedly was made public before AD 60 when its veracity could easily have been checked.
As for lying, many of these witnesses were put to death because they refused to retract their testimony.
"Maybe Christ survived his crucifixion and convinced his friends that he had died and risen."
There is no evidence that his friends were daft. They experienced him living a new life, not barely clinging to the old one.
Sceptics tend to suppose that anyone who reports something they find unbelievable must be terribly gullible. This is fine so long as you admit that it is your preconception, not anything you know about the witnesses. If you start by assuming that Christ cannot be alive, of course no amount of evidence will convince you. Similarly, I am sceptical about the Loch Ness Monster (for instance) in spite of the many witnesses, but this is because I think I know enough to be pretty sure that the reports cannot be true, not because I am in a position to discredit the witnesses. All I ask here is that you be clear about your prejudices.