Although I have been reviewing Tim and Lydia McGrew's argument on the resurrection, I have decided to give a brief rundown of Richard Carrier's Why the Resurrection is Unbelievable which is a chapter of that (highly recommended) book The Christian Delusion: Why Faith Fails.
Carrier's Basic Contentions
1. Herodotus, who was an educated, careful, and generally reliable historian, reports all kinds of fantastic tales, such as a fortress that magically defended itself with armaments. But no one would believe any of Herodotus' wild tales, and since Herodotus' credibility is equal to or greater than the Gospels, we shouldn't believe the Gospels when they tell us that a man came back from the dead.
Point of interest: yesterday I posted about how the gospels had some degree of archaeological support, a real boasting point for Tim and Lydia McGrew. Well, guess what: Herodotus has recieved some fantastic corroboration, and even some corroboration for issues about which some historians thought he was full of it. His fantastic tale of giant ants, for example, probably refers to something real (!), he correctly identified the first pharaoh and the builders of the pyramids, he correctly reported that Medes was overthrown by Cyrus, and he's been vindicated by various topological and archaeological surveys, as has been reported in the Encyclopedia of Historians and Historical Writings.
2. The Resurrection of Jesus is an extraordinary claim. Extraordinary claims require extraordinary evidence. The evidence for the resurrection is not extraordinary because it comes from poor sources, and, even if those poor sources were right about basic things such as an empty tomb, such evidence could never be called truly "extraordinary."
On the sources: Our Sources are (1) Paul and (2) the Gospels. Paul is not reliable because, as he tells us in Galatians 1, he gets his gospel from Old Testament Scripture and from personal revelation of God. We wouldn't accept the word of a cult leader today who claimed God revealed the truth to him or that he could find hidden messages in Old Scripture (such claims are reminiscent of Charles Manson believing that the Beatles were giving him messages through their songs). Therefore Paul is not a reliable source for true historical events, because he does not use a method we would consider to be reliably tracking the truth.
The gospels aren't reliable either, for a number of reasons:
(a) they are wildly contradictory (just read the resurrection stories of each one).
(b) they report extravagent events that aren't reported anywhere else, even though such fantastic things would have been reported if they really happened. For example, they report that the temple curtain was torn after Jesus' death. But that isn't reported anywhere by anyone, even though there were priests whose sole duty was to attend the temple veil.
(c) The gospels are full of symbolic fiction, as Carrier demonstrates with his example of the passion narrative imitating the scapegoat ritual, and has been shown by others in works such as Gospel Fictions and The Homeric Epics and the Gospel of Mark.
(d) they contain interpolations and later additions, which makes their original content somewhat suspect (I don't fully agree with Carrier on this point, and I'll elaborate on that later).
(e) the gospels were born in an environment that was short on skepticism and full of credulity and fraud, which doesn't give us any reassurance that the gospels must be true; the fact that they were passed down to us is not an indication that they were considered credible by any careful, critical, and skeptical person(s).
3. Natural explanations of Christian beliefs are more credible. This true because (a) natural explanations are intrinsically more likely (b) they have greater explanatory scope, they explain why Christianity has so much in common with other religious movements of the time and (c) natural explanations explain why Jesus was only seen by a Paul and a handful of others after his death, instead of appearing to the whole world, which is something God would certainly do if he endorsed the Christian religion.
Where I Disagree with Carrier
On page 302 Carrier tells us that Mark 16:9-20 was "'snuck in'" by "dishonest Christians." He says that the story of the woman caught in adultery, long known to be a later addition to the text of John, a "forgery" which was "deceitfully inserted after the fact." He finishes up with, "We have no way of knowing what got added to the version we now have in the Bible."
I think this is a little uncharitable. First, the insertions and additions that occurred in the New Testament may not be dishonest. Maybe a scribe figured that Mark's ending had been "cut off" from his copy of the Gospel (as some scholars have proposed today), and decided to fill in the blanks as best he could by writing a new ending. Such an action wouldn't be dishonest to my mind. The same goes for the story of the woman in adultery: it could be an illicit forgery, or it could simply be some piece of oral tradition or something that got inserted into the gospel by a Christian who wanted to see it preserved; by a Christian who thought he was doing nothing more than augmenting someone else's gospel.
And as for Carrier's statement: "We have no way of knowing what got added to the version we now have in the Bible." That is way off. The field of lower criticism has ways of knowing (such as: when a verse isn't present in our earliest manuscripts, which is how we know Mark 16:9-20 is a later addition). The field of higher criticism has ways of telling when something is out of place or uncharacteristic, an example being 1 Thessalonians 2:13-16 which, to my mind, is certainly an interpolation because of its antisemitism (not characteristic of Thessalonian's author) and because the chapter reads just fine when the passage in question is removed.
Carrier may have meant something along the lines of, "We have no way of being absolutely certain about the original text of the New Testament." Which is true. If some addition or change was made to the New Testament in the early time from which we have no manuscripts, and if the finished text reveals no clues showing us that the passage in question is interpolated, then we won't know about it. And that is a significant concern which ought to decrease our confidence in the evidence for the resurrection, at least slightly.
And that's it. Those are my only concerns with Carrier's chapter. Other than that, I approve of it and highly recommend it.