Among other things, I would observe that there is a certain deductive argument, or argument to the best explanation involved in the question.
The existence of the multiple historical claims about the resurrection, by numerous (former) skeptics of such, is indisputable, of course. We do have to ask what is the explanation for all these numerous people embracing this idea.
So if we reject the idea that they all testified to this event, often on pain of persecution and death, because they had actually seen it happen, then what is the best alternate explanation?
And, for what it is worth, I would devote some of your natural and healthy skepticism to Richard Carrier’s own writings and arguments. I have found him to be extremely polemical, often being very selective or misleading or careless in his data in order to affirm his predetermined conclusion. Just one example in the article you linked… he says that
“This was an age of fables and wonder. Magic and miracles and ghosts were everywhere, and almost never doubted. This was an age of fables and wonder. Magic and miracles and ghosts were everywhere, and almost never doubted… Only a small class of elite well-educated men adopted more skeptical points of view, and because they belonged to the upper class, both them and their arrogant skepticism were scorned by the common people, rather than respected.
Carrier here is either entirely ignorant of, or glossing over and covering up, the consistent and persistent skepticism of all the original disciples when they were first told by other eyewitnesses about the resurrection. This is not a small error. This is one example of many I found just in this article.
I would be very careful in giving too much weight on this question to someone who is as committed to his atheism as Richard Carrier appears to be, and certainly don’t read him as anything approaching an “objective” perspective in the topic. If there is any good evidence for the resurrection, someone with his philosophical commitment will be all but assured to miss it, or misinterpret it.
So if I may be so bold… If Jesus did not rise from the dead, what would be your alternate explanation for the historical facts involved? Hypnosis? Group Hallucination? Conspiracy?