Stephen Law recently wrote an article arguing for skepticism regarding the existence of a historical Jesus. It can be found in its entirety here. It is an interesting article, written purely from a philosophical perspective, and not from a historical one. I should note he doesn't endorse mythicism, the belief that Jesus did NOT exist. He simply advocates for a skeptical position regarding the whole thing. Also, the rest of this post won't make sense unless you go read his article.
Law argues for 2 claims, using some thought experiments to intuitively justify them. He then uses those claims to form his argument for skepticism.
P1 Where a claim’s justification derives solely from evidence, extraordinary claims (e.g. concerning supernatural miracles) require extraordinary evidence. In the absence of extraordinary evidence there is good reason to be sceptical about those claims.
I am willing to grant this one. The bottom line he is going for is that we don't have enough evidence from the NT documents to justify the miracle claims therein. I think this is reasonable for the point he is trying to make, even if there is some argument over what counts as "extraordinary."
P2 Where testimony/documents weave together a narrative that combines mundane claims with a significant proportion of extraordinary claims, and there is good reason to be sceptical about those extraordinary claims, then there is good reason to be sceptical about the mundane claims, at least until we possess good independent evidence of their truth.
I disagree that this claim is reasonable, as I hope to show in my thought experiments. The background information we possess is just as important in evaluating testimony as any independent evidence of the mundane claims in question. Unless Mr. Law is willing to say that background information counts as independent evidence, P2 is invalid. If background information does count, it is unclear that P2 undercuts belief in Jesus' existence.
I will present an alternative to the "Ted and Sarah" thought experiment and another that I think better represents the evidence we have in the New Testament, and argue that the conclusions we draw are different in my situation, even though there is no additional evidence on the specific mundane facts we have in question.
Consider "The Magician Pranksters."
You read online about a group of anonymous individuals who are inviting themselves into peoples houses and performing magic tricks for them, then leaving without any explanation. The article gives good evidence that this is happening, as some sort of new prank kids are pulling these days.
Your friends Ted and Sarah come to you one day explaining that some people came into their house and did some really miraculous things. One of them made their couch float in the air, and the other one cut off her hand and then reattached it. Then, they both got up and walked through the front door while it was still closed. Both Ted and Sarah are absolutely convinced of the miraculous nature of these events, and neither mentions or knows anything about the online article you read. They stand by their story while you question them, insisting on what they saw.
Note that the story they tell involves a multitude of miraculous happenings integral to what happened, and that you have no independent evidence that Ted and Sarah had people to their house. According to P2, we have "good reason to be skeptical of the mundane claims" being made here, but intuitively that is not the case. If the example seems far fetched, or if you feel the article constitutes independent evidence, try this one.
"The Faith Healer"
A friend tells you she went to a big tent revival and saw a faith healer. She then regales you for a half hour on all the miraculous things she saw there. These include a man in a wheelchair getting up and walking, demons being cast out, long lasting pains being healed, and even a dead man in the basement being brought back to life. She tells you that the healer prophesied things about her that nobody could have known. You didn't read about the gathering in the paper or anything, and have no other evidence regarding it having taken place.
This is a perfectly realistic scenario, and according to P2 we are justified in doubting our friend ever went to a big tent revival. I think most people would find that conclusion absurd. In fact, the only evidence you would expect to find for a faith healer, regardless if you believe in that or not, is reports of a miraculous nature. It would be silly to assume that most faith healers didn't exist on account of the fact that testimony in regards to them often mixes the miraculous with the mundane. While we have every right to doubt the miraculous nature of what she witnessed, we recognize that such experiences are incredibly probable in the context of a big tent revival.
So there is a problem with P2 as it stands, and I would further suggest that the situation we have with regards to Jesus is closer to those I mention than to Mr. Law's examples. The reports we have of Jesus suggest he was a faith healer, and also a religious and political leader (a messiah). We know from non-biblical sources that healers and messiahs were relatively common during the time Jesus supposedly was teaching. We also know from current as well as ancient evidence that faith healers have miracles ascribed to them as a result of their vocation (it's right there in the title for God's sake). Further, we know from almost ALL ancient historical evidence that movement leaders have apocryphal and legendary stories attributed to them.
So the evidence we have for the existence of Jesus is consistent with his being recognized by his followers as an extraordinary individual. Much like our faith healer exists in a role today where we would expect miraculous stories to abound around them, Jesus was in a role in which we could expect miraculous stories to flock to him as well. Though this in no way is meant to prove he did exist, I think it shows that we have no more reason to be skeptical of his existence on account of the stories surrounding his life. There are certain contexts where those stories are expected, even if they are false.