Winky-face noted and appreciated!

But seriously, by my accounting, every standard of evidence I know includes an element of faith. The only differences between them are (a) what is taken on faith and (b) how credulous that faith is.

Namely, I find faith elements in believing:

• first/second/third-hand reports, even by trained, neutral observers

• expert consensus

• single expert opinion

• by contradiction

• the evidence standards of American civil and criminal trials (note the plural, "standardS". The standards are different between them.)

• induction, including (perhaps) mathematical induction

• "engineering quality" proof

• "mathematician quality" proof

My professional practice as an aircraft mishap investigator is to identify and apply the highest feasible standard from the above list, based on what information is available. "Best practice" in this industry dictates that selection and application of a standard of evidence is a matter of prudential judgement, based on the consequences and probabilities of being wrong, the resources available (evidence, time and $), while being scrupulously open about ones methods.

On historical questions about events of 20 centuries ago, the quality of evidence is not very good. About pretty much everything. What we are left with is Bayesian stuff. Anybody who goes to 0% or 100% draws the raised eyebrow from me. :-)

And there is serious historical thought that Mohammed, too, was fictional

Yeah, that's a ludicrous idea too. Some people seem to think that "fictional" is the null-hypothesis, to be believed by default unless there's an extraordinary amount of evidence to the contrary. This is nonsense: Fictional characters of historical influence aren't more common than real people of historical influence.

This is bias at its most obvious.

If you believe that someone made a fictional character up, and then he made thousands of near-contemporaries believe in his existence, that's a rather extraordinary hypothesis, which has a very low prior given that nobody else seems to have ever managed this feat ever.

Muhammed existed. Jesus of Nazareth existed. The evidence are overwhelmingly in their favour -- including the various bits of inelegancies and clumsinesses in their life-stories that only real-life people display, not fictional characters constructed at their time-period. And there's not a single piece of evidence that someone authored them as fictional characters.

The real problem with either question is the excessive interest in getting the "right" answer.

Right in quotes? Are we now pretending that truth has a subjective value now? This is about being less wrong, and people that assume "fiction" to be the default hypothesis, and that discount religious texts as evidence just because they are religious texts, they are more wrong than other people.

If e.g. Socrates turned out to be a fictional character invented by Plato, philosophy wouldn't care.

Socrates existed too.

Nor do I know of any fictional characters that are so deliberately placed recent history and yet their existence is believed by their contemporaries as real.

How about Huangdi?

"Throughout most of Chinese history, the Yellow Emperor and the other ancient sages were considered to be real historical figures. Their historicity started to be questioned in the 1920s by historians like Gu Jiegang, one of the founders of the Doubting Antiquity School in China. In their attempts to prove that the earliest figures of Chinese history were mythological, Gu and his followers argued that these ancient sages were originally gods who were later depicted as humans by the rationalist intellectuals of the Warring States period. Yang Kuan (楊寬), a member of the same historiographical current, noted that only in the late Warring States had the Yellow Emperor started to be described as the first ruler of China. Yang thus argued that Huangdi was a late transformation of Shangdi, the supreme god of the Shang pantheon.

[snip]

Most scholars now agree that the Yellow Emperor was originally a deity who was later transformed into a human figure."

These all seem to me to be false dichotomies, which assume that it's impossible either for a single creator to have embroidered their story as they went along, or for multiple creators or editors to have changed the story at different points in time.

According to the messianic prophesies (of which Jesus fulfilled practically none even according to generous interpretations) the messiah was supposed to be born in the land of David, which was Bethlehem. Being from somewhere else was inconvenient for a prospective messiah, so his followers had an incentive to claim that he was from there even if he really wasn't. The hypothesis of a real cult leader whose followers wanted to believe he was the messiah predicts the nonsensical census story better than the hypothesis of an imaginary figure who was invented to be a messiah; much simpler and more convenient to simply say that his family was from Bethlehem.

These all seem to me to be false dichotomies, which assume that it's impossible either for a single creator to have embroidered their story as they went along, or for multiple creators or editors to have changed the story at different points in time.

You know there's no impossibility -- that's why I said "I assign less than 5% probability", I didn't say "I assign 0% probability". I'm talking about the probabilities of each scenario. Conditional and prior.

If you considered that, and you didn't treat "completely fictional" as the default, needing extraordinary evidence to decide against it, but having hardly any evidence in its favour, I think you'd reach the same conclusion as I

Also we don't have any evidence that Jesus' contemporaries believed he was real. The reports of people believing Jesus was real come from long after Jesus supposedly died.

And considerable evidence of belief in the first century that Jesus was not corporeal, but an ideal (docetism). This was a major point of theological contention. The notion of a human Jesus did not achieve popularity until well into the second century.

There were quite a few troublemaking preachers who fell afoul of the law in Judaea at the time, many of whom were called Jesus - it was a very common name at the time.

However, one of the big problems with assuming one of these fellows (or another we have no documentation of) was the human seed for Christianity is the early Christian tradition of docetism - that Christ had no corporeal existence at all, and was just an idea. Paul of Tarsus certainly seems to think along these lines, despite the later caution against said notion in John.

This also helps explain the curious lack of non-Biblical evidence for such a person, in histories where one would expect it.

It is often noted by apologists that scholars think there's enough evidence to say there was a human seed for Christianity. However, "scholar" in this context is a weasel word - most are Christians and theologians, who would have tremendous trouble (personal and professional) coming to the opposite conclusion at all. The epistemological standards accepted in Biblical history in particular are generally bloody awful and an embarrassment to other ancient historians.

For a pile of stuff on this issue I recommend the RationalWiki article, which I have worked extensively on. (One of the other main contributors just so happens to be an atheist who was a student of Biblical history.)

(I find this stuff fascinating, if only for the psychopathology. And, as such strident atheists as Mencken, Dawkins and Hitchens have noted, you can't be highly literate in English without knowing the KJV, much as you need to know Shakespeare and Greek mythology. The trouble is that ... well, it's like you wanted to study the Odyssey or the Iliad but the only people to learn from were people who (a) actually believed in all the gods named therein (b) really wanted you to as well.)

Documentary evidence that dates from the time of Jesus' supposed life and death, which describes a religious leader called Jesus who started a splinter sect of Judaism would do it.

What documentary evidence for any other religious leaders that started other splinter sects of Judaism at the time do you have?

If you don't have any direct evidence for any specific one of those leaders, does that mean there didn't exist any such splinter sects at the time?