Do you believe Socrates is historical? By the standard of evidence you seem to require, we can't consider him anymore than a mythical "philosopher-type" invoked as a mythic character to further particular points.
If Socrates wasn't historical, what would it matter? For example, would the strength of the writings attributed to him diminish if we found out that it was some other person, or maybe several people, who wrote them?
I think this is a key distinction between Jesus and other historical figures. For example, if Euclid didn't really exist as Euclid, for most purposes, so what? I may be overly generalizing here, but I think the interest in most ancient figures flows from their works; we deem
Elements to have merit in its own right, so we want to find out more about the person who created it. In the case of the Gospels, though, to a large degree the situation is reversed: much of the merit of the work is dependent on the merit of the subject. Even if Euclid was a fictional character,
Elements still describes a monumental work of mathematics. OTOH, if Jesus was a fictional character, then the merit of the New Testament is diminished.
The most basic question behind whether or not the gospels, or anything in them, can be regarded as historical is one of genre. If the gospels are merely myths, than we can safely regard virtually everything in them as unhistorical. The same holds true if they are plays, or ancient novels, etc. However, if the gospels were written with the intent to record factual information (in other words, an attempt at ancient history or biography) then a more serious consideration of their content is required.
Why this distinction? And does it even work?
I mean, there's quite a bit of information in the Gospels that is obviously meant to record fact: place names, date references to kings of Judea and Caesars, details of life and social organization in Judea and Jerusalem, etc., etc. At the same time, there's quite a bit of information that's (IMO) obviously mythical; it seems clear to me that the author's intent isn't just to record happenings in Judea 2,000 years ago, it's to launch a religion.
I think the most reasonable position is that the Gospels (and arguably the Bible as a whole, but that's a whole other matter) are a mixture of both history and myth. The question is where the line between the two sits.
Also, I think we need to factor into all this the problem of accuracy: consider certain details in the Gospels that appear to be historical. Did Herod's slaughter of the infants actually happen? If it did, it seems exceedingly odd to me that Josephus wouldn't have commented on it among the many details he wrote on Herod.
Did Nazareth actually exist in Biblical times? From what I've read, it was a cemetery during the lifetime of Jesus and would have been considered an "unclean" place to Jews.
When was the Roman census, and was it actually required for all the citizens to return to their family hometowns to be counted?
I'm not sure if this is the case among Biblical scholars, but I think that the term "historical" implies "reliable", or at least "potentially reliable". When you use the term "historical" to describe Jesus and events of the Bible, what exactly are we supposed to be able to conclude from that?
Interestingly enough, however, there is still a nugget of historical information, even within this clearly mythic story handed down over hundreds of years, with little attention paid to accuracy in transmission (in fact, innovation and variety were important aspects of oral mythic tradition for the Greeks). Scholars at one time doubted whether or not Troy ever existed, and then we found it. So despite the fact that the genre here is clearly myth, the possibility for historicity remains.
However, the fact that there was a city of Troy doesn't necessarily mean that the Trojan War occurred, or that any of the central characters of the Iliad actually fought in it if it did. It certainly doesn't mean that the war was sparked by divine interference in human affairs at a dinner party.
Take another story:
The Day of the Triffids. Its details of English geography and world politics circa 1950 are likely very accurate. Is The Day of the Triffids "historical"?
You mentioned the possibility of fantastic events occurring in otherwise-historical works. However, how exactly are we supposed to decide what's historical and what's not in a work like that without some outside frame of reference with which to judge what's reasonable and what's not?
So where do the gospels fit into all of this? What I have been trying to establish is that just because an ancient work includes theology or miraculous stories does not mean it should be excluded from the genre of ancient history. Ancient histories contained these things. Nor should the fact that there are inaccuracies (such as the census in Lukes birth narrative) exclude it, as ancient historians often relied on rumor and often made mistakes.
That isn't just mentioned in passing, though: the census is presented as
the reason why Jesus was born in Bethlehem. I personally think that it points toward a later attempt to make the Jesus story fit Jewish Messianic prophecy.
Another common criterion is that of embarrassment. Many things in the gospels actually do not make Jesus look that good, and yet are recorded. For example, Jesus baptism by John make John look superior to Jesus, or Johns disciples asking if Jesus was the one foretold, when John was supposed to know that Jesus was the messiah. The gospel authors may try to explain these events, but they are nonetheless recorded, indicating once again the authors are writing a form of ancient history. Scholars look at those aspects of the gospels which are embarrassing to Christians, and tend to judge them as having a greater chance of actually having happened, because the gospel authors wouldnt make up stories to make Jesus look bad, nor would others add to the Jesus tradition narratives or sayings or stories which were embarrassing.
I really don't see how you can call the baptism story "embarrassing" for Jesus. If Jesus being baptized by John makes John look "superior" to Jesus, doesn't this fit in with a theme that runs throughout the Gospels of Jesus lowering himself? "Blessed are the meek", the washing of feet and all that?
Also, I don't think you can look at it so much as a matter of embarrasment as
disbenefit: it might be true that people won't lie unless they think they can get something out of it, but sometimes that's served by looking slightly foolish if it means getting what you want.
From what I gather, there was a group paralleling the early Christians who considered John the Baptist to be the Messiah. I can see the passages about John, including the baptism story, as a way to try to bring them in... almost like a celebrity endorsement:
"See! Even the person you think is the Messiah realized that our Messiah is the real Messiah! Come and join us!"
This effect could potentially be of great benefit to the Gospel authors, regardless of any "embarrasment" that it implies (though I don't think it actually implies that anyhow).
A third fairly common criterion of historicity is the recording of an event of saying multiple independent sources. Matthew and Luke appear have both used Mark, and to have drawn from a source we call Q, in addition to having access to other parts of the Jesus tradition. Many scholars argue that the extra-canonical gospel of Thomas is also independent from the Synoptics. So when a saying is found in Thomas, Q, and Mark, it is more likely to be historical, as it is confirmed by multiple sources.
But if Thomas, Q and Mark are all products of the community of early Christians, are they really multiple independent sources?