What are the arguments that Bible specialists, historians, and classicists pursue when they define the historical JC?
That's a bit like asking "what are the arguments that linguists pursue when they define grammar"? A simple answer is possible, but pretty useless. They use the same arguments historians use everywhere.
There are, however, central issues particular to this case. One is genre. A final paper I wrote as an undergrad for my classical languages degree was a comparison between the historical Socrates and the historical Jesus, both in terms of the history of research on the two, and ways methods used in historical Jesus studies could be applied to the historical Socrates. I have already posted a very brief (relative to the paper) extraction on this issue in a former thread:
http://www.religiousforums.com/forum/2805645-post157.html
http://www.religiousforums.com/forum/2805647-post158.html
Genre is one part of determining the probability (not numerical) that a source contains historical information. But it is not the only part for many reasons. One is that clearly mythic or literary sources can contain historical information and do.
I refer more to Attic plays than I do something like the Iliad. Yet for the sake of illustration (perhaps comparison?) you may know or have heard of the ongoing debate over certain Hittite texts and their relation to Ilium and the Achaeans.
Now, while I consider it a fairly well established but by no means unquestionable hypothesis that archaeological excavations have found "Troy" or Ilium (that is, the Ilium of the Iliad is a real place), the idea that there is anything more we can say about the history of "the Trojan war" and Homer's characters borders on conspiracy level speculation. Yet this has been an ongoing debate among historians, linguists, and archaeologists almost since the Hittite texts were recovered. The most infamous scholar here is (I believe) Latacz, whose book
Troia und Homer. Der Weg zur Lösung eines alten Rätsels I did not know was the German original of the book I bought (
Troy and Homer: Towards a Solution of an old mystery) until I received it, which really annoyed me because
1) It means that at some point I'll have to buy the German edition and I've wasted my money and
2) It was a stupid and easily corrected mistake that I have only myself to blame, which is the worst possible situation when it comes to laying blame for a problem one has at the feet of anyone or doors of any establishment.
That said, Latacz's final section opens with a reference to a chapter from Bryce's
The Kingdom of the Hittites: "In 1998 one of the leading Hittite scholars, Trevor Bryce, attempted to collate some of these facts, if far from all, in order to present a general picture in a separate chapter of his book,
The Kingdom of the Hittites, which he entitled The Trojan war: myth or reality? He concludes that there can no longer be any doubt that the story of the Trojan War has a basis in history". Latacz concurs, and closes his book with "We can then formulate our conclusion thus: at the point which research has now reached, it may be that we cannot yet say anything definite about the historicity of the Trojan War. However, the possibility that a historical event could underlie the tale of Troy/Wilios...has not diminished as a result of the combined research endeavours of various disciplines during the last twenty years or so. Quite the reverse: it has grown ever stronger.
The abundance of evidence pointing precisely in this direction is already almost overwhelming. And it grows with every month in which new shafts are driven into the mine of mystery by archaeologists, scholars in Anatolian, Hittite, and Greek studies, linguists, and many other representatives of divergent disciplines, all working with strict objectivity and all under the spell of the problem of Troy...The earlier uncertainty dissolves and the solution seems nearer than ever. It would not be surprising if, in the near future, the outcome states: Homer is to be taken seriously."
Thankfully, although there are those who, to varying degrees, would say they agree with the above, it is by no means unchallenged and (although I have not done the research necessary to say this with certainty) I would hazard a guess that most scholars who have participated in the research describe would
not agree.
In a nice tie in with biblical studies, we find in the volume
Epic and History a paper by Jonas Grethlein: "From Imperishable Glory to History: The Iliad and the Trojan War". The paper criticizes Latacz for many reasons, but more importantly makes a much more reasonable claim about epic and history:
"What, then, can we conclude about the
Iliad and history? Greek epic may not be the best instance for elaborating on the use of epics as historical sources, since our comparative evidence is basically the archaeological record. Yet for this very reason Homer is an indispensable source for the student of ancient Greece. While using the
Iliad as a
Quelle is highly problematic, the
Iliad does provide rich insights as an
Überrest.
Homer is not of much use as a guide to the history of events, but he presents important evidence for social history."
In "
Homer and History: Old Question, New Evidence" provides a better (IMO) description of those like Latacz: ""This paper seeks to apply new evidence...to enduring Homeric questions. To some, of course, any discussion of possible elements of historicity in the Homeric epics provides an example of the credulous in pursuit of the tenuous, futiley attempting to circumscribe chronologically the imagination of the poet."
I refer to this source for three reasons:
1) I tried to find something that I could link to, and this was available
2) I like the poetic flourish present in "an example of..."
3) If you follow the link and look at the final page (32) before the notes, there is a quote that begins with "The second millennium before Christ". It is of no direct relevance to the historical Jesus other than to situate the time period of the discussion of historical events we are talking about with the Homeric epics and that of Jesus. So not only do we have something that everybody agrees is epic poetry, that nobody knows who (if any single person did) compose or when it was composed, but finally it is describing events that everybody agrees at least happened several hundred years before the early dates for the composition of the Iliad (8th/9th century BCE).
We don't know who wrote it. We don't know when the wrote it. It is clearly epic poetry filled with myths. We have terrible manuscript attestation to use for textual criticism and there are even words that are used only once in all of Greek literature in Homer so that we aren't even sure what they mean.