From a historiography standpoint, this is mostly an 'academic' exercise, since the 'existence' of Jesus of Nazareth could easily be established with only a tiny fraction of our New Testament documents. The mere existence of someone in history is (often) easily established on the basis of small textual samples (sometimes even single paragraphs). The amount of data (especially historically 'incidental') we have about Jesus in the New Testament--and the appearances that the authors were not collusive--gives us a very, very high level of assurance in this matter.
Again, professional and academic scholars of the period -- Christian, Jewish, Secular -- accept the New Testament as an adequate witness, both for historical 'existence' and for many pieces of historical detail about Jesus.
I should also mention at the outset that, in spite of the sporadic complaints on the Internet about the matter(!), the manuscript evidence in support of the iron-clad, "pre-accretions" reference to Jesus in Jospehus is strong, stable, and accepted by the mass of professional historians. Between the NT and Jospheus, there is no serious reason whatsover to doubt the historical 'existence' of the Jesus of Nazareth behind those references.
The internet debate about this subject (generally NOT participated in by the more historically-informed skeptics and Christians) is a very peculiar phenomenon. Graham Stanton is a New Testament scholar of a 'moderate' position. In the most recent edition of his excellent "The Gospels and Jesus" (Oxford:2002), Professor Stanton includes this section commenting on the debate [GAJ2, 143-145]:
"Many readers will be surprised to learn that the very existence of Jesus has been challenged. From time to time since the eighteenth century a number of writers have claimed that our gospels were written C. AD 100 (or later) and that only then did the early Christians 'invent' Jesus as a historical person. During the communist era Soviet encyclopaedias and reference books consistently made that claim. In recent years the existence of Jesus has been debated heatedly on the Internet.(Also, it should be noted that I am MERELY dealing with the issue of evidences for Jesus' EXISTENCE--NOT for his character, words, deeds, etc.)
"The most thoroughgoing and sophisticated statement of this theory has been set out in five books by G. A. Wells; the most recent is The Jesus Legend (1996). His case is quite simple: until the beginning of the second century AD Christians worshipped Jesus as a mythical 'Saviour' figure; only at that point did they make their 'Saviour' a historical person who lived and taught in Galilee.
"This intriguing theory rests on several pillars, all of which are shaky. Nonetheless it is worth taking it seriously, for it raises important issues for the student of the gospels.
"Wells argues that before C. AD 150 there is no independent non-Christian evidence for the existence of Jesus. The slender Jewish and pagan references to Jesus all echo Christian insistence that Jesus died under Pontius Pilate-and Christians began to make this claim only at the end of the first century. Why did Roman writers such as Tacitus, Suetonius, and Pliny say hardly-anything about Jesus and his followers? As Wells himself concedes, from their point of view Jesus and earliest Christianity were no more important than the many other charismatic religious leaders and movements which were two a penny all over the Roman empire-and Palestine was a remote corner of the empire!
"Wells stresses that in the earlier New Testament letters there is a strange silence about the life of Jesus and his crucifixion under Pontius Pilate. Wells notes (correctly) that the very earliest Christian credal statements and hymns quoted by Paul in his letters in the 50s do not mention either the crucifixion or Pilate, or in fact any events in the life of Jesus. But as every student of ancient history is aware, it is an elementary error to suppose that the unmentioned did not exist or was not accepted. Precise historical and chronological references are few and far between in the numerous Jewish writings discovered in the caves around the Dead Sea near Qumran. So we should hardlyexpect to find such references in very terse early creeds or hymns, or even in letters sent by Paul to individual Christian communities to deal with particular problems.
"Wells claims that the four gospels were written C. AD 100 and that the evangelists largely invented their traditions about the life of Jesus. But by this date Christianity was flourishing in many parts of the Roman Empire: it had hardly survived at all in Palestine and the four gospels were almost certainly not written there. If, as Wells claims, they were largely invented in a Roman and Hellenistic cultural setting, it becomes much harder than he supposes to account for the numerous details, many of which are purely incidental to the purposes of the evangelists, which do fit into our knowledge of first-century Palestine.
"As we have stressed repeatedly in the preceding chapters, traditions about Jesus were preserved and to a certain extent modified in the light of the convictions about his significance held by his followers in the period after Easter. But indications of modification do not (as Wells supposes) necessarily imply invention. If the gospel traditions were invented about AD 100 why is it far from easy (with the exception of John's gospel) to find in them traces of the convictions, emphases, and problems of the Christians of that period?
"Why would proclamation of Jesus as a historical person assist Christian evangelism more than proclamation of a mythical figure? If the historical existence of Jesus was invented only in about AD 100, why was it necessary to create so many detailed traditions?
"We have a good deal of information about the polemical and often bitter arguments Christians, Jews, and pagans had with one another in the early centuries. But the early Christians' opponents all accepted that Jesus existed, taught, had disciples, worked miracles, and was put to death on a Roman cross. As in our own day, debate and disagreement centred largely not on the story but on the significance of Jesus.
"Today nearly all historians, whether Christians or not, accept that Jesus existed and that the gospels contain plenty of valuable evidence which has to be weighed and assessed critically. There is general agreement that with the possible exception of Paul, we know far more about Jesus of Nazareth than about any first- or second-century Jewish or pagan religious teacher."
Jesus lived His public life in the land of Palestine under the Roman rule of Tiberius (ad 14-37). There are four possible Roman historical sources for his reign: Tacitus (55-117), Suetonius (70-160), Velleius Paterculus (a contemporary), and Dio Cassius (3rd century). There are two Jewish historical resources that describe events of this period: Josephus (37-100?), writing in Greek, and the Rabbinical Writings (written in Hebrew after 200, but much of which would have been in oral form prior to that time). There are also sources (non-historians) writing about the Christians, in which possible mentions are made (e.g., Lucian, Galen).
Of these writings, we would NOT expect Velleius to have a reference to Jesus (i.e. the events were just happening OUTSIDE of Velleius' home area), and Dio Cassius is OUTSIDE of our time window of pre-3rd century. Of the remaining Roman writers--Tacitus and Suetonius--we have apparent references to Jesus (discussed below), even though the main section in Tacitus covering the period 29-32ad is missing from the manuscript tradition. If these are genuine and trustworthy 'mentions' of Jesus, then we have an amazing fact--ALL the relevant non-Jewish historical sources mention Jesus! (Notice that this is the OPPOSITE situation than is commonly assumed--"If Jesus was so important, why didn't more historians write about Him?" In this case, THEY ALL DID!).
Of the Jewish resources--Josephus and the Rabbinical writings (e.g. Talmud, Midrash)--BOTH make clear references to the existence of Jesus (even though the details reported may be odd). So ALL the Jewish sources refer to Him.
In addition, there are three OTHER candidates for historical 'mentions' of Jesus that fall in the 2nd century: one Roman (Pliny the Younger) , one possibly Syrian (Mara Bar Serapion), and one Samaritian (Thallus). [We can also include here the writings of Celsus, Galen, Lucian]
I would like to take these in probable historical order.
Let me also just mention something about the Josephus issue. Every now an then I get an email about someone abjectly 'dismissing' the data from Josephus, without even interacting with the data and the positions of solid scholars. This is inappropriate. By far and away, the bulk of modern scholarship accepts that Josephus makes two independent references to Jesus--to argue otherwise requires the objector to dismantle the historical consensus, and this requires argumentation instead of simple assertion (and disallowance of Josephus as a witness!). One of the leading scholars, translators, and commentators on Josephus is Steve Mason. In his book on Josephus and the New Testament (Hendrickson:1992), he discusses the two references to Jesus in Josephus' writings, and concludes that "if it were needed", they would provide independent testimony to the existence of Jesus. He writes:
"Taking all of these problems into consideration, a few scholars have argued that the entire passage (the testimonium) as it stands in Josephus is a Christian forgery. The Christian scribes who copied the Jewish historian's writings thought it intolerable that he should have said nothing about Jesus and spliced the paragraph in where it might logically have stood, in Josephus' account of Pilate's tenure. Some scholars have suggested that Eusebius himself was the forger, since he was the first to produce the passage…Most critics, however, have been reluctant to go so far. They have noted that, in general, Christian copyists were quite conservative in transmitting texts. Nowhere else in all of Josephus' voluminous writings is there strong suspicion of scribal tampering. Christian copyists also transmitted the works of Philo, who said many things that might be elaborated in a Christian direction, but there is no evidence that in hundreds of years of transmission, the scribes inserted their own remarks into Philo's text. To be sure, many of the "pseudepigrapha" that exist now only in Christian form are thought to stem from Jewish originals, but in this instance it may reflect the thorough Christian rewriting of Jewish models, rather than scribal insertions. That discussion is ongoing among scholars. But in the cases of Philo and Josephus, whose writings are preserved in their original language and form, one is hard pressed to find a single example of serious scribal alteration. To have created the testimonium out of whole cloth would be an act of unparalleled scribal audacity." (p.170-171)
This will take a while, but I plan to take these in chronological order in my analysis.