Answer
With regard to historical writings not included in the Bible, it has never been the Christian position that these are necessarily reliable. Whether the authors are outside the church like Josephus and Philo, or within the church like the earth church fathers, these historical writings are not infallible. So, inconsistencies between their accounts and the accounts in the Bible are to be expected, and should not in and of themselves cast doubt on the reliability of Scripture.
With regard to other historical data, such as the findings of archaeology, etc., the data is always open to interpretation — this is true whether it appears to support or to refute the Bible. We should not rely too heavily on science either to prove or to disprove our faith. The reality is that scientific historical reconstructions are speculative at best. Most of the data from those periods has been lost. Yes, there are buildings, writings, etc. But when you compare the data that we currently possess to the vast amounts of data that have been lost (millions of people, the entire records of all their lives, their buildings, their writings, their conversations, their possessions, objects, etc.), what we have is a pittance. We can know some things with a bit of clarity, but most of what we claim to know is speculation. It is a bit like trying to reconstruct a huge jigsaw puzzle based on one or two pieces. We can see the extant pieces relatively well, but we have no idea how the recovery of the missing information might affect our understanding of those extant pieces.
The Bible itself teaches that our faith is counter-intuitive from a human perspective (1 Cor. 1:18-25). Therefore, it is mistake to base our faith on science, archaeology, Josephus, etc. If we base our faith on these things, it will only be as strong and as secure as the latest scientific theory (and we all know that scientific theories change all the time). A right interpretation of science will always confirm our faith, but it is very hard for fallen human beings to arrive at right interpretations of the natural world, particularly when it comes to God's interaction with it. Moreover, our faith is grounded first and foremost in a person, namely God, and our confidence in history as a reliable record of the facts is based on our confidence in the God of history.
Jesus was a typology
It is not unreasonable to think that the people of the first century might have constructed a typology and invented a character to embody it. Christians accuse other religions of doing this all the time. But just because the time and place are ready for such an invention does not imply that any such character who arises must be an invention. Besides this, there are far too many problems with such a reconstruction, not the least of which is that it fails to take account of the way Jesus embodied the Old Testament. Whatever similarities there are between Jesus and pagan gods, these are dwarfed by the similarities between Jesus and the Old Testament.
Jesus did not exist
It is essentially impossible to prove a universal negative in the class of "Jesus never existed." In fact, even most liberal scholars these days have realized the futility of this kind of argument and have abandoned it. One problem is that the lack of evidence for a person's existence is not proof of his non-existence. For example, we know that millions of people lived and died in that time period, yet we have proof of the personal existence and identity of very few individuals. A second problem is that it is arbitrary to discount the New Testament evidence for Jesus' existence, which must be done in order to support this claim. In this regard, there are glaring inconsistencies in the ways certain scholars accept some historical writings as trustworthy and reject others. In Christianity, we have a basis for making these distinctions: faith and tradition. But science cannot appeal to these bases, and therefore ends up making selections according to arbitrary standards — typically standards that are conveniently designed to support the conclusions of the researcher. For example, nearly every modern critic employs the scientific method, which is an insufficient method for discovering realities beyond the natural realm, and which is incapable of properly incorporating data that can't be verified or repeated.
There are many good books responding to these types of issues. A couple that I have found useful over the years are The Historical Reliability of the Gospels by Craig Blomberg (IVP, 1987) and The Modern Search for the Real Jesus by Robert B. Strimple (P&R, 1995). Obviously these won't deal with every new argument since their publishing, but they do help orient readers to the issues involved in any attempt at historical reconstruction. You might also be interested in the apologetics of Cornelius Van Til, who provided persuasive philosophical reasons to accept the worldview of Christianity as the only sufficient explanation for the world we know.
Hope this helps,
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.