The Anonymous Gospels -- So What?
When I first started debating the truth of Christianity on the Internet, I was immediately challenged with the idea that we don't even know who wrote the Gospels. I responded, naturally enough, that the Gospels were the Gospels of "Matthew, Mark, Luke and John." Seemed easy enough to me, but it was quickly pointed out to me that nowhere in the Gospel accounts themselves do the authors identify themselves. From this the skeptics with whom I was discussing Christianity concluded that we couldn't know who wrote the Gospels -- after all, the Gospel accounts themselves don't identify the authors.
If you are ever challenged with this, the question that can be asked is to the Skeptic is: "So, you then would acknowledge the authenticity of the Pauline Epistles as well as the Epistles of Peter and John that identify Paul, Peter and John as the authors, correct?" This will put the skeptic over a barrel because they can only answer one of two ways: yes or no. (If they try a different alternative, press them for a yes or no.) Here's why this is important.
If they say yes, then you have won a major concession. Many scholars do not believe all of the letters of Paul were written by Paul (particularly the Pastorals), and there are questions about 2 Peter and 2 and 3 John. But if the skeptic is willing to concede that Paul, Peter and John actually wrote all of his letters, then the letters themselves establish the most crucial elements of the truth of the Gospels, i.e., Jesus was crucified for our sins and was raised again from the dead. Paul, while not an eyewitness, testifies to his conversations with the apostles (Peter, etc.) from which he knows about Jesus' crucifixion, and he also knows from first-hand experience that Jesus as risen (as the result of his experience on the Road to Damascus).
If the skeptic says that the mere identification of the author in the Epistles does not mean that Paul, Peter or John (respectively) actually wrote the Epistles then the follow up question becomes "So, what's your point?" You see, suppose that the Gospel of Mark had as its opening paragraph the statement: "This is the Gospel of Jesus written by John Mark, companion to Peter." Do you suppose that such an introduction would satisfy a skeptic that the Gospel was in fact written by John Mark? Of course it wouldn't. They would argue either (1) the paragraph wasn't part of the original, but was added later, or (2) the identification of the author is a fabrication (there may be other possibilities, but these will make the point).
You see, to the skeptic's way of looking at the Gospel, the mere identification of the author would not be enough to establish the authenticity of the identification. That must be shown, if at all, by other evidence that exists outside of the text itself. Since that is already the argument that takes place (is there good evidence that Matthew wrote the Gospel of Matthew, etc.?), then the failure to identify the authors in the text is simply one small piece of missing information that would make virtually no difference to those who want to doubt the authenticity of the Gospel.
But another question remains: Why are the Gospels anonymous? Since part of our apologetic to skeptics is that two of the books (Matthew and John) were written by eyewitnesses, that another (Mark) was written by a companion of an eyewitness, and the last (Luke) was written by a man who traveled with Paul and interviewed eyewitnesses (such as Mary, Mother of Jesus), why didn't these authors use their names in the title or the opening paragraphs? The New Advent Encyclopedia article on Gospel and Gospels when discussing the Titles of the four Gospels (which are admittedly not traceable to the four authors themselves) states a reason:
". . . the historical books of the New Testament differ from its apocalyptic and epistolary literature, as those of the Old Testament differ from its prophecy, in being invariably anonymous, and for the same reason. Prophecies whether in the earlier or in the later sense, and letters, to have authority, must be referable to some individual; the greater his name, the better. But history was regarded as a common possession. Its facts spoke for themselves. Only as the springs of common recollection began to dwindle, and marked differences to appear between the well-informed and accurate Gospels and the untrustworthy . . . did it become worth while for the Christian teacher or apologist to specify whether the given representation of the current tradition was 'according to' this or that special compiler, and to state his qualifications".
Make no mistake about it, the fact that the authors of the four Gospels did not identify themselves in the Gospel texts or titles is not only not conclusive that Matthew, Mark, Luke and John did not write them, it is almost irrelevant to the question.