One often hears the claim, made frequently by skeptical scholars and laypeople alike, that we have no grounds on which to think the four canonical gospels were actually written by the people to whom they are ascribed. The original documents, we are told, were written in anonymity, the attributions being added by scribes at a later date. This claim is made frequently by the notorious textual critic Bart Ehrman. Is Ehrman's assessment correct here, however? Do we have any evidence which might indicate the authorship of the four gospels?
Ehrman is actually mistaken in his assertion that we know the original documents did not bear the name of their author. As Ehrman knows full well (he's constantly reminding us), we don’t have the original documents in our possession (as is the case for all sources of that time period) and so we couldn’t possibly know for sure one way or the other. But I think there is positive indication that the gospels were written by the persons to whom they were attributed by the early church (Matthew, Mark, Luke and John).
One example would be the fact that two of the gospels are ascribed to such minor characters as Mark and Luke -- neither of whom, by any accounts, were themselves eyewitnesses. Had a forger wanted to acquire credibility for his writing he would undoubtedly have attributed it to someone like Peter, Thomas or James (as the later second and third century Gnostic gospels did).
Actually, there is some compelling evidence (both external and internal) that Mark penned the eyewitness accounts of Peter. For example, Justin Martyr, writing around A.D. 150, spoke of Mark's Gospel as "the memoirs of Peter." He suggested that Mark wrote down his material when he was in Italy (which concurs with other early tradition which indicates that the gospel of Mark was penned in Rome for the benefit of the Christians there. Iraeneus (writing approx. A.D. 185) referred to Mark as "the disciple and interpreter of Peter." Most famously, Papias, the bishop of Hieropolis (writing approx. A.D. 140) wrote,
"And the presbyter [the Apostle John] said this: Mark, having become the interpreter of Peter, wrote down accurately whatsoever he remembered. It was not, however, in exact order that he related the sayings or deeds of Christ. For he neither heard the Lord nor accompanied Him. But afterwards, as I said, he accompanied Peter, who accommodated his instructions to the necessities [of his hearers], but with no intention of giving a regular narrative of the Lord's sayings. Wherfore Mark made no mistake in thus writing some sayings as he remembered them. For one thing he took especial care, not to omit anything he had heard, and not to put anything fictitious into the statements."
It is curious, then, that Mark's gospel did not become “the gospel according to Peter” but, rather, “the gospel according to Mark”.
I also think that the gospel traditionally attributed to John claims that authorship. It refers throughout to the certain “disciple whom Jesus loved”, a disciple who is clearly John but who is never mentioned by name. Given that John is a very prominant disciple in the three other gospels (the synoptics name the Apostle John approximately 20 times), this is very curious indeed, and suggests that the author assumed his readers would know who the author was. In the final chapter of John’s gospel, he writes, “This is the disciple who testifies to these things and who wrote them down.” In addition, there is some strong external corroboration for the Johanine authorship of John's gospel. Irenaeus (A.D. 130-200), who was a student of Polycarp (A.D. 70-160), who in turn was student of the apostle John, testifies to the Johanine authorship of John and asserts that it was written when John was in Ephesus and when he was well on in years.
There is also some supportive evidence, I think, for the traditional authorship of Luke. Apart from being another fairly minor character (and not one of the twelve disciples), we also know that Acts of the Apostles is written by the same individual as Luke’s gospel. From Acts 16 onwards, the narrator routinely employs the pronouns “we” and “us”, which suggests that the narrator is in close contact with Paul and his companions. Moreover, much of the information relayed in Acts is unlikely to be known by an individual who had not completed that trip -- or, at the very least, been in contact with someone who had. Indeed, Paul, in his letters, refers to his companion Luke three times (Colossians 4:14; 2 Timothy 4:11; Philemon 1:24).
The evidence for the authorship of Matthew's gospel is weaker than for the other three. Matthew's gospel would certainly have to have been written by someone who was familiar with the time and place (e.g. see Peter William's lecture
here). The Gospel's authorship, as is the case for all four gospels, goes unchallenged in the early church. In his
Ecclesiastical History, the church historian Eusebius (A.D. 265-339) quotes Origen (A.D. 185-254), stating,
"Among the four Gospels, which are the only indisputable ones in the Church of God under heaven, I have learned by tradition that the first was written by Matthew, who was once a publician, but afterwards an apostle of Jesus Christ, and it was prepared for the converts from Judaism."
To conclude, there is no good reason to doubt the traditional authorship of the four gospels, and there are various internal and external indicators to suggest that the traditional authorship is correct. I could continue in the same vein, listing such evidences, for some time. For a fuller discussion of the topic, I refer readers to Richard Bauckham’s book
Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony.
This was previously posted at my personal blog here. 
