So it was a delight to receive an email from one of our trainee teachers at Maryvale Institute was asked this question:
Can you give me a definitive answer to the authors of the Gospels please Fr Peter? I think Mark and John were apostles of Jesus and Luke was a follower of Peter I think? I am confused. When I did RE A level John was probably the Elder and not the apostle or the Beloved. Anyway if you have a minute I would be grateful if you could give me an answer.
Here is my quick (and rather unreferenced) answer:
The authorship of the Gospels has long been discussed and debated. If you delve into a good Bible commentary, such as the Jerome, it will give you an overview of the debate. Suffice to say there are traditional answers and the current critical consensus. The latter should not be considered to be definitive.
(A recent book on some of these issues has been written by Fr John Redford, entitled "Who was John?" It is available in the Maryvale bookshop!)
To a certain extent, we should be cautious about the term 'author'. A reading of what we call the Synoptic Gospels (Mt, Mk and Lk) shows that to a large extent they were editors, forging together material they had collected. John seems to put more creativity into the task, but continues to follow the inherited outlines of the story - especially in the passion.
Bear in mind also that only Luke's Gospel actually includes a reference to the evangelist in the text itself. Some would argue that the names of Mark, Matthew and John (esp Mt) are later ascriptions (though surely very very early).
Another point to remember is that in the ancient world (as indeed today), the name on the top of the document (or at the bottom) does not necessarily indicate that that person wrote every word. Quite beside the matter of sources, writers would also have those who wrote for them (amanuenses) who might have been like modern day copy typists, but at other times - like a modern day secretary - might have had more freedom. The end of John's Gospel certainly appears to have been 'completed' by a disciple of the 'author', and it could well be that the writing of the Gospels were collaborative activities.
So, when we use the term evangelist (better than 'author') we probably means the principal director or authority behind the Gospel project, the precise extent of whose involvement it is impossible for us to know.
The traditional identifications are that Matthew (aka Levi) and John were amongst the apostles of Jesus. Mark (aka John Mark) was a follower of St Paul, who took Peter as a major source. Luke is the only gentile evangelist, who also wrote the Acts of the Apostles, and was a doctor who accompanied St Paul on some of his journeys.
Much critical scholarship in the 19th and 20th centuries has rejected all these identifications, mainly because there has been a desire to see the writing of the Gospels to be much later than the lives of the individuals themselves. However, this is very much an open question, and more recent writing has tended to move back to earlier dates.
For my own part, I think it is pretty safe to operate on the basis that the traditional ascriptions are broadly correct, especially if you are to qualify what you say and write by saying, for Mark for example, 'thought to be the John Mark mentioned by Paul' - this indicates that you are aware of the debate, which is by no means final.
My one hesitancy is over Matthew. Though the matter is still hotly debated, the critical consensus remains that Mt depends on Mk for much of his text, and it is hard to see how this could be if Mt was an eyewitness.
However, more to the point is whether this matters at all in most circumstances. When writing about the content of the Gospel, we can comfortably say 'Matthew writes ...' (though remember to say Jesus says when Jesus says). If asked in the classroom, we can honestly say that Mt is traditionally thought to be one of the apostles, though we can't be sure. (After all, the Gospel itself doesn't tell us). Who the evangelist Matthew was - or were - does not have very much bearing on the content at all from a spiritual-theological point of view, and only limited importance for historical studies.
From a Catholic understanding, each of the Gospels is part of holy Scripture, as defined by the Church, which teaches that the writers were inspired by the Holy Spirit to give us God's word, but also wrote as human authors. Who these people actually were is relevant to understanding what they wrote, but whoever they were, their words remain part of Scripture.
Of course, when these issues would really matter is if you were writing an essay with the question "Who was Matthew?" If you ever do so, I would be delighted to read a copy!