Slimboyfat,
I'm not sure if it's a miscommunication issue on my part or if you're just being obtuse but let's give it one more try shall we? You made the claim:
This professor says the names Matthew, Mark, Luke and John were not applied to the gospels in the manuscript tradition before the mid-fourth century.
Plain and simple, the professor did NOT say this nor did he remotely imply it. He even went so far as to specifically point out that, for the Gospel of John, we have a late second century manuscript that includes the name. No one here is saying that the early manuscripts lacked these titles.
You attacking this guy for a position he doesn't hold.
More importantly, the reason the Gospels are "anonymous" is because the names were never meant to establish authorship. Rather, they were place holders to tell the narratives apart.
We know this for several reasons:
1.) The Greek preposition κατά (speculative - "handed down", "according to") is used to identify the Gospels instead of a proper genitive case that would imply an author's ownership or identity.
2.) None of the Gospels identify the Author's in the body of the work which was common practice at the time.
3.) The Gospels are written in the 3rd person instead of being first hand accounts.
4.) When the Gospels are quoted by early writers (Ignatius, Polycarp, Justin Martyr, etc.) they never use the Gospel names.
5.) It's highly unlikely that a fisherman (John) and a tollbooth collector (Matthew) would be literate. Even worse, as Galileans, they spoke Aramaic. Not the Greek the books are written in.