“We think that Matthew used Mark and undefined other sources, while creating some of the sayings material. Luke used Mark and Matthew, as well as other sources, and the author also created sayings material.”
So says E.P. Sanders and Margaret Davies in their book, Studying the Synoptic Problem.
I tend to be of the persuasion to argue against the inclusion of oral tradition because it, like Q, cannot be proved. Instead of allowing that the authors were creative, and used orality creatively to produce literary works that aren’t based on any particular tradition (think of the ways that first and second century Jewish theology that made analogies of previous Rabbis).
Here’s my argument:
Mark is first. While we might like to suggest that Mark just used a free hand to create his exposition, it is neither logical nor supported by the internal archaeology. By this, I mean that the Gospel contains at least one historical exorcism from which it is easy to see that the other exorcisms were based upon.
Matthew uses Mark, but makes it a religious, sectarian Jewish document, perhaps as some argued, while sitting in Antioch rather than Rome (Mark). This explains the push for Peter, among other things. More on that in the book. There is also some archaeological evidence in Matthew of early teachings that dated better to the time of Jesus.
Luke, a second generation now-Christian writer, uses Mark and Matthew and then builds his own work. I believe that while I can show this in several places (because that is not the topic of the book, or rather, the topic of this book) for Matthew, I can only for the moment show a theological expansion in Luke. This needs more study on my part, but I’m not sure that given the nearness of completion of my project that I will have enough time, nor if a mimetic synopsis of the Gospels isn’t warranting of a fuller publication. In at least one parable of Jesus, there is an archaeological artifact that dates to the time of Jesus and would not have been understood later had it not been preserved by the Jesus tradition. I also tend to think that the economic focus in Luke’s Gospel is generally something more in line with an early first century movement than an early second century creation.
So, while I am not sure I want to get into the idea of oral traditions, I do like the use of “undefined sources” which do not have to be limited to oral or literary traditions but could very well be theological reflections and mini-pre-midrashs of Rabbi Jesus that had been passed on in a sectarian Jesus community.