According to John S. Kloppenborg (2017) The Synoptic Problem is the problem of the literary relationships among the first three “Synoptic” Gospels (Matthew, Mark, and Luke). Peter Leithart (2018) boils down the synoptic problem to a matter of literary dependance. There are many similarities among the synoptics yet they still divert in significant ways. These similarities raise questions about whether there was direct/incident  literary dependence among the synoptics or whether there was common dependence on another source by the synoptics that lead to the similarities they display. 

Who Came First?

The first part of the Synoptic problem we need to address in examining the literary dependancy among the synoptics is answering the question of who came first. We have to establish an order of writing.  As it relates to Luke there seems to be congruence of thought that it was a dependent of the writings of Mark. In some older theories it is a dependent of Matthew.  When we consider the construction of a genealogy of the development of the Synoptic Gospels, the major theories seem to find bifurcation on the position that the book of Matthew should occupy in the mix of things. While more modern theories agree to an account where Mark was first, and Matthew and Luke are dependents. There are some older theories that place Matthew as the priemier (Augustine, Griesbach, etc.).  To be fair, Mark actually moved up in prominence over time. Augustine in the 3rd and 4th century, presented a Matthew - Luke - Mark  order. Then later on in the 17th Century you had scholars like Johan Griesbach that proposed an order where Matthew was first. Luke reworked Matthew and then Mark used them both. Then later, you have the position emerge that Mark wrote first around ~AD 68 and was then refined and reworked independently by Matthew and Luke into their own writings a few years later. Peter Leithart (2018) points out that this is the consensus among modern scholarship that “the gospel of Mark is the first of the gospels while Matthew and Luke draw from Mark.”  

“Q“ who?

So great, Mark was first, then Matthew and Luke came from Mark. But now we come to another issue that needs resolution. And Here is where the postulating begins. There is common material that is found in Matthew and Luke that is not found in Mark. This is believed to originate from a second main source known as Q. This Q hypothesis was popularised by British biblical scholar and textual critic, Burnett Hillman Streeter (1924). Streeter (1924) postulates that this source Q in theory could have been either a written source, an oral source or a combination of both. This is the main premise of the Two Document Hypothesis (2DH), of which scholars like Werner Georg Kümmel (1975) are major proponents. Although Streeter himself would later push a Four Document Hypothesis as an expansion of the Two document Hypothesis. Something we should cover later. Other voices like Mark S. Goodacre (2001) will argue for “Markan priority” and the dependence of Luke on Matthew. Creating another school of thought. The Mark without Q Hypothesis (MwQH). Which was further supported by voices like Austin M. Farrer (1955). Personally, MwQH is a bit hard to hold on to, with glaring examples such as the passages in Matthew and Luke which recount the lords prayer (albeit slightly different versions of the Lord's prayer). We have to ask. How could Matthew and Luke’s only source of reference be Mark, when Mark does not record the Lord’s prayer at all? Where did it come from? What was the source? Is this an argument for another source Q? Possibly. 

Streeter (1924), in his attempted deconstruction of the Matthew/Luke agreements help us further understand the relationship between Mark and Luke. Streeter (1924) posits that the agreement between Matthew and Luke were due to coincidence resulting from the two authors' reworking of Mark into more refined Greek. The idea being that Luke refined and reworked portions of Mark incorporating them into the corpus of his gospel. Thus the first five chapters of Mark contain material that is also recounted in Matthew and Luke. With Luke roughly following the same order of events as Mark. None of this is intended to refute the inerrancy of scripture. It is only meant to provide an introduction into the genealogical construction of the Synoptic Gospels.

References:

• Kloppenborg, J. (2017). Synoptic Problem. Oxford Bibliographies.

• Leithart. P. (2018). Lecture by Peter Leithart on the Synoptic Problem. Theopolis Institute. Retrieve from:

• Kümmel, W. (1975). Introduction to the New Testament. Rev. ed. Translated by Howard C. Kee. Nashville: Abingdon,

• Goodacre, M. (2001). The Synoptic Problem: A Way Through the Maze. The Biblical Seminar 80. London: Sheffield Academic Press.

• Farrer, A. (1955) On Dispensing with Q. In D. E. Nineham (ed.), Studies in the Gospels: Essays in Memory of R. H. Lightfoot. Basil Blackwell Publishing.

• Streeter, B (1924) The Four Gospels, a Study of Origins treating of the Manuscript Tradition, Sources, Authorship, & Dates. Macmillan Publishing.