I’ve been immersing myself in the Synoptic Problem of late. Based on the limited studies I’ve done before, I’ve always gravitated towards the four source theory (Mark, Q, L, M). Although I have had my curiosity aroused by the Farrer-Goulder-Goodacre theory of Mark–>Matthew–>Luke (eliminating the need for Q). And I have to say that Mark Goodacre has, at least, sown seeds of doubt in my mind about Q.
For those who think the Synoptic Problem is dull, they should read Mark Goodacre’s Is the Synoptic Problem Tedious? Any way, I’m gravitating towards a solution to the Synoptic Problem that is not necessarily new, but I think an underrated one in the discussion. Here’s what I think …
1. Marcan priority.
2. Double tradition is Q-lite and other synoptic traditions like non-Marcan narrative material (OST).
3. Matthew used Mark, Q-lite, OST, and M.
4. Luke used Mark, Q-lite, OST, L, and Matthew .
(Diagram from Stephen Carlson’s Synoptic Problem Website).
The Synoptic Problem is so complicated and challenging that it can make the most determined researcher want to put his or her head in the sand to somehow escape from the frustration, or else incline them to take a yoga class in the hope that attaining nirvana might bring release from the intense intellectual suffering and provide closure to their curiosity. Such respite has eluded every Synoptic researcher apart from the most self-assured.
Skepticism aside, I wish to optimistically put forward a tentative solution for the Synoptic Problem. Nearly half a century ago, E.P. Sanders proffered his opinion on future for the Synoptic Problem: “I rather suspect that when and if a new view of the Synoptic problem becomes accepted, it will be more flexible and complicated than the tidy two-document hypothesis. With all due respect for scientific preference for the simpler view, the evidence seems to require a more complicated one.” I think that is indeed the case. While I think that the two (four) source hypothesis is basically correct, there are several features of the theory that need to be tweaked in order to accommodate to what I believe to be the slightly more complex nature of the problem, specifically, that Luke used Mark, Q, and Matthew.
I call the position the Holtzmann-Gundry hypothesis (though it has also been called the “three source hypothesis”). It is named after the German scholar H.J. Holtzmann its first proponent and American scholar Robert H. Gundry its most well-known proponent. In a nutshell this view is (1) Marcan priority; (2) Matthew used Mark; (3) Luke used Mark, Q, and other traditions; and (4) At a later point, Luke has incorporated Matthew into his own work.
To give a brief history of this position, H.J. Holtzmann argued for Marcan priority and postulated the existence of Q (or L as he called it called for “logia”) in his celebrated Die synoptischen Evangelien, but he modified his view in a journal article published fifteen years later that tacitly suggested that Luke also used Matthew. Holtzmann afterward declared in his Einleitung that he had come to change his mind on three areas of the Synoptic Problem:
1) Not everything in Matthew and Luke that goes beyond Mark can be accommodated in the sayings collection. At times elements from the collection are more highly modified by Luke than they are by Matthew. It is possible that it contained narrative sketches that formed undetachable frames for the sayings of Lord [In der Spruchsammlung lässt sich nicht Alles unterbringen, was Mt und Lc von Redegehalt über Mc hinaus darbieten; ihre Elemente sind zuweilen von Lc noch mehr überarbeitet als von Mt; sie enthielt möglicher Weise auch skizzenhafte Erzählungen als Umrahmungen davon unabtrennbarer Herrnssprüche].
2) Other sources for Matthew are unprovable; but such a question remains open for Luke [Weitere Quellen sind für Mt unerweislich; dagegen bleibt für Lc die Frage nach solchen offen].
3) Luke knew Mark and Matthew even if he might not have used them [Lc hat neben Mc auch Mt, wenn nicht benutzt, so doch gekannt].
4) Consequently, at least most of the motives for distinguishing between an Ur-Mark and Mark are eliminated [In Folge dessen kommen wenigstens die Meisten Motive zur Unterscheidung eines Urmarcus von Mc in Wegfall].
Eduard Simons, a student of Holtzmann, argued for this hypothesis more fully in his Hat der dritte Evangelist den kanonischen Matthäus benutzt? (Bonn, 1880), but was basically ignored, the direction of his own career didn’t help either, working as he did in practical theology rather than New Testament.
However, Simons’ approach was noted and affirmed by Edward Y. Hincks in the US in the late nineteenth century. Hincks noted the main rival hypotheses of the time including the Ur-Mark theory (H.J. Holtzmann) and Mark-used-Matthew’s-Logia theory (B. Weiss) and rejected them both as problematic and inadequate explanations. Instead, Hincks found Simons’ argument compelling since Matthew’s Gospel circulated widely, Luke was written later so Luke could have had access to Matthew, and the divergences between Matthew and Luke can be accounted for without requiring Luke’s independence of Matthew. Furthermore, for Hincks, Luke’s use of Matthew explains the Luke-Matthew agreements against Mark. He also posits that Mark and the Logia source (Q) may have had independent reports of the same account that were used by Luke and Matthew. This is said to explain the contours of the mission discourses and the accusation of Jesus’ alliance with Satan (i.e., the Mark-Q overlaps).
Robert Gundry has been the most successful advocate for a three source approach although his views have largely gone unnoticed among those outside the field of Synoptic Problem studies. Gundry has written two major commentaries on Matthew and Mark and also explored the presence of so-called Matthean “foreign bodies” in Luke. According to Gundry, both Matthew and Luke used Mark and non-Marcan tradition held in common. While this sounds like the standard two-source theory, Gundry adds:
Gundry still remains convinced of the existence of Q on the grounds that “Luke’s borrowing wholesale from Matthew” remains problematic because it leads to “Luke’s equally wholesale disarrangement of Matthew’s materials.” The postulation of Q does not prevent Gundry from arguing that Luke used Matthew because it accounts for the presence of a number of Matthean foreign bodies in Luke.
Because Mattheanisms occasionally appear as foreign bodies in Luke, we also have to think of Luke’s using Matthew as an overlay on his primary sources. That Matthew’s gospel did not provide one of those sources is shown by the disarrangement of Matthean material we would otherwise have to suppose. But that the Matthean foreign bodies come from our present Gospel of Matthew, not from an earlier source, is shown by their conforming to Matthew’s distinctive diction, style, and theology as evident elsewhere and by their frequently depending for their point on Matthew’s context (often stemming from Mark), whereas in Luke they lack contextual point. Therefore we need not free over the numerous minor agreements of Matthew and Luke that do not fall into the category of Mattheanism … They, too, may represent a Matthean overlay in Luke, though apart from the Matthean foreign bodies we would not have known so with any confidence.
Ron Price has also argued for this position and even has a webpage dedicated to it (see here). See the below diagram:
1. I think Marcan priority is, as Mark Goodacre puts it, the “cornerstone” of the Synoptic Problem. So much of the data makes sense on the premise of Marcan priority.
2. I think Q is still a valid postulation given that it accounts for the fluctuating primitivity between Matthew and Luke on several sayings and there is no need to revert to Luke’s wholesale use of Matthew which leaves us wondering why he broke up Matthew’s speeches quite so abruptly and artlessly.
3. But Luke probably used Matthew as an “overlay” or as a Nebenquelle (tertiary source) at a later stage in the production of his Gospels as this accounts for minor agreements (esp. in the passion narrative [like Mark 14:65/Matt 26:67-68/Luke 22:64]) and gives us a further way of explaining the Mark-Q overlaps.
 E.P. Sanders, Tendencies of the Synoptic Tradition (SNTSMS 9; Cambridge: CUP, 1969), 279.
 H.J. Holtzmann, Die synoptischen Evangelien: Ihr Ursprung und geschichtlicher Charakter (Leipzig: W. Engelmann, 1863).
 H.J. Holtzmann, “Zur synoptischen Frage,” Jahrbücher für protestantische Theologie 4 (1878), 533-54.
 Some like William Farmer (Synoptic Problem, 20, 40, 47) think that Holtzmann was influenced by his doctoral student Eduard Simons’ dissertation Hat der dritte Evangelist den kanonischen Matthäus benutzt? (Bonn: Carl Georgi, 1880) in coming to this conclusion. Though Edward C. Hobbs (“A Quarter-Century Without ‘Q’,” Perkins School of Theology Journal 33.4 , 11) points out that Holtzmann more probably influenced Simons instead because Holtzmann published such a view two years before Simons’ thesis was submitted and taught Simons for a number of years earlier.
 H.J. Holtzmann, Lehrbuch der historisch-kritischen Einleitung in das Neue Testament (Freiburg: Paul Siebeck, 1892), 2:350 trans. with adjustments from Stoldt, History and Criticism of the Marcan Hypothesis, 92.
 Edward Y. Hincks, “The Probable Use of the First Gospel by Luke,” JBL 10 (1891), 92-106.
 On the Matthew–Luke divergences, Hincks argues (“Use of the First Gospel by Luke,” 96-97): (1) Luke used the Logia source (i.e., Q) differently; (2) In the infancy narrative, Luke shows the influence of Matthew’s genealogy but otherwise follows different sources; (3) Luke uses Mark different to Matthew because Luke esteemed Mark more than Matthew; (4) Luke’s omission of material from Matthew, but if they were in the Logia source where Matthew found them, the problem of omission would still remain; (5) Luke does not use Matthew’s pragmatic way of referencing the Old Testament because of Luke’s independent “doctrinal conception”; and (6) Luke used different sources for his resurrection accounts.
 Hincks, “Use of the First gospel by Luke,” 99-101.
 Robert H. Gundry, Matthew: A Commentary on His Handbook for a Mixed Church under Persecution (2nd ed.; Grand Rapids, MI: Baker, 1994); idem, Mark: A Commentary on His Apology for the Cross (Grand Rapids, MI: Baker, 1993); idem, “Matthean Foreign Bodies in Agreements of Luke with Matthew Against Mark: Evidence That Luke Used Matthew,” in The Four Gospels 1992, eds. F. van Segbroeck et al (FS F. Neirynck; BETL 100; Leuven: Leuven University Press, 1992), 2:1466-95; idem, “A Rejoinder on Matthean Foreign Bodies in Luke 10,25-28,” ETL 71 (1995), 139-50; idem, “The Refusal of Matthean Foreign Bodies To Be Exercised from Luke 9,22; 10,25-28,” ETL 75 (1999), 104-22.
 Gundry, Matthew, 5.
 Gundry, Matthew, xvi.