Proponents both of the majority two-document hypothesis (2DH) and of the main alternative, the Farrer Hypothesis (FH), have usually approached the debate by arguing that the existence of Q depends on whether Luke and Matthew were independent.
Proponents of the 2DH have argued that the material shared by Luke and Matthew (but not found in Mark) must not only derive from a shared source (ie, Q) but is used in such different ways that Luke could not have known how Matthew used the Q material, nor Matthew how Luke used it. The latter point, that Matthew and Luke are independent, is often defended with the strongest rhetoric, with Burnett Hillman Streeter providing the parade example:
Subsequent to the Temptation story, there is not a single case in which Matthew and Luke agree in inserting the same saying at the same point in the Marcan outline. If then Luke derived this material from Matthew, he must have gone through both Matthew and Mark so as to discriminate with meticulous precision between Marcan and non-Marcan material; he must then have proceeded with the utmost care to tear every little piece of non-Marcan material he desired to use from the context of Mark in which it appeared in Matthew–in spite of the fact that contexts in Matthew are always exceedingly appropriate–in order to re-insert it into a different context of Mark having no special appropriateness. A theory which would make an author capable of such a proceeding would only be tenable if, on other grounds, we had reason to believe he was a crank.
– The Four Gospels: A Study of Origins, p. 183
Proponents of the FH have argued just as strenuously not only for Luke’s knowledge of Matthew (L/M), but that such dependence precludes the existence of Q.
So, for example, Austin Farrer argued that all was needed to dispense with Q was to show that Luke had read Matthew:
The Q hypothesis is not, of itself, a probable hypothesis. It is simply the sole alternative to the supposition that St. Luke had read St. Matthew (or vice versa). It needs no refutation except the demonstration that its alternative is possible. It hangs on a single thread; cut that, and it falls by its own weight.
– “On Dispensing with Q”, p. 62
More recently, Francis Watson has written:
Q’s existence can only be sustained if Matthew and Luke write independently of each other.
– Gospel Writing, p. 121
In each case, strong conclusions are made about the necessity for / redundancy of Q, based on the independence of Luke and Matthew / dependence of Luke on Matthew.
Let us assume, at least for argument’s sake (although, I happen to agree), that the recent defences of Luke’s use of Matthew have been successful. The “coincidences of Q” – the agreements between Matthew and Luke that cannot be well explained under the 2DH – compel us to accept that Matthew and Luke are not independent. If that is the case, there is still no logical reason why Luke might not have used both Matthew and Q (that is, some common source of Matthew and Luke in addition to Matthew). The dependence of Luke on Matthew does not logically entail that there is no Q. The case against Q is not made out by merely showing that Luke is dependent on Matthew.
In order to dispense with Q, we would instead need detailed study of every double tradition saying, to determine whether any are better attributed to a common source rather than Matthew. Luke, after all, did not necessarily think like William of Ockham: economy in the use of sources was not necessarily Luke’s modus operandi and neither should it be our approach to Luke. Luke’s reference to “many” (πολλοὶ) earlier “orderly accounts” of the events in the life of Jesus, and more traditions handed down besides – despite its vagueness and ambiguity – suggests that early authors of accounts of Jesus’ life had no great aversion to redundancy.
One might counter that my objection remains in the realms of possibility, and that we still require a good reason for considering whether parts of the double tradition were based not on Matthew but on a shared source (Q). And that would be a fair objection. But a good reason is not difficult to find in Synoptic scholarship.
We already know that Luke employs one source of Matthew to the exclusion of Matthew itself: the Gospel of Mark. Some sections of Luke follow Mark without including Matthew’s distinctive additions. For example, in Luke 4:14-6:19 there is a significant number of triple tradition pericopae in a row which follow Mark’s content, but not Matthew’s (the return to Galilee; rejection at Nazareth; healings of Simon’s mother-in-law and others; preaching of Kingdom at synagogues; the calling of the first four disciples; healing of a leper; healing of a paralytic; the calling of Levi/Matthew; the question about fasting; the question about the Sabbath; the man with the withered hand; choosing of 12 apostles; teaching and healing before crowd from Judea, Tyre and Sidon). There are too many of these pericopae in a row to claim that all of the Matthaean variants were not “Luke-pleasing”, ie., that Luke rejected them because they did not please his own authorial preferences. Luke has rather followed one of his sources for an extended sequence, to the exclusion of one of his later sources. The pericopae in Luke 4:14-6:19 form a marked contrast to those in Luke 3:1-4:13//Mt 3:1-4:11, where Luke repeatedly includes Matthew’s additions – hardly coincidentally – in the same locations: Mt 3.7b-10//Lk 3.7-9 (JBap on brood of vipers); Mt 3:12//Lk 3:17 (JBap on winnowing fork); Mt 3.27-30//Lk 11.19-23 (Beelzebub); Mt 4.3-11//Lk 4:1-13 (the temptation).
Luke’s tendency, also evident in the works of other ancient historians, is to sometimes rely on a single source to the exclusion of parallel sources. This is also this pattern in the nativity, wherein Luke excludes Matthew’s wise men, Herod’s murder of infants, and the flight to Egypt, preferring a group of family traditions which are strongly coloured by traditions about Jesus’ mother and other women. This is the pattern too in Luke’s Passion and Post-resurrection narratives, which excludes many of Matthew’s expansions (eg resurrected saints, guards, earthquake, disciples go to Galilee to see Jesus).
So if Luke possessed Mark and Q as sources, we could justifiably expect Luke to have relied on one source (Matt or Q) but not the other for the double tradition. On this basis, we have good prima facie grounds to expect that Luke sometimes preferred the source or sources underlying Matthew in preference to Matthew itself. To determine the matter, we would require a careful weighing of all double tradition pericopae, in order to ascertain whether it is more probable that they derive from Matthew or from a shared source of Matthew and Luke. In addition, we should be open to the possibility that the shared source might not be the same shared source used in other pericopae, might originally have been written in either Greek or Aramaic (or other), or may be part oral in addition to written components which are evident in certain verbatim similarities within the double tradition – and therefore may not be a unified Q. Given the baggage of Q – which today typically connotes much more than the undefined shared source(s) underlying some or all of the double tradition – it might even be better to employ a new siglum. Or an older one, like uppercase Λ (for logia).
In conclusion, the dependence of Luke on Matthew does not determine the question of Q’s existence. The Farrer Hypothesis’ compelling challenge to the Two-Document Hypothesis may, rather, be the first step in rehabilitating a reappraised Q.