What Exactly is Q?

See also Evidence of Q? and The Making of the Double Tradition.

Much of the text of the gospels of Mark, Matthew, and Luke is very similar to, and in some places identical to, text in either one or both of the other two gospels. For this reason they are collectively referred to as the Synoptic (or ‘seeing together’) Gospels, or sometimes just 'the synoptics.’ The existence of the parallels in these gospels raises the question of how they came to exist, e.g. was one gospel used as a source for another, or did two of the gospels share a different (unknown) source, and several hypotheses using an unknown source have been created in an attempt to solve what is known as The Synoptic Problem. 

The Two Source Hypothesis (2SH)

One such hypothesis is the Two Source Hypothesis (2SH, or Mark-Q hypothesis), in which an additional hypothetical source (usually, but not necessarily, considered to be a single document) known as Q is required to explain how Matthew and Luke can contain parallel versions of text that does not exist in Mark. NB: Q is sometimes used in a more general sense as simply an unknown source, but here it is used specifically to refer to the form of the source as used in the Mark-Q hypothesis.

By definition this parallel text is what is generally known as the Double Tradition (because it only exists in two of the synoptic gospels). However, this does not mean that Q (the source) = the Double Tradition (the text). Instead, it means that Q must contain at least the Double Tradition text, but there is no barrier to Q containing more, either text that is also found in other synoptic sources (e.g. in Mark), or text for which we currently have no known source, e.g. Sondergut (unique) Matthew or Sondergut Luke. In a footnote to ‘Jesus in Oral Memory: The Initial Stages of the Jesus Tradition,’ James Dunn stresses this point:  

To avoid the confusion which has been endemic in discussion of Q, I use ‘q’ for the actual material common to Matthew and Luke, and ‘Q’ for the hypothesized document from which q was drawn. The working assumption that Q = q is one of the major weaknesses in all Q research.

Dunn makes a good point regarding the problem of associating Q both with a hypothetical source and the content of that source, but it is unfortunate that he then instead equates ‘q’ with “the actual material common to Matthew and Luke,” rather than using the more common term ‘the Double Tradition.’ It is worth noting here that some people also equate ‘M’ (a document) with ‘Sondergut Matthew’ (text), and ‘L’ (a document) with ‘Sondergut Luke’ (text), but it should always be remembered that we simply do not know whether the source of any of these hypothetical texts (if they existed as such) would have been oral, one or more documents, or a combination of the two. 

We also do not know the exact text of Q, because in reality there is no one text of Q, not least because the possible extent of Q has varied since it was first hypothesized. For example, Q did not originally contain just the Double Tradition, but instead it was considered to be a ‘sayings source’ (believed by some to be the ‘Logia’ referred to by Papias), and this view was buttressed by the discovery of the Gospel of Thomas. However, the relationship between Q and Thomas is not direct, as Paul Foster describes in ‘Is It Possible to Dispense with Q?’:

The significance of Thomas, specifically in relation to Q, is summarized by Davies in the following terms:

Both Q and Thomas are lists of sayings, having about one third of their sayings in common, but they are not otherwise connected. Thomas is not Q, nor a source for Q, nor is Q a source for Thomas. The Q hypothesis does, however, gain strength from the fact that Thomas proves that lists of sayings did circulate in the early churches.

Yet the discovery of Thomas has not convinced Q skeptics either of the possibility of the existence of Q or of the appropriateness of the comparison. Rather the criterion has been somewhat changed to try and remove Thomas from the debate. Goodacre dismisses the positive evidence that Thomas offers for the Q hypothesis in the following cursory manner:

The disappointing news for the Q theory is that the document looks nothing like Q as it is commonly reconstructed. Thomas is quite lacking in the kind of ordered arrangements that characterize Q, especially the all-important narrative sequence in Q's first third. Thus, far from corroborating the existence of documents like Q, the blatant contrast between Thomas and Q gives one major pause for thought.

Contrary to Goodacre, the significance of Thomas was seen by Q supporters as at least providing solid evidence, despite previous assertions to the contrary, that amorphous sayings collections could circulate in the early church, although to describe either as amorphous is to miss certain structural features in both documents. Now that Thomas has been discovered, the charge has changed and it appears that Q is not amorphous enough, since it does not match Thomas exactly. Of course it does not, for Thomas is not Q. However, what Thomas and the synoptic gospels do is mark end points on a continuum of Christian writings about Jesus, and to find that the genre of Q sits comfortably between these two extremes gives plausibility to inferring that the genre of reconstructed Q is well within the realms of possibility.

Although some people had begun to add introductory narrative elements to Q before Thomas was discovered, as Thomas was purely sayings this expansion was then resisted. In addition the strong influence of Adolf von Harnack, who stated: “It is a priori probable, indeed quite certain, that much which occurs only in St. Matthew or in St. Luke is derived from Q,” led to reconstructions of Q being largely restricted to sayings in the Double Tradition, with very limited narrative introductions. However, this restricted form of Q was not capable of being a complete solution to the Synoptic Problem, as Nancy R. Heisey notes in ‘The Current State of Q:’

E.P. Sanders and Margaret Davies agree that from a broad perspective the two-source theory and related Q hypothesis handle the data reasonably well. When more detailed analysis is undertaken, however, the problem of the minor agreements between Matthew and Luke or the overlaps between Mark and Q require either a continually expanding Q, the pushing of data back toward unknown earlier documents or strata, or shifting the problem to the Mark-Q relationship. They argue that most New Testament scholars have long accepted some uncertainty and complexity of the history of traditions behind the Synoptic Gospels, while referring in general terms to the two-source theory. They thus call for a more overt admission of this uncertainty.

Heisey’s comments here point out the ‘dirty little secret’ that the International Q Project (IQP) would appear to had been trying to hide by heavily promoting the view that the Critical Edition of Q, backed by the multiple volumes of the Documenta Q, define the one and only text of Q. The 'secret' is that in reality there are a vast range of possible texts, all of which are able to fulfill the role of the second source in the Mark-Q hypothesis, and so all of which are Q. There is in effect (as Foster above notes) a continuum of Qs, or (with apologies to Star Trek) a ‘Q Continuum,’ the history of which is explained by David B. Sloan in ‘Q as a Narrative Gospel.’ 

Minimal Q

The fact that the history of Q shows how varied the definition of the contents of Q has been since it was first hypothesized should give us pause, a point on which Stewart Petrie elaborates in ‘’Q’ Is Only What You Make It’:

Nothwithstanding any pretensions to the contrary, one of the gravest shortcomings in the search for ‘Q’ is its lack, or the avoidance, of objectivity. What is ‘Q’? Nobody answers with real conviction. Usually the best that can be offered is so-and-so’s reconstruction of ‘Q’. There is even a reconstruction based on the common features of other reconstructions – a sort of ‘Q’ of ‘Q’s, and surely a reductio ad absurdum. The argument is in constant danger of becoming a circular one: a decision having been reached as to what ‘Q’ should be, its reconstruction is undertaken accordingly, and the result is then presented as convincing evidence for ‘Q’. It is here that the whole discussion of ‘Q’ presents an air of unreality, in that in each case it is never quite the same thing that is under consideration.

In his conclusions to ‘The Progressive Publication of Matthew: An Explanation of the Writing of the Synoptic Gospels,’ B. Ward Powers (coincidentally referring to Petrie) also comments on "the vagueness, dubiousness, and insubstantial nature of Q:"

This hypothesized documentary source is invoked to account for one particular class of Matthew-Luke agreements against Mark: those where Matthew and Luke agree in the inclusion of substantial material not in Mark. There is not (and in the nature of the case, could hardly be) unanimity about the scope and extent of Q, because each scholar decides the contents of Q based on his own criteria. As an article by S. Petrie point out, “Q is only what you make it” – a point numerous others have reiterated. There is a sizeable gap between postulating a Q and adducing any objective evidence in support of its existence. And if one depends on logical arguments, then those logical arguments will, if carried through fully and consistently, establish a different conclusion because of the Mark-Q overlaps.

Unfortunately ‘the general synoptic public’ (if there is such a thing) is not aware of the great flexibility inherent in the definition of Q, and the 'popular' or ‘traditional’ view of Q (the source) is that it contains just the Double Tradition (the text), referred to by some as a ‘minimal Q.’ For example, the Wikipedia page on Q promotes this view, as can be seen in the diagram on that page, and it is reinforced by scholars such as Mahlon H. Smith, who in 1998 wrote that:

Today there is greater consensus than ever among synoptic scholars about the contours of Q. Its general boundaries are defined objectively by non-Markan parallels in Matthew and Luke, with additions limited to:

Single-tradition pericopes beyond the border of the double tradition are few and generally restricted to units with obvious stylistic and/or thematic echoes of the adjacent section of Q. Scholarly debate about the internal tradition history of the Q material does not disturb this consensus, since Q is by definition the version of the text known to Matthew and Luke. Current scholarly debate about the contours of this document Q is no greater than disagreement about the original ending of Mark. Uncertainty about whether Mark originally ended at 16:8 or 16:20 or somewhere else has not kept it out of the canon, so questions about Q’s contours should present no obstacle to canonizing it.

Notwithstanding this view, others theorize a Q that contains additional text, as Kloppenborg describes in the essay ‘The Sayings Gospel Q’: 

… the literary analysis of the Sayings Gospel is dependent upon a more or less probable reconstruction of the extent of Q. While an impressive consensus exists among specialists in study of the Sayings Gospel regarding its contents, there are nonetheless important disagreements. These varying estimations of the original extent of Q depend upon whether one adheres to the “minimal Q text” – that is, only those pericopae in which Matthew and Luke display substantial agreements, either in the absence of a Markan parallel or against the existing Markan parallel – or whether one includes other pericopae as well.

Expansions beyond the minimal Q text fall into two general categories: (1) special material (Sondergut) in Matthew which Luke may have omitted for editorial reasons (or special Lukan material which Matthew may have omitted), and (2) triple tradition pericopae which contain a small number of “minor agreements” of Matthew and Luke against Mark and hence betray a Q Vorlage.

As Kloppenborg indicates, even the “minimal Q text” contains agreements of Matthew and Luke where there is also a Markan parallel (as described above), but having Mark and Q contain the same text in these particular instances is extremely damaging to the ‘minimal Q’ Mark-Q theory as a whole, as there is then no valid basis on which to deny the possibility of Mark and Q containing common text in other instances. The whole basis of the Mark-Q theory relies on the independence of Mark and Q, and consequently once it is allowed that they are actually not independent in at least some places, the whole rationale on which the content of ‘minimal Q’ relies is overturned. As Christohper Tuckett states: 

A theory of direct dependence of Mark on Q would thus appear to demolish one of the strongest arguments in favour of the very existence of Q in the first place.

Once it is accepted that Q must have contained more than just the Double Tradition (even if the addition is just a small fraction of what we see in Mark), then it becomes impossible to accurately define the extent of Q. In The Present State of the Q Hypothesis Howard Bigg comes close to realizing that this is fatal to any attempt to limit the content of Q to just that necessary to fulfill its role in the Mark-Q hypothesis, and more recently Marco Eilers convincingly argues the point in his blog post The Problem with Mark-Q Overlap. Powers also sees that existence of the Mark-Q overlaps makes it impossible to identify any text in Mark that could not also exist in Q. Again, from his conclusion:

There are numbers of places where Matthew-Luke positive agreements are so many and so significant in a Markan context that the Two-Source Hypothesis is led to conclude that Q and Mark overlapped at the point; that is, they both contained an account of the same pericope, and accordingly, Matthew and Luke each (in his own way and to varying extents) conflated Q and Mark. But if some events recorded in Mark are thus acknowledged also to have been in Q, on what basis (other than pure arbitrariness) can it be decided that all the various other pericopes in Mark could not also be in Q? In other words, if Q existed at all, on what objective basis can its boundaries be drawn so as to exclude the rest of the Markan corpus? There is no way that Q can be confined to being merely a “sayings source.” Once we face the significance of Mark-Q overlaps, we find that carrying the argument for Q to its logical conclusion leads us to Q being a full Ur-Gospel, used by Matthew and Luke. It would seem that the argument for Q “proves” too much! But in any case it is clearly invalid to conclude that something cannot have been in Q simply because it also occurs in Mark.

Maximal Q

Suppose that Q contained not just the Double Tradition, but some of the Triple Tradition (not just the Mark-Q overlaps) as well. How would this affect the content of Matthew and Luke? The answer is that it quite possibly would have no effect at all. Both aMatthew and aLuke would know some of the Triple Tradition text from Q as well as from Mark, and whatever reasons they had for including that text in their own gospels would simply be re-enforced as a result of knowing the text from both Mark and Q instead of from Mark only. Of course, if whatever Triple Tradition text was in Q was not in the same order as that in Mark, then aMatthew and aLuke could have chosen to include the same text, but in different orders. One could have preferred the order in Mark and the other the order in Q, or either, on knowing two different orders, could have chosen to re-order the common material and/or place the material not from Mark (the Double Tradition material) in different locations. If this was the case then it would provide a natural reason why the order of the material in Matthew differs from that in Luke, with Matthew purely by choice differing more from the order in Mark than does Luke. 

Q could also have contained some or all of the text of Sondergut Matthew and Sondergut Luke, as if this was present in Q then it would simply mean that aMatthew and aLuke selectively chose which Q material they did or did not include in their respective gospels. Essentially there is no barrier to Q having contained not only the Double Tradition, but also parallels to some or all of the Triple Tradition, Sondergut Matthew, and Sondergut Luke. Although having all of this material in Q seems unlikely, in particular as it would raise the question of why aMatthew did not choose anything in what we see as Sondergut Luke and aLuke did not choose anything in what we see as Sondergut Matthew, the idea that Q contained only the Double Tradition seems equally unlikely. We are therefore left with the distinct possibility that Q could have contained very much more than just the originally hypothesized ‘sayings source’, to the point where it could easily be seen as a complete gospel in its own right. 

Whatever the extent of any hypothesized Q, from ‘Minimal’ to ‘Maximal,’ there is the constant problem that in the Mark-Q hypothesis aMatthew and aLuke used the same two written sources: Mark and Q, containing exactly the same text, and consequently it is hard to explain why Matthew and Luke are as different as they are. Of course, there is no a priori reason why aMatthew and aLuke should copy text from either Mark or Q exactly word for word, why they should use text from Mark and Q in the same order, or why they should exclude exactly the same portions of Mark and Q from their respective gospels, so we would expect differences between Matthew and Luke. However, because there are so few places where Matthew and Luke have exactly the same text as in Mark, such a great difference in order between Matthew and Mark, and such a difference in which portions of Mark are excluded from Matthew and Luke, it is hard to explain such differences as due purely to independent redactional choices having been made by the two authors. What would have caused aMatthew and aLuke to have treated their (identical) sources so differently? 

The above ignores the issue of any additional sources (not specified in the Mark-Q theory) that either aMatthew or aLuke (but not both) might have used. This is important because while Mark is a source (but not necessarily the source) of all the Triple Tradition material, and all the hypothesized forms of Q contain at least the Double Tradition material, neither Mark nor Q (at least in the case of the traditional or ‘Minimal’ Q) contain either the Sondergut Matthew or Sondergut Luke material. In addition, as Q is hypothesized to have followed the order of Luke (to the point where verses in Q are referred to using the chapter and verse numbering from Luke), we are left with the following questions: 

We have seen above that the ‘Minimal Q’ is just the smallest ‘valid’ Q that can be hypothesized within the Mark-Q theory, and the same applies to M and L. The four sources (Mark, Q, M and L) contain just enough text to be capable of being sources for everything in Matthew and Luke, with no overlap between any pair of them, and nothing extra. Except …. except for those annoying Mark-Q overlaps, and the fact that Sondergut Matthew and Sondergut Luke cannot be considered to be complete documents in their own right. So, Mark and Q shared at least some common text, and M and L contained more than just Sondergut Matthew and Sondergut Luke respectively. With three hypothetical sources, each with no clearly defined boundaries, it is not surprising that attempts have been made to reduce the uncertainties by ‘combining’ sources and/or reducing their scope by resorting to oral traditions instead where possible. 

The ‘Maximal Q’ hypothesis avoids the problem of aMatthew and aLuke each apparently knowing text from either M or L but not both, and also avoids the issue of having three hypothetical sources. It achieves this by the simple expedient of having Maximal Q include all the Sondergut Matthew and Sondergut Luke text, but as a result it means that in this scenario aMatthew knew the text we know as Sondergut Luke and aLuke knew the text we know as Sondergut Matthew. This of course adds to the redactional issues facing aMatthew and aLuke, since with the text of both Sonderguts within Q there has to be something to explain why aMatthew rejected Sondergut Luke, and aLuke rejected Sondergut Matthew. It also moves Q away from being purely a ‘sayings gospel,’ or even just the Double Tradition, to essentially being a fully-fledged narrative gospel in its own right. Not only do we have no evidence (e.g. extant mss or patristic writings) for the existence of this gospel, but even if we only counted the Double Tradition, Sondergut Matthew, and Sondergut Luke (i.e. ignoring any Mark-Q overlaps or any other part of the Triple Tradition) this gospel would have been more than one-third larger than Luke, the largest of the synoptic gospels. The idea that such an important (and large) source of gospel material once existed but has left no direct trace seems very improbable. 

There is another problem with Maximal Q: With it containing so much text (At least the Mark-Q Overlaps, the Double Tradition, Sondergut Matthew, Sondergut Luke, and some other portions of the Triple Tradition), it becomes very hard indeed to see how it could be a single coherent document. For example, how could a Q of this extent contain what are essentially conflicting versions of several passages in Matthew and Luke that, while clearly related, are, at best loose parallels with significant differing details? Then, assuming that Maximal Q agrees with Minimal Q in following the order of the text in Luke (for the Triple Tradition material, the Double Tradition, and the Sondergut Luke material), how could the Sondergut Matthew material be accommodated within this structure without significant ‘disconnects’ when transitioning between the Sondergut Matthew material and the rest? What would be needed is the addition of some ‘linking passages’ to smooth over the cracks, so adding what could only be called ‘Sondergut Q’ material (Material in Q but not in Mark, Matthew, or Luke). 

The Three Source Hypothesis (3SH)

Powers sees that the existence of the Mark-Q overlaps makes it impossible to identify any text in Mark that could not also exist in Q. Again, from his conclusion:

… the argument for Q removes the necessity for seeing Mark as a source for Matthew and Luke. All the common material in Matthew and Luke can be attributed to the Q source, and not merely material that is not in Mark. Thus the way is open to view Mark as also derived from the Q Ur-Gospel, or from Matthew and Luke. In practice, Q advocates will not follow the logic of their arguments to this conclusion. Rather, they argue for Q from the existence of material that is common to Matthew and Luke but that is not in Mark, without justifying their basis for deciding that other common Matthew/Luke material could not also be in Q if it is also in Mark. The recognized Mark-Q overlaps continue to point to the deficiency in their reasoning.

From the above it should be clear that the Mark-Q theory has problems with the selective incorporation of the text from M and L into Matthew and Luke respectively, while at the same time allowing aMatthew to not use what we see as Sondergut Luke, and aLuke to not use what we see as Sondergut Matthew. These problems exist whether the Sonderguts were text within two additional source documents (M and L), or were part of a Maximal Q, and as a result the Sonderguts are often considered to be derived from oral sources instead, so making it easy for aMatthew and aLuke to have received different information from different people. 

The obvious problem this raises is that it is impossible to know who these people might have been, and what they might have said to aMatthew and aLuke. As a result, once the possibility that Sondergut Matthew and Sondergut Luke came from oral sources is raised, there is then no basis on which to say that the Double Tradition was not common material that was known to the oral sources used by both Matthew and Luke. The only defensible positions are either that Q, M, and L were all one or more written sources (with the problems described above), or that none of them were, and if none of them were the whole rationale for the Mark-Q hypothesis collapses, since the only written source left is Mark. Essentially, if any one of Q, M, or L is allowed to be at least partly oral, then there is no argument on which to insist that the others must have each been a single written source, or even both part of a single written source.

One way to at least reduce the scope of this problem is to allow either aMatthew to have seen and used Luke, or for aLuke to have seen and used Matthew. For various reasons (of which the different orders in Matthew and Luke is one) it is more common to hypothesize aLuke using Matthew than the reverse, and the Three-Source Hypothesis [3SH, or Mark-Q-Matthew model, or Holtzmann-Gundry hypothesis] has exactly this configuration. As Michael Bird notes, the features of this hypothesis are: 

In item 2 above Bird refers to a ‘Q-lite,’ highlighting the fact that (although his phrasing actually obscures this) the source that in the Mark-Q theory is called Q is not the same as the equivalent source in the 3SH, because in the 3SH it no longer has to include all the Double Tradition. Instead, the text of the Double Tradition is non-Markan text in Matthew, that only actually became the Double Tradition when aLuke chose to use it in his gospel as well. As the Double Tradition text is the ‘heart’ of Q (all versions of Q contain it), a source without the Double Tradition should not be called Q, and so for this discussion I will follow Bird, and refer to Q-lite. However, there is another problem: If Q-lite is Q without the Double Tradition, then the contents of Q-Lite can vary from ‘Minimal Q’ without the Double Tradition to ‘Maximal Q’ without the Double tradition, i.e. from nothing at all to all of Sondergut Matthew, Sondergut Luke, and the Mark-Q overlaps, plus some other parts of the Triple Tradition. In a reply post on Mark Goodacre's NT blog Stephen C. Carlson commented that this is a significant problem for the 3SH: 

One major drawback to the 3SH is that once Luke's use of Matthew is admitted, it becomes very hard to delineate what's in this Q because all the controls that the 2SH people have with independence are gone. Even the Q under the 2SH is hard to delineate because of the lack of control given by the Mark/Q overlaps. With the additional possibility of Matt/Mark/Q overlap, the Q of the 3SH becomes almost unreconstructable. Perhaps some people will find this to be a feature rather than a bug.

In another reply, 'Michael' commented on Gundry’s lack of definition of Q: 

Gundry's Q is so flexible (flimsy?) that it easily encompasses oral and written traditions shared by Matthew and Luke. This echoes Stephen's point above. So do we even know what Q is under the 3SH?

I am one of the “some people” referred to above by Carlson, because the sheer flexibility afforded by the 3SH when it comes to the content of Q-lite means that it can be hypothesized in such a way as to maximize the number of synoptic issues (e.g. alternating primitivity, the source of the doublets (see the Introduction to Doublets), the Mark-Q overlaps, the minor agreements, Matthews additions to Triple Tradition text) for which it provides explanations, while at the same time minimizing those for which it does not. In addition, not only can the content of Q-lite be ‘varied to suit,’ but so can its relationship to Mark. Although there is in general great resistance to the possibility that Q depends on Mark (but some of the Q community think that Mark depends on Q), there is no such restriction on Q-lite. This leads to a number of possibilities, not least because Q-lite can now be considered to a text 'part way' between either Mark and Matthew, or between Mark and Luke. As there is evidence for a shorter version of Luke (omitting Luke Chapters 1 and 2 and with other differences) the latter appears more likely.

Conclusion

Q only exists as a corollary of the hypothesis that neither Matthew nor Luke knew the text of the others’ gospel, because on that hypothesis one cannot have created the Double Tradition by seeing and using non-Markan text in the other. However, this does not restrict Q to being just one specific text, and instead there is an almost infinite number of different Q texts that aMatthew and aLuke could have seen, with the smallest being just the Double Tradition, and the largest including large portions of the Triple Tradition and the Matthean and Lukan Sonderguts, subject only to the constraint that it did not contain a version of enough of the text we see in either Matthew or Luke to overrule the arguments for the independence of their authors. As indicated above this means that the hypothesized text of Q can vary greatly, and begs the question of why the IQP expended so much effort on trying to define the text of Q as though it could only be one specific text.

As suggested above: “’Q’ Is Only What You Make It”. At one end of the spectrum there is the Q as defined by the IQP, which contains just the smallest subset of the text common to Matthew and Luke necessary to allow aMatthew and aLuke to have not known each other's gospels. At the other end of the spectrum there is ‘Maximal Q,’ essentially a complete gospel in its own right, in most cases overlapping with Mark to a considerable degree. However, all variants of Q contain at least the Double Tradition text, because Q can only have existed if Matthew and Luke were created independently.

If Matthew and Luke were not independent then the situation changes. Effectively, the addition to the Mark-Q hypothesis of a link from Matthew to Luke (or Luke to Matthew), and the consequent change of Q into Q-lite by the removal of some or all of the Double Tradition text, leads to the 3SH/Mark-Q-Matthew hypothesis being much more flexible than the 2SH/Mark-Q hypothesis, and as a result being able to resolve a number of synoptic issues that the 2SH/Mark-Q hypothesis cannot. In addition, because the definition of Q-lite allows for so much variation, depending on its contents it could be considered to be either a deutero-Mark or an early version of Luke, as discussed in MwEL: A New Synoptic Hypothesis. It's not a question of defining what IS (or rather, has to be) in Q - that's easy - it's the Double Tradition. The problem is defining what ISN'T (or MUSTN'T be) in Q.

References

Bigg, Howard C: The Present State of the Q Hypothesis, 1988 

Bird, Michael F: The Holtzmann-Gundry Solution to the Synoptic Problem (Three Source Hypothesis). Also Goodacre, Mark: Mike Bird on Luke's use of Matthew and Q 

Bogs Christopher R.: Q on the Chopping Block: Dissent in the Synoptic Problem, 2003

Burkett, Delbert Royce: Rethinking the Gospel Sources: Volume 2: The unity or plurality of Q, SBL, 2009 

Carlson, Stephen C: The Synoptic Problem Website 

Davies, Stevan: Thomas, Gospel of, in D.N. Freedman(ed.), Eerdman's Dictionary of the Bible (Grand Rapids, Michigan: Eerdmans, 2000) p1303

Derrenbacker, Robert A, Jr and Kloppenborg Verbin, John S: Self-Contradiction in the IQP? A Reply to Michael Goulder, 2001 

Dunn, James D. G: Jesus in Oral Memory: The Initial Stages of the Jesus Tradition, University of Durham 

Eilers, Marco: The Problem with Mark-Q Overlap 

Foster, Paul: Is It Possible to Dispense with Q? , 2003 

Goodacre, Mark: The Case Against Q: Studies in Markan Priority and the Synoptic Problem. Online: The Case Against Q, Ten Reasons to Question Q, A Monopoly on Marcan Priority? Fallacies at the Heart of Q, and Beyond the Q Impasse or Down a Blind Alley.

See also Mark Q Overlaps I: Terminology, II: Major Agreements Between Matthew and Luke, III: Minor Agreements between Mark and Luke, IV: Back to the Continuum, V: the degree of verbatim agreement, VI: The Direction of Dependence 

The Gospel of Q at The Nazarene Way 

Gundry, Robert H: A Response To “Matthew And Midrash”, JETS 26:1 (Mar 1983) 

Head, Peter M. and Williams P.J: Q Review, Tyndale Bulletin 54.1, 2003 

Heisey, Nancy R: The Current State of Q, TIC TALK 39, 1997 

Hogan’s Blog: A Critique of the approach and evidence of the Q theory in light of the Synoptic Gospels. MA assignment, 2012 

Kirby, Peter: The Existence of Q

Kloppenborg, John S: Synoptic Problems: Collected Essays, 2014, which includes On Dispensing with Q?: Goodacre on the Relation of Luke to Matthew, 2003 

Kok, Michael J.: Euangelion Kata Markon, The Case For and Against Q 

Lindemann, Andreas (Ed): The Sayings Source Q and the Historical Jesus, 2001 

Mattila, Sharon Lea: A Problem Still Clouded: Yet Again – Statistics and “Q” 

McNicol, Allan J: Has Goulder Sunk Q? An Assessment of Mark Goodacre’s ‘Goulder and the Gospels: An Examination of a New Paradigm’, Institute for Christian Studies,  1997

McNicol, Allan J, (Ed) with Dungan, David L., and Peabody, David B: Beyond the Q Impasse: Luke’s Use of Matthew, 1996 

Passantino, Bob and Gretchen: The Mysterious Case of the Missing Q, 2002

Petrie, Stewart: 'Q' Is Only What You Make It, Novum Testamentum, Vol. 3, Fasc. 1/2 (Jan., 1959), pp. 28-33

Poirier, John C. and Peterson, Jeffrey (Ed): Marcan Priority Without Q: Explorations in the Farrer Hypothesis , 2015 

Powers, B. Ward: The Progressive Publication of Matthew: An Explanation of the Writing of the Synoptic Gospels, 2010

Sloan, David B: Q as a Narrative Gospel, 2015 

Smith, Daniel A: The Trouble with Q, 2012 

Smith, Mahlon H: The Canonical Status of Q, 1998

Tuckett, Christopher: Q and the History of Early Christianity: Studies on Q, Edinburgh: T & T Clark, 1996, pp. 7-8, and From the Sayings to the Gospels, Mohr Siebeck, 2014 

Turton, Michael: Is Mark Q? 

Watson, Francis: Q as Hypothesis: A Study in Methodology