# The Existence of Q

This web page is a summary of the arguments for the existence of Q. It largely follows the essays given in The Two-Source Hypothesis: A Critical Appraisal / edited with an introduction by Arthur J. Bellinzoni, Jr., with the assistance of Joseph B. Tyson and William O. Walker, Jr, published Macon, GA by Mercer University Press 1985.

Please also see my page on The Priority of Mark.

I also recommend Daniel Wallace's essay on The Synoptic Problem. Wallace's essay is itself a summary of the arguments given in Robert H. Stein's The Synoptic Problem: An Introduction (Grand Rapids: Baker 1987).

I also recommend Stephen Carlson's summary of The Two-Source Hypothesis.

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The Question of Q

Q is the term given to the second source supposedly used by Matthew and Luke in addition to Mark. The existence of Q has been challenged by such able critics as Austin Farrer, Michael Goulder, and Mark Goodacre. The alternative model proposed to the Two-Source Hypothesis is termed the Farrer-Goulder hypothesis. In this hypothesis, both Matthew and Luke have used Mark, but Luke has also used Matthew. Although the Farrer hypothesis does have a number of points to commend it, on balance I concur with the majority of scholarship that it is more likely that Matthew and Luke used Mark and Q independently. The purpose of this essay is to set forth the reasons for this judgment, which does not attain certainty but rather a probability.

The Two Source Hypothesis states that Matthew and Luke independently used Mark and a second source termed Q. Against the Farrer-Goulder hypothesis, it is maintained that it is improbable that the author of Luke consulted the Gospel of Matthew. The relative independence of Matthew and Luke is established by the convergence of several different arguments.

Independence in the Special Material

The Infancy and the Resurrection

Absence of Matthew's Use of Mark

Absence of Matthean Redaction in the Triple Tradition

Absence of Matthean Redaction in the Double Tradition

Primitivity of the Double Tradition in Luke

The Order of the Double Tradition in Luke

Different Markan Contexts for the Double Tradition

The Evidence of Doublets in Matthew and Luke

The Infancy and the Resurrection

The most serious discrepancies between the Gospels of Matthew and Luke are found in the infancy and resurrection narratives. The most obvious explanation for this phenomenon is that the agreement between the narratives of Luke and of Matthew is due to their common knowledge of Mark while the disagreement is due to their independence from one another.

There are several discrepancies in the infancy narratives of Matthew and Luke.

In Matthew the news of the coming birth of Jesus is conveyed to Joseph in a dream; in Luke, Mary is told directly by the Angel Gabriel.

Matthew implies that when Jesus was born his parents lived in Bethlehem and they left when King Herod began a search to find and kill Jesus. In Luke Jesus' parents traveled from their home in Nazereth to Bethlehem for a Roman census.

There is no census, inn, or manger in Matthew - indeed he says that Jesus was born in their "house" (2:11).

The geneaologies disagree, for example, on as fundamental a matter as the name of Joseph's father.

The resurrection accounts also diverge most seriously after the ending of Mark in 16:8, with Matthew narrating the appearance to the disciples in Galilee, while Luke tells only of appearances in the Jerusalem environs. Another example where the author of Luke-Acts disagrees with the author of Matthew is in the details of the death of Judas (Mt 27:3-10, Acts 1:16-20). These divergences are best accounted on the independent use and elaboration of Mark by Matthew and Luke.

Raymond Brown writes (An Introduction to the New Testament, p. 114):

Where Luke and Matt have almost contradictory accounts, why did Luke not make some effort to reconcile the difficulty? For example, Luke's infancy narrative is not only massively different from Matt's, but also in details is virtually irreconcilable with it, e.g., about Joseph and Mary's home (in Bethlehem in Matt 2:11 [house]; in Nazareth in Luke 2:4-7, with no home in Bethlehem) and about their travels after the birth of Jesus (to Egypt in Matt 2:14; to Jerusalem and Nazareth in Luke 2:22, 39). Or again, Luke's acctount of the death of Judas in Acts 1:18-19 is scarcely reconcilable with Matt 27:3-10.

In his essay "In Defense of Q," E.L. Bradby suggests a "rough-and-ready method" of testing the Farrer hypothesis. Bradby looks at four passages found in the triple tradition: the walk through the cornfields and its sequel (Mk 2:23-3:6, Mt 12:1-21, Lk 6:1-11), the parable of the sower (Mk 4:1-20, Mt 13:1-23, Lk 8:4-15), the charge to the apostles (Mk 6:7-11, Mt 10:1-42, Lk 9:1-5), and Peter's confession at Caesarea Philippi (Mk 8:27-9:1, Mt 16:13-28, Lk 9:18-27). In each case, Matthew has an expanded and fuller version of the pericope than does Mark, yet in no case does Luke reflect any of these Matthean additions to the triple tradition. Bradby concludes (ibid., p. 293):

If St. Luke had Matthew as well as Mark before him when he wrote, we can picture him following Mark verbatim whenever he had him, and Matthew verbatim when he had not Mark. But what, then, would happen when he had rival versions of an incident from Mark and from Matthew? What we should normally expect any conscientious historian to do is to take the later and fuller version, in this case Matthew (since ex hypothesi Luke knew as well as we do that Matthew had incorporated Mark's shorter Gospel in his longer one). We might, however, concede that for certain literary reasons he might follow sometimes one and sometimes the other. But if we find, as we have found in four important passages, that the later and fuller version is consistently spurned in favor of the earlier and shorter, and that there is not one clear instance in these sections of any non-Markan passage which Luke has derived from Matthew, we can hardly be blamed if we fall back, with relief, on the alternative hypothesis, that in many passages Luke has used Mark and in many others Luke and Matthew have each used a common source other than Mark, that is, Q.

Fitzmyer also makes use of this argument as follows (ibid., pp. 247-249):

. . . the apparent reluctance of Luke to reproduce typically Matthean "additions" within the Triple Tradition. In thus phrasing the matter, I may seem to be prejudging the issue. But I am only trying to refer to the fuller Matthean formulation of parallels in Mark, such as the exceptive clause on divorce (Mt. 19:9; cf. Mk. 10:11); Jesus' promise to Peter (Mt. 16:16b-19; cf. Mk. 8:29); Peter's walking on the waters (Mt. 14:28-31; cf. Mk. 6:50); and the peculiar Matthean episodes in the passion narrative [e.g., the death of Judas, the earthquake, the resurrection of the saints -ed.]. . . the real issue is to explain Luke's failure to adopt the extra Matthean materials in his parallels, or at least some of them, if he has written in dependence on Matthew - or used Mark as his main source and quarried Matthew only for such material as would suit his own edifice. The few examples cited above, having to do with pericopes, do not give a full picture of this phenomenon; it is necessary to compare a whole list of smaller Matthean additions to Mark, which are absent in Luke.

Fitzmyer provides this list to which more could be added:

Lk. 3:22 Mt. 3:17 (the public proclamation) Cf. Mk. 1:11

Lk. 5:3 Mt. 4:18 ("who is called Peter") Cf. Mk. 1:16

Lk. 5:27 Mt. 9:9 ("Matthew") Cf. Mk. 2:14

Lk. 6:4-5 Mt. 12:5-7 (plucking grain on the Sabbath) Cf. Mk. 2:26-27

Lk. 8:18b Mt. 13:12a (being given in excess) Cf. Mk. 4:25

Lk. 8:10-11 Mt. 13:14 (quotation of Is. 6:9-10) Cf. Mk. 4:12

Lk. 9:1-5 Mt. 10:7 (nearness of the kingdom) Cf. Mk. 6:7-11

Lk. 9:20b Mt. 16:16b (Peter's confession) Cf. Mk. 8:29b

The most probable conclusion is that Matthew and Luke have used Mark independently.

Absence of Matthew's Use of Mark

In his essay "Towards the Rehabilitation of Q," F. G. Downing examined "Luke's supposed use of passages where Matthew has apparently conflated a Markan record of teaching with similar but distinct material of his own from some other source." These passages include the Baptist narrative (Mt 3:1-4:11; Mk 1:1-13; Lk 3:1-22, 4:1-13), the Beelzebul controversy (Mt 12:22-45; Mk 3:20-29; Lk 11:14-26, 12:10, 6:43-45), the sending out of the Twelve (Mt 9:35-10:16; Mk 6:13-19, 6:6-11, 34; Lk 9:1-5, 6:13-16, 10:1-12), and the synoptic apocalypse (Mt 24:4-26, Mk 13:5-37; Lk 21:8-36). Downing divides the text of Matthew into A, in which Matthew follows Mark very closely; B, in which Matthew has material parallel to Mark; and C, in which Matthew presents material without Markan parallel.

Concerning the Beelzebul controversy, Downing argues (ibid., p. 277):

If Luke has Matthew and Mark before him, fairly obviously he is using only Matthew. He reproduces Matthew's C material (Matthew, not Mark) almost entire; and where Matthew has parallels with Mark is much closer to Matthew's than to Mark's version. Matthew has retained more or less the Markan context (he has only displaced the Call of the Twelve which immediately preceded the Beelzebul controversy in Mark); Luke has not even preserved that. He has no significant independent parallels with Mark.

If Luke has Mark and Matthew before him, fairly obviously he is using only Matthew. But is he using Matthew? We have noticed that Luke uses none of the A material, none of the material in which Matthew is at all obviously or precisely reproducing Mark. He uses most of the C material (Matthew only), and a lot of the B material, which may well, we suggested, have in large part originally been integral with the C material in Matthew's source. Luke in fact seems to be using Matthew's extra material without Matthew's obviously Markan additions. But Matthew's extra material without the Markan additions is not Matthew's Gospel; it is Matthew's other source(s).

Downing concludes that the use of a common source behind Matthew and Luke is the only sensible solution to the problem of "the Lukan omissions of pure Mark from his rendering of material similar to that which Matthew has conflated with Mark." Downing explains the difficulty that this presents for the Farrer hypothesis (ibid., p. 278):

On Dr. Farrer's argument, we have to suppose that Luke sat down (or stood) with Matthew's and Mark's works before him. He must have then, we have suggested, decided to follow Matthew (he has only three Markan words not in Matthew, and two in another context). But for some incomprehensible reason, he decides not to follow Matthew throughout, but to follow Matthew only where the latter has added new material to Mark or has largely altered him. He notes that one and a half sentences exactly quote Mark, and so omits them. It is not that he is going to use them somewhere else. He just arbitrarily excludes them, in one case actually in favor of writing his own version (verses 21-22): so it is not even that he finds the Markan material repetitive. It is not that he objects either, to Mark as such, for on Dr. Farrer's thesis, Luke does not know (as we have noted) that the B material is not basically Mark, but slightly emended; and he includes this, quite happily. All that he excludes is the material in Mark that Matthew obviously saw fit to include pretty well as it stood!

It seems very much more sensible to assume that Luke did not know Matthew's use of Mark, and in fact here reproduced his own version of the B and C (= Q) material, with no reference either to Matthew or Mark.

Downing presents further examples of this phenomenon. Concerning the baptism narrative, Downing writes (ibid., p. 279):

Again, Luke reproduces almost all the C material (less any equivalent of Mt. 3:14-15), the preaching of John, very faithfully, the Temptation less so. For the B material he has often his own version of Mark (so this time, if he has Matthew and Mark before him, he is surely using both) but reproduces almost all of it. Of the A material, Matthew's faithful quoting of Mark, he omits completely the larger part, 3:4-5a (he uses 5b independently, Lk. 3:3a) and verse 6. He does include the quotation from Isaiah (and omits Malachi from Mark); but the correction is obvious, and the remaining quotation essential to the Markan context that he retains. So again, Luke seems deliberately to ignore just the Markan material that Matthew has seen fit to reproduce exactly. Again, he seems to be reproducing Matthew's material independently of Matthew's use of Mark.

And on the sending out of the Twelve, Downing writes (ibid., p. 280):

In Matthew's version of the Sending out of the Twelve (Mt. 9:35-10:16) there is a considerable amount of C (Matthew not Mark ) material (9:35b, 37-38; 10:1b, 5-8, 12-13, most of 14 [?], 15-16). There is B material (Matthew // Mark), 9:35a, 10:1a, 2-4, 9-11 (14a?). There is A class material (Matthew = Mark): Matthew cites Mark precisely in 9:36. And again, Luke reproduces a lot of the C material, almost verbatim. He reproduces most of the B material, but often offers his own version of Mark: if he has Matthew and Mark before him, he is using both. But he omits Mt. 6:36 = Mk. 6:34, the only verse of Mark that Matthew has included as it stood in his own conflation of his two sources. It has every sign of 'Luke-pleasingness' (to quote Dr. Farrer: cf. Lk 7:13; 10:33; 15:4-6, 20). He does not use it elsewhere. He just omits it, though he preserves parallels to both sides of its Matthean context. He just does not seem to know Matthew's clear uses of Mark.

Downing goes on to adduce further examples to build his case. He concludes: "We would suggest it is much more reasonable to suppose that Luke's apparent ignoring of every clear use by Matthew of Mark is due to Luke's ignorance of Matthew's use of Mark. Luke knew Matthew's source (or sources) 'before' it had had its parallels with Mark conflated with the latter; and this source (or 'these sources') is what has come to be known in part as Q."

Absence of Matthean Redaction in the Triple Tradition

Concerning the phrase "Son of David," Wallace argues:

This phrase occurs eleven times in Matthew, four in Mark and Luke. Sheer numbers do not do this justice. Matthew begins his gospel with this phrase (1:1). Further, when a comparison is made, pericope by pericope, it can be seen that this is truly a Matthean emphasis. Cf., e.g., Matt 12:22-24/Mark 3:22/Luke 11:14-15. If Matthew were the first gospel, why would Mark and Luke omit this phrase seven times? That they have no aversion to it is seen from the four references. Further, the four references in Mark match the four in Luke, suggesting that Luke used Mark but was unaware of Matthew.

Following Stein, Wallace argues: "Matthew's ten (or eleven) introductory formulae ('this was to fulfill...') are not duplicated exactly in either Mark or Luke. Since both Mark and Luke use other introductory formulae (such as 'it is written'), this shows that they too were interested in linking the life of Jesus to the OT. But would they omit all of Matthew's formulae?" This suggests that Luke (like Mark) was not aware of Matthew.

Absence of Matthean Redaction in the Double Tradition

Here is another example, found in both the triple tradition and in the double tradition. The phrase "the kingdom of the heavens" is a well-known, tell-tale redactional phrase of the evangelist Matthew. It appears in Matthew thirty-two times, several times in place of the phrase "kingdom of God" that was found by Matthew in Mark. It also appears several times in the double tradition in Matthew, yet not once does Luke take over the Matthean phrase. This makes best sense on the hypothesis that Matthew and Luke have independently used the Q document, which Matthew has rewritten while Luke has retained the original wording.

Mt 5:3. Blessed [are] the poor in spirit, for theirs is the kingdom of the heavens.

Lk 6:20. And he, lifting up his eyes upon his disciples, said, "Blessed [are] ye poor, for yours is the kingdom of God."

Mt 8:11. But I say unto you, that many shall come from [the] rising and setting [sun], and shall lie down at table with Abraham, and Isaac, and Jacob in the kingdom of the heavens; but the sons of the kingdom shall be cast out into the outer darkness: there shall be the weeping and the gnashing of teeth.

Lk 13:28-29. There shall be the weeping and the gnashing of teeth, when ye shall see Abraham and Isaac and Jacob and all the prophets in the kingdom of God, but yourselves cast out. And they shall come from east and west, and from north and south, and shall lie down at table in the kingdom of God.

Mt 11:11-12. Verily I say to you, that there is not arisen among [the] born of women a greater than John the baptist. But he who is a little one in the kingdom of the heavens is greater than he. But from the days of John the baptist until now, the kingdom of the heavens is taken by violence, and [the] violent seize on it.

Lk 16:16. The law and the prophets [were] until John: from that time the glad tidings of the kingdom of God are announced, and every one forces his way into it.

Mt 13:33. He spoke another parable to them: The kingdom of the heavens is like leaven, which a woman took and hid in three measures of meal until it had been all leavened.

Lk 13:20-21. And again he said, To what shall I liken the kingdom of God? It is like leaven, which a woman took and hid in three measures of meal until the whole was leavened.

There is one occasion in the double tradition where Matthew has the phrase "kingdom of God," and in this case it appears that Matthew was retained the phrase from his source because to do otherwise would have destroyed the parallelism.

Mt 12:28. But if I by [the] Spirit of God cast out demons, then indeed the kingdom of God is come upon you.

Lk 11:20. But if by the finger of God I cast out demons, then the kingdom of God is come upon you.

I consider this, perhaps, to be an example of "fatigue" in Matthew's use of Q (which Goodacre says could not be found in his article). Prior to this verse, Matthew had never once used the phrase "kingdom of God" and consistently substituted the phrase "kingdom of the heavens," but subsequent to this verse Matthew's use is mixed.

The Primitivity of the Double Tradition in Luke

In the case of Mt 12:28 // Lk 11:20, we also see that Luke has retained the more primitive form of the saying with "the finger of God," while Matthew has rephrased the saying with "the Spirit of God," a phrase found elsewhere in the Gospels only in Matthew 3:16, where Matthew has also rephrased Mark 1:10.

Christopher Tuckett provides an example (Q and the History of Early Christianity, pp. 24-25):

To take a concrete example, many would argue that at Q 11:49, Luke's version is more original in having the doom oracle spoken by the 'Wisdom of God' in the past ('Therefore the Wisdom of God said "I will send to them . . ."') by contrast with Matthew's version in which the oracle is spoken by JEsus in the present ('Therefore, behold I am sending to you . . .'). From the side of the Q hypothesis, Luke's version looks decidedly un-Lukan. Nowhere else in Luke (apart from Luke 7:35 which is also a Q passage, or one borrowed from Matthew) does Wisdom appear as an almost personified being. On the other hand, Matthew's replacement of 'Wisdom' with the 'I' of Jesus is part of a consistent pattern whereby Matthew's Jesus takes the place of Wisdom in such texts (cf. above). Thus Luke's version seems to represent the more original Q version which Matthew then redacts.

Other examples could be adduced. For example, in the Sermon on the Mount, Matthew writes about "the poor in spirit" and those who "hunger for righteousness," while Luke simply writes of the poor and the hungry. Matthew's version of the Lord's Prayer is also more elaborate. It has been suggested that the influence of oral tradition could explain how Luke had access to a more primitive form of these sayings. But such an explanation is seen to be ad hoc when it could be argued that Luke would prefer to use the more developed Matthean forms in any case. The phenomena of alternating primitivity in the double tradition is what is to be expected of the hypothesis that Matthew and Luke have independently used a common source, and this consideration adds to the viability of the Q hypothesis.

The Order of the Double Tradition in Luke

Fitzmyer argued as follows:

. . . it is difficult to explain adequately why Luke would want to break up Matthew's sermons, especially the Sermon on the Mount, in order to incorporate a part of it in his Sermon on the Plain and scatter the rest around in an unconnected and disjointed fashion in the loose context of the travel account. Even though one must admit that this central portion of Luke is redactionally very important in the composition of the Third Gospel and that it constitutes a "mosaic" in its own right, yet the tension between its matter and its form (that is, between its loosely connected or almost unconnected episodes or sayings and its unifying preoccupation with Jesus' movement toward Jeruasalem that appears from time to time [Lk. 9:51, 53; 13:22; 17:11; 19:28]) has always been a problem. Whatever explanation is to be given for it and for Luke's redactional purpose in constructing this central section, the explanation that he has quarried the material from Matthew's sermons is the least convincing.

However, the argument from order can be finessed. The argument that Luke's order is the more original order of the double tradition does not rest upon any assumptions about inferior artistic ability. It arises from a close examination of the texts such as was made by Vincent Taylor in his article "The Original Order of Q."

Kloppenborg has usefully offered a summary of Taylor's work (The Formation of Q, pp. 68-69):

Rather than comparing Matthew and Luke in two parallel columns, Taylor offered the brilliant solution of dividing Matthew into six components: the five large sermons and the remainder of the Gospel (see table 2). When this was done, Taylor was able to show that there is a large measure of agreement in order when one compares each of the six Matthean columns with Luke. In effect, Taylor suggested that Matthew scanned Q several times, removing material appropriate to each of the five sermons, and reproducing these smaller sets of sayings in Lucan order. He conceded, however, that the agreement in order is "not continuous throughout [each sermon] but visible in groups and series of passages in the same order in both Gospels." Finally, he tried to provide explanations for each transposition or dislocation of Q material, almost invariably attributing the change to Matthew. Conflation with Mark and influence of M tradition were his usual ways of accounting for Matthean alterations.

Although Kloppenborg has some methodological reservations, he offers the following observations (The Formation of Q, p. 78):

. . . the observation that Matthew collected related materials is of only limited value in defending Lucan priority in order. In many instances it does not yield particularly convincing conclusions. In one case, however, its force is considerable. The mission speeches in Matthew and Luke begin with a cluster of Q sayings (see above). At 10:16 Luke finished his speech and turns to other subjects. But Matthew continues, employing diverse materials, some drawn from Mark (13:9-13) and some from Q passages which are scattered throughout Luke. What is striking is that Matt 10:24-39, comprising ten Q sayings, reproduces these sayings in Lucan order (##14, 65-69, 76-77, 87-88) even though they do not appear together in Luke. Here it appears that Taylor's type of explanation has special merit (even though Taylor did not treat these particular sayings). After reproducing and rearranging the Q mission speech, and after interpolating part of Mark 13, Matthew scanned Q and removed, in the original Q (= Lucan) order, 11 sayings appropriate to the theme of mission and used these as the balance of his mission speech. Only in the case of Q 17:33 (Matt 10:39), which occurs with a cluster of discipleship sayings (Q 14:26, 27 // Matt 10:37, 38), is it likely that the Matthean order is primary. Otherwise, it is the most economical and intelligible solution to suppose that Matthew scanned Q and collected these sayings than to argue that Luke distributed them in a capricious fashion.

Taylor himself stated one conclusion of these observations (ibid., p. 317):

The investigation has confirmed the view that Luke has preserved the order of Q and has followed it with great fidelity. It has shown further that Matthew knew the same order and was aware of it when he made editorial adjustments and conflated Q with Mark and M. If we reject, as we must, the hypothesis of Luke's dependence on Matthew, the result of comparison of the order of the sayings in Matthew and Luke is to demonstrate the existence of Q, so far as this is possible in the case of a source known to us only from its use in the two Gospels. Q is not 'an unnecessary and vicious hypothesis,' but a collection of sayings and parables which actually existed when Matthew and Luke wrote.

Different Markan Contexts for the Double Tradition

In a famous passage, Streeter observed the following (ibid., p. 223):

Sir John Hawkins once showed me a Greek Testament in which he had indicated in the left-hand margin of Mark the exact point in the Markan outline at which Matthew has inserted each of the sayings in question, with, of course, the reference to chapter and verse, to identify it; on the right-hand margin he had similarly indicated the point where Luke inserts matter also found in Matthew. It then appeared that, 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 Markan outline. If Luke derived this material from Matthew, he must have gone through both Matthew and Mark so as to discriminate with meticulous precision between Markan and non-Markan material: he must then have proceeded with the utmost care to tear every little piece of non-Markan 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 reinsert 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.

This argument is also taken up by Fitzmyer (ibid., p. 250):

. . . aside from 3:7-9, 17 and 4:2-13 Luke has never inserted the material of the Double Tradition into the same Markan context as Matthew. If he derives such material from Matthew - and otherwise manifests such respect for a source that he is following, as his dependence on Mark would suggest - it is surprising that at least some of the remaining Double Tradition does not occur in contexts that parallel Matthew, which are often quite appropriate to this material. The frequent disagreement with the Matthean order in this regard is crucial to any judgment about Luke's dependence on Matthew; in fact it suggests that he does not depend.

The Evidence of Doublets in Matthew and Luke

This argument is advanced by Werner Georg Kummel (ibid., pp. 232-233):

The decisive evidence for a common, written source for Matthew and Luke is offered by the doublets, or double traditions (double traditions are texts presented by both evangelists, but in different forms; doublets are texts which one evangelist presents twice). It is noteworthy that Luke reports the sending of disciples twice: Lk. 9 and Lk. 10, the first time in parallel with Mk. 6:7-13 and the second in parallel with Mt. 10. Of course, in Lk. 10:1 there are seventy disciples, but as Lk. 22:35 shows, the saying in Lk. 10:4 was originally addressed to the twelve. Mt. 10:1-16 makes contact alternately with Mk. 6:7-13 and Lk. 10:1-12. Similarly there are doublets in Matthew, some of which parallel Mark while others parallel Luke's sayings material, for example, Mt. 18:8-9, and 5:29-30; 19:9 and 5:32.

Furthermore, there is a string of sayings of Jesus appearing twice in Matthew and Luke, once in a setting which Mark also has, a second time in a sayings setting which is found only in Matthew and Luke. The most important examples of this are:

a) "He who has, to him will be given" (Mt. 13:12; Mk. 4:25; Lk. 8:18; cf. Mt. 25:29; Lk. 19:26).

b) "If any man will follow me, he must deny himself" (Mt. 16:24-25; Mk. 8:34-35; Lk. 9:23-24; cf. Mt. 10:38-39; Lk. 14:27; 17:33).

c) The eschatological retribution for the rejection of Jesus (Mt. 16:27; Mk 8:38; Lk. 9:23-24; cf. Mt. 10:32; Lk. 12:8-9).

d) Persecution of the disciples on account of Jesus (Mt. 24:9, 13; Mk. 13:9, 13, Lk. 21:12, 17; cf. Mt 10:19-20, 22; Lk. 12:11-12).

e) Mk. 3:23-30 is lacking in Luke; but Lk. 11:17-23 offers a different version of the defense of Jesus against the charge of complicity with the demons. Mt. 12:25-31, however, recalls alternately Mk. 3 and Lk. 11.

When this evidence of doublets and double traditions in Matthew and Luke is placed beside the fact that Mark presents a single doublet (Mk. 9:35; 10:43), it is incontrovertibly proved that Matthew and Luke must have used a second source in addition to Mark.

Conclusion

I do not pretend to have achieved a certainty but only a probability in favor of the Q hypothesis. Perhaps each of these arguments are surmountable, but each points in a certain direction, and the cumulative force of these arguments lead me to favor the Q hypothesis as the best explanation of the synoptic data. The presence of the minor agreements is the only one very serious argument against the Q hypothesis, and it has been successfully addressed in detail by writers from Streeter to Neirynck. An assessment of the totality of the evidence indicates a balance in favor of the Q hypothesis, and thus it is my working hypothesis.