I propose 2 major arguments and 3 minor arguments supporting the view that Mark was dependent upon Luke.
Major Argument 1--The Argument from Order
The argument from order suggests that Mark was third by comparing the order in which pericopes are presented. Matthew & Luke frequently alternate “following” Mark’s order, especially in the first half of Mark. Where Matthew stops following Mark, Luke starts following Mark, and vice-versa. Furthermore, Matthew & Luke never agree in order against Mark.
Malcolm Lowe examined the Argument from Order mathematically and through formal logic and showed that the explanatory power of each hypothesis strongly favors Mark being third.
In other words, how often does the order of materials in the Gospels align with what would be predicted based on Matt & Luke copying from Mark, versus what would be predicted based on Mark copying from Matt & Luke. Any synoptic theory acknowledges exceptions, but how many exceptions are we talking about?
How often does the prediction match what’s actually in the Gospels:
- With Mark first: 57/90
- With Mark third: 88/90
Lowe’s paper and formal proof are excellent—you can find them here.
As for the alternating pattern, let’s look at this pattern 3 ways:
If Mark were first and the other two authors wrote independently, then by pure happenstance where one stopped following Mark the other started…over and over again. This is what David Barrett Peabody pithily referred to as "they neatly divided Mark's Gospel between them" (and more improbable still, that they did so by accident).
Since Matthew & Luke do sometimes agree in order where Mark is not present, suggesting that their common order derives from Mark cannot adequately explain the phenomenon of shared order. Note that some have said that Mark must be first because where there’s no Mark to follow Matt & Luke go their separate ways. This is backwards. Even where there is Mark to follow Matt or Luke regularly disagree with Mark’s order anyway!
If Mark were first and the third author knew both Mark and the second Gospel, then the third author went to the extraordinarily laborious effort of making sure he followed Mark where the other one didn’t, but was ambivalent about following Mark where the other one did.
Since both Matthew & Luke have a clear structure to their Gospel—and it has nothing to do with this alternating Markan pattern of order—the idea that the third author complicated their task by inserting this obscure alternating pattern into their work is both ad-hoc and inexplicable. Unless we want to get into conspiracy theories on coded messages (I don't), I conclude that it would be wildly improbable to produce this pattern by accident, and irrational to do it on purpose.
If Mark were third, then the process is clean and straightforward: where his sources agreed in order, he followed their order. Where they did not agree in order he necessarily could not follow both and so chose one or the other.
(This argument is most helpful when visualized—my channel has a deeper discussion of this argument with whiteboard drawings: see Macro argument from order & Micro argument from order)
Major Argument 2--Hebrew language
This argument was made by Robert Lindsey (see a summary in this post on the site). Though both are composed in Greek, Luke is considerably more Hebrew in syntax and expression than Mark. This is exceptionally difficult to explain if Mark came first (Luke would have had to re-Semitize the material he was copying from Mark), but very straightforward if Luke preceded Mark (the more Semitic material is the earlier material).
Since (at least most of) Jesus' teachings originated in a Semitic language, which is more likely?
a) Semitic material in Luke became more Greek in nature as it was transmitted through Greek audiences
b) Greek material in Mark became more Semitic in nature as it was transmitted through Greek audiences
"A" is by far the simpler hypothesis, and it supports Luke preceding Mark.
Borrowing of words
Eduard Zeller's work on borrowed words in the Synoptic Gospels didn't presuppose which Gospel was first (like most such theories do), and concluded Mark borrowed from both Matthew & Luke. An excellent summary in English is in the Introduction to One Gospel from Two Mark's Use of Matthew and Luke.
For every example where it looks like Luke has borrowed wording from Mark, there are multiple examples going the other direction. The aforementioned discussion of Robert Lindsey's work provides another example of this pattern, in which Mark appears to be editing Luke's verb-tenses, not the other way around.
Clement of Alexandria
The early, well-placed scholar Clement of Alexandria suggests that Mark's Gospel was written third (after Matthew & Luke):
Again, in the same books, Clement gives the tradition of the earliest
presbyters, as to the order of the Gospels, in the following manner:
The Gospels containing the genealogies, he says, were written first.
The Gospel according to Marks had this occasion. As Peter had preached
the Word publicly at Rome, and declared the Gospel by the Spirit, many
who were present requested that Mark, who had followed him for a long
time and remembered his sayings, should write them out. And having
composed the Gospel he gave it to those who had requested it (see HE
(to be sure, Clement's student Origen does appear to disagree with him on this matter)
There are hundreds of places in the triple tradition (material in all 3 Synoptic Gospels) where Matthew & Luke agree in a minor detail, and Mark disagrees.
The following thought experiment is interesting. I give a story to two students, tell them to work separately, and ask them to re-write the story, add their own touch to it, and make it nearly twice as long. Later, the students come back with their revisions—and although there are numerous differences, they have also made exactly the same change in the same place in the story not once or twice, but hundreds of times! Am I going to appeal to chance or to collusion? I’m going to strongly suspect the latter.
David Barrett Peabody has written:
If the hundreds of ‘minor agreements’ scattered throughout the Triple
Tradition are seen to merge with and form a pattern with the scores of
‘major agreements’…then it becomes increasingly apparent that Luke was
primarily dependent on Matthew and not Mark, and there is no need for
Q or the priority of Mark. (One Gospel from Two - Mark’s Use of
Matthew and Luke, p. 6)
This then works against the idea that Matthew & Luke copied from Mark, and is decent support for the view that it was Mark who blended material from Matthew & Luke.
(a more detailed discussion, including objections to this view, is found here)
Markan Priority (the view that Mark was the first of the Synoptic Gospels) remains extraordinarily popular in New Testament scholarship today. I share in this post why I do not believe the arguments for or the popularity of Markan Priority are compelling reasons to believe it is true.
If the case for Luke preceding Mark is allowed a fair analysis, without the pressures of academic conformity, the evidence stands up reasonably well.