Premises of this response:
- There was no Q document (per the OP)
- Luke (writing to a gentile audience) used Matthew’s Gospel (written
to a Jewish audience) as a source. For a more thorough discussion of
the greater Jewish focus of Matthew, and why it indicates that
Matthew preceded Luke, see my thoughts here.
What Luke leaves out
You have heard it said
This is a reference to the Mosaic Law. Matthew, writing to Jews, would be able to reference the Torah and his audience would know what he was talking about. For Luke, writing to a gentile audience, references to the Torah would be a distraction at best and a source of confusion at worst. Unsurprisingly then, Luke omits the “you have heard it said” passages found in Matthew.
Pagans & Tax Collectors
Matthew’s reference to pagans would be an effective message to the Jews, who prided themselves on being different from pagans. It’s a sharp remark: how good are you if you’re only doing what the pagans do?? It’s an effective and poignant observation of hypocrisy, if people are doing the same things they criticize their “out-group” for doing.
But to Luke, whose readers may well have been pagans (past or present), rather than driving the point home he might actually offend his readers. They didn’t grow up believing in the Lord and probably won’t take well to be referred to as an “out-group”. Even if some of the Jews looked down on the pagans, Luke doesn’t score any points by pointing it out.
On a related note, where Matthew speaks tax-collectors—a group despised by many Jews who saw publicans as traitors in the service of a foreign power—Luke changes the reference to sinners. An educated Greco-Roman audience would likely not feel the same way about tax-collectors as Matthew’s audience did.
In general, Luke portrays Rome in a remarkably positive light (just two examples of many would be Pilate really hard to let an innocent man go & Gallio being evenhanded in the Corinthian trial of Paul); he may in fact be doing so in order to try to keep Christianity & Rome on positive terms. As such, he’s not going to go out of his way to gratuitously criticize Rome’s tax-collectors. John Mauck goes into great detail on the context of Luke’s portrayal of Christianity & Rome here.
Go the second mile
This classic teaching from the sermon on the mount (Matthew) is conspicuously absent from the sermon on the plain (Luke). I do not claim to know for certain why, but I can offer a hypothesis. Matthew’s audience would generally be people who were being asked to go a mile, whereas Luke’s audience may well include people who were in positions of authority to compel others to go a mile. It is widely held that Luke's target audience was educated Greco-Romans--the high Greek of his preface (Luke 1:1-4) supports this.
Luke thus leaves this passage out so as not to 1) justify the abuse of power or 2) create the impression that Christians should be targeted for public mistreatment because they’re too nice to say no.
Assuming Matthew wrote first and was used as a source by Luke, there is no need to explain why Matthew leaves out passages found in Luke.
What Luke adds
Approximately half of the Gospel of Luke is material not found in Matthew or Mark. Whether we call this “L” or “Luke’s notes from eyewitness interviews” or something else, clearly Luke has material and commentary beyond what’s in Matthew (in many contexts) that he wants to include.
Perhaps the most parsimonious solution to what Luke adds in the sermon on the plain is this: the sermon on the plain was a different time and place than the sermon on the mount, and Jesus said some things during the sermon on the plain that he didn’t say on the mount.
If Jesus gave multiple versions of the sermon (traveling preachers do this all the time), then Luke may have heard different versions of the sermon. If Luke had heard several versions of the sermon and really liked certain passages, why not include them even if Matthew had left them out?
I’m hesitant to try to dive too far into speculating what is in the mind of the author (I think this has been the shipwreck of many an exposition on the synoptic problem), but at the very least, whatever his source, Luke had some material that wasn’t in Matthew and it was quite appropriate in the context in which he presented it.
The Golden Rule
This is one of Jesus’ most iconic teachings. To those who see the sermon on the mount and the sermon on the plain as evidence of fabrication I would ask: find me an itinerant preacher in any time or place who never taught the same ideas more than once. Given that every word attributed to Jesus in the Gospels can be read aloud in under an hour, it is a virtual certainty that over the course of a multi-year ministry He would have said many things—including telling stories more than once & teaching principles not found in the Gospels.
I find it inconceivable that so profound a statement as the golden rule (which to my knowledge is never found in its positive form prior to Jesus) would only have been uttered once.
But even if Jesus taught the same parables & principles many times, we shouldn’t expect the Gospel authors to write it many times. A document of this magnitude would be a significant and expensive undertaking—so even if you have a really profound statement to make, you might make it only once.
As such, Matthew & Luke each took the golden rule, probably spoken by Jesus on a number of occasions, and put it in the context they thought would be most effective.
Chronology isn’t the #1 guiding principle here
Some have been surprised to discover that the Gospels are not designed to be strictly chronological documents. True the infancy narratives are at the beginning and the passion narratives at the end, but in between there appear to be other interests besides chronology.
This is less surprising when we consider that early on, the Gospels were much more likely used as memory aids (see HE 3.24.6) for preachers than as treatises to be read aloud from end to end as a sermon (have you ever tried this with a massive scroll that has no chapters, verses, or spaces between words?). The narrative context then serves a very valuable purpose--it's much easier to remember a story than a long dialogue. A Gospel written in bite-sized pieces (pericopes) would serve the preachers' needs quite well.
(For those who want to really geek out on the synoptic problem, I gave an in-depth presentation of the argument from order which can be found here)
Matthew organizes much of his material by topic and builds his narrative around the major sermons. Luke, on the other hand, organizes a decent portion of his gospel by geography. E.g. Jesus spent time in city A, here are things in said and did there; He spent time in city B, here are things in said and did there, etc. These aren’t hard and fast rules but they are frequent patterns. I believe they explain a decent portion of the dislocations between material shared by Matthew & Luke.
The parable of the stained-glass window
(described in greater detail here from 3:42 to 5:48 )
You see two photographs, both of the same stained-glass window. In one, the window is intact and it is a masterpiece. In the other, it is in shards and fragments in front of the frame—which is bent—as there’s a rock on the ground next to the window. The photographs don’t have timestamps on them, and you’d like to know which was taken first.
In theory it’s possible that either photograph was taken first—it’s possible to restore a broken window so well that nobody can tell it’s a restoration—but it is far more likely that the intact picture was taken first, and then somebody threw a rock through the window.
I see this phenomenon in Matthew & Luke. Matthew has put together magisterial sermons. Luke regularly breaks them up (this is not just the sermon on the mount) and scatters them throughout his Gospel based on his own plan of what content will be covered where. That Luke would break up Matthew’s sermons is easier to believe than that Matthew found all these pieces scattered throughout Luke and managed to assemble a masterpiece from scattered remnants.
This isn’t intended as an attack on Luke; he just has a very different set of organizing principles than does Matthew.
Bringing Q into the mix doesn’t help—the same problem remains. If Matthew used Q, did Matthew patchwork together a stained-glass window from fragments in Q? It’s no more likely than that he did so from Luke. But if Luke is willing to break up sermons he could do it whether his source is Matthew or Q.
Thus, the simplest solution is to get rid of the middleman and drop the Q assumption. If Luke’s use of Q and Luke’s use of Matthew require an (essentially) identical explanation, appealing to Q would only serve to multiply entities beyond necessity.
Insight from Shem Tob Matthew
The 14th century Shem Tob polemic against Christianity includes a copy of Matthew—in Hebrew—which does not appear to be a translation from Greek or Latin, but rather a descendent of ideas originally put down in Hebrew. (Here is a summary on what Shem Tob is, and here is a detailed scholarly discussion of what it means.)
A fascinating observation has been made regarding the way the Sermon on the Mount is recorded in Shem Tob:
When the sayings in Luke are placed alongside their parallels in the
Hebrew text of Matthew 5-7, every time the Hebrew is interrupted by
the words “Jesus said to his disciples,” without exception Luke jumps
to a different place in his Gospel or has a void. See here p. 254
This data point, in conjunction with the discussion of the parable of the stained-glass window above, leads me to the conclusion that early on the sermon on the mount—though an unparalleled masterpiece in its entirety—was regularly thought of as a source from which individual lessons could be broken out and used in a variety of contexts (in the ministry you'll find a lot more opportunity for a 2 minute lesson than a 30 minute sermon).
This is exactly what Luke appears to do with the sermon, and if Matthew was already written in a form that made these bite-sized pericopes easy to separate from the whole, there is no need to appeal to Q at all in these passages.
- Jesus almost certainly gave the same/similar sermons more than once; variations in different settings should not surprise us.
- When Matthew says something that would be misunderstood by or offensive to Luke’s audience, Luke usually leaves it out.
- When Luke has material (from another source and/or setting) that fits contextually very well with material he is obtaining from Matthew, Luke is happy to add it in. Since about half of Luke is not found in the other Gospels, Luke was clearly willing to add material he liked to whichever documents he used as sources.
- Matthew organized material into effective, self-contained sermons, but they were made up of individual pericopes that were sometimes presented together and sometimes presented on their own. Luke sometimes did one and sometimes the other based upon the themes he was emphasizing in a given place in his Gospel.
- Q is unnecessary to explain any of this behavior.