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Matt.5:1,2: "And seeing the multitudes, he went up into a mountain: and when he was set, his disciples came unto him: And he opened his mouth, and taught them, saying...."
Luke6:17,20: "And he came down with them, and stood in the plain, and the company of his disciples, and a great multitude of people...came to hear him.. And he lifted up his eyes on his disciples and said..."
Was this sermon on a mountain, or on a plain? And just what was it's content? Luke and Matthew vary so widely.
Some like to say that Matthew and Luke are reporting two different sermons, but this is untenable - both are followed by the same story of the healing of the centurion's servant.
In terms of place this is easy -- The Greek in Matthew is to be interpreted as referring not to "on a mountain" but "in mountain country" - it is a regional rather than a specific reference. (See D. A. Carson, "Exegetical Fallacies".)
The issue of content might appear more complex, but it is actually just as easy to explain. When reckoning with any teaching of Jesus that appears in more than one gospel, one should observe the dictum of N. T. Wright: That Jesus taught these same basic things, in slightly different forms, perhaps hundreds of times. As long as the basic message is intact, it matters not at all which "version" is recorded.
At the same time, Matthew's structure as a "teaching" gospel, a manual with a structure designed with education in mind. Matthew has clearly designed the Sermon on the Mount as a compendium (which his readers, seeing the structure of his Gospel, would recognize), rather than as a straight historical report (like Luke's version would be expected to be, as he is reporting in the Hellenistic historiographic tradition).
Keener's commentary on Matthew explains :
...[A]ncient writers exercised the freedom to rearrange sayings, often topically. Writers who collected such sayings summarizing the thrust of a famous teacher's message (such as Epictetus' Encheiridion, Menander's epitome, or the Qumran Temple Scroll) called their collections "epitomes"; Matthew has exercised an analogous literary liberty, collecting many of Jesus' sayings on the topic of ethics, even if the precise comparison with Greek "epitomes" may be overstated.
Keener notes as well that rabbinic collections of sayings could vary on details just as the two sermon "versions" could. There is no need to resort to any other harmonizations, such as that e.g., Jesus said the same things twice, varying them by saying them once in the third person and the other in the first person.