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Various features of the setting contribute to Matthew's portrait of Jesus.
First, "mountain" settings in Matthew are usually significant (17:1; compare 15:29; 28:16; although Moses is not alluded to in 4:8). Many scholars think that Matthew probably recalls Moses' revelation on Mount Sinai (Ex 19:3) here. If so, Jesus' superior revelation also makes him superior to those who "sit in Moses' seat" (Mt 23:2); the One greater than Moses, first encountered in 2:13-20, has begun his mission.
Second, Matthew's depiction of Jesus' teaching is appropriate. That Jesus sat to teach (5:1; compare 13:1-2; 23:2) fits expected patterns of Jewish instruction (see also Lk 4:20). Thus Jesus takes the role of the scribes, but Matthew also indicates that Jesus is greater than the scribes (Mt 7:29).
Finally, Jesus' audience is also relevant to Matthew's point. Jesus' ethics specifically address disciples, but Jesus also invites those who are not disciples to become disciples and live according to the values of God's kingdom. The crowds following Jesus (4:25-5:1) function as at least potential disciples; disciples in the Gospel provide models for later believers (Guelich 1982:53). Matthew explicitly indicates that Jesus taught his disciples (5:1-2) but also that the crowds were present (5:1; 7:28-8:1), implying that Jesus wanted both to hear, calling both to decision (7:24-27; see Guelich 1982:60).