So by his actions, Jesus clearly presents Himself as a new lawgiver, in the mold of Moses. If one does not want to go that far and speak to Jesus’ private intentions, one could certainly insist that His biographers wished for their audiences to draw that conclusion.
In Jesus’ case however, His status goes beyond that of Moses. Unlike Moses, Jesus does not point to the finger of God as having written the commandments in stone at a time in the distant past, thus pointing to an entity separate from himself in the process. Jesus does not appeal to the ancient working of the finger of God in the way that one may appeal to an established and recognized authority figure. Rather, Jesus is reported as speaking of Himself using the same finger of God language that was most assuredly meant to communicate something which He believed to be true of Himself. Undoubtedly, this is what Luke wants His audience to grasp.
Later on in the same setting, Jesus goes on to say “For just as Jonah became a sign to the people of Nineveh, so the Son of Man will be a sign to this generation” (11:30). This use of “Son of Man” is part of a building process within Luke. That process effectively culminates with Jesus’ linking the coming of the Son of Man, referencing Daniel chapter seven and the Son of Man coming on the clouds to the Ancient of Days in order to receive His kingdom, to the destruction of the Temple, with a repetition of “this generation” in connection with the sign, while also speaking of the Son of Man during the course of His passion (an entirely different subject matter altogether).
Jesus then, in Luke’s highly structured and structural setting, speaks of Himself in connection to the finger of God (with this functioning on multiple levels), and then speaks of the Son of Man, which can be shown to be self-referential. Making the connection then, the Son of Man is obviously meant to be understood as a divine figure, and it is the Son of Man (the king of the kingdom of God, the Messiah, the Creator God manifest) that is speaking when providing new laws for the people of that God and casting out demons.
As this study works backwards through the defining and definitive historical narrative that is the Hebrew Scriptures, the final instance of the finger of God is found in the eighth chapter of Exodus. There, Moses has struck his staff on the ground, with this striking resulting in the dust of the ground becoming like “gnats throughout all the land of Egypt” (8:16b). As they had done with the previous signs from Israel’s God that had been provided to Moses in order to prove the veracity of the message he delivered, the magicians of Egypt attempted to match the feat. However, they were unable to do so. In response, “The magicians said to Pharaoh, ‘It is the finger of God!’” (8:19a)