These two verses are central to Paul's Christology. Two fundamental truths are asserted of "His (God's) Son", and their close parallelism is impossible to miss:
"who was born" / "who was appointed"
"from the seed of David" / "Son of God with power"
"according to the flesh" / "according to the spirit of holiness"
There are three primary competing views of this passage:
1) One view takes v. 3 as descriptive of Christ's humanity or his human nature, whereas v. 4 describes his deity or his divine nature. Thus the contrast is between the two components of Christ's person. He is one person with two natures: one human (hence flesh) and one divine (hence spirit; not a reference to the HS).
2) According to another view, the contrast between "flesh" and "spirit" is between the outward and the inward. Externally Jesus may be said to have descended from the seed of David. Internally he was perfected in the spirit (or by the Spirit) which fitted him to be the Son of God with power.
3) The most likely view contends that the focus of the contrast between v. 3 and v. 4 is not between his human nature and his divine nature but rather between his humiliation and his exaltation. In other words, the contrast is not between two different components in Christ's person but between two successive stages or phases in Christ's experience. Cf. Phil. 2:5-11.
Humiliation = his birth, earthly life and ministry, sufferings.
Exaltation = resurrection, ascension, enthronement.
According to this view, flesh refers not so much to the body (far less to the sinful nature) but to the present, natural, earthly realm in which we live. The flesh/spirit contrast is historical; it is a contrast between this present, fallen, earthly, temporal world in which we live, and the future, redeemed, heavenly, eternal world which is yet to come.
The phrase "according to the flesh" refers not so much to Christ's human nature but to the historical realm/environment with which humanity is necessarily associated. The eternal Son of God entered the sphere of the flesh, i.e., this present, fallen, evil age. But as v. 4 goes on to point out, by virtue of his resurrection he has entered the sphere of the spirit, the new age, the heavenly realm where he now lives and reigns.
The word translated "declared" (NASB) is significant. It is the Greek word horizo, from which we get the English term "horizon". Some insist it means that the resurrection marks out or declares Jesus to be the Son of God. But in its 7 other occurrences in the NT it means to determine, to appoint, to fix (Lk. 22:22; Acts 2:23; 10:42; 11:29; 17:26,31; Heb. 4:7). In some sense, then, Christ Jesus was appointedSon of God by virtue of his resurrection from the dead.
This would appear to create a theological problem, for how can the eternally pre-existent Son be appointed Son of God? But note: Paul does not say Jesus was appointed Son of God, but Son of God with power. Paul is describing an event in history whereby Jesus was instated in a position of sovereignty and invested with power (cf. Acts 13:33; Phil. 2:9-11). At the resurrection and exaltation Jesus began a new phase of divine sonship. While on earth Jesus was certainly the Son of God. But he was not the Son-of-God-with-power. Paul is not saying Jesus became the Son at the time of the resurrection (the heresy of Adoptionism). After all, it is the Son who is appointed Son. "The tautologous nature of this statement," Moo explains, "reveals that being appointed Son has to do not with a change of essence -- as if a man or human Messiah becomes the Son of God for the first time -- but with a change in status or function. . . . [Thus] the transition from v. 3 to v. 4 . . . is not a transition from a human Messiah to a divine Son of God (adoptionism) but from the Son as Messiah to the Son as both Messiah and powerful, reigning Lord" (41). It is a transition from the Son of God in weakness and frailty and submission and humiliation to the Son of God in power and strength and authority and exaltation.
Paul's use of Lord with reference to Jesus is eternally significant. Lord translates the Hebrew YHWH more than 6,000x in the LXX. To speak of Jesus as Lord is to identify him with YHWH, God of Israel! It also points to his absolute sovereign right of rule over us: over our minds, wills, emotions, lives, time, money, talents, over all.