From Schreiner:

“Paul must explain in his gospel how Jesus Christ has accomplished redemption.  Human beings are freed to honor and praise God because Jesus in his person and work has vindicated God’s honor.  He has succeeded where Adam and Israel failed.  He is the promised seed of Abraham and David, the Lord of heaven and earth, and he even shares in the divine nature.  He fulfills the promises of the new covenant, and through him the promise made to Abraham that all nations would be blessed is inaugurated” (152).

“The promises of salvation made to Israel were not yet fulfilled, and the nation continued to live under Roman control because of its sin.  The pattern of sin that permeated Israel’s history demonstrated that the glorious promises of deliverance and salvation were not yet a reality.  The history of Israel shows that for God’s promises to be fulfilled, a new humanity is necessary; and for a new humanity, we need a new Adam.  Paul proclaims that Jesus the Messiah is the new Adam” (152).

Schreiner notes that Israel had not seen the fulfillment of the OT prophecies regarding their ultimate salvation (159).  He rightly sees that the promise to Israel in the Abrahamic Covenant is limited to the area of Palestine, but the whole of the Abrahamic promises makes Abraham the heir of the world (160), involving descendants that are broader than Israel as a nation (but not detrimental to the literal fulfillment of those promises to Israel either).

“The lordship of Jesus cannot be confined to an initial decision where one submits to his lordship.  Paul often appeals to the lordship of Jesus in his exhortations, showing that the lordship of Jesus carries through all of life.

“Often kyrios functions as the translation of Yahweh when God himself is the referent (Rom 4:7-8 = Ps 32:1-2; Rom 9:27-29 = Is 10:22-23; 1:9; Rom 11:34 = Is 40:13; Rom 15:9, 11= Ps 18:50 or 2 Sam 22:50; 1 Cor 3:20 = Ps 94:11; 2 Cor 6:18 = 2 Sam 7:8).  More significantly, in a number of texts Paul identifies the kyrios as Jesus Christ, even though the Old Testament allusion or quotation clearly refers to Yahweh (Rom 10:13 = Joel 2:32; Rom 14:11 = Isa 49:18; Jer 22:24 and Isa 45:23; 1 Cor 1:31 = Jer 9:24; 1 Cor 2:16 = Isa 40:13; 1 Cor 10:22 = Deut 32:21, 26; Phil 2:10-11 = Isa 45:23-24; 1 Thes 3:13 = Zech 14:5; 2 Thess 1:8 = Isa 66:15)” (168).

On Philippians 2 and “Christ emptied himself.”  “Some have understood this to mean that he surrendered himself completely of his deity in becoming a human being.  Close attention to the text is necessary to discern Paul’s meaning.  The main verb he emptied (ekenosen) is modified by two participles:  taking (labon) and becoming (or being made – genomenos).  Both of these participles should be understood instrumentally, in that they describe the manner in which Christ emptied himself.  That is, he emptied himself by taking the form of a servant and by being made in the likeness of human beings.  The emptying of Christ, then, consisted of an adding.  He emptied himself by becoming fully human” (172).

“Often people define grace only in terms of an unmerited gift.  Such a definition is certainly fitting.  But grace is more than an unmerited gift in Paul, for the word gift could convey the idea that one may choose to open the gift or, conversely, that one may choose to reject the gift.  Grace in Paul is also a power that effects what is demanded.  The gift of righteousness is not merely offered to human beings; it is secured through the work of the second Adam.  The last Adam does not merely offer life; he grants life” (187).