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“God has elected Christ as the means of salvation”. (Cf. Gal. 3:16). God’s choice was about the lineage through which the Messiah would come.
Romans 9:15 “For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.” — Answered in section of verse 18.
In Romans 9:16, Paul is saying man (of Jewish descent) cannot be given the mercy/compassion of God solely and entirely based off their bloodline, ethnicity, as if they can will or work for His mercy/compassion of being a Jew. That is what Paul is saying in verse 16.
In Romans 9:17, God wanted his power and glory to be known for two different groups of people. One, for the Jewish people when they left egypt, they would say “God is so powerful, look at all the things that he did. This is the God that we serve. This is the God that we need to be faithful to.” He wanted his glory and power to be known so people would revere him, so people would see what kind of God he is, and that would certainly strengthen the faith of the Israelites. Two, it also strengthened the nations around them. Example, when the Israelites went to Canaan, they went to Jericho. And what they heard the people in Jericho saying is we've heard about the power of God, and so all these things were in the minds of the people. Rahab proves this “We have heard how the LORD dried up the water of the Red Sea…” (Joshua 2:10).
Paul is showing the Jews who “the people of God” are, and is using OT examples of how others who were chosen (when it was supposed to be the firstborn chosen), yet God was making a point.
Firstborn (Gen. 25:31–34, 49:4).
Ishmael is the firstborn
God says: “No — My covenant line goes through Isaac.”
This is not about salvation.
It’s about who carries the covenant line that leads to the Messiah.
Jacob over Esau (vv. 10–13)
God says: “No — Jacob will be the covenant line.”
Again:
Not salvation.
Not eternal destinies.
This is about how God is structuring redemptive history.
What was the point? “You Jews should not be shocked that God is including Gentiles. God has always chosen unexpected groups or people to advance His covenant plan.”
Isaac instead of Ishmael. Ishmael was the first born, but God chose someone outside of the first born. Same for Jacob over Esau.
Even back then, God was showing He was not bound to the firstborn rule, and He has the sovereign freedom to choose the covenant line. This becomes the point Paul is making: Do not tell God who He can and cannot include, and it was to show His covenant purposes are not bound to flesh, birth order, or human expectation.
Rom. 9:18ff When a nation or individual conforms to God’s will by allowing Him to mold them (the clay) into vessels of mercy or honor that God has prepared beforehand for glory. Since God does not want anyone to perish, He gives the clay chances to want to decide what kind of vessel they will be. Anyone can choose to be a vessel of mercy/honor prepared beforehand for glory if they so choose based upon their obedience, or a vessel of wrath/dishonor based upon rebellion.
It doesn’t say God prepared before birth or God created them that way. So what has He prepared beforehand? He has prepared beforehand the result of what kind of vessel a nation or individual will be based upon their obedience or rebellion. We have the ability and decision to choose the kind of vessel the Potter makes us (as does a nation) which He has prepared beforehand based on our obedience or rebellion to Him.
God has sovereignly chosen what he will do regarding the clay, (sinner), in that he has chosen to respond to the clay, (sinner), according to its repentance or lack of repentance. By quoting the potter/clay metaphor Paul essentially tells the Jews that God will deal with men based on their repentance—as he has always said he would deal with them.
Isaiah 29:13-16; Jeremiah 18:1-12
The metaphor is distinguishing between two opposite classes of people - Believers and unbelievers, and emphasizes God's right to establish the standard of justification. The Jews were rejecting God's power to save men (the gospel, Rms. 1:16), and set out to establish their own way (10:1-3). We certainly have the power and responsibility to make ourselves vessels of honor, and our faith, or lack thereof, will determine which type of vessel we are.