Romans 9:16

Romans 9:15-16  (see also Romans 9:30-32)
For He says to Moses, I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion. So then it does not depend on the man who wills or the man who runs, but on God who has mercy

Continuing from Romans 9:1-5, within the overall theme of Jewish evangelism, “it,” meaning God’s “mercy,” does not depend on our ability to establish our own self-righteousness through the Law, but rather depends on admitting our unrighteousness and accepting His forgiveness, which is perfectly summed up in Romans 9:30-32:

Romans 9:30-32: “What shall we say then? That Gentileswho did not pursue righteousness, attained righteousness, even the righteousness which is by faith; but Israelpursuing a law of righteousness, did not arrive at that law. Why? Because they did not pursue it by faith, but as though it were by works.” 

Gentiles: Sinners admitting their unrighteousness and welcoming the mercy of God.
Israel: Jesus is not the Messiah, and our only righteousness comes from living righteously.

Arminians do not claim that salvation is according to human perfection in the flesh. The mercy of God is instead for those who confess their sins and ask for forgiveness, which God grants to anyone who comes to Him. Consider the following parable:

Matthew 18:23-27: “‘For this reason the kingdom of heaven may be compared to a king who wished to settle accounts with his slaves. When he had begun to settle them, one who owed him ten thousand talents was brought to him. But since he did not have the means to repay, his lord commanded him to be sold, along with his wife and children and all that he had, and repayment to be made. So the slave fell to the ground and prostrated himself before him, saying, “Have patience with me and I will repay you everything.” And the lord of that slave felt compassion and released him and forgave him the debt.’ 

Calvinist, Peterson and Williams: “The next verse is particularly difficult for Arminianism. ‘It does not, therefore, depend on man’s desire or effort, but on God’s mercy’ (Rom 9:16). Paul explicitly excludes human desire (literally, ‘willing’) or effort (literally, ‘running’) as the determining factor in salvation.” (Why I am Not an Arminian, p.61, emphasis mine)

No. Paul is refuting assurance by works, specifically in regard to supposed righteousness established through the Law. The unbelieving Jews didn’t believe in the Messiah, and instead believe that the only path to righteousness is living righteously. While we are certainly to live in obedience to God, the Scriptures show that there is none righteous, and all we like sheep have gone astray. True righteousness comes from God bestowing mercy and forgiveness to those who confess their sins and receive His for forgiveness by faith. Since Calvinists don’t have the correct Jew and Gentile context in focus, they end up on a wild path that imagines Paul rebuking free-will. 

Calvinist, Peterson and Williams: “Paul’s conclusion to the redemptive history lesson begun in Romans 9:6 devastates theologies based on free will.” (Why I am Not an Arminian, p.61, emphasis mine)

The context is not about free-will vs. determinism. It’s about Jew and Gentile, in terms of the works of the Law versus receiving God’s righteousness by faith.

Calvinist, Peterson and Williams, continue: “Romans 10 gives a complimentary answer: God’s word has not failed, but unbelieving Israel reaped what it deserved for its unbelief--God’s judgment. Paul thus sets God’s absolute sovereignty (Romans 9) side by side with genuine human freedom (Romans 10).”  (Why I am Not an Arminian, p.64, emphasis mine)

That is incoherent, and completely gets off course from the real context.

Arminians, Walls and Dongell: “If Paul’s focus all along has been upon that large body of unbelieving Jews who imagine that their physical connection to the people of Israel guarantees salvation, then it is quite likely that the ‘doing of good or bad’ and ‘works’ and human ‘desire or effort’ have reference to what Paul has targeted again and again throughout Romans: Jewish confidence that possessing and doing (specific features of) the Mosaic law will guarantee salvation (e.g., Rom 2:17-29).” (Why I am Not a Calvinist, p.93, emphasis mine)

​Obviously that commentary gets the context right, and ends up with the same conclusion that Paul reaches at Romans 9:30-32.

Adrian Rogers: “Listen, none of it depends upon you. It is all God. Do you understand that? That’s grace. … It’s either grace or works, not grace and works. If you were hanging over a precipice, two thousand feet below are jagged rocks, and there’s a chain of 100 links, 99 of them made of forged steel, 1 of them made of crepe paper, how safe are you? As safe as that 1 link. Now if any part of your salvation depends upon you, you’re not going to make it. You’re not going to make it. It is by grace. What did this man preach to him? He preached to him that hes a sinner, that Christ died for him. If he will put his faith where God has put his sins, that he will be saved.” (Every Christian An Evangelist: Acts 8:26-39, emphasis mine)

And the grace of God is indicative of the king, according to Matthew 18:23-27, who had compassion on the person who begged for mercy. 

For the unbelieving Jews who believe that they are righteous by keeping the Law, will sadly discover too late in their Life-Review at Judgment before God that they fell short of perfection and will be in desperate need God’s forgiveness, but by then it will be too late. God’s mercy must be received in this life, because in eternity, it will be too late.