Having mentioned Romans 9, it seems like a good idea to spend a few minutes reading through that chapter. Not to give a real exegesis, but to give an overview of the argument in that chapter.
vv. 1–5, the problem of Gentile belief and Jewish unbelief
Romans 9:1–5 sets out an apparent contradiction with Romans 8:29 ff. Israel "according to flesh" (Romans 9:3) has largely not believed in Christ, so they're excluded from the Romans 8 blessings. At the same time, gentiles who have believed are promised them. But there are eight blessings to Israel listed in Romans 9:4–5, including Christ Himself. So how can we understand this conundrum?
The answer takes three chapters to develop, but if we limit ourselves to this chapter, we'll see that it builds on "Divine sovereign individual election". That argument takes up basically all of this chapter.
vv. 6–7 The Word of God has not failed
The thesis is given in Romans 9:6 – the word of God has not failed. That's the central point, and the same verse tells us why: because "not all [are] Israel which [are] of Israel" (Romans 9:6). This is the point that will be argued for the rest of the chapter, but it's the point that seems most frequently missed when I hear people discussing Romans 9.
The argument that the word of God hasn't failed is that not all of Israel's descendants are counted as the nation of Israel, nor are all of Abraham's descendants counted as children (Romans 9:6–7). It's possible that someone can be descended from Israel (Jacob), but not be part of the nation of Israel as far as God is concerned. It's possible for someone to be a descendant of Abraham, but not be included in God's reckoning of Abraham's children.
vv. 8–9 Isaac is a son, Ishmael is not
Let's pause here and say that this explains the strange and repeated assertion in Scripture that Isaac is Abraham's only son (Genesis 22:1–2, 15–19; Hebrews 11:17–19) even though we're explicitly told that Isaac had an older brother (Genesis 21:9) and several younger siblings (Genesis 25:1–6). We know for a fact that Isaac was not Abraham's only begotten son, but Scripture describes him that way.
So Romans 9:8–9 explains that Isaac is Abraham's only son as far as God is concerned, because he is the son of promise. Ishmael is Abraham's physical descendant, but God doesn't count him as a child of Abraham.
vv. 10–13 Jacob is chosen, Esau is not
Romans 9:10-13 applies this same principle to the next generation, saying that although Jacob and Esau were twins, having the same father and the same mother, Jacob is chosen but Esau is not. And here were have an amazing parenthesis that introduces a very important point (Romans 9:11), that it wasn't a matter of what they did. Indeed, we're explicitly told that God chose Jacob over Esau when neither of them had done either good or evil. And we're told why: "that the purpose of God according to election might stand."
summary of vv. 6–13 election is individual
One interpretation of these verses is national election: the idea being that Ishmael, Esau, and Jacob all represent nations, and God was effectively choosing the nation of Jacob (Israel) as opposed to the nations of Esau (Edom) and Ishmael. I held that view for many years, but it doesn't stand up to the opening statement in Romans 9:6–7 – "not all are Israel who are of Israel, nor are all children who are seed." We know this is the point of these stories, because the text has already told us where the argument is going. The argument isn't to support national election (which is a real thing), it's the opposite: membership in an elect nation isn't an indication of individual election. That's the statement in Romans 9:6–7, and it's the argument that's being developed in Romans 9:8–13. Ishmael and Esau both had the right father, and Esau even had the right mother (notice that's explicitly mentioned in Romans 9:10), but they weren't themselves chosen.
So we could stop right there and we have our answer to the conundrum of Romans 9:1–5. Being born into the [elect] nation of Israel doesn't mean that God considers you one of Abraham's descendants. It's brutal, it's harsh, but it's the argument of Romans 9.
v. 14 is God unrighteous?
But of course there's more, and now we get to the part that really angers the flesh. Romans 9:14 asks the question, is God unrighteous? And of course the answer is no. But the argument to establish it actually makes things "worse".
v. 15–16 what about Israel?
The thesis of our argument is that the word of God hasn't failed because, "they are not all Israel who are of Israel, nor are they
all children because they are the seed of Abraham" (Romans 9:6–7). vv. 8–13 has given us examples of the second statement – Ishmael, Isaac, Esau, and Jacob are all descendants of Abraham, but only Jacob is the chosen. But we haven't seen a case where someone is of Israel, but not Israel. So now we come to an example from later in the story – from Israel.
Romans 9:15 takes us back to Exodus 33:19–23. The entire nation of Israel (except Moses and Joshua) had committed idolatry at the foot of Sinai, and God had threatened to wipe them all out. And in fact, Exodus 32:25–29 tells us that Moses had ordered the summary execution of three thousand of the people, right then and there; so not all the nation is shown mercy. So now Moses has been pleading with God for the people, and at the end, God says, "I will be merciful to whom I will be merciful."Now we're looking at the whole question of election from the other side. In Romans 9:8–13, the argument has been about excluding individuals from the elect nation. Now we're discussing an entire nation that has sinned, that all deserves to be wiped out (Exodus 32:7–10). And God says that He will not treat them like they deserve: He will choose – not because of any merit on their part – to be merciful to them, because that's what He chooses. So now we're discussing God's choosing (election) in terms of inclusion: in terms of including people who have done nothing to deserve it. So Romans 9:16 reiterates the statement of Romans 9:11, that the issue is whom God chooses. God shows mercy to whom God chooses to show mercy, it's not an issue of what you do, nor even what you choose, but whether God chooses to show mercy.
So now we hit the hardest verses: as soon as we find that God chooses to show mercy to some who don't deserve it (Romans 9:16), we find the story of Pharaoh. And here we find that God chose not to show mercy to someone. Indeed, God chose to harden Pharaoh's heart (Romans 9:17). God raised Pharaoh up – notice Romans 9:17–18 doesn't start the discussion with Pharaoh already on the throne, but with God raising him up – to show His power through Pharaoh. And Romans 9:18 tells us that God's choice to show mercy is mirrored in His choice to harden: He has mercy on whom He wills, and He hardens whom He wills.
summary of vv. 6–18 God chooses individuals
Before we look at Romans 9:19, let's remind ourselves of the context. The problem in Romans 9:1–5 is that Israel has been given promises that we just don't see fulfilled. Gentiles are getting blessings in Christ (Romans 8:28 ff.), but Israel is not. And the answer given is that the word of God hasn't failed, because God chooses individuals. Not every person descended from Abraham is counted as a child of Abraham. Not every person born into Israel is counted as part of the chosen nation. There is national election, but Romans 9 is arguing that an individual's place in an elect nation is itself a choice of God. That God has the right to exclude individuals from their national election.
And Romans 9:18 answers directly to the conundrum of Romans 9:1–5. Why has Israel largely (not entirely! Romans 11:1–6) rejected Christ? The first answer is given in Romans 9:6–7, not all those individuals are in God's reckoning of Israel. The second answer is given in Romans 9:18, God has chosen to show mercy to some, and has chosen to harden others.
vv. 19–20 how can God judge, if His purpose is always fulfilled?
So now we see the reaction, “Why does He still find fault? For who has resisted His will?” (Romans 9:19). Let's remind ourselves that this is the test of whether we've been paying attention in the previous 18 verses. If we have, we'll also conclude that no one can resist God's purpose. He chooses to show mercy to some, and to harden others. So how can God judge them? Isn't that unfair?
Paul's answer is brutal and direct, who are you to judge God? (Romans 9:20).
Romans 9 goes on to develop this idea, but it's worth pausing here to let this one sink in. God doesn't have to explain Himself to us. He has every right to harden Pharaoh's heart, and then destroy Pharaoh because he wouldn't humble himself. That's pretty much what God promised Moses He would do (Exodus 4:21–23). Before Moses returned to Egypt, before he stood before Pharaoh the first time, before he ever mentioned letting the children of Israel go, God said He'd make sure Pharaoh didn't obey, and then He'd punish Pharaoh for it.
God doesn't owe us an explanation: He has every right to make vessels of honor and vessels of dishonor.
vv. 22–24 vessels of mercy and vessels of wrath
Romans 9:22–24 brings this whole discussion back to the opening conundrum of Romans 9:1–5. There are vessels of wrath, prepared for destruction (Romans 9:22). There are vessels of mercy prepared beforehand for glory (Romans 9:23). God has made both. The vessels of mercy are identified as "us whom He called, not of the Jews only, but also of the Gentiles" (Romans 9:24). Notice how it ties this back in with Romans 8:30. And notice that these vessels of mercy aren't defined by lineage or any form of national election: they are individuals, called from Israel and from the Gentile nations.
Romans 9:25–29 goes on to substantiate this claim quoting Hosea and Isaiah, which we'll skip for the sake of brevity.
vv. 30–33 righteousness by faith, not by law
We should mention Romans 9:30–33, though, because it carries the argument forward from Romans 9:1–5, and ties it into Romans 10:1–4. Here "Israel" refers to the nation, effectively the people who aren't considered children of Abraham in Romans 9:6–7. This is "Israel according to flesh" as in Romans 9:1–5.
And what do we find? That gentiles (not all gentiles, surely) have attained righteousness through faith (Romans 9:30), while Israel (not all Israel, certainly) has failed to attain righteousness, attempting to earn it by law (Romans 9:31–32).
That "Israel" here doesn't mean the whole nation (i.e., God has a remnant in Israel) is clear both from context (cf. Romans 11:1–6) and from the preceding statement. We don't understand "the Gentiles... have attained to righteousness" (Romans 9:30) to mean that all the gentiles are believers. This isn't teaching a sort of a reverse national election! But the bulk of Israel – Abraham's and Jacob's physical descendants – have rejected Christ, and thus have rejected God's righteousness. Gentiles, who have no claim to blessing as descendants of Abraham, have found God's righteousness. This is developed more fully in Romans 10 and 11.
But notice that the issue in Romans 9:30–32 isn't some temporal blessing. The issue is righteousness before God. [Some] gentiles are righteous before God, having believed. [Some] Israelites are unrighteous before God, having not believed. So yes, the argument of Romans 9 is indeed an argument of election to salvation. It encompasses more than just salvation (the eight blessings to Israel in Romans 9:1–5), but any claim that Romans 9 isn't about salvation ignores vv. 22–32.
So that's my take on Romans 9. I apologize it was so long, but following my comments on the significance of Romans 9:19 earlier, it seemed worthwhile to write down. I've read too much on the chapter not to have picked up ideas from others on it, but I've deliberately avoided referring to commentaries to keep the flow of the text. So I'm sure there's nothing I could say that's not in one of Darby's expositions, or in Newell's Romans, Verse by Verse.