“Then what becomes of our boasting? It is excluded. By what kind of law? By a law of works? No, but by the law of faith.” -Romans 3:27
Paul has already proven in verses 17-24 that because the Jews disobeyed the Law and thus dishonored God causing his name to be blasphemed among the Gentiles, there is nothing for them to boast about regarding their own righteousness.
But here he takes a slightly different approach to drive the final nail in the coffin. There are legitimate things for which the Jews may boast (Romans 9:4-5), but the law of works is not one of them. Boasting is excluded because righteousness is obtained by the law of faith in Christ—apart from the works of the Law.
To say it another way, the Jews may boast in their heritage and special anointing of God to be priests to the world (and all the privileges that come with that) but they do not obtain righteousness any other way than through faith in the true Israel, Jesus Christ—just as the Gentiles do (See also Galatians 3:16, 24-29).
In regards to righteousness, the only boasting that is allowed is boasting in the cross of Christ (which he is about to unpack in chapter 4).
Nota Bene: The Greek reads: Ποῦ οὖν ἡ καύχησις; ἐξεκλείσθη. διὰ ποίου νόμου; τῶν ἔργων; οὐχί, ἀλλὰ διὰ νόμου πίστεως.
Law (νόμου = nomou) in this instance is being used more generally than specifically referring to Tora. It’s more like principle (I.e., law of gravity, law of supply and demand, etc.).
Literal translation
Ποῦ οὖν ἡ καύχησις = Where is the boasting?
ἐξεκλείσθη = It is shut out! [often rendered, “it is excluded!”] (it is the aorist passive indicative third person singular verb form of κλείω, which means “to shut”) See its use in Galatians 4:17: “They make much of you, but for no good purpose. They want to shut you out, that you may make much of them.”
διὰ ποίου νόμου = by which law?
τῶν ἔργων = of works?
οὐχί = negated adverb (i.e., No, Not)
ἀλλὰ διὰ νόμου πίστεως = but by (a, the) law of faith.
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