Where then is glorying? The Apostle, after having, with reasons abundantly strong, cast down men from their confidence in works, now triumphs over their folly: and this exulting conclusion was necessary; for on this subject, to teach us would not have been enough; it was necessary that the Holy Spirit should loudly thunder, in order to lay prostrate our loftiness. But he says that glorying is beyond all doubt excluded, for we cannot adduce anything of our own, which is worthy of being approved or commended by God. If the material of glorying be merit, whether you name that of congruity or of condignity, by which man would conciliate God, you see that both are here annihilated; for he treats not of the lessening or the modifying of merit, but Paul leaves not a particle behind. Besides, since by faith glorying in works is so taken away, that faith cannot be truly preached, without wholly depriving man of all praise by ascribing all to God's mercy -- it follows, that we are assisted by no works in obtaining righteousness. Of works? In what sense does the Apostle deny here, that our merits are excluded by the law, since he has before proved that we are condemned by the law? For if the law delivers us over to death, what glorying can we obtain from it? Does it not on the contrary deprive us of all glorying and cover us with shame? He then indeed showed, that our sin is laid open by what the law declares, for the keeping of it is what we have all neglected: but he means here, that were righteousness to be had by the law of works, our glorying would not be excluded; but as it is by faith alone, there is nothing that we can claim for ourselves; for faith receives all from God, and brings nothing except an humble confession of want. This contrast between faith and works ought to be carefully noticed: works are here mentioned without any limitation, even works universally. Then he neither speaks of ceremonies only, nor specifically of any external work, but includes all the merits of works which can possibly be imagined. The name of law is here, with no strict correctness, given to faith: but this by no means obscures the meaning of the Apostle; for what he understands is, that when we come to the rule of faith, the whole glorying in works is laid prostrate; as though he said -- "The righteousness of works is indeed commended by the law, but that of faith has its own law, which leaves to works, whatever they may be, no righteousness." [1]

Footnotes

1 - Grotius explains "law" here by "vivendi regula" -- rule of living;" Beza, by "doctrina -- doctrine or teaching," according to the import of the word tvrh in Hebrew; and Pareus takes "the law of works," metonymically, for works themselves, and "the law of faith," for faith itself; and he quotes these words of Theophylact, "The Apostle calls faith a law because the word, law, was in high veneration among the Jews." He uses the term, law, in a similar manner in Romans 8:2, "The law of the spirit of life," etc. "He calls here the gospel; the law of faith,' because faith is the condition of the gospel covenant, as perfect obedience was the condition of the covenant of nature and of that of Moses, (conditio foederis naturalis et foederis Mosaici.)" -- Turrettin

Where is boasting then? - Where is there ground or occasion of boasting or pride? Since all have sinned, and since all have failed of being able to justify themselves by obeying the Law, and since all are alike dependent on the mere mercy of God in Christ, all ground of boasting is of course taken away. This refers particularly to the Jews, who were much addicted to boasting of their special privileges; See the note at Romans 3:1, etc.
By what law? - The word "law "here is used in the sense of "arrangement, rule, or economy." By what arrangement, or by the operation of what rule, is boasting excluded? "(Stuart)." See Galatians 3:21; Acts 21:20.
Of works - The Law which commands works, and on which the Jews relied. If this were complied with, and they were thereby justified, they would have had ground of self-confidence, or boasting, as being justified by their own merits. But a plan which led to this, which ended in boasting, and self-satisfaction, and pride, could not be true.
Nay - No.
The law of faith - The rule, or arrangement which proclaims that we have no merit; that we are lost sinners; and that we are to be justified only by faith.

Jew. Where is boasting, then? - 'η καυχησις, This glorying of ours. Have we nothing in which we can trust for our acceptance with God? No merit of our own? Nothing accruing to us from our circumcision and being in covenant with God.
Apostle, It is excluded - εξεκλεισθη, It is shut out; the door of heaven is shut against every thing of this kind.
Jew. By what law? - By what rule, doctrine, or reason is it shut out? by the law of works? The rule of obedience, which God gave to us, and by which obedience we are accepted by him?
Apostle. Nay - Not by the law of works; glorying is not cut off or shut out by that; it stands in full force as the rule of life; but you have sinned and need pardon. The law of works grants no pardon, it requires obedience, and threatens the disobedient with death. But all glorying in the expectation of salvation, through your own obedience, is excluded by the law, the doctrine of faith: faith alone, in the mercy of God, through the propitiation made by the blood of Jesus, (Romans 3:25), is that by which you can be justified, pardoned, and taken into the Divine favor.

(11) Where [is] boasting then? It is excluded. By what (e) law? of works? Nay: but by the law of faith.
(11) An argument to prove this conclusion, that we are justified by faith without works, taken from the result of justification. The result of justification is the glory of God alone: therefore we are justified by faith without works: for if we were justified either by our own works alone, or partly by faith and partly by works, the glory of this justification would not be wholly given to God.
(e) By what doctrine? Now the doctrine of works has this condition attached to it, that is, "if you do", and the doctrine of faith has this condition, that is, "if you believe".

Where is boasting then?.... There is no room nor reason for it, either in Jews or Gentiles: not in the Jews, who were very apt to boast of their being Abraham's seed; of their circumcision; of their being Israelites; of their having and keeping the law; of God being their God; and of their knowledge of him: nor in the Gentiles, who were ready to boast of their philosophy, wisdom, and learning; of their self-sufficiency, freewill, and of the things they had in their own power.
It is excluded; it is shut out of doors; the key is turned upon it; it is not allowed of; it is entirely exploded:
by what law? of works? nay; for, that establishes boasting when men seek life, righteousness, and salvation by the works of it, and fancy they shall be able to attain them this way:
but by the law of faith: not by a law requiring faith; nor as if the Gospel was a law, a new law, a remedial law, a law of milder terms; but the word "law" here answers to the Hebrew word which signifies any "doctrine" or "instruction", and oftentimes the doctrine of the Gospel, as in Isaiah 2:3, and here particularly, the doctrine of a sinner's justification by faith in the righteousness of Christ; according to which doctrine the most unlikely persons are justified, even ungodly persons, the worst and vilest of sinners; and that without any consideration of works, by faith only, which is freely given them; and by faith in Christ's righteousness only: so that there is not the least room for boasting in the creature, but all their boasting is in Christ, who is made unto them righteousness, and by whom they are justified.

God will have the great work of the justification and salvation of sinners carried on from first to last, so as to shut out boasting. Now, if we were saved by our own works, boasting would not be excluded. But the way of justification by faith for ever shuts out boasting. Yet believers are not left to be lawless; faith is a law, it is a working grace, wherever it is in truth. By faith, not in this matter an act of obedience, or a good work, but forming the relation between Christ and the sinner, which renders it proper that the believer should be pardoned and justified for the sake of the Saviour, and that the unbeliever who is not thus united or related to him, should remain under condemnation. The law is still of use to convince us of what is past, and to direct us for the future. Though we cannot be saved by it as a covenant, yet we own and submit to it, as a rule in the hand of the Mediator.

INFERENCES FROM THE FOREGOING DOCTRINES AND AN OBJECTION ANSWERED. (Romans 3:27-31)
Where is boasting then? . . . excluded. By what law?--on what principle or scheme?.
of works? Nay; but by the law of faith.

Where is boasting then? If we are justified, not by our own righteous works, not by the law of Moses, but as a free gift of God through a law of faith, where is the ground for Jew or Gentile to boast?
Therefore. The conclusion of the line of argument is now reached. No man is justified by works of law (no article in the Greek), but by faith, the faith that brings into loving obedience to Christ.
Is he the God of the Jews only? If God is the God of all nations, it ought to be regarded a reasonable thing that he would justify through faith Gentiles as well as Jews.
As there is one God, there is one plan of justification.
The circumcision, the Jews are justified by faith, a faith not in God, whom they already acknowledged, but a faith in Christ, God manifest in the flesh. In the same way the uncircumcision, the Gentile world, are justified through the faith. The Gospel is meant by the faith (the article is found in the Greek). The salvation of both is by faith in Christ crucified.
Do we then make void the law? Do we make it useless through the faith; i. e., through the Gospel? (the article is found before faith in the Greek).
We establish the law. Rather, law (the article is not found in the Greek). Law is confirmed and rendered sacred, when its just demands are met by the suffering of the Son of God himself.

Where is the boasting then of the Jew against the gentile? It is excluded. By what law? of works? Nay - This would have left room for boasting. But by the law of faith - Since this requires all, without distinction, to apply as guilty and helpless sinners, to the free mercy of God in Christ. The law of faith is that divine constitution which makes faith, not works, the condition of acceptance.