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We are justified by the obedience of faith in Christ and by the obedience of faith of Christ, not by circumcision or other religious rituals of Judaism.
Notice that, in my view, Paul's message is not the simplistic message from Luther about faith versus works. The works that count (the works of agape and mercy, that is) are included in the Pauline phrase "obedience of faith," a phrase that frames the Letter to the Romans by appearing in Romans Ch. 1 and in the last chapter of Romans (Ch. 16). Scholars like to call such literary framing an inclusio or envelope structure that tips us off on what the author thinks is extraordinarily important. Don't trust me--look up the "obedience of faith" in the first and last chapters of Romans.
Thus, good works (as opposed to ritual works) are already included as intrinsic to faith. It is a false choice to present faith and good works as exclusive of each other. In my view, Martin Luther's reading of Paul was a caricature with tragic consequences of unnecessary division that continue to this day.
Notice that, in my statement, the obedience of faith is, as we would expect as Christians, in Christ; but also notice that it is the obedience of faith of Christ--the Christ's whose own obedience to the Father won us liberation from bondage.
Paul argues ferociously against works, but we have to ask: which works? Paul targets circumcision and the other ritual works of the old religion. In contrast, Paul emphasizes the need to engage in a life of obedience and good works as a result of faith. There is no contradiction between Paul and James. But there is a contradiction between the caricature proposed by Martin Luther and the actual writings of both Paul and James.