That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.
That ('In order that') the righteousness of the law, [not dikaiosunee (G1343), but dikaiooma (G1345)] - 'the righteous demand of the law;' the practical obedience which it calls for (see the notes on this form of the word in Romans 5:16),
Might be fulfilled in us - or, as we should express it, be 'realized' in us. Calvin, Fritzsche, Hodge, and Philippi take this to mean, 'that the justifying righteousness of the law might be imputed to us; partly (in the case of some of them) because they take justification still to be the subject discoursed of; partly because they hold it untrue that the righteousness of the law is any otherwise fulfilled in us; and partly because they think that if our own personal obedience were meant, the second clause of the verse would be but a repetition of the first. But is it not unnatural to suppose that the apostle is still dwelling on justification, of which he had already treated so largely? And what is it that this verse conveys which had not been over and over again expressed, and, according to their own interpretation, once or twice said even in the preceding verses? Nor is it a wholesome thing, as we think, to be so very jealous of any expression that sounds like an assertion that Believers fulfill the requirements of the law? For, do they not do so? And is it not the express object of Romans 6:1-23, in the first part of it, to show that they do, and in the second to bid believers accordingly see that they do? That their obedience is not perfect is no more a truth than that it is a real and acceptable obedience through Christ. (As to the use of the passive voice here, "might be fulfilled" in us, it seems far-fetched to infer-as DeWette, Olshausen, and Alford do-that it is, used 'to show that the work is not our's, but God's by His grace.')
Who walk. This is the most ancient of all expressions to denote 'the bent of one's life,' whether in the direction of good or of evil (see Genesis 5:24; Genesis 6:9; Genesis 48:15; Psalms 1:1; Isaiah 2:5; Micah 4:5; Malachi 2:6; Luke 1:6; Ephesians 4:17; 1 John 1:6-7).
Not after (according to the dictates of) the flesh, but after the Spirit. In this and the following verses it is difficult to say whether by "the Spirit" as opposed to "the flesh," the apostle means the Holy Spirit, as the indwelling principle of the new life in believers, or the renewed mind itself, under the operation of that indwelling Spirit. Both are in active operation in every spiritual feeling and act. While the whole gracious frame and activity of the soul is due to the Holy Spirit as the indwelling Source of it - "the Spirit of life in Christ Jesus" (Romans 8:2) - the thing done is not done passively, mechanically, involuntarily in us, but is the spontaneous life and frame, emotions and actings, of the renewed mind. But from Romans 8:9, it would seem that what is more immediately intended by "the spirit" is our own mind, as renewed and actuated by the Holy Spirit. (See Philippi, pp. 288, 289.),