Those who object to a distinctive third use place the "doing good to others" under the first use -- it is part of keeping and promoting order in society. Or, in other terms, achieving civil righteousness.
This can really only be true in a society that considers itself explicitly Christian. However, in a society that is not so, the positive commands enumerated by Luther in the SC aren't so easily applied to civil society as a whole. They are expectations for Christians, but can't be enforced on non-Christians. Thus, third use can't merely be collapsed into first use.
Have to disagree with this because in the Ten Commandments we are dealing with natural law. They are found universally throughout cultures, Christian and pagan, in words similar to the Biblical ten. So when Paul speaks of 'elemental principles' in Galatians, for instance, he is speaking of the laws written on the heart. Luther made no such distinction in his explanations to the ten commandments, that this part of the law is for everybody, and this part is solely for Christians...
It is part and parcel of our righteousness coram mundo. I had posted a quote several months ago from The Genius of Luther's Theology by Kolb and Arand which speaks about this notion of two kinds of righteousness.
I've been thinking lately about the two kinds of righteousness as related to the uses of the Law.
Civil righteousness comes about by obedience to the first use of the law, which some of us refer to as the curb and the prod. It curbs bad behaviors and prods us to do good deeds. Both the curbing and prodding functions help bring order to society, to a household, or to a church. In a sense, civil righteousness is about creating right relationships between peoples on earth. As I have studied the fruit of the Spirit, it struck me that many of those are about our relationship with other people (so also are many of the works of the flesh).
I'm not sure of Luther's term for the other righteousness, but I'll call it divine righteousness -- it's concerned about creating the right relationship between God and humankind. It comes about only as a gift from God to sinners. For this the second use of the law and the Gospel work together. We are convicted of sins and our sinfulness state so that we might repent and throw ourselves on the mercy of God's grace by by Jesus through the gospel.