The Obligation Principle. For any act φ, we have a moral obligation to do φ (or refrain from doing φ) if and only if God commands us to do φ (or refrain from doing φ).
The Compliance Principle. For any act φ, if God commands us to do φ (or refrain from doing φ), then we have a moral obligation to comply with Her command to do φ (or refrain form doing φ).
So if God commands one to honor the sabbath, by Obligation we have a moral obligation to honor the sabbath; and equally, by Compliance, we have a moral obligation to comply with God's command to honor the sabbath. Brown and Nagasawa argue that these are distinct moral requirements; it is very unclear, however, how these two principles relate to DCT, at least as Brown and Nagasaw understand them. The nut of their argument is that Obligation only requires honoring the sabbath, for whatever reason, whereas Compliance, given their definition of 'comply', requires that we honor the sabbath because God commanded it. The first of these inferences does not seem correct. Nothing about Obligation tells us at all what it is to fulfill an obligation; it just tells us obligations obtain when God commands, and vice versa. And it is not clear that the Divine Command theorist is really committed to Compliance in Brown & Nagasawa's sense. Indeed, unless I'm mistaken, the most famous Divine Command theorist historically, William Warburton, is not committed to it. Warburton holds that morality is sustained by a 'threefold cord': rational perception of what is appropriate to what, sentiments cultivated according to good moral taste, and the authority of a superior to command. Any of these three is an adequate reason for acting morally, and you can act morally while acting for any of these three reasons. But because Warburton holds that morality is, strictly speaking, established only by obligation, which depends on the authority of a superior to command, and fundamentally on the ultimate authority of God, it is the divine command that obliges actions (or nonactions) and makes them moral rather than just reasonable or tasteful. This means that the act of obligation does not itself have to be the motivating reason for acting that way: it's just what establishes the standard by which you can say, yes, that was a genuinely moral thing to do, rather than just a very reasonable or a very tasteful thing to do. Indeed, Warburton is very clear that one of the reasons God gives us the ability to perceive the rational relations between things, and also the rudiments of good sentiments and the ability to cultivate them, is precisely to give us internal motivating reasons for acting morally; each strand of the threefold cord can provide a good moral motivation. It's just that only one of these actually makes the act itself moral or immoral.
Thus DCT as such is only committed to Obligation, not to Compliance, as Brown and Nagasawa understand it -- although, of course, there may be individual Divine Command theorists who commit themselves to Compliance.
