Thick and thin obligations

Suppose that all fundamental thick moral obligation terms can be put in the logical form: "required by virtue v". Then we have a plausible and neat account of thin obligation in terms of thick obligation:

1. A is obligatory if and only if there is a virtue v such that A is required by v.

Can we define the thick terms via thin obligation? A promising start is:

2. A is required by virtue v if and only if facts about v explain why A is obligatory.

But this is only a start, since there are obvious counterexamples. Suppose I promise you to give you ten dollars if courage is a virtue. Then a fact about courage, namely that it is a virtue, explains why it is obligatory for me to give you ten dollars, but I am not required by justice, and not by courage, to give you ten dollars.

To make something like (2) work, we would need to specify the way in which facts about v explain why A is obligatory. It is implausible to suppose that this can be done without recourse to something circular, like saying that facts about v explain in a requirement-inducing way why A is obligatory.

This suggests that it is easier to account for thin obligation in terms of thick obligation. And this, in turn, suggests that it is better to take as our fundamental concept of obligation not "is obligated to" but "is obligated by ... to".