There is a close family of arguments that shows up, first I know, in the neo-antiquity of analytic philosophy, the time of Moore and Prichard; then in Onora O'Neill's Constructions of Reason and, more colorfully, as Christine Korsgaard's map-reading disanalogy in the comparison of theoretical and practical reasoning (I think it's in The Sources of Normativity, but I'm not 100% sure). The argument is roughly as follows (I am mainly adapting Prichard's formulation):
- Before I have performed some action a, a doesn't really exist.
- If an obligation were a property of a, it would be a property of a non-existent object.
- But no property is had by a non-existent object; existence is a precondition of having properties.
- Therefore, if obligations are properties of actions to be done, then the property of being obligated is not actually instantiated anywhere at all.
O'Neill makes the point in terms of the notion of subsumption-of-particulars-under-concepts (practical reasoning is not the application of a concept to an already-given action, but produces the action according to the concept in itself); Korsgaard contrasts knowing how to read a map generally from knowing how to use a map for particular purposes, saying something about how normative reasoning isn't about looking for little "normative flags" attached to intended spots on a normative map.
So all that could seem like a reason to try out quantifying over obligations instead. But the next problem is that the nonexistent actions of which obligatoriness was predicated, are now somehow properties of obligation-objects. ∃o(Ao), read as, "There is an obligation such that it is an obligation to do A," turns "to do A" into a predicate of the obligation.
But next, we could also try out relations, here. Let's throw in B for some agent. Say ∃oB(oRB), for some relation R. Would this work? The least I can say is that Prichard argued against a relationalist picture as much as a monadic-property one, saying that a nonexistent relatum doesn't sustain the existence of a relation. On the other hand, by relating obligations to agents, maybe we can somehow squeeze a description of an action into the meaning of R, and avoid the problem of non-existent functions. Or we need a three-place relation between some o, some B, and some nonexistent a, and we are still doomed. I'm not sure.
At any rate, Wansing[??] contemplates the matter in important detail:
Note that quantifying over obligations would also make the generic duality with permission into a more complicated affair. It is no longer possible to take some o and say ~o~ = p, because o is not a sentence/proposition. Maybe we might write something like ~∀o~(Ao) = ∃p(Ap), but I don't really know if that makes sense. (I was going to ask about these topics in a new question on this SE, but yours showed up in the "similar questions" prompt window.)
P.S. Ward[70] uses the phrase "quantify over obligations," though I'm not sure to what effect. Rothschild and Yablo[20] mentions that, "The idea of quantifying over obligations figures prominently in Moltmann’s work, e.g., Moltmann [2017]," the reference apparently being to this.