First, it proposes an interesting analysis of distinctively moral normativity (something that has puzzled me before) in terms of the fittingness of feelings of obligation. While there's clearly an intimate connection here, it's natural to wonder about the direction of explanation: If you are morally obligated to Φ, that would provide a straightforward explanation of why it's fitting to feel obligated thus. On the other hand, if the distinctive phenomenology is meant to explain what it is to be morally obligated, we might feel that some other explanation is needed of when and why such phenomenology is fitting. Insofar as emotions (like fear) have fittingness conditions, these seem derivable from their cognitive content: the implicit claim being made by the emotion in question (e.g. that you're in danger). But what is the cognitive content of a feeling of obligation? Surely not just the vacuous reflexive thought that this very feeling is fitting.
Perhaps a more promising avenue is to analyze obligation in terms of its cognitive role, e.g. the fittingness of ruling out of consideration certain options. On the other hand, as previously noted, this would seem to make moral obligation a potentially "derivative" notion, e.g. if what should be "ruled out of consideration" is something that is appropriately determined on broadly utilitarian grounds.
None of which is a problem for Nye, Plunkett & Ku -- as explained in note 52, they don't really need the explanatory claim -- I just think it's an interesting issue.
Secondly, and more centrally to the paper, they propose a distinction between state-directed and act-directed motivations (suggesting that the fittingness of the latter can "demystify" deontological practical reasons in much the same way that the fittingness of state-directed motivations makes broadly consequentialist -- "teleological" -- practical reasons seem so natural/unproblematic). They illustrate the distinction with the following contrasting pairs of motivations (p.8):
1. wanting to yell at someone in a fit of anger vs. wanting it to be true that one has yelled at him so he doesn’t walk all over you,
2. an aversion to killing someone vs. an aversion to there being killings in the world, and
3. wanting to exercise now vs. wanting the world to be such that one exercises now.
The former motivation in each pair is directed at an act; the latter, at a state of affairs. Since we have reasons to act on fitting motivations, a fitting act-directed motivation will give rise to a reason to act thusly, potentially independently of any consequences for the broader state of affairs. The authors illustrate (p.16):
For instance, suppose (as seems plausible) that the fact that your conduct has harmed someone makes for the fittingness of feeling [...] guilt for what you have done. Since guilt essentially involves intrinsic motivation to make amends, [plausible bridging principles entail ...] an intrinsic reason to make amends for what you have done.
Is the impartial consequentialist then committed to claiming that it's no more fitting to feel guilt when you act badly than when anyone else does? That seems problematic! Better, I suppose, to deny that these "act-directed motivations" have fittingness conditions at all, but the authors do an excellent job here of "shifting the burden" on to the consequentialist.
In consequentialism's defense, there are serious worries (arising specifically for non-consequentialists) about possible incoherence between the fittingness of acts (or act-directed motivations) and fitting preferences about how we should act. The authors bite the bullet on this one (pp.17-18, n.40):
If you could save five individuals by killing one (say, by pushing the one into the path of a trolley about to kill the five), we are inclined to think that you should more strongly prefer that the five live, more strongly prefer that the one is pushed, and thus more strongly prefer that you push him, even though you should not push him. It might seem strange at first to think that we should hope that we will act as we should not act. But it is actually a familiar phenomenon that we should hope that we will have motives that it is unfitting to have (e.g. unwarranted anger towards one if that is the only way to prevent an evil demon from killing five). If, as we have argued, what there is reason to do just is a matter of what it is fitting to be motivated to do, it should be no more surprising for it to be reasonable to hope that we will do what it is unreasonable to do (e.g. unreasonably kill one individual if that is the only way to save five). While it is plausible that we should intrinsically value our acting reasonably, the value of this, even from our own perspectives, should be absolutely trivial compared to that of someone’s life (let alone four lives). To look more fondly upon one’s following the dictates of reason than upon one (or certainly four) other individuals’ surviving would be monstrously narcissistic.
There's something very puzzling about this passage as a defense of deontology. If it would be "monstrously narcissistic" to "look... fondly upon following the dictates of reason" rather than saving more lives (as, indeed, seems right), why is it not equally monstrous to act so? And if so acting is indeed monstrously narcissistic, and so out of line with what really matters, then surely reason could not "dictate" such a terrible action after all? So it cannot be true that you should not push the one.
More broadly, the analogy to reasonably wanting unfitting motives breaks down because of the Motivations-Actions Principle introduced on p.12: a fittingness reason to want to Φ is ipso fact a reason to actually Φ. If you've reason to want and hope that you push the one, these are equally reasons to bring it about that you push the one (most straightforwardly: by pushing him -- but you may be able to achieve the same end more indirectly by taking a "pushy" pill, or the like -- would the authors endorse the latter action, or will it inherit the same prohibiting deontological reasons as directly pushing did?). By contrast, there is no such general link between fitting reasons to desire some other desire and the fittingness of that other desire.
So I'm still inclined to think that the rationally fitting agent would not have conflicting act-directed and state-directed motivations, so the fittingness conditions for the two should likewise not come apart, which may in turn suggest that the distinction is not all that significant after all. (It's striking that the most intuitively compelling examples of the distinction -- #1 and #3 above -- both seem to involve a kind of weakness of will, making sense of how we can have the state-directed motivation without the act-directed one, i.e. by being irrational!)
For these sorts of reasons, my Phil Quarterly Fittingness paper recommends interpreting non-consequentialists as positing special deontic reasons for (state-directed) desire/preference, that "override" our pre-moral reasons to prefer the greatest impartial good. But that does bring out an important respect in which non-consequentialist views are structurally much messier, and less unified, than consequentialist ones, and which may ground a residual sense of "mystification".