In physical laws, there are a number of numerical parameters. Some of these parameters are famously part of the fine-tuning problem, but all of them are puzzling. It would be really cool if we could derive the parameters from elegant laws that lack arbitrary-seeming parameters, but as far as I can tell most physicists doubt this will happen. The parameters look deeply contingent: other values for them seem very much possible. Thus people try to come up either with plenitude-based explanations where all values of parameters are exemplified in some universe or other, or with causal explanations, say in terms of universes budding off other universes or a God who causes universes.
Ethics also has parameters. To further spell out an example from Aquinas' discussion of the order of charity, fix a set of specific circumstances involving yourself, your father and a stranger, where both your father and the stranger are in average financial circumstances, but are in danger of a financial loss, and you can save one, but not both, of them from the loss. If it's a choice between saving your father from a ten dollar loss or the stranger from an eleven dollar loss, you should save your father from the loss. But if it's a choice between saving your father from a ten dollar loss or the stranger from a ten thousand dollar loss, you should save the stranger from the larger loss. As the loss to the stranger increases, at some point the wise and virtuous agent will switch from benefiting the father to benefiting the stranger. The location of the switch-over is a parameter.
Or consider questions of imposition of risk. To save one stranger's life, it is permissible to impose a small risk of death on another stranger, say a risk of one in a million. For instance, an ambulance driver can drive fast to save someone's life, even though this endangers other people along the way. But to save a stranger's life, it is not permissible to impose a 99% risk of death on another stranger. Somewhere there is a switch-over.
There are epistemic problems with such switch-overs. Aquinas says that there is no rule we can give for when we benefit our father and when we benefit a stranger, but we must judge as the prudent person would. However I am not interested right now in the epistemic problem, but in the explanatory problem. Why do the parameters have the values they do? Now, granted, the particular switchover points in my examples are probably not fundamental parameters. The amount of money that a stranger needs to face in order that you should help the stranger rather than saving your father from a loss of $10 is surely not a fundamental parameter, especially since it depends on many of the background conditions (just how well off is your father and the stranger; what exactly is your relationship with your father; etc.) Likewise, the saving-risking switchover may well not be fundamental. But just as physicists doubt that one can derive the value of, say, the fine-structure constant (which measures the strength of electromagnetic interactions between charged particles) from laws of nature that contain no parameters other than elegant ones like 2 and π, even though it is surely a very serious possibility that the fine-structure constant isn't truly fundamental, so too it is doubtful that the switchover points in these examples can be derived from fundamental laws of ethics that contain no parameters other than elegant ones. If utilitarianism were correct, it would be an example of a parameter-free theory providing such a derivation. But utilitarianism predicts the incorrect values for the parameters. For instance, it incorrectly predicts that that the risk value at which you need to stop risking a stranger's life to certainly save another stranger is 1, so that you should put one stranger in a position of 99.9999% chance of death if that has a certainty of saving another stranger.
So we have good reason to think that the fundamental laws of ethics contain parameters that suffer from the same sort of apparent contingency that the physical ones do. These parameters, thus, appear to call for an explanation, just as the physical ones do.
But let's pause for a second in regard to the contingency. For there is one prominent proposal on which the laws of physics end up being necessary: the Aristotelian account of laws as grounded in the essences of things. On such an account, for instance, the value of the fine-structure constant may be grounded in the natures of charged particles, or maybe in the nature of charge tropes. However, such an account really does not remove contingency. For on this theory, while it is not contingent that electromagnetic interactions between, say, electrons have the magnitude they do, it is contingent that the universe contains electrons rather than shmelectrons, which are just like electrons, but they engaged in shmelectromagnetic interactions that are just like electromagnetic interactions but with a different quantity playing the role analogous to the fine-structure constant. In a case like this, while technically the laws of physics are necessary, there is still a contingency in the constants, in that it is contingent that we have particles which behave according to this value rather than other particles that would behave differently. Similarly, one might say that it is a necessary truth that such-and-such preferences are to be had between a father and a stranger, and that this necessary truth is grounded in the essence of humanity or in the nature of a paternity trope. But there is still a contingency that our world contains humans and fathers rather than something functionally very similar to humans and fathers but with different normative parameters.
So in any case we have a contingency. We need a meta-ethics with a serious dose of contingency, contingency not just derivable from the sorts of functional behavior the agents exhibit, but contingency at the normative level--for instance, contingency as to appropriate endangering-saving risk tradeoffs. This contingency undercuts the intuitions behind the thesis that the moral supervenes on the non-moral. Here, both Natural Law and Divine Command rise to the challenge. Just as the natures of contingently existing charged objects can ground the fine-structure constants governing their behavior, the natures of contingently existing agents can ground the saving-risking switchover values governing their behavior. And just as occasionalism can have God's causation ground the arbitrary-seeming parameters in the laws of physics, so God's commands can ground the arbitrary-seeming parameters in ethics (the illuminating analogy between occasionalism and Divine Command is due to Mark Murphy). Can other theories rise to the challenge? Maybe. But in any case, it is a genuine challenge.
It would be particularly interesting if there were an analogue to the fine-tuning argument in this case. The fine-tuning argument arises because in some sense "most" of the possible combinations of values of parameters in the laws of physics do not allow for life, or at least for robust, long-lasting and interesting life. I wonder if there isn't a similar argument on the ethics side, say that for "most" of the possible combinations of parameters, we aren't going to have the good moral communities (the good could be prior to the moral, so there may be no circularity in the evaluation)? I don't know. But this would be an interesting research project for a graduate student to think about.
Objection: The switchover points are vague.
Response: I didn't say they weren't. The puzzle is present either way. Vagueness doesn't remove arbitrariness. With a sharp switchover point, just the value of it is arbitrary. But with a vague switchover point, we have a vagueness profile: here something is definitely vaguely obligatory, here it is definitely vaguely vaguely obligatory, here it is vaguely vaguely vaguely obligatory, etc. In fact, vagueness may even multiply arbitrariness, in that there are a lot more degrees of freedom in a vagueness profile than in a single sharp value.