Feser and Bessette structure their argument for capital punishment carefully. Their fourth general premise is that some wrongdoers deserve death, but they spell out as a fifth and separate premise the notion that someone has the authority to inflict that death upon the wrongdoer:
Public authorities have the right, in principle, to inflict on wrongdoers the punishments they deserve.
As I noted in my original post on the death penalty, the fact that someone deserves death does not of itself imply that any human being has the authority to impose it. Accordingly, F&B devote an entire subsection of their argument to showing that the government in particular does have that authority.
However, I think there is a small gap in their case. They start from the general notion that every order tends to put down what opposes that order, so that the order of reason raises pangs of conscience against the individual in his wrongdoing and the order of divine providence inflicts punishments on those who disobey the divine law. Then they add the point that the government is entrusted with the social order, so that those who offend against the social order can be legitimately punished by the government. Finally, both from reason and by appeal to the Church’s teachings, they urge that the authority of the government is given to the government by God, and this regardless of whether we are talking about hereditary monarchs or democratically elected officials. The conclusion: the government has a divinely established authority to punish offenses against the social order.
The gap to which I refer is this: the fact that the government has divine authority to inflict punishments does not of itself imply that the government has divine authority to inflict all kinds of punishment.
For example, F&B mention in the course of their argument that the father of a family has a divinely given authority over the familial order and hence over his children. It follows that he can legitimately punish his children—but no one maintains that a father can impose the death penalty on his children.
Or to take another example, the Church has a divinely given authority over her members, and according to Canon Law can even punish a wayward member for offenses. And yet no one has ever maintained that the Church has authority to punish people for, say, a speeding violation. As F&B point out, different orders have different authorities over them, and so the range of a given authority depends on the kind of authority implied by its particular order.
My point is simply this: the fact that God has given authority to the government does not immediately imply that God has given all authority to the government, so that the government can inflict any kind of punishment. The case F&B make is good as far as it goes, but they need to add something further to establish that the particular kind of authority given by God to the government includes the authority to impose even the death penalty.
In other words, they need a closer discussion of this “social order” entrusted to the government. That points us toward another topic they omit, which I will raise in an upcoming post.