Natural law concerns not doing evil. In this sense, it is profoundly theistic, even Christian. This is because physical death is not sufficient punishment for breaking laws of nature: everybody dies, whether saint or sinner. The wages of sin rather is spiritual death in hell. And only Christianity has the notion of hell somewhat fleshed out in its doctrine.
Anyhow, notice how the Rothbardian “two eyes for an eye” theory of punishment regarding natural law is entailed by each of the 4 theories of punishment. The idea is that the criminal not only must pay restitution but himself loses the exact same rights and amount of happiness that he dared to take away from his victim.
1. Rehabilitation. If the criminal loved his victim, then the pain to the victim would be the criminal’s pain, as well. Since the criminal has no regard for the victim at all, the only way to simulate love is by inflicting the exact same unhappiness on him as he inflicted on the prey. Though crude, this is the beginning of the criminal’s metaphysical reformation.
2. Retribution. The cosmic order of things, the integrity of the hierarchy of good and evil is preserved. Did Smith attempt to lower Jones status unjustly and raise his own at Jones’ expense? Well then, Smith has corrupted his nature by the exact amount of happiness that he bit off Jones. His own status in God’s kingdom must therefore be lowered by that amount.
3. Deterrence. The more heinous the crime, the greater the punishment the criminal expects in return. There is a double utility to society: the criminals are intimidated into becoming productive citizens and thereby into avoiding condemnation; the potential victims are spared the ordeal of being brutalized by the criminals.
4. Condemnation. If an incorrigible defiant criminal has set his mind on hating society, then he is according to natural law (if not perhaps grace) to be hated back and as a result to be permanently restrained for life or killed altogether. There is now a double disutility to the criminal signified by the two eyes: pain of loss, as his wicked desires to hurt his fellow men are unsatisfied; and pain of sense, as he is physically destroyed.
For natural law, each theory is sufficient to yield two eyes for an eye. (Or perhaps, an eye and a leg for an eye, because poking out two eyes blinds entirely, while poking out one eye does not.)