Positive law concerns the doing of good. The main area of positive law is to control non-culpable externalities, pollution, for example. Not doing evil is mandatory, if one’s nature is not to be destroyed in hell; doing good — any good — is supererogatory.
Natural law need not be promulgated; everybody knows that one shall not kill. Positive law is a complex web of rules that need to be made public explicitly.
Notice that the code of laws and the stipulated punishments for breaking them are supposed to move society closer to the greatest good for the greatest number (GGfGN). This is distinct from the deterrence theory of punishment which seeks to balance the harm to the criminal in a particular case and the good of society. The first concerns lawmaking and is addressed to the legislator; the second, punishment and is addressed to the judge. We are interested, among other things, in the second aspect.
A judge who tries a criminal for a violation of a positive law can no longer blithely rely on the “two eyes for an eye.” No theory of punishment suggests this principle.
Therefore, the 4 theories take a different form.
1. Retribution is simply the penalty fixed by law, e.g., $X – $Y fine or Z – W years in prison.
2. Deterrence comes next, and the judge needs to ascertain the most optimal punishment in regard to our GGfGN.
3. With the total punishment fixed, the actual suffering is split between internal penance and external coercion. If a person repents (i.e., is rehabilitated), the external punishment can be lowered.
4. On the other hand, if the criminal glories in his corruption, the external punishment is maximized in order to protect society from this person’s future crimes.