Asking "Do they deserve it?" is another way of asking "Is the punishment just?". If we unpack the question, we get "Does the punishment prevent further injustice?" and "Is justice restored?". The objectively correct punishment is the one that answers "yes" to both questions (if possible). But I only see a matter of facts here. Why do you say this is a matter of values? — Samuel Lacrampe
Because the question I offered is not asking, "Does the punishment prevent further injustice?" and "Is justice restored?", but rather "Does the person who is deserving of punishment deserve this punishment?" -- It's a question of how we interpret justice, and what we mean by justice. In the case of the death penalty it is thought of as just when the person in question has done something so wrong that the worst punishment we have is the only possible way to rectify what they have done. Justice, in this sense, is seen as a kind of balance. One person kills, and so is killed in return.
Another sort of justice would just be restorative justice. Killing a murderer only creates more death, rather than rectify the wrong. Seeing as we can do nothing to bring back the dead the debt owed by the murderer is unpayable, and so they are given some sort of life sentence.
Another sort of justice would be rehabilitative justice. Killing a murderer not only fails to rectify a wrong, it also misses out on what the truly just act would be: turning the murderer into a productive member of society. Justice, in this sense, is more about the health of a community than rectifying wrongs.
Given that we agree that morality is objective, this question becomes virtually irrelevant; because objective truth is found by reason and not opinions — Samuel Lacrampe
I'd say this confuses truth with justification. So while we agree that moral statements are truth-apt, in that they seem to be describing things which are or are not the case invariant of one's point of view, what I am asking is how you determine whether such a statement is true or false. Agreement seems to be the metric on hand, so we'd have to ask how it is we determine that people agree.
I'd say that this is not enough:
Moral systems on the other hand are very similar in different places and times. The Golden Rule is called such because it is universal. It occurs in some form in nearly every religion and ethical tradition — Samuel Lacrampe
For the reasons against the golden rule I already mentioned, one, and also because "moral systems" could just be read as synonymous with "systems with the golden rule". So any system with the golden rule is a system with the golden rule, meaning that definition-ally they'd all be similar. But this just begs the question.
I'd say that, for instance, the Nazi system you propose contra moral systems is another example of people acting on moral impulses. These were moral impulses of disgust and a fascination with human unity in the state. There is a certain desire for purity in Nazi emotions, as well as a desire to be rid of a previous embarassment and rectify wrongs done to the people. But I would call it an immoral system, in the evaluative sense -- but in the descriptive sense, just like capitalism, communism, or feudalism, I'd say that it counts as a system of prescripts for society, and so is in that sense at least a normative system. It would count when looking at whether or not people agree on goodness.