If murder is wrong, why is it right to execute a murderer?
"But wait!" You say. "That question assumes that it is right to kill a murderer. It is never okay to commit murder, even against murderers. There. Problem solved."
Okay, but then what do you do with the murderer? Incarceration? Forced rehabilitation? Is it not wrong to kidnap people and hold them against their will? Why is a wrong suddenly a right when dealing with criminals?
This is the punishment paradox.
You can cheat by invoking the non-aggression principle, which is that the initiation of force is wrong except in self-defence. However, punishing a murderer after the fact is not really self-defence. And besides, where does the non-aggression principle come from?
Intuitively, we all understand that you can't just turn the other cheek and let criminals go. They're a threat to society, and we need to deter others from committing crime. However, this is an argument from effect. In other words, you want 'B' to happen, therefore 'A' is justified. We want to stop crime (B), therefore punishment (A) is justified.
There are two problems with this kind of argument. First, you don't know that 'A' will lead to 'B' in the absence of conclusive scientific evidence, which is very difficult to obtain in the realm of sociology and psychology. Second, even if 'A' is the most effective means of obtaining 'B', that does not mean that 'A' is moral. Here's an example to illustrate this point:
'I want sex, therefore rape is justified.'
This is an absurd example, but it demonstrates that arguing from effect provides zero insight into morality. Perhaps for this person, rape is the best way to obtain sex, so rape is justified in terms of its effectiveness. This does not mean that rape is morally justified. Clearly, arguing that you want 'B' therefore 'A' is justified does not help us resolve the punishment paradox.
In order to resolve the paradox, we must start with a few basic premises:
1) Morality is the set of rules that everyone should follow. Note the wording. I did not say that morality is the set of rules that everyone does follow. It is the set of rules that everyone should follow.
***Side note. What separates moral rules from law is that moral rules are universal. Laws are local. If the idea of universal rules is distasteful to you, stop using the language of morality. You cannot talk about right or wrong, and you cannot talk about good or evil without invoking the idea of universal rules. You can only talk in terms of legal or illegal. That means you cannot complain that corporations or the government is committing evil when they are operating within the law. If you complain that they are evil, it is because you assume the existence of rules above the ones created by politicians. In other words, universal rules that exist independently of governments.
2) If everyone should follow the same rules, then whatever rules you apply unto others, you must also apply unto yourself and vice versa.
3) Therefore, whatever you permit yourself to do unto others, you must permit others to do unto you.
How does this resolve the punishment paradox?
The answer is that it's not wrong to kill. It's wrong to kill if you don't allow others to kill you. It's not wrong to steal. It's wrong to steal if you don't allow others to steal back from you. It's not wrong to hit. It's wrong to hit if you don't allow others to hit you. Otherwise, universality is violated, and we no longer have a moral rule.
So why is it right to kill a murderer? Because he permitted himself to kill others. Therefore, he must permit others to kill him.
"But wait!" You say. "Doesn't this mean that it's not wrong for a suicidal man to go on a killing spree?"
Yeah, and neither is it wrong for anyone else to kill him. Problem solved.
As a mathmetician would say after proving a mathematical equation:
quod erat demonstrandum! (Q.E.D.)!