By what definition, and extent, and to what purpose do we as humans classify the idea and act of murder as evil? To most people I ask this question seems ludicrous and the answer alarmingly obvious, but I have yet to understand why we identify this occurrence as ‘evil.’ I can understand that the intent of murder and its outcome can result in a way that selfishly benefits the murderer at such a terrible cost, and I can understand that the action of taking someone’s life is just as cruel to the deceased as it is to the people that knew and loved that victim, but it seems hypocritical to me that we as a society generalize the idea of killing as evil when relatively many of us favor capital punishment, strong military, and, at least in fiction, vigilante justice. We send men and women to violent battlefields yet, before they leave, indoctrinate the poor souls into thinking that the very act of murder is evil just by itself. They come back scarred because of this. ‘Do unto others as you would have them do unto you.’ This doctrine assumes that everyone, or at least others, innately both self-preserve and love themselves. To me, this idealized world is instantly refuted the second one realizes that the occurrence of murder exists at all. Otherwise, why act in such a needlessly violent manner? Why do as a society define murder as ‘evil’ and ignore the intent of it when the intent clearly outlines the motive and the scope of its effect?

Well, we think that murder is wrong, and that it's often (usually?) not just wrong but very wrong—wrong enough to count as evil. Robbing someone of their purse is bad; robbing them of the life is worse. What you say you don't understand is why we count murder as (typically? often? almost always?) evil in spite of the fact that we think killing isn't always wrong. You see some sort of hypocrisy here. But why?

After all: not all killing is wrong. The obvious example: killing in self-defense, which I hope we can agree is morally acceptable in a way that murder isn't. Even more so: killing by a police officer to protect the life of an innocent person threatened by an assailant. Capital punishment is a harder case. I think it's wrong, but I don't think people who believe otherwise are therefore morally blind. War is complicated business, but there's a case to be made that going to war is at least sometimes morally acceptable too.

The place where what you're saying seems to miss the mark is here:

it seems hypocritical to me that we as a society generalize the idea of killing as evil when relatively many of us favor capital punishment, strong military, and, at least in fiction, vigilante justice.

and it misses the mark because to think that some but not all killing is wrong is exactly not to generalize the idea of killing as "evil." It's to make distinctions. That's consistent with a rule of thumb that says killing is presumptively wrong and always needs justification. But it seems clear that some killing in some circumstances can be justified. That's true even if killing is usually wrong. It's true even if most (but not all) killing is positively evil.

I'd add one more thing: talking about "we as a society" is usually not helpful. "Society" isn't one thing. Different people within a single society hold different views, and hold them with different levels of conviction. Rather than worrying about what "we as a society" think or say, better to analyze the views themselves. And the word "hypocritical" applies to societies, if at all, only as a not-very-helpful extension of its primary use: as a way of describing individual people who are guilty of a certain sort of moral weaselry.

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