A parent is legal guardian of a child until they are of age, or longer/shorter as prescribed by law
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Well, yes; a police officer can take someone into custody, because he's allowed to by law.
I think we're mostly in agreement, in the sense that the law can give authorisation for people to have extraordinary rights over other people (such as parents vs children, police vs civilians). To note, I feel all that to be quite right and just. However, if we go by the idea that law is something brought into being by mutual agreement, and is separate from morality, then we will need to accept that someday the law might grant greater powers to others over ourselves than we might feel is proper. Such as the right of a Head of State to order lethal force to be used against aiders and abetters of separatist guerillas who are allied with an external enemy with whom the nation is currently at war (I'm talking about Saddam gassing the Kurds).
I agree with what you're saying, but strictly speaking, the Law can't proclaim someone judge over someone else - and certainly not judge and jury, without possibility of a higher appeal (with the exception of very specific instances such as spies and deserters in wartime).
I think it is unlikely to fully happen, turning police officers into Judge Dredd-type figures or something. But laws can and do change, and I'm not sure it is entirely accurate to say that it can't happen. At least the current legislative apparatus has nothing procedural to prevent it from happening, and I don't see anything conceptually that would make it have a probability of even close to zero. I understand that a constitution-type document usually outlines how such things are to be arranged, and if you can change that, then it is only a question of how far you can go.
It appeared to me (and apparently KO as well) that you meant that a police officer going rogue/using excessive force/killing someone without need/etc is, in certain cases, acceptable, as a deterrent. With which I don't agree, since any deterrence it would offer would be....what? "If you make me mad, I'll break my own rules and hurt you, but as long as you're not too bad, we'll stick to our rules"? That's ridiculous. You need to be able to deter them while staying inside the lines of the law.
Nah, as I said earlier, deliberately setting fire to the cabin to kill this guy would have been neither right nor legal. I doubt anyone is claiming that is the way this was supposed to go, though opinions may differ on exactly how bad it is. Personally, as I think I mentioned, I'm not shedding too many tears if it actually went down that way, and speculate on whether some good might actually have come out of it. And I imagine the primary deterrent in this case would be directed against going after cops and their families, which I think is far less ridiculous than you make it sound.