I agree with @Bad Alias - JB makes it clear that intent & believing something ought to happen is pretty important.
JB also makes clear, when discussing the first law, that intent, while important, is less important than consequences.
I have trouble with the first law because I can't help wanting to apply the legal concept of proximate cause to the magical act. For example, if a wizard scratches someone using magic, then the scratch becomes infected, and the someone dies, that is clearly not a proximate cause of their death. I'm not sure it isn't a violation of the laws of magic because there is no intervening choice that causes/allows the death.
If you blast someone with enough fire to kill them, that means you believed in what you were doing enough to use that level of magical mayhem. I think it doesn't matter that you finished them off with a mundane weapon. Barring self-defense, because the other person was trying to kill you first, you committed a First Law violation when you hit that person with a lethal level of magic because it was clearly your intent to kill them.
I don't think intent is that important to JB. Additionally, the intent might have been to injure them enough to incapacitate but not kill. Then to finish them off through mundane means.
Isn't the defense when someone is using black magic against you? I thought I read that somewhere, but in chapter 7 of Storm Front it's just stated as self defense and defense of the defenseless, which is probably just others.
Everyone seems focused on intent, but the law says not to kill. We have different words for different kinds of killing. Murder, manslaughter, non-culpable homicide. The difference between all of these is intent. Murder is the unlawful killing of another human being with malice aforethought, express or implied. I'll spoiler an explanation below. Manslaughter is the criminally negligent killing of another human being. An accident caused by inexcusable behavior. Non-culpable homicide is a catch all for any form of lawful killings (self defense, war, executions, accidents, etc.). In the DF, self defense isn't a legal defense; it is a mitigation. That's why he's given the Doom instead of complete freedom. He violated the First Law, but he got a reduced sentence. JB has made clear that even manslaughter with magic, and possibly all other homicides with magic, are First Law violations. Intent is the less important part. It is my understanding that a less culpable intent leads to less black magic taint.
Another point is that the intent that matters is the intent to kill with magic. The intent that magic kills the victim. In the first example, that may not be the intent. The intent could be that the results are a death by mundane means. The first example is not a violation because the practitioner did not kill with magic. They killed with mundane means, not magic. Had the practitioner let the victim die of his wounds, that would have been a violation regardless of intent.
There are four ways to meet the intent element, malice aforethought, for murder.
1. Intent to cause death.
2. Intent to cause grievous bodily harm.
3. Depraved heart (recklessness far beyond that which is required for manslaughter, such as burning a house down that you know people are in because you love fire so much).
4. Felony murder (when someone dies as a result of the commission of a felony).
I doubt that the White Council depends on American or Western legal system definitions to enforce their laws of magic.
The proper translation of the first law into English would depend on common law legal definitions, which is what I was using. Though I do believe the "human being" part of the definition is a "recent" American change from the original "person."
I don't think the first law is violated when there is an intervening sufficient cause of death. That is, a cause that would have resulted in death even if magic hadn't been involved. For example, if in the first example, the bullet through the head would have killed the person regardless of whether or not they had been burned.
I do think that the only thing intent effects is the amount of stain.
I do think some amount of intervening causes, even if they have nothing to do with choice, removes the taint. Think Butterfly Effect.The term, closely associated with the work of Edward Lorenz, is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. https://en.wikipedia.org/wiki/Butterfly_effect (https://en.wikipedia.org/wiki/Butterfly_effect)