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A beam is going to fall on top of two people. When it does so, its weight will be distributed evenly over their two heads, injuring both but not killing either. Had that weight been distributed over one person, it would kill him.

Is one allowed to push one of the people out of the way, leaving the beam to fall solely on the other guy?

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Can you come up with a less contrived case? I can't imagine there would ever be a case in real life where somebody knows that a beam will only injure two people, but will definitely kill one person. In both cases there is likely a chance for death. (what if one of them moves their head, and it hit's their neck breaking it?) –  avi Jan 30 at 7:12
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You mean causing one person to die to avoid two people to be injured? I can't see why that would be permissible. (Now we likely wouldn't charge someone for murder if he was acting to save himself from injury, that might be considered asking too much self-control. But a bystander?)

Redirecting a lethal force (e.g. switching the tracks of the runaway train) may not be considered a "full act of murder" or liable to the technical death penalty, but it's still prohibited and I couldn't see why it would be allowable to prevent injury. (Preventing death is a different story.)

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This case is not like the runaway train. I am allowing a person who is already in harm's way to die to prevent one person from being injured. –  Clint Eastwood Jan 29 at 15:18
    
@ClintEastwood "in harm's way" doesn't matter. The point is he wasn't going to die, and now he is. "Someone who is going to die" is known in the Gemara as gavra katila -- "a dead man." We have no halachic category called "someone who was going to be hurt." –  Shalom Jan 29 at 15:27
    
So you are saying that I am forced to allow someone to be injured? –  Clint Eastwood Jan 29 at 15:35
    
@ClintEastwood Yes, why would you think otherwise? If the choice is death or injury, a million people being injured is better than having one person die. –  avi Jan 30 at 7:11
    
Ah. Now that you've brought in absolute values (million v. 1) you have fallen for the freight train fallacy. If I had made the train run over the toes of a million people instead of killing one, I would still be in the wrong. I am not simply choosing who gets to be hit by the train, I am deciding that one person does not get hit by the train who would have already been hit by the train. –  Clint Eastwood Jan 30 at 13:06
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