Imagine this scenario: A serial killer is pointing his gun at an innocent person John and wants to kill John. An arahant is near the killer and knows that the killer will kill 5 more innocent people after he kills the innocent person John. The arahant can choose to kill the killer before the killer kills John and the other 5 innocent persons. Would the arahant kill the killer? Would a Buddha kill the killer? If yes, why? If no, why?
"Would the arahant kill the killer? Would a Buddha kill the killer?"
'Yes, Sutavā, you heard correctly [...]. A bhikkhu who is an arahant [...] is incapable of transgression in nine cases. (1) He is incapable of intentionally depriving a living being of life"
-- AN 9.7 (Bodhi trans.)
"Here, Visakha, a noble disciple considers thus: 'For all their lives the arahants dwell having abandoned killing living beings, refrain from killing living beings, they have laid down their staffs, laid down their weapons, they are conscientious, sympathetic, compassionate for the good of all living beings; so today I dwell, for this night and day, having abandoned killing living beings, refraining from killing living beings, I am one who has laid down my staff, laid down my weapon, I am conscientious, sympathetic, compassionate for the good of all living beings. By this practice, following after the arahants, the Uposatha will be entered on by me.'"
-- AN 8.43
"If no, why?"
Through greed a covetous man kills breathing things [...]. Through hate a malevolent man kills breathing things[...]. Through ignorance a deluded man kills breathing things... Will that be long for his harm and suffering?" — "Yes, venerable sir." [...]
Through non-greed an uncovetous man does not kill breathing things [...]. Through non ill-will an unmalevolent man does not kill breathing things. [...] Through non-delusion a man with true knowledge does not kill breathing things... Will that be long for his welfare and happiness?" — "Yes, venerable sir." -- AN 3.66
Summarizing, it's wrong action:
And what is wrong action? Killing, taking what is not given, illicit sex. This is wrong action.
-- MN 17
Such a question assumes death is the cessation of existence. This is not the Buddhist view. Killing the murderer won't solve anything, it merely brushes the dirt under the carpet. Since violent thoughts will reemerge in the killer's next life, and grow once more because they weren't ever eradicated, nothing is achieved by killing.
Killing someone is passing the buck, and an attempt to make it someone else's problem in the next lifetime. It is wrong view to believe there is an "I" to preserve and that there is a someone else out there to load our burdens on. Karma takes care of such problems by presenting us with the same problems we ran away from in our subsequent lives until we learn to handle it with enlightened wisdom.
A lotus isn't born by waging a war on dirt, it is a transformation of dirt that produces the lotus.
The only solution for ignorance is wisdom. Even before the murderer was pushed to the brink of action, there was deep suffering in him or her, and it was permitted to grow. Thus the well meaning Buddhist is constantly working to heal the suffering in others around them, to eradicate pain and suffering everywhere so that such deep suffering leading to murderous thoughts don't manifest.
What would an arhat or Buddha do is immaterial. What would each of us do is more pertinent.
Also known at the Trolley Problem from Game Theory. My answer is that this kind of question is a red herring. Ethics is about how you wrestle with experience to try to minimise suffering. Hypothetical questions like this one are pointless because they will never occur as real dilemmas. Buddhist ethics is focussed on how one actually behaves in every day life. This kind of scenario has never happened in anyone's life. The fact is that presently there is no Buddha and as far as I know, no arahants. So the answer to the question can make no possible different to how you or I conduct ourselves. And what's worse is that while we spend time on such problems we are being distracted from what is actually going on right now.
This kind of thing comes under the heading of samphapalāpa - frivolous speech. And as such is something to be avoided.
MN 1.3.1 Kakachupama sutta
Majjhima Nikāya 21 - Kakacūpamasutta
The Parable of the Saw
"Monks, even if bandits were to savagely sever you, limb by limb, with a double-handled saw, even then, whoever of you harbors ill will at heart would not be upholding my Teaching.
Monks, even in such a situation you should train yourselves thus:
'Neither shall our minds be affected by this, nor for this matter shall we give vent to evil words, but we shall remain full of concern and pity, with a mind of love, and we shall not give in to hatred. On the contrary, we shall live projecting thoughts of universal love to those very persons, making them as well as the whole world the object of our thoughts of universal love — thoughts that have grown great, exalted and measureless. We shall dwell radiating these thoughts which are void of hostility and ill will.' It is in this way, monks, that you should train yourselves.
An arahant would certainly have perfected the 5 precepts at the least and would abstain from harming anyone. I also belive that the Buddha might have said that an arahant was even incapable of killing. Any enlightened being would certainly try and find another option even if doing so resulted in failure.
Here is an alternate perspective from the Mahayana tradition. (I'm not equating arahant & bodhisattva, but if you are asking what a Buddha would do it is perfectly legitimate in my mind to consider also what a bodhisattva would do.) In 'Words of My Perfect Teacher,' Patrul Rinpoche says:
"For all good or bad actions, the intention is by far the most important factor that determines whether they are positive or negative, heavy or light. It is like a tree: if the root is medicinal, the trunk and leaves will also be medicinal. If the root is poisonous, the trunk and leaves will be poisonous too. Medicinal leaves cannot grow from a poisonous root. In the same way, if an intention develops from aggression or attachment and is thus not entirely pure, the action that follows is bound to be negative, however positive it might seem. On the other hand, if the intention is pure, even acts that appear negative will in fact be positive."
He then tells a story (also found in Gampopa's 'Jewel Ornament of Liberation' I believe) to illustrate the point:
"Once in a previous life, the Buddha was a captain called Compassionate Heart. He was sailing upon the ocean with five hundred merchants when the evil pirate called Black Spearman appeared, threatening to kill them all. The captain realized that these merchants were all non-returning Bodhisattvas, and that if one man killed them all he would have to suffer in the hells for an incalculable number of kalpas. Moved by an intense feeling of compassion, he thought: "If I kill him, he will not have to go to hell. So I have no choice, even if it means that I have to go to hell myself." With this great courage he killed the pirate, and in so doing gained as much merit as would normally take seventy thousand kalpas to achieve. On the face of it, the act was a harmful one, since the Bodhisattva was committing the physical act of murder. But it was done without the least selfish motivation. In the short term, it saved the lives of the five hundred merchants. And in the long term it saved Black Spearman from the sufferings of hell. In reality, therefore, it was a very powerful positive act."
Of course, I will not pretend to have even a shadow of this level of insight and freedom from the poisons of afflictive emotions; and therefore I try my best to abide by the precept of not killing. But it is important for us no matter where we are on the path to remember that motivation is essential in determining karmic consequences, not mere outward acts. It reminds us to look deeply into our own hearts in order to skillfully respond to such ethical quandaries when they actually arise in our lives.
The arahant would not kill the killer. A Buddha would not kill the killer.
Even if by killing the killer, lives would be saved in thousands, the arahant or a Buddha would not kill the killer. Even if by killing the killer, lives would be saved in millions, the arahant or a Buddha would not kill the killer. Even if by killing the killer, lives would be saved in billions, the arahant or a Buddha would not kill the killer.
Why is that so? Because the action of the arahant or a Buddha killing the killer would lead to more suffering.
Why is that so?
If by killing the killer, one life would be saved, what would the consequence of killing the killer be? The thought "It's ok to kill killers" would sprinkle in people's minds.
If by killing the killer, thousand lives would be saved, what would the consequence of killing the killer be? The thought "It's ok to kill crazy people" would sprinkle in people's minds.
If by killing the killer, millions lives would be saved, what would the consequence of killing the killer be? The thought "It's ok to kill evil people" would sprinkle in people's minds.
If by killing the killer, billions lives would be saved, what would the consequence of killing the killer be? The thought "It's ok to kill destructive people" would sprinkle in people's minds.
And what does a delusioned mind, seeking liberation from pain, permeated with pain and the thought "It's ok to kill killers, crazy people, evil people and destructive people" think? "It's ok to do evil for lesser evil"
When a delusioned mind, seeking liberation from pain, permeated with pain, thinks "It's ok to do evil for lesser evil", that mind, to liberate from this same pain, because of its delusion, will do evil for more evil. And the seed of suffering would spread.
Thus, the action of "justifying killings", leads to more suffering.
When an arahant or a Buddha abstains from killing any living creature in any way, what would the consequence of such action be? The thought "It's not ok to kill no matter what, even if it needs to be for lesser evil" would sprinkle in people's minds.
When a delusioned mind, seeking liberation from pain, permeated with pain, thinks "It's not ok to kill no matter what, even if it needs to be for lesser evil", that mind, even though he is delusional, because of that same thought, to liberate from pain, will not do evil for more evil. And the seed of wisdom would be spread.
Thus, the action of "always abstaining from killing no matter what", leads to less suffering.
Volitionally taking the life of another living being is only possible if one has defilements left. Killing is rooted in hatred (dosa).
An enlightened being such as an Arahant or a Buddha has eradicated all defilements and fetters and are therefore not capable of killing since the unwholesome root is simply not there.