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TuviaDulin comments on Circular Altruism - Less Wrong
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Define "serious". Specify one harm X that is just barely not serious, and one Y that is just a little worse, and is serious. Verify that you can find an N such that YN > 1 human life, and that there is no N such that XN > 1 human life.
X = losing a finger. Y = losing a hand.
Losing a finger is traumatic and produces chronic disfigurement and loss of some manual dexterity, but (as long as it isn't a thumb or index finger) it isn't going to truly handicap someone. Losing a hand WILL truly handicap someone. I would rather everyone lose a finger than one person lose a hand.
Actually, let's make it closer. X = losing a finger, Y = losing a thumb. My answer would still be the same. Missing a finger isn't a huge setback. Missing a thumb is.
I'm pretty sure that if an invading alien fleet came and demanded every human lose a single finger, there'd be more than enough people that'd be willing to sacrifice their very lives to prevent that tribute -- and though I'm not sure I'd be as brave as that, I'd most certainly be willing to sacrifice my hand in order to save a finger of each of 6 billion people.
People would sacrifice their lives for it. However, would that choice be rational? Especially if we consider the likelihood that a war with the aliens might result in massive civilian casualties? Fighting is only a good idea if winning puts you in a better position than you would otherwise be in.
Being willing to sacrifice your hand is noble, and I would probably do the same thing. But if you're talking about someone ELSE'S hand, you need to look at what losing a finger really costs in life experience and working ability versus losing a hand.