Is it right to value the life of a family member over a random person of equal moral values?

It depends on what you mean. I'd be mistaken if I thought that members of my family were more valuable or worthy than other people just because they're my family. In the general scheme of things, my children's well-being is not a bit more important than the well-being of anyone else's children. The same goes, of course, for parents, siblings, spouses, lovers, friends, fellow citizens. But I have a feeling that's not the question you're asking. Im guessing you're asking whether it's okay to treat one's own family, friends, etc. preferentially. In some cases the answer is no. Suppose I'm in charge of hiring a new employee. It would be wrong to hire my daughter instead of another candidate simply because she's my daughter. That would be giving my daughter an unfair advantage. The right thing to do, if at all possible, would be to turn the decision over to someone who doesn't have a personal stake in the outcome.

On the other hand, to use a sort of example well-known among philosophers, if I have to choose between saving my daughter's life and saving the life of a stranger, my view is that I'd be a monster if I didn't prefer my daughter.

More generally, in a wide variety of situations there's nothing wrong with preferring friends and family to others. There are many reasons for this, but the most obvious is that the world would be a far poorer place if it didn't make room for the intimate attachments and special relationships that are an integral part of friendship, romantic love, family ties.

Of course all this can go wrong. The worse way is tribalism, nationalism, and the violence that those sentiments can lead to. But the fact that some ways of preferring one's friends, family, fellow citizens... are wrong doesn't mean they all are.

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