Revlid beat me to quoting Julian so I won't bother repeating why future generations are very much relevant here.
That aside, what kind of dumb logic is that? "That girl is dead"? No, for fuck's sake, she isn't. She's alive and healthy, standing right before you. And you are suggesting that it is right to kill her if that saves the world? That is not a justification, it's an excuse. Excuse for your own weakness, inability to find a better solution or even just accept that you are committing yourself to evil because you want to live a while longer, or for your children to have a shot at life.
But looking at the later posts, at this point, this is becoming not a discussion about a Type-Moon work but rather, a general discourse on ethics and morality, something I'm disinclined to argue due to the sheer amount of time it can take.
No. In Miyu's world, Gaia is dying. Science as we know it can't do shit about that because Gaia's will is what enforces physical laws. Without it, the world as we know it simply crumbles away and all scientific constants are liable to become unknown variables, if they even retain any kind of meaning. And I won't even delve into the fact that the collapse of Gaia's RM leaves the planet completely unprotected from incursions of Lovecraft-esque eldritch abominations from beyond that are vaguely alluded to in the setting.