Sylvie is a little more likely to write off how fragile life is when people live. We doubt she'd be casually thinking about this "fine line" had this been one of the timelines in which her baby dies.
"Life must go on," [Sylvie] said. (9.51)
Sylvie says this because she thinks it's silly to be scared of influenza. She's right in a the show must go on kind of way, but without caution, life won't go on. At least not for the ones who die.
Life was going on. A think of beauty. (9.67)
Ursula thinks this as she dies of influenza. Life is going on, but not for her. Everyone else will continue to live, and it's only a thing of beauty in the painful, poetic sense of the word.
"Thirteen is quite grown-up nowadays. And life can be very short, you know." (20.3)
The irony drips off this line like snot from a runny nose in allergy season. Ursula, who is being spoken to, knows better than anyone how short life is, having already died at birth, at age four, at five, at eight…
"Reincarnation," Dr. Kellet had said to her. "Have you heard of that?" Ursula, aged ten, shook her head. She had heard of very little. (20.47)
It's hard to tell if a psychologist who is discussing reincarnation with a ten-year-old is a genius or a crackpot. In any other book, he might be a kook, but in Life After Life, his diagnoses are spot on.
"One must nose forward," [Dr. Kellet] said. "Nudge one's way through the chaos of our thoughts. Unite the divided self." (20.49)
Ursula is made up of many divided selves. In each life, she feels weird echoes of past ones. While she might never be able to unite them all, she eventually becomes able to listen to them and either change them or let them be.
"Nirvana is the goal. Non-being, as it were." At ten it seemed to Ursula that perhaps being should be the goal. (20.76)
Ursula's views on life change as she relives her life over and over. As she gets older, she starts to see the circularity of things, so that as she relives life over and over, she becomes a very wise ten-year-old, who even at that tender age starts to yearn for non-being.
What a world of difference there was between dying and nearly dying. One's whole life, in fact. Ursula felt she had no use for the life she had been saved for. (20.339)
Sometimes people change the course of their life after a near-death experience. Ursula, however, is able to change the course of future lives if there isn't anything she can do to remedy things in her current one.
It seemed to Ursula that how you got there was the whole point but there was nothing to be gained from arguing with Sylvie on the days when she was mired in gloom. (21.17)
Sylvie is fatalistic in an almost apathetic way. Her philosophy seems to be life stinks (sometimes), and then you die. And because people die, she doesn't see any reason to live a good life. Maybe that's why she has no qualms about cheating—she's going to die anyway, and no one will be around to remember it.
"Life is too precious to be unhappy." (22.31)
Even if, like Ursula, you have more than one life to live, why not make the best of each and every one?