It's an interesting problem imo. We don't know for certain that, for example, chemo will work, so we have a kind of faith, say a faith in scientific probability. Others have a faith in some other force, and if the child survives then their view is vindicated, though not from the scientific perspective. The starting point for some in this discussion is that life is greater than death. Others put life and death on equal footing, indeed, as two sides of the same coin. (Smiling at Tsing's last paragraph re "weird".)
Others can put life and death on equal footing all they want. They just can't make that decision for someone else.
No, we never know if treatment will be successful. But we do know that the probabilities of doing nothing favor death. Again, if the child is too immature to have a voice, it's up to us to go with the probabilities.
Agreeing with both of you for situations where we're talking about one too young or otherwise unfit to decide for themselves. But the "go with the probabilities" answer is the rub. Who says we have to go with probabilities (a secular view) over faith?
The life or death of a child? I'd say a mature society would go with the probabilities. It is not after all the 14th century.
Forced to agree with db (cannot believe I am saying that). But the morally superior answer to the child question is that "we did all we could" to ensure their survival and protection. That means trying all options. Prayer and medicine are not mutually exclusive. Faith that requires you to do nothing or ignore science is potentially dangerous and not in the best interest of the child. I can see this going into a vaccination debate.