If you take one or more rules as absolutes that ought never be violated, like typical deontology does, then what happens if you are ever faced with a situation where every choice available violates at least one of them?
You get into a gridlock - all possible ways events could progress from that situation are blocked. You want some standard to be met but that option does not exist. So you must either fix the rules or have a way of weighing things to pick the lesser evil.
Maybe you think that such gridlock is always the result of a flawed or incomplete set of rules - that for a correct set of rules, all possible problems present a choice that does not require violating any of them. Or maybe you think deontology inevitably leads to gridlock.
Either way, I consider this a very useful name for a fairly common variant of logical contradiction that often occurs - and is often overlooked - in deontological thinking and values.
If we concede the right to bodily autonomy from birth at least as far as possible (with a person that has yet to orient themselves in the world, but must be taken care of meanwhile), as I believe we should, then the decision of a child in need of medical procedures to survive to reject them in accordance with the believes it was raised in, should be accepted as any other wish to die [1/2]
(after a carefully neutral talk about possible options and consequences respectively perspectives on the matter), no? Currently pondering the issue and interested in other people‘s angle. (Sorry for the awkward phrasing, Englis is not my first language.) [2/2]
I think the biggest thing I want to point out is that "beliefs the child was raised in" might have damaged the child's reasoning ability, and also that the child might have insufficient ability to see that their choice to reject treatment is actually a choice to die or really appreciate the weight of that until it's too late.
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For that first part, there is a parallel to how trauma, beliefs, and other aspects of upbringing can influence the emotional factors of wanting to die. Suppose upbringing hurt a kid in a way that causes them to feel self-loathing and pessimism about having a life experience worth living through. Hopefully we can all see how infancy and childhood trauma can cause such strong and practically-inevitable cause-and-effect ripples that if a sufficiently traumatized kid asks for death and you grant it, that's less like you respecting a truly autonomous choice and more like letting them drown after they were tied up and thrown overboard. Their autonomy was already taken from them before they got to you. Their mind was chained and weighed down by outside actors and forces... you just don't have any clean, absolutely autonomy-respecting choices anymore. That's not an option that exists. The choices available are respecting/violating their current injured "autonomy" by granting them death, or violating/respecting their potential healthy "autonomy" by healing or freeing them enough so that they can make the decision without their upbringers or trauma violating their autonomy.
So I think it's important to recognize that beliefs can be the same way. It's just that the mechanism of action is more perniciously subtle than the stereotype of severe and blatant emotional trauma. It warps the very faculty with which we reach conclusions, judge evidence and arguments, and so on. If you wouldn't let me reach into your mind and magically shape what your feel/perceive/sense/think is logical, then you recognize on some level what I mean about how external influences that shape your sense of logic could be robbing you of autonomy. And early exposure to beliefs, information, and modeling of logic are poweful influences that shape your sense of logic.
And thus, in principle, I don't think we can just treat all beliefs a kid was raised in as equivalent. In practice there aren't easy answers about how we as a society decide which beliefs are unacceptably wrong... in practice societies are making this decision all the time, and different societies make different choices, and many of those choices are viewed by some people as unacceptably bad, wrong, or downright evil. But those choices are inevitably being made, and there's no non-choice here since a lack of formal policies and choices just defers it to informal cultural norms and smaller-scale power dynamics "on the ground" in hospital rooms, local courts, village mobs, and so on. Best I got for that problem is the same as my answer for improving all problems of governance, rule-making, coordination, and consensus - decision shares.
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More generally, I think "autonomy" as a value has the problem that "autonomy" (and relatedly, "free will") as a concept fuzzes out the more you "zoom in on it", in particular as you consider what causes you to make any given choice, feel any given feeling, think any given thought, remember or not remember something, and so on, at any given moment. Minds and brains are concentrations of cause-and-effect interplay. Exceptionally complicated, large, rapidly evolving, and slow to totally lose any causal ripple, but cause-and-effect interplay nonetheless.
So to me, respect for autonomy is a derived value - I value respecting autonomy because I can see how in most situations it causes harm and suffering to not respect autonomy, especially when we consider indirect effects, integrate the future, and remember that we are rarely able to see into other minds as well as they see inside themselves. In particular, the odds of us being right when we think we know someone's mind better than they themselves do are low. It's also a game theoretic necessity: brains which don't insist on enough respect for their autonomy get used as a resource by those who for one reason or another end up exploiting them - so as a pragmatic ethics engineering constraint, we are working in a world where it is both common and healthy for people to expect some degree of respect for their autonomy.
But I think that's clarifying. Notably, part of the derivation is about the difficulty of knowing another mind as well as that mind knows itself. But kids are in the most amateur stages of knowing themselves. So while it's important to treat them with a large amount of respect for their autonomy, because that's part of raising them into healthy and competent adults, it's also important to recognize that they have much higher odds of being wrong about themselves, especially for things which require longer experiences of being a human: who they are or what they mean.
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As a small child I was hospitalized twice.
I had to receive injections, at the peak of my treatment three times a day, including a week or so when I was being woken up while it was dark in what felt kinda like the middle of the night to take them.
I would've absolutely rejected any treatment that involved a needle if I had been given a choice in the matter. As-is, I was the most persistently difficult kid around - thrashing and crying and fighting every time. A couple times I did other creative things that took the full defiance willpower I could muster as a little kid, like running off in the hospital halls and hiding or diving under a table and refusing to come out.
Being literally told at least once that I could die if I stopped getting treated did not change this. I remember kinda knowing death as a concept at the time, but I still would've chosen to stop getting treated if I could. I am pretty sure I explicitly said that death would've been preferable, but...
As a kid, that wasn't choosing to die. That was the result of being chronically triggered and feeling thoroughly compelled to do anything to get out of the cycles of mounting dread, a massive fight-or-flight response constantly in tension with resignation and perpetual real or imagined emotional/interpersonal conflict of my little child will against the authority of my mom and the hospital staff, the vigorous desperate physical flailing at the end, the pain of the actual injection made worse by my fully clenched muscles needing a much more forceful needle jab, and the attendant emotional trauma, two to three times a day, every day, for weeks. The distant abstract risk of a descent into vaguely worse symptoms or whatever and eventual cessation of experiences was scary if I thought about it, but crucially it was totally abstract - the treatments I begged to decline weren't. It wasn't even a decision to take my chances and gamble that I wouldn't die. It was desperately motivated wishful thinking. My emotionally-real time horizon was the next four hours.
As it so happens, in my case I was misdiagnosed. The treatments weren't actually helping (although being outside of the building my family was living in at the time was helping). So you could maybe really charitably interpret this as in part influenced by some sort of accurate awareness on my part - and that maybe if I really was sick in a way that my treatment was helping, I would've sensed it and my attitude would've changed.
But even that implies that someone would've had to violate my autonomy for however many injections it took for me to notice the pattern and make an informed judgement on whether or not it was "worth it".
And if I hadn't been misdiagnosed, if I really was in need of such treatments to not die, and there was an opt-out option, I would've been dead like 25+ years ago.
Not exactly a rejection based in beliefs I was raised in, but factor that in as you will.
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There's this anecdote I heard recently, about a kid who died because his parents were in the "Christian Science" movement and their entire community thought the right way to deal with the kid's illness was to pray it away. As I understand it they specifically view it as somehow wrong and bad to pursue medical treatment.
But the most relevant bit was that none of the people involved had even remotely enough relevant knowledge to have remotely accurate beliefs about the risks. Towards the end they thought the kid was getting better because he stopped having seizures. He stopped because damage to his brain got bad enough.
What would the kid have said if you had a chance to ask him how he should be treated, at any point after getting sick? What conversation could you have about options, consequences, and perspectives could you have with a kid raised with those beliefs - let alone a carefully neutral conversation - that would've given him a snowball's chance in hell to get out of "faith in Jesus will save me, and to think otherwise is dangerous" or whatever?
Sometimes valuing autonomy for a child is actually functionally equivalent to valuing some adult's autonomy to harm the child - whether intentionally or not.
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Remember the stories of COVID patients who refused to take precautions and did not bother getting the vaccine, only to die in the ICUs begging doctors to give them the vaccine?
Grown-ass adults, and it still took them until the raw reality of suffocating to death was upon them, until they were viscerally feeling it in-the-moment and it was indisputable.
Death from a lack of treatment is far too often only abstract until it's too late to treat, especially when you're so so so far away from truly understanding any of the science or filtering out the bullshit....
When you're not feeling like you're literally about to die, it's very easy to convince yourself at an emotional level that your chances of survival are really good actually. Abstract medical knowledge is something you really have to learn to trust and feel as predictive.
But at least for an adult, you could say they have had enough opportunity to know better, to learn enough of the necessary logic and evidence and find their way to the truth if they had just made enough effort. (Given how bad at reasoning and truth-finding many people are, and how the deck is stacked against many people circumstantially, I feel like society should seriously start to recognize that this is a kind of ableism and classism, but at least an argument could be made.)
So again, what chance does a child have, armed with the kind of beliefs that would cause them to refuse treatment, to really understand and appreciate what risk they're taking on?
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So my own view is that in principle, sure, there's something correct in this thought - but in practice, I think there are some serious ethical risks with letting a child opt out of medical treatment, due to beliefs or otherwise. I'm open to the possibility that those risks could be overcome on a case-by-case basis with at least some children, but I think if you want to be maximally ethical for the children, the bar needs to be really high and you'd need to be really careful (higher and more careful than just a few really good conversations with the child) or you end up effectively just respecting upbringers' autonomy to launch their kids into a suicide trajectory before they even have the ability to meaningfully decide if they want to change course.