I agree, but what I’m really looking for is an answer as to how you can judge if someone is of sound mind or not and therefore judge the morality of the decision by the doctor.
I think the answer relates to a person being in touch with reality or not.
From a moral POV, this specific case is crystal clear: intervention would have been immoral. The higher level principle is that one may not rightly initiate force against a person’s will (it is allowable to hit a person if they agree to be hit). The concept of implicit permission will play an important role in this discussion.
To take a non-psychotic example, you may not grab a person and shove them. However, if a person steps into the street apparently unaware that a truck 10 feet away is hurtling towards them, you should assume that they did not pick this particular moment to snuff themselves. The facts known to you indicate that the person continues to affirm the fundamental choice – to exist – and your only rational conclusion is that they are not in full possession of the facts (they are looking the wrong direction). Another fact is that a calm exposition of Objectivism ethics and the truck / life dichotomy leading to the person’s choice to step back is not possible. (If the truck were 100 feet away, you could say something like “Truck on your left, dude! Splat!”). Your choice to grab the person and move them out of harm’s way is technically force, but it is reasonable to assume that it is force with implicit permission. The assumption is that if they had perceived the truck, they would not have stepped in front of it.
In an extreme case I can think of someone with paranoid Schizophrenia who would do as this woman did, but the explanation in the letter for the suicide would be out of touch with reality. His explanation could be that aliens have told him to kill himself, if he doesn’t then aliens would kill his friends and family.
We would be assuming, as we did in the truck case, that the person was fundamentally inclined to exist, but because of certain perceived “facts” he concluded that life would be unbearable. At some point we might ask why a person would ever decide that life qua man is not possible, but let’s take it that the person has reached that conclusion. Well, that conclusion (in this hypothetical) is completely conditioned by the belief that aliens would kill his friends and family. Were it not for that belief, the person would not have abandoned the ultimate goal. His conclusion is based on a false premise, which is caused by “broken axioms”, that is, perception that is caused by seriously malfunctioning sensory apparatus. Furthermore, it is reasonable to believe that his perceptions can be corrected, though it’s slower than in the truck case (needing a course of medication). If his perceptions are corrected, his ultimate conclusion (“life is possible”) would also change.
There is an analogy with the truck case, a significant mismatch between reality and perception. In both cases, they are not perceiving reality correctly (and without correct perception, conceptual conclusions also cannot be correct). There are obvious difference between the truck case and the alien case, but what they have in common is a failure to perceive reality, and that their false perceptions lead to choices that they would not have made if they had perceived reality correctly. Just as we would forgive a man for using force to prevent a blind person from stepping out in front of a truck that he did not perceive, we would forgive a man for using force to prevent a madman from taking his life based on patently false perceptions of aliens.
In this case, for the doctors not to intervene to save his life, they would be condemned as immoral since it is clear that he is of not sound mind and instead mentally ill to an extent that his right to life, specifically his right to take his life, should not be recognized in this situation.
I don’t think you can conclude based on mental illness that the person has no right to life because of his mental problem. If that were correct, you could conclude “Aha, he’s nuts, we can harvest him for spare parts!”. However, you’re also complicating the question by injecting doctors and evaluations of immorality for inaction into the discussion. I think it would be better to focus on the more accessible question of whether it is morally permissible to use force to prevent a person from ending their life because of fundamentally false perception. From that we could get to a conclusion about doctors, but that involves bringing into the discussion the specific nature of doctors and why they should act in certain ways.