In one of Raymond Smullyan's (quite excellent) puzzle books, he offers the following proof that everyone is either conceited or inconsistent. The argument is quite simple: consider all the things that you believe. Do you think they're all correct? If so, well, you're conceited, because only a conceited person would think they're never wrong. But if you don't then you believe something and also believe it's wrong, which is inconsistent.

(Smullyan is an actual math professor in logic, so it's not surprising that this proof is related to a real mathematical phenomenon known as omega-inconsistency.)

I was thinking about this paradox because of an episode of Law and Order: SVU which I saw a few weeks ago. The show centers on a doctor who denies that HIV causes AIDS, and some of his patients, and the show unambiguously condemns the doctor. Strikingly, despite the fact that it's fairly clear that the doctor genuinely believes in what he's saying, he is treated more like a willful criminal than someone dangerously mistaken. Indeed, in at least one point, a police officer suggests (without evidence) that his views must be maliciously negligent, in a manner that suggests the viewers are expected to agree.

But Smullyan's paradox is in play here. We believe, with justification, that the doctor is wrong in this case, and causing harm to his patients. But, somewhere, there's probably another doctor refusing to give a treatment, and that doctor happens to be making the right choice, and will someday be feted, while their persecutors will one day be condemned as cruel agents of an inflexible and indifferent establishment.

I don't have a particular brilliant summing up to give here. My point is just that there doesn't seem to be much general thought about how to strike this balance. When the issue comes up, the response seems to be dominated by emotional disgust, mixed with an abstract idea that there are some limits, but no effort to reason to an actual decision that's independent of the particular case. (Strikingly, the SVU episode dealt outcomes to characters pretty much in linear order of how sympathetic the character was.)