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ChaosMote comments on Does utilitarianism "require" extreme self sacrifice? If not why do people commonly say it does? - Less Wrong Discussion
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My view, and a lot of other people here seem to also be getting at this, is that the demandingness objection comes from a misuse of utilitarianism. People want their morality to label things 'permissible' and 'impermissible', and utilitarianism doesn't natively do that. That is, we want boolean-valued morality. The trouble is, Bentham went and gave us a real-valued one. The most common way to get a bool out of that is to label the maximum 'true' and everything else false, but that doesn't give a realistically human-followable result. Some philosophers have worked on 'satisficing consequentialism', which is a project to design a better real-to-bool conversion, but I think the correct answer is to learn to use real-valued morality.
There's some oversimplification above (I suspect people have always understood non-boolean morality in some cases), but I think it captures the essential problem.
It might be useful to distinguish between a "moral theory" which can be used to compare the morality of different actions and a "moral standard" which is a boolean rule use to determine what is morally 'permissible' and what is morally 'impermissible'.
I think part of the point your post makes is that people really want a moral standard, not a moral theory. I think that makes sense; with a moral system, you have a course of action guaranteed to be "good", whereas a moral theory makes no such guarantee.
Furthermore, I suspect that the commonly accepted societal standard is "you should be as moral as possible", which means that a moral theory is translated into a moral standard by treating the most moral option as "permissible" and everything else as "impermissible". This is exactly what occurs in the text quoted by OP; it takes the utilitarian moral system and projects it on a standard according to which only the most moral option is permissible, making it obligatory.