So, getting back to human beings, just as the proper treatment of vehicles to care for and maintain them long term, isn’t merely to “Do no damage to them,” the proper long-term view of human morality is more than merely “Do no harm.”
To properly care for a vehicle long term means knowing some basics about what kind of thing a car is, how to properly maintain its various components, how to change or repair those that are wearing out, and how to operate it on a daily basis, etc.
By analogy, then, human morality – if it is to be objective in the same sense that vehicle maintenance is objective – must involve knowledge of the kind of thing a human being is, how to develop and maintain its various aspects – physical, mental, emotional – and how to monitor when parts or aspects are wearing and in need of maintenance.
I suspect your “subjectivity” view plays a part here when we observe how cars can be used for different purposes. You might say that some vehicle owners purchase cars just to drive the crap out of them, some as purely functional transportation devices and because they have lots of cash they may not care to maintain them, etc.
Similarly, you might insist people have some kind of right to decide for themselves whether they choose to “care for the well-being of others” and the extent to which they ought to be compelled to do so.
That would, again, depend upon what kind of thing, precisely, human beings are.
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Thing is, though, it isn’t what we imagine to be the case that is the significant thing. What matters is what really is the case. And THAT isn’t up to us to decide. It is the objective truth of the matter – what human beings really are – that counts.