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It is often useful if not required to clarify which usage of the word “objective” youre using when discussing this topic. There are three that I’ve found people using:
Usage 1: Objective as in exists in and as part of tangible reality. This is what people want morality to be. But alas anvils do not fall on peoples heads when they do bad things. Hume murdered this one.
Usage 2: Objective as in applied to all humans whether or not they want it to be applied to them. I mean, you can choose to behave like your morals apply to everyone but this isnt really objective at all. Just poor language.
Usage 3: Objective as in not including or affected by anything subjective (feelings, desires, opinions, time, location, etc). Things like math, gravity, and the NAP fit this usage.
One may choose to elevate the word “evil” out of the subjective morass that priests, kings, lawyers, and cult leaders have kept it in for centuries by applying an objective equation to determine it. The NAP is a uniquely well suited option as it is both objective and universalizable.
But it is still up to individuals to choose to do so and to apply it and reciprocate it with other people. (see: What are Rights and Who Gets Them)