Proving that moral facts exist.

Not just consequential reasons but also deontological reasons.

Sorry. Ethics do not exist, there are merely value preferences. I prefer to follow the NAP because I like the concept, I find it pleasing, I find it noble. I don’t steal from others for similar reasons.

You can decide directly that you personally follow a certian principals for certian reasons, I will not kill those who I consider innocents because I consider the idea despicable and evil, but this is merely preference, I cannot make my preferences a direct part of the universe outside of my mind, nor can you.

Very few consider eating until you vomit to be immoral, but most do consider it despicable, disgusting, and abusive to one’s body and therefore refrain from doing so and attempt to convince others to do so. Most do not care about it enough however, to go and force the person to stop doing so, the major difference between what is percieved to be “moral” and what most percieve to be merely preference.